Platonic Realism & Scientific Method
Scientific method relies on the ability to capture just those attributes of objects in such a way as to be able to make quantitative predictions about them. This is characteristic of Galilean science, in particular, which distinguished those characteristics of bodies that can be made subject to rigourous quantification. These are designated the 'primary attributes' of objects, and distinguished, by both Galileo and Locke, from their 'secondary attributes', which are held to be in the mind of the observer. They are also, and not coincidentally, the very characteristics which were the primary attributes of the objects studied by physics, in the first place.
It was subsequently discovered that if you can represent something mathematically, that you can use mathematical logic to make predictions about it. The greater the amenability of an object to mathematical description, the more accurate the prediction can be: hence the description of physics as the paradigm of an 'exact science' (as per The Unreasonable Effectiveness of Mathematics in the Natural Sciences' by Eugene Wigner.)
Bertrand Russell said that 'physics is mathematical not because we know so much about the physical world, but because we know so little; it is only its mathematical properties that we can discover.' And within the domain of applied mathematics, the applicability of mathematical logic to all kinds of objects yields nearly all of the power of scientific method.
In other words, what can be expressed in quantitative terms can also be subordinated to mathematical analysis and, so, to logical prediction and control. It becomes computable, countable, and predictable by mathematical logic. That is of the essence of the so-called 'universal science' envisaged on the basis of Cartesian algebraic geometry.
But this also challenges the naturalist dichotomy of mathematics being 'in the mind' and the world being 'out there', which is how we are inclined to instinctively construe it. As we have seen, things that can be quantified can be made to conform to mathematical predictions in the same way that they conform to logic. We know by logic the laws and axioms which are visible to thought itself - Frege's 'laws of thought' - and so requiring no empirical validation, on account of their being logically necessary; they're not 'out there' but are known true a priori. And through the quantitative method of science, the ability to reduce an objective to its mathematical correlates, the certainty provided by logical prediction can be applied to phenomena of all kinds with mathematical certainty (which is, I think, the point of Kant's 'synthetic a priori). It's the universal applicability of these logical and mathematical procedures to practically any subject which opens access to domains of possibility which would be forever out of reach to a mind incapable of counting.
Hence the necessity of Platonic realism to the natural sciences.
@Banno - as discussed.
It was subsequently discovered that if you can represent something mathematically, that you can use mathematical logic to make predictions about it. The greater the amenability of an object to mathematical description, the more accurate the prediction can be: hence the description of physics as the paradigm of an 'exact science' (as per The Unreasonable Effectiveness of Mathematics in the Natural Sciences' by Eugene Wigner.)
Bertrand Russell said that 'physics is mathematical not because we know so much about the physical world, but because we know so little; it is only its mathematical properties that we can discover.' And within the domain of applied mathematics, the applicability of mathematical logic to all kinds of objects yields nearly all of the power of scientific method.
In other words, what can be expressed in quantitative terms can also be subordinated to mathematical analysis and, so, to logical prediction and control. It becomes computable, countable, and predictable by mathematical logic. That is of the essence of the so-called 'universal science' envisaged on the basis of Cartesian algebraic geometry.
But this also challenges the naturalist dichotomy of mathematics being 'in the mind' and the world being 'out there', which is how we are inclined to instinctively construe it. As we have seen, things that can be quantified can be made to conform to mathematical predictions in the same way that they conform to logic. We know by logic the laws and axioms which are visible to thought itself - Frege's 'laws of thought' - and so requiring no empirical validation, on account of their being logically necessary; they're not 'out there' but are known true a priori. And through the quantitative method of science, the ability to reduce an objective to its mathematical correlates, the certainty provided by logical prediction can be applied to phenomena of all kinds with mathematical certainty (which is, I think, the point of Kant's 'synthetic a priori). It's the universal applicability of these logical and mathematical procedures to practically any subject which opens access to domains of possibility which would be forever out of reach to a mind incapable of counting.
Hence the necessity of Platonic realism to the natural sciences.
@Banno - as discussed.
Comments (244)
Quoting Wayfarer
Interesting point of view as all the debate you opened here. But I am somehow disagree in Frege’s laws of thought explaining those axioms were supposedly we don’t need empirical validation because somehow is innate upon us.
Despite the concepts are clear to understand the perfect science and how physics works quoting John Locke’s primary and secondary attributes there is another philosopher which I guess is important here to disagree in these statements: George Berkeley.
George Berkeley said: if neither primary qualities nor secondary qualities are of the object, then how can we say that there is anything more than the qualities we observe? he established this question criticising John Locke’s one: If you put one hand in a bucket of cold water, and the other hand in a bucket of warm water, then put both hands in a bucket of lukewarm water, one of your hands is going to tell you that the water is cold and the other that the water is hot. Locke says that since two different objects (both your hands) perceive the water to be hot and cold, then the heat is not a quality of the water.
Then debating Plato Berkeley said: "an abstract object does not exist in space or time and which is therefore entirely non-physical and non-metal"
It is interesting because he tried to abolish all kind of platonic realism or classic empiricism. At least John Locke, as you pointed out, defended somehow primary attributes but Berkeley rejects it all saying about gravity (for example) gravity, as defined by Newton, constituted "occult qualities" that "expressed nothing distinctly. Berkeley thus concluded that forces lay beyond any kind of empirical observation and could not be a part of proper science.
A final statement of him was that the object of science should be purified the perceptions not explaining it.
Well this is why Berkeley is remembered as a extremist empiricist but I guess it is interesting bring his ideas in this debate.
Wise words there. I just realized that, although right now my mind draws a blank, there possibly are non-mathematical questions we can ask about the world or reality. For instance, off the top of my head, as a rocket blazes off in the direction of the red planet following Newton's equations of motion to a T, I could ask, "what does the rocket mean for humanity?" This is the best non-mathematical question I could think of at the moment, hopefully it'll do the job of illustrating the point that not everything about a rocket or anything else for that matter has to do with math. We're, as Bertrand Russell elucidates, perceiving only one facet of reality - there might be more interesting things going on in the non-mathematical domains of reality that we have absolutely no idea how to mine for valuable information. I could be wrong though as historians, anthropologists, sociologists, psychologists, fields as yet to undergo a mathematical revolution could very well be the ones that have their own unique answers to the question, "what does the rocket mean to humanity?" Of course all this assuming our thoughts and thus the answers to the question themselves are irreducible to some equation involving biochemical molecules.
If, the distinction between primary and secondary attributes is broken down in this way, so as to allow for the universality of mathematical applications, then why conclude that all is "of the object" rather than all is "of the mind". As javi2541997;511801 indicates, Berkeley demonstrated that all is "of the mind" is the more logical conclusion. The other conclusion, that all is "of the object", requires the unsubstantiated assumption made by Kant, of the thing-in-itself, noumena, an assumption rejected by skeptics.
I don't know how far this is relevant or true or reasonable but looking as math as "in the mind" as opposed to the world "out there" seems to be a misconception; after all to believe that would be to overlook a very conspicuous fact - the two seem to be "inexplicably" compatible with each other [ref: The unreasonable effectiveness of mathematics in the natural sciences]. This can't be a coincidence, right? If math works in describing reality once or twice, it can be a coincidence but ALL the time (till date of course)? Smells fishy! :lol: We have, it seeems, in this the seed of a conspiracy theory of cosmic proportions.
Keep in mind, that at some point , the regressive description of existing things (atoms, protons, neutrons, electrons...) ultimately, right now, have no other explanation other than that of abstract mathematics (mathematical structures that are discovered) or a Platonic reality, of sorts.
However, to advance Berkley's idealism from modern day discoveries as you suggest, I think he provides for an nice backdrop or theory of metaphysical existence of consciousness. And that in turn squares with abstract qualities and structures existing in the universe, including our own conscious existence.
So you have consciousness itself and mathematical abstracts themselves, both existing without a so-called existential or complete material (or even logical) explanation. But instead, an abstract one.
Correct me if I'm wrong, but I don't think Berkeley actually resolved/reconciled consciousness requiring space and time to exist, or maybe he did... .
There are varieties of mathematical realism other than Platonism. The fact that certain relations among phenomena hold regardless of what anyone thinks about them does not entail that the corresponding mathematical objects metaphysically exist in a realm of concrete forms. As Charles Peirce maintained, echoing his father Benjamin, mathematics is the science of drawing necessary conclusions about hypothetical states of things. Abductive/retroductive explanations (theories/models) are fallible idealizations that require deductive explication (predictions) and inductive evaluation (experiments/observations) to ascertain whether and how well they match up with reality.
You are not wrong. Berkeley escalated a bigger step trying to emphasise what powerful the consciousness instead of trying to explain what is going on with primary/secondary stimulus. This is why authors say he is even more empirical than John Locke. At least this one explained how some attributes are needed to be explained/taught because without it we don’t really know what are we talking about.
For example, John Locke received this letter in his An Essay Concerning Human Understanding
[i]If we block a child in a room all of his childhood teaching him the green colour while is actually yellow. Will he name all of his life “green” when he would actually see yellow? In this topic John Locke answered this is a perfect empirical experiment so he put the following sentence:
What you are trying to say is that complex terms like colours are not innate because we can teach children to misunderstand mixing them. I guess this is the same example of fearness. You can feel the fear because previously someone taught you what is darkness, witches, demons, etc...[/i]
Somehow John Locke understood there are some primar and secondary attributes but depends a lot how they are taught, thus experience
But Berkeley goes furthermore, he says that these are just flawed comments. We are wrong if we try to explain everything instead of purify it. The only truth is our perception doesn’t matter what we are taught.
Nevertheless, Berkeley is contradictory when he speaks about God defining him as perfect (idea)
Why did he do that? Why did not he defend exactly the same in Plato realism?
I want to address a methodological question, if I may. Whether the speculation should be in sensory or extrasensory terms can turn into its own entire debate, but we have to articulate what constitutes an intuition. I have many times advocated on the forum, that ultimately, all of our epistemic efforts rest on preconceptions, persuasions, whatever we want to call them. That we don't access any self-evident facts, but only have attitudes that establish sustainable epistemic allostasis, guided towards epistemic homeostasis
In this regard, it serves well to divide our mental experiences into two aspects. Those that we consider to determine ourselves, and those that we recognize as extrinsically compelled. Essentially, we ascertain that there are boundaries on our personal freedom. The division, even if partly psychological, is not phenomenally inconsequential and it does maintain continuous character. From our point of view thus, some persuasions are self-regulated, consciously or subconsciously, while others are compelled from uncontrolled sources. Some of those which are privately controlled are sustained and some are contradicted by subsequent experience with the externally compelled ones.
Which leaves the question, how to preemptively outgrow your labile persuasions before their character is exposed by external forces. Or otherwise put, which persuasions are evidently bad. There isn't a single way to address the question. Maybe all persuasions eventually perish and are philosophically vacuous. (This is what I consider the argument for absurdism.) But lets limit the scope a bit. One way to thread towards persistence is to be open to experience. Your purview expands and hopefully your lability decreases. The second way to rectify defects is to reconcile contradicting persuasions. For example, I am persuaded to believe in reason. I am also persuaded to believe in sensory experience. But the overall picture of my sensory experience can contradict my reason, in which case I will have to rectify this incompatibility. You have to follow methodological balance that guarantees that you are open to knowledge, while maintaining and improving the quality of your knowledge.
Although this sounds simple, the problem is that you cannot directly infer fundamentals. You can rely on external cues for corrective, but not for synthetic guidance. We don't have some privileged capacity for inferring structure from experience, unless it subclasses the structure we already have. We start with blind assumptions and experiment. Those innate impulses to synthesize or reassign priorities work differently from sorting within the preestablished mental order. It relies on continuous trial and error. If a fundamental persuasion makes no positive difference to the individual, or even detracts from their experience, it should be consequently eliminated.
This does not always happen, however. If a systemic phenomenon, or fragment of the collective behavior contributes functionally, or catalythically, or becomes absorbed, it might not be removed. Objective truth can be overshadowed by group interdependencies. A persuasion may also be sustained overdue for its utility, such as the attainment of happiness. Happy persuasions might be deemed more important then the predictive ones. Such importance is not its own justification however, because in the long term, it vanishes if it is not provisioned by predictive sustenance.
But even stoic persuasions are not directed through a faultless process. As I said, the synthesis of fundamentals depends on trial and error. Sometimes we will spontaneously discover sustainable fundamental idea, such as rationality, the inductive method, statistical inference, objectivity, etc and maintain it henceforth. Or, we will spontaneously discover some unsustainable persuasion. In which case, assuming no group function to justify its existence, either the idea, the specimen or the species will be repressed from reproducing. But failing to affirm some belief also indirectly contributes to the reproduction of the emerging sustainable persuasions.
The point I am trying to make is, that persuasive impulses are not subject to reason at their prima-facie stage, because they represent openness to experience. Sometimes, they mask social signaling, but other means of social interaction eventually tend to displace them. Primitive intuitions are, in a sense, defended by their very existence, for however long it lasts. I don't propose that everyone should defend any spurred belief for the sake of the value of spontaneity. People who believe in the apparent primacy of empiricism and rationality should support the epistemics they choose, including through the politics of banishment of extrasensory claims in science. Active political position helps in the discovery of social value.
But the nature of the mind is a special subject of philosophy. It lacks determination. And I believe that we have to concede that if philosophy was always conservative, we wouldn't make the progress to our present day epistemic understanding. We should approach the question from a hypothetical point of view and debate the consistency of arguments, impartiality, interrelationships with other intuitions, and not treat our conjectures as privileged. Within reason...
I will try to come back for discussion of possible hypotheses. I have said before, I am not literate. But I can try to discuss a few ideas in broad strokes. Emphasizing the distinction between the interactionist and supervenience account of substance dualism would be useful, and how the former can be confirmed or refuted empirically. I think we should discuss some kind of empirically compatible hypothesis, such as property dualism, panpsychism, pantheism or emergent materialism. We should probably also discuss some type of idealistic existence monism (we are all fiction in the mind of the diety) and enactivism.
You say that you are not literate. I think that you are extremely literate, but just need to break up your great long paragraph. I found my eyes could not cope, but it seems well written and as if it is really worth reading.
I made some crude editing.
(I wrote the text in an external editor, then pasted it in a hurry. It was originally displayed on a wider content area.)
Yes, I think that makes it a lot better, and it was not a criticism, just a wish to be able to read what you had written.
In a different thread, Metaphysician Undercover made a great point that an ideal object doesn't actually exist regardless of how well it approximates a real object. Reality is quantized, with a heterogeneously fractal geometry no matter the negligibility of this geometry to a perceptual frame of reference. Even a circle has microscopically fractal texture, so that the fact of a unit circle's area being pi, an infinite decimal, is only actually present in our thoughts. It seems impossible for an infinite geometrical quantity to exist on humanity's observational scale, at least from the vantage point of current science. This indicates a deep distinction between mathematical concept and mathematical object, mind and matter. An ideal shape is like a unicorn, a completely imaginary entity, but this discrepancy averages out to negligibility in many circumstances, allowing us to make the philosophically naive yet practical analogies of relativity so crucial to the logic of mathematical modeling. Math is a language describing fundamentally fictional entities.
I think that the reason I was interested in your discussion is the way you spoke of the philosophy of mind. I have been reading this thread today, finding it fascinating, more on the level of consideration of mind, because I am most certainly not a mathematician. I am interested in your view of mind lacking determination. The angle I am coming from is one arising in the thread I made on pessimism and optimism, and realising that in the discussions which I am having, I am coming from the angle of believing that our consciousness, perhaps as part a larger consciousness may have a determining factor in our lives, and realising that others don't necessarily have that view at all.
However, I am not sure whether this is relevant
what you are querying, but I am probably responding to yours because it is a more general one within the thread.
Science and mathematics knows how to measure quantity and often defines reality by quantity. However we have our subjective definitions of quality but unable to define objective quality. We don't know how to measure objective values so unable to feel "meaning" such knowledge offers. A may equal B in quantity but not in objective quality. Simone Weil wrote:
[i]Now, ordinary language and algebraic language are not subject to the same logical requirement; relations between ideas are not fully represented by relations between letters; and, in particular, incompatible assertions may have equational equivalents which are by no means incompatible. When some relations between ideas have been translated into algebra and the formulae have been manipulated solely according to the numerical data of the experiment and the laws proper to algebra, results may be obtained which, when retranslated into spoken language, are a violent contradiction of common sense.
If the algebra of physicists gives the impression of profundity it is because it is entirely flat; the third dimension of thought is missing.[/i]
A person understands in the complete meaning of the term when they can experience the external world with the third dimension of thought as opposed to the usual duality which limits us to measures of quantity and subjective values.
Necessity? Or rather contingency?
I made an assumption that mathematical truths cannot be irreducibly complex, which holds for mathematical proof design or quantification of mathematical proofs. Meaning that mathematics seems to be invented rather than discovered.
Quoting javi2541997
I agree Berkeley is an important philosopher and that his arguments are ingenious but I don't know if I would want to reference him, at least not without doing a lot more reading.
As for Frege, from that essay I linked:
[quote=Tyler Burge, Frege on Knowing the Third Realm]Frege believed that number is real in the sense that it is quite independent of thought: 'thought content exists independently of thinking "in the same way", he says "that a pencil exists independently of grasping it. Thought contents are true and bear their relations to one another (and presumably to what they are about) independently of anyone's thinking these thought contents - "just as a planet, even before anyone saw it, was in interaction with other planets." '
Furthermore in The Basic Laws of Arithmetic he says that 'the laws of truth are authoritative because of their timelessness: "[the laws of truth] are boundary stones set in an eternal foundation, which our thought can overflow, but never displace. It is because of this, that they authority for our thought if it would attain to truth."[/quote]
The key point is that 'number is real in the sense that it is independent of thought' - but at the same time, it can only be grasped by a rational intellect. This is the key point in my view.
Quoting aletheist
No, they're abstracts, by definition. It is the nature of the reality of number that is the point at issue.
There's another recent essay, What is Math? from the Smithsonian Institute, which notes:
I think this brief paragraph speaks volumes. At issue is the sense in which numbers can be said to exist. They don't exist as phenomena - unlike phenomena, they don't come into or go out of existence, and are not composed of anything (save other numbers) - so they're of a different order to phenomenal existents. And it seems to me that this is what is being furiously resisted by current orthodoxy. As the SEP article on Platonism in Philosophy of Maths says:
I think the statement that this 'would be' an important discovery is unintentionally ironic, as if it's something which has never been considered.
Quoting TheMadFool
Of course, no disputing that.
I watched that Penrose interview shortly after it was published. Those Closer to Truth interviews are a goldmine. I commented on that video:
Quoting simeonz
Isn't this 'biological reductionism'? That being the effort to 'explain' reasoning and mathematical capacity in terms of purported underlying regulative biological systems? The conceptual difficulty here is that science itself relies on the cogency of rational argument to establish any kind of explanatory framework. You can't examine the nature of rational thought from some point outside of it, treating it as an external or objective phenomenon, because any such explanation is already an exercise in rational thought. This point is discussed in some detail in Thomas Nagel's Evolutionary Naturalism & the Fear of Religion.
Quoting simeonz
I don't think present day philosophy of mind has much going for it, really. It places severe a priori limits on the nature of knowledge. Sure we have much better science and technology but are we superior in wisdom to the ancients?
I'm not sure how the technical definition of a fractal applies here. Explain what you mean, please.
Doesn't quite sound right from a philosophical perspective. Realism is about things and objects, but science is not. Both math and science are primarily about relations where point objects only serve as instances to an equation or to a law. 'Platonic' realism in science only acts as mental scaffolding to assist in visual modelling of possible worlds of whatever specialty is under examination. Thus the 'reality' of a mathematician might be in the world of tessellations or knots, that of a chemist in spatial orientation and partial charges of molecules in interactions. Plato himself of course had nothing to do with any of these 'realities', numbers were copies or combinations of Ideal metaphysical objects.
You are right, my bad--but that is precisely why I maintain that mathematical objects cannot exist in the strict sense of reacting with other like things in the environment. In accordance with that metaphysical definition, anything that exists is concrete.
Quoting Wayfarer
I agree, and I maintain that reality is being such as it is regardless of what anyone thinks about it. In accordance with that metaphysical definition, the mistake that Platonism has in common with nominalism is treating reality as synonymous with existence. On the contrary, although whatever exists is real, there are realities that do not exist--including numbers and other mathematical objects.
Wasn't the whole issue of scholastic realism versus nominalism is that the former accepted the reality of universals (in Aristotelian form, as mediated by Aquinas), while the nominalists did not? It was, i believe, Duns Scotus who introduced the idea of the 'univocity of being', which denies that there are different modes of being, although I admit this is a very thorny issue and I need to read a lot more about it.
My technical rigor is surely not spot on, but what I mean is if you draw or construct a precise circle out of actual materials, the circumference's surface contains imperfections, no matter how slight (depending on the technique: pencil, machinery or whatever), and these average out to a fractal-like structure of negligible nesting proportions. This differs from a quintessential fractal in that the compositional detail is less homogeneous and prominent, but is still structures nestled within structures, so basically analogous.
Current physics instructs us that any geometrical object instantiated in the real world will be quantized at the most basic level and is thus fundamentally angular, so an area of pi for example is probably impossible in matter, as the Hilbert program intuited at a relatively early stage of scientific math (I'm getting that information secondhand, you're welcome to correct me).
Motion of course takes effect at a very essentialized level, and this is the source of both the existence and perception of continuity. Whether motion is more like pixels synchronized on a computer monitor or the wild gyrations of a seismograph seems uncertain, but I intuitively lean towards the chaos theory seismograph picture. I think quanta are extremely disequilibrated due to the complexity of their emergent relations while in motion.
That was indeed the medieval debate, but its modern manifestation is affirming the reality of generals in addition to the existence of individuals. Peirce described himself as an extreme scholastic realist in this sense, maintaining that reality includes some possibilities and some conditional necessities, rather than consisting only of actualities.
Quoting Wayfarer
Well, for what it's worth, turbulence
[quote=Wikipedia]The onset of turbulence can be predicted by the dimensionless Reynolds number, the ratio of kinetic energy to viscous damping in a fluid flow. However, turbulence has long resisted detailed physical analysis, and the interactions within turbulence create a very complex phenomenon. Richard Feynman has described turbulence as the most important unsolved problem in classical physics.[/quote]
Math, not as effective as Eugene Wigner thought, eh?
The Unreasonable Ineffectiveness Of Math
The device you're communicating with depends on the unreasonable effectiveness of maths. Interesting article, but the sense in which I'm arguing for Wigner's view, is certainly not that maths or the mathematical sciences are in any sense omniscient in principle or practice. Very well aware of that.
I think that since the success of the nominalist attitude, which was one of the main forerunners of empiricism generally, that scholastic realism has been forgotten to such an extent that there is barely any awareness of what it meant.
[quote=Joshua Hochschild, What's Wrong with Ockham]...[C]ritics of Ockham have tended to present traditional [i.e. scholastic] realism, with its forms or natures, as the solution to the modern problem of knowledge. It seems to me that it does not quite get to the heart of the matter. A genuine realist should see “forms” not merely as a solution to a distinctly modern problem of knowledge, but as part of an alternative conception of knowledge, a conception that is not so much desired and awaiting defense, as forgotten and so no longer desired. Characterized by forms, reality had an intrinsic intelligibility, not just in each of its parts but as a whole. With forms as causes, there are interconnections between different parts of an intelligible world, indeed there are overlapping matrices of intelligibility in the world, making possible an ascent from the more particular, posterior, and mundane to the more universal, primary, and noble.
In short, the appeal to forms or natures does not just help account for the possibility of trustworthy access to facts, it makes possible a notion of wisdom, traditionally conceived as an ordering grasp of reality.
This point is interesting. I understand now what Frege is trying to tell us. I like that characteristic of “timelessness” and so he is somehow right too despite Berkeley theories.
If some statements made by the humankind understanding or investigating the nature or reality are so efficient that literally are passing through the centuries without doubt of their existence probably is due to they are true.
For example: 1 + 1 = 2. Why? Because I count it as an act with my fingers. We can argue here if 1 + 1 equals to zero or infinite. But the law of truth or primary attribute that equals to 2 doesn’t need to drive to error. Despite of Berkeley criticism about not purifying at all the nature around us.
I wasn't trying to be ambivalent towards people's preconceptions, or indifferent towards my own preconceptions. I elaborated my rational and empirical, but possibilian persuasions. I explained how I reconcile those qualities of attitude. Such as, why a rational empiricist can be possibilian, which could then allow this discussion to progress further, without being divided between people of different persuasions. I made a case, hopefully epistemically justified, that possibilianism is natural consequence of rational empiricism, for philosophical subjects which lack clear determination. And I challenge you to make a case on your end for epistemic justification of empiricism, if you felt it was necessary or you felt that my claims were inherently condescending towards yours.
First, my persuasions demand to be recognized and reconciled. I cannot become irrational, simply because I see chance to be in this forum. I can not become rejecting of my sensory experience, simply because I have the opportunity to do so now. This is not how I have structured my personality. If I were to switch mine with yours, I would be just Wayfarer's doppelganger, and we would agree on more subjects, but this is not how my nature works. And believe me, whether rational empiricism is right or not, this is not how my nature works.
But, as a rational, empirically trusting (to a point) person, I do realize that my knowledge has limits, and those limits lie in my own intuitions. That is, I realize that I have attitudes without justification, but hold to them until proven wrong. Then, it seems to me that it would be hypocritical to deny any explanation for philosophically indeterminate subjects, whether it would be theistic or not, dualistic or not, even if it is a creative conjecture. My only conditions were, that we keep the discussion hypothetical, to keep it open to everyone, out of political necessity this time. I also proposed that we try to explain how our hypotheses contrast with each other, their compatibility and incompatibility, their similarity and dissimilarity, consider any possible internal inconsistencies, internal redundancies, or internal sources of incompleteness and vagueness, where by internal, I mean self-exposed or self-confessed.
Quoting Wayfarer
As I have stated in our previous discussions, while there might be a different point of view from the outside, of which I confess, I am not aware, I don't feel that I am compelled by this hypothesis or by epistemic necessity to explain my knowledge. I am not denying that the universe is partially intellectually cognizable, thanks to the fact that it is inherently orderly. Paraphrasing what you stated in some earlier conversation, in rational empiricist terms order is that which explains. But my cognition is just reproduction of order within order, which captures a measure of what the explanation is. The full explanation rests on its own existence, not mine. I don't require that I can explain orderliness through my cognition, because that suggests that my cognition, which is just homomorphic fragment of order within order, is central to the nature of order, and not contingent to the complete picture of orderliness. Orderliness is its own nature. It doesn't require to be explained by me. It justifies itself, however it does. I could synthesize such a construction, where order has underlying explanation, from a greater vantage point, which I somehow antropomorphize. Meaning, it becomes explained in terms that reduce in complexity to my own complexity. Sure. But that just embeds our universe in a super-universe. If I could hypothesize a final antropomorphically cognizable universe, what would distinguish it from ours? Do I do that, just because I cannot fully grasp my own? What I am getting at, is that nature explains itself to itself, but no to me.
Quoting Wayfarer
This gets us to the fundamental distinction between my point of view and yours, which ties beautifully with @Jack Cummings 's question about optimism and pessimism. I see a board of chess on which human beings serve purpose. In the game, they receive the gift of overtaking other pieces, which is just the virtue of their function, but at their level of abstraction or sense of meaning, it appears the logical conclusion of the game. But it is completely unrelated to the game's objective, which wouldn't translate to them at all, and never will, because a pawn has a different sense of purpose. The game has its own unrelated purpose. The game will find its objective, but the pawn will not appreciate it. You see a classroom, where human beings are challenged by lessons, aimed to teach them fundamental truths of a greater vantage point. From my purview, there is no greater wisdom then getting a sense of your identity in the moment, while appreciating your limitations, continuously adapting, hoping that the game is not over for you. To you, there is no greater error then the assumption than the lesson is understood, before reaching a self-evident self-explanatory conclusion. You are ontological optimist and I am ontological pessimist. You believe in benevolent antropocentric antropomorphic universe, I believe in every men as its own universe, clashing against the tides of the exterior motives, trying to adapt without losing its dignity and personally established purpose.
Edit: As I said, I do intend to come back and try to outline my take on a some hypothetical propositions in broad strokes. It might take a day or two. Not that I am that knowledgeable, but we need some kind of enumeration of major ideas.
I didn't mean to say you didn't know this stuff but what I want to bring up is there are certain areas in physics where math, as they claim, "breaks down" e.g. black holes, the Big Bang singularity, to name a few. I wonder if this means anything? Does it shake scientists' faith in math as a complete, self-contained, tool for studying the world at large?
The essay itself is interesting. You can find a copy here. Frege was not at all like Berkeley, from what I can see - more cautious, not prone to sweeping statements or grand metaphysics.
Quoting simeonz
I'm not familiar with this term 'possibilian' and I can't find it on the Web. Perhaps you could explain?
But, beyond that, I fear we're talking past one another. Let's go back to the beginning of your first post in this thread:
Quoting simeonz
Which 'question' do you mean? What question do you think I'm posing that 'can't be answered without some kind of speculation?'
Quoting TheMadFool
Yes, true, although black holes, in particular, were theoretically posited as a direct consequence of Einstein's laws, weren't they? And again I'm not claiming that science is all-knowing even in principle. Look carefully at the OP again. The topic I'm interested in is: are numbers real? And if so, in what sense are they real?
The view that numbers are real, independently of any mental activity on a human's part, is what is generally known as mathematical platonism. The point is, this is unpopular in today's academy; there are many very influential mathematicians, who are far greater experts than I could ever hope to be, who are intent on showing that it's mistaken. But according to this article Benecareff's influential argument against platonism was made 'on the grounds that an adequate account of truth in mathematics implies the existence of abstract mathematical objects, but that such objects are epistemologically inaccessible because they are causally inert and beyond the reach of sense perception.' In other words, this argument denies that we can have the innate grasp of mathematical truths that Frege asserts in the paper mentioned above. That's the 'meta-argument' I'm trying to get my head around.
Possibilianism is mostly concerned with theistic claims, but it is essentially attitude open towards the exploration of unproven claims, as long as they are suggested hypothetically.
Quoting Wayfarer
The question about the nature of experience. What explains having experience and hence knowledge. How does it form - does experience emerge from the innate ability of the material substance to be self-cognizant of its configuration (panpsychism, emergent materialism, pantheism), does it emerge by virtue of connection to higher cognitive self (substance dualism), does it emerge as creative fictional introspection (idealistic existential monism), or does it emerge through collaborative enactment (enactvism). Those are some ideas. All of those ideas explain science in different manner and with somewhat different consequences. Some justify the attitude of empiricism completely, and others explain this attitude, but do not justify it.
Do you agree that abstractions "in the mind" can be formed differently according to each of those hypotheses?
Thank you for sharing it with me. I am going to check it out.
I will try to briefly summarize my take on each idea. Those are my interpretations, so you could argue with them or not, but I am not sure that any of them coincide completely with Spinoza, or Leibniz, or some established authority.
Panpsychism proposes that nature is self-cognizant. The problem is how do the constituents of matter enact mental coherence and unity between each other, to form singular consciousness. But if some kind of emergentistic view applies, then matter simply perceives matter and captures knowledge and ideas by representation. This representation automatically traps the abstractions that homomorphically approximate the environment (also panpsychic matter). Pantheism is very close, but emergentism follows more naturally, because the deity is capable of self-awareness (possibly unrelatable to our understanding) and the material constituents just capture local fragmented perspectives of it.
Substance dualism keeps the ideas in the mind separate from the physical world. The brain and the world are a computational device. The mind is the actual carrier of experience. The problems that it faces are - where and how is the mind created, is the knowledge captured in a supervening manner preserved after the physical embodiment is disassociated, what happens when the body is mentally impaired or the amount of bodies decrease, etc.
I may be coining the term idealistic existential monism, but the idea is that our identity is fictional and our experience of the world happens within the confines of single cognizant entity that also creates it. (Edit: We are the split personalities of a deity that willingly experiences disassociative identity disorder. This is similar to pantheism, but doesn't require allocation of cognizant potential to matter. In fact, I see no apparent obstruction to creating and destroying identities in this hypothesis, because they serve only as epistemic device to the creator.) The problem here is primary motivation, but cognition and understanding is trivially possible.
Enactivism is as close to what was referred on the forum as intersubjective idealism. Each person is a creative force, but the collective effort is contingent and self-regulating. How it self-regulates constitutes the challenge for this hypothesis.
Edit. Obviously, you are free to amend and adapt my take on the ideas or propose your own.
You’re clearly a deep and well-read thinker about these questions, but I still feel that in respect of this particular thread, we’re talking at cross-purposes. The rhetorical question I’m posing is, why is mathematical Platonism out of fashion?Why is it that many serious mathematicians and philosophers seek to discredit it, and to explain our ability to mathematise in naturalistic or reductionist terms? It’s really rather a specialised question, and one I am barely qualified to consider, considering how technical many of the arguments are. But it’s a question I’m intrigued by, in fact my first forum post in 2010 was about this very question, and to me it’s still very much a live issue.
I’m very much attracted to that idea. I find the key figure there is Husserl. His ideas of the umwelt and lebenswelt, as kind of ‘meaning-environments’, speaks volumes to me.
Yes. In retrospect, I realize that I got a little carried away from the topic. I got stuck on the issue of the nature of experience. I'll think about whether I can research and contribute something more topical later (edit:...or much later).
Well, what exactly does "real" in "numbers are real" mean? I'm no mathematician but I can say with some degree of confidence that numbers are, at the end of they day, abstractions - they are, in the most basic sense, patterns in sets: The number 1 is the pattern in the sets {0}, {a}, {red}, {fox} and the number 3 is the pattern in the sets {good, 3, pee}, {%, fee, bravery}, {love, dog, +} and so on. The question then is, are abstractions real? Finding an answer to this question is the first order of business, no? So, what do you think? Are abstractions real?
A good starting point is to realize that all it takes is a mind sensitive to patterns, with a pattern-recognition module so to speak, to see that there is a pattern in the world as we know it that humans have named numbers. Any system capable of detecting patterns will, sooner or later, hit upon the idea of number from its observations of the world. Doesn't that indicate that though it takes a mind or a pattern-detecting system to conceive of numbers, the pattern has to exist outside of the mind, in the world "out there" as opposed to "inside our minds"? How can the mind perceive of something that doesn't itself exist in some sense of that word? Beats me.
Have you also looked into Imaginary Numbers? The square root of -1, according to mathematicians, doesn't exist and that means, the aptly named, real numbers exist. How exactly are mathematicians using the words "exist" when making statements about the reals compared to imaginary numbers?
I don't think this is right. Imaginary numbers exist as mathematical entities used by mathematicians. In exactly the same way that the real numbers exist for mathematicians: they exist because they are used. The imaginary numbers are just plotted on a different number line (not the real axis).
The term imaginary number is considered to be a misnomer by many mathematians.
@Wayfarer Corrigendum.
By the way, if imaginary numbers exist, what is the square root of -1? I know the square root of 4 is 2, a number; I know the square root of 2 is 1.414..., another number.
All real numbers are (probably?) instantiated in the universe. Take for example pi, wherever you see something circular/spherical, it's there as the ratio between circumference and diameter.
Where is a real-world instantiation of the square root of -1? Electronics? Semiconductors?
They exist as abstractions, mathematical concepts.
Quoting TheMadFool
There are certainly mathematical abstractions without a concrete actualisation, and these include real numbers. I think uncomputable real numbers would be an example (chaitins constant). Or a number a billion times larger than the atoms of the observable universe. I mean, there is always a larger number in abstract land..
Yet real numbers and "imaginary" numbers aren't exactly like each other. I can easily express any real number with the numerals, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 and a decimal point but not an "imaginary" number. This difference, how does it impact the OP's concerns?
You seem to have missed the point but it's entirely my fault. What I meant was real numbers - as a category - has real-world instantiations i.e. there's at least one real number that's actually, let's just say, measurable with a straight edge. Not so for "imaginary" numbers.
Edit: The strength of an electromagnetic field can be measured by complex numbers (apparently).
That mathematical Platonism is unpopular in today's academy presents an odd dilemma for mathematicians. Platonist principles support a huge part of modern mathematical systems, underpinning extensionality and set theory, to begin with. These mathematical axioms require that a term signifies an object. Only Platonism can support this prerequisite. So, if there are proficient and influential mathematicians who openly deny Platonism, then these same mathematicians must be prepared to revisit, denounce and replace, all the fundamental mathematical axioms which are based in Platonism, or else they are simply being hypocritical.
Yep. Sir Paul Davies is at least one of many theoretical physicists who would agree with that! :up:
:up:
[math]i[/math] appears in the Schrodinger equation:
[math]i\hbar\frac{\partial}{\partial{t}}|\Psi(t)\rangle=\hat{H}|\Psi(t)\rangle[/math]
That is a historical question, and my understanding is that mathematicians refer to "real" numbers only to distinguish them from so-called "imaginary" numbers; the latter term actually came first.
Quoting TheMadFool
In general philosophy, "real" means being such as it is regardless of what anyone thinks about it. In philosophy of mathematics, realism ascribes this nature to mathematical objects, including both real and imaginary numbers.
Quoting TheMadFool
Yes, it is routinely used in circuit analysis and design.
This is false, since it is not necessary for something to exist--in the metaphysical sense of reacting with other like things in the environment--in order to be the object of a sign. It does not even have to be real--it could instead be fictional, as some philosophers consider mathematical objects to be. Also, as I have explained elsewhere, signs denote their objects; what they signify are their interpretants.
Cheers. Not quite the direction I thought you had in mind, but that will make it more interesting. I will do some reading.
https://plato.stanford.edu/entries/platonism-mathematics/
https://math.dartmouth.edu/~matc/MathDrama/reading/Wigner.html
https://www.smithsonianmag.com/science-nature/what-math-180975882/
Quoting TheMadFool
That is the point at issue! If numbers are real, but not corporeal, then it's a defeater for philosophical materialism - there are reals that are not material. I think this is why platonic realism is so firmly resisted - it cuts against the grain of naturalism.
I don’t think this includes imaginary numbers or fictitous entities (like Sherlock Holmes or Bugs Bunny). Once mathematics becomes thinkable, then all kinds of fictionalised and imaginary systems can be invented, but I don’t think it detracts from the point at issue.
I think it what platonic realism does include is an astonishingly wide range, however. Think of the 'elements of reality' that are likewise only intellectual in nature, but are nevertheless real: 'interest rates, mortgages, contracts, vows, national constitutions, penal codes and so on. Where do interest rates "exist"? Not in banks, or financial institutions. Are they real when we cannot touch them or see them? We all spend so much time worrying about them - are we worrying about nothing? In fact, I'm sure we all worry much more about interest rates than about the existence or non-existence of the Higgs boson! Similarly, a contract is not just the piece of paper, but the meaning the paper embodies; likewise a national constitution or a penal code’ ~ Neil Ormerod.
The human 'meaning-world' is constituted from these elements, but they’re not 'out there somewhere'. They don't exist in the same way that flowers or pens or chairs exist but are real nonetheless.
This only supports my point. To justify calling an imaginary thing "an object" requires some form of Platonism.
It seems to me that number is obviously real. There is a real concrete difference between two apples and three apples. Numerals also are obviously real, they can be written and spoken. I can't see what all the controversy is about if one side (the platonic realists) are not arguing that numbers as actual entities of some kind "exist somewhere" (although obviously not in spacetime) or at least somehow.
The question for them is where or how do numbers as actual independent entities exist, or what would it mean to say they are real beyond saying that they are (real) abstractions?
No, it does not. Hamlet, the fictional character in Shakespeare's play, is the object of the sign that is the first word of this sentence. No form of Platonism is required to affirm this.
Not if you subscribe to fictionalism.
Quoting Janus
The whole debate is exactly about the ontological status of abstracts. Mathematical Platonism says that the real numbers are not dependent on any mind, i.e. they’re not the product of thought. As Frege puts it, that they are grasped by the mind ‘in the same way the hand grasps a pencil’. But if they’re real, then what kind of existence do they have? What does it mean to say abstract objects exist? Where are they? This then circles back to - why, they exist ‘in the mind’.
If you glance at those refs I provided to Banno above, these arguments are discussed. Last one is the best starting point.
What more could be said about the ontological status of abstracts other than that they are real abstracts? Analogously what more could be said about real physicals other than that they are real physicals?
At the risk of belaboring the point, it is an all-too-common nominalist mistake to insist that if abstract objects are real, then they must also exist. These are two very different concepts--whatever is real is such as it is regardless of what anyone thinks about it, while whatever exists reacts with other like things in the environment. Again, there are varieties of mathematical realism other than Platonism.
I agree with you, but thousands wouldn’t. I’ve had many exchanges with others on this Forum who believe that ‘existence’ and ‘reality’ are synonyms, and who can’t imagine what it would mean for them to differ.
Quoting Janus
Surely you can see how this poses a problem for naturalism? If you can’t see it, then sure, there’s nothing to discuss.
This might help the case for some version of idealism (non-materialism).
Quoting Wayfarer
This maybe the stumbling block for idealism (non-materialism).
Even if we were to all agree that immaterial numbers exist, we still have to contend with the fact that numbers aren't like "...flowers or pens or chairs..." We're not out of the woods yet.
Where's your grammar? Fictional characters are known as subjects, not objects. Your claim that "Hamlet" refers to an object is unsupported by any conventional grammar.
Even if I grant you that fictional, imaginary things may be called objects, my point was that some form of Platonism, as an ontology is required to support the claimed reality of such objects. So this line of argument is not really getting you anywhere.
Quoting aletheist
Trying to establish a separation between "real" and "existent" just muddies the water by creating ambiguity, and is counterproductive toward understanding. As well as being "real", ideas, concepts and abstractions are obviously "existent". They have a significant effect on the physical world as clearly demonstrated by engineering.
So defining "existent" as having causal interaction, then attempting to remove ideas from this category is a mistake because ideas obviously have causal interaction. Then this proposed separation between "real" and "existent", which would put ideas into some category of eternal inert objects which cannot have any influence in our world in any way, is just child's play. It's an imaginary scenario which in no way represents reality.
... An all-too-rarely credited nominalist insight, rather.
Quoting Metaphysician Undercover
Quoting Quine, On What There Is
Again, in semeiotic a subject is a term within a proposition that denotes one of its objects. "Hamlet" is a sign, a subject of a proposition such as "Hamlet killed Claudius." The fictional character in Shakespeare's play is its object. Other subjects of that proposition are "killing" and "Claudius," which denote a relation and another fictional character in Shakespeare's play as their objects. The predicate is signified by the syntax, conveying that something called "Hamlet" stood in the relation of "killing" to something called "Claudius" within the universe of discourse, which in this case is Shakespeare's fictional play--not the real universe.
Quoting Metaphysician Undercover
It is firmly supported by what is known as speculative (theoretical) grammar within semeiotic, the science of all signs.
Quoting Metaphysician Undercover
No one is claiming that fictional, imaginary things are real. In fact, being fictional is precisely the opposite of being real. That which is fictional is such as it is only because someone thinks about it that way; Hamlet was the prince of Denmark only because Shakespeare created a story in which that was the case. By contrast, that which is real is such as it is regardless of what anyone thinks about it; Platonism is one form of mathematical realism in this sense, but not the only one.
Quoting Metaphysician Undercover
On the contrary, I have found that carefully drawing the proper distinction between reality (whatever is such as it is regardless of what anyone thinks about it) and existence (whatever reacts with other like things in the environment) is extremely clarifying and helpful. Treating them as synonymous is what muddies the water by imposing nominalism, effectively begging the question against realism.
Quoting Metaphysician Undercover
The first sentence is false, but the second is true. The kind of effects that ideas, concepts, and abstractions have on the physical world is obviously very different from the kind of effects that physical things have on the physical world. The former are not like things in the (physical) environment, so they do not exist in that sense. Nevertheless, some of them are real--they are such as they are regardless of what anyone thinks about them--but this does not require them to be "located" in a Platonic realm.
I don't think there is any problem with saying that numbers exist in logical space just as objects exist in 'physical' space. Numbers react with "like things" (other numbers) in their environment just as physical things do in theirs. Also number, quantity, is a significant, integral part of all physical interaction, so it's not like number (quantity, as opposed to the abstraction from quantity; numbers as distinct entities) doesn't exist in the physical world. As I said before there is an actual difference between three apples and four apples.
Quoting Wayfarer
It depends on what you mean by "naturalism". For me number is an obvious part of nature, and abstraction is a natural part of being a self-reflective being. If you don't want to posit a supernatural reality, or you don't associate naturalism per se with the kind of reductive scientism that thinks everything can be explained in objectivist terms or even more extremely, in terms of physics, then what is the problem with naturalism? I see naturalism at its most general as simply a rejection of the supernatural as a separate or higher non-physical reality or realm.
The most striking thing about The Unreasonable Effectiveness of Mathematics in the Natural Sciences is that the argument is not about reason, so much as about Wigner's sentiment. That maths has been used with such success feels wrong to Wigner.
One is tempted to answer: so what?
A child who learned chess by watching adults play might insist that it is "self-evident" that the bishop stays on its original colour.
But it isn't. It's just how we play the game.
Frege might insist that there are primitive truths that are self-evident.
But there aren't. It's just how we play the game.
We might add a rule to Chess such that when the Bishop moves to a corner at the far end of the board it may move immediately to an adjacent square, changing colour. We could continue to play despite having broken the self-evident rule.
We add a rule to mathematics naming the square root of -1 'i'; and we continue to play the game.
What looks like an intuition — that the bishop stays on its own colour and that there is no root to -1 — is mere convention.
I'm picturing the issue as one of as direction of fit, as in Anscombe. That the number of things in the box is 3 is something we do; the direction of fit is from us to the world.
Add to that, that concepts are not things so much as a way of behaving; that is, concepts are best not considered as things in people's minds, but as ways of talking and acting.
Then we have a way of talking that goes "one, two, three" while pointing to each thing in turn. And we can use this way of talking to talk about lot of different things. And then we can talk about this way of talking when we find ourselves adding, then multiplying, then differentiating...
SO even though numbers are not things, we develop mathematics by treating them as if they are. And in the end they become things just by our having treated them as such.
So, the extension of "Wayfarer" is Wayfarer. The extension of "red" is each and every red thing. But the extension of "1"? Well it's literally every individual. And as such it seems to me, at least in my present mood, that the extension drops out of the game, and what we have is the intension, the rule, concept or game we play in counting.
And the consequence of that is that talk of extension in mathematics becomes fraught with ambiguity. Hence, Wittgenstein's argument that mathematical extensions must be finite, and hence his adoption of finitism, seems misguided.
...all this to say that Platonic Realism towards mathematical objects is not wrong, but just one way of treating those objects. It comes about by extending the notion of what is real to encompass numbers.
Tosh. When Einstein discovered relativity, he was not ‘behaving’ or ‘acting’, or rather, his ‘behaviour’ and ‘action’ was mainly sitting and writing, and, I imagine, staring into space, and taking long walks. Many people ‘behave’ and ‘act’ like that, but that doesn’t give rise to a monumental scientific discovery. That was made by virtue of rational insight and unique mathematical intuition. Einstein had to devise a mathematical lexicon to articulate what he saw. And as is well known, those insights have proven predictive time after time. How many times have we read the headline ‘Einstein Proved Right Again’?
I think the issue around Platonic realism is simply that it torpedoes one of the beloved dogmas of empiricism, ‘no innate ideas’. There’s your ultimate sacred cow in our day and age. Read these snippets from the various sources I’ve referred to:
And from the Internet Encyclopedia of Philosophy article on the Putnam-Quine Indispensability argument:
And are our ‘best epistemic theories’? Why, they’re grounded in neo-Darwinian materialism, which can never allow that we could have intuition of mathematical verities:
Oh, what a quandary. So why not admit the obvious: that ‘our best empirical theories’ leave something fundamental out? Because then, ‘you’re opening the door to Religion’, and ‘empiricism might as well go out the window’. Well - splendid idea - better alternative than having to devise these tortuous rationales like the Indispensability Argument or Fictionalism.
It’s politics, at the end of the day. There’s certain ways you’re supposed to think, and if you don’t go along with that, woe betide unto you.
Quoting Wayfarer
Relativistic is a way of calculating relative velocities at speeds approaching c - a way of behaving.
Quoting Wayfarer
I think the issue around Platonic realism is simply that you wish it to torpedo one of your despised dogmas of empiricism, ‘no innate ideas’.
But this is not getting the conversation very far at all.
SO we might try this: if you think mathematical objects are real, perhaps we might look at how "real" works.
It's a real car, not a toy. It's a real dollar note, not a forgery. It's a real boy, not made of wood.
It's a real mathematical object, not...?
What?
1. Despite the title, Wigner is merely expressing a sentiment .
2. Edit - I left out Frege. What is self-evident to one person may be rejected by another. In particular Frege's desire to develop a logical basis for arithmetic and hence for maths as a whole has been show impossible. Maths cannot be derived in its entirety from self-evident truths.
3. There are alternatives — I offered by way of example good reasons to suppose that numbers do not refer to anything — and so no need to jump to your believe in Platonic Realities
4. The use of "real" in Platonic realism needs justification. It is not at all clear what it is that Platonic Realism claims is real...
Bare assertion with no supporting argument.
Quoting Banno
You simply referred to behaviourism, which has been obsolete since the 1940's.
Quoting Banno
It's not clear to you. The Indispensability Argument is a good starting point. But this controversy is about something.
Then show me were Wigner does more than I say - the arguments are there, but I think them of little merit. Choose one to discuss.
Quoting Wayfarer
You know that is not an accurate rendering of Wittgernsteon's attitude towards mathematics. You can do better.
Quoting Wayfarer
If it is clear to you what it is to be real in Platonic realism, you should be able to share. You will be aware that this is the most common criticism, so you presumably have a reply. Where can I find a real platonic circle?
It's a real physical object - it's not an illusion, it's not a reflection, its not a mirage...
It's a real abstract object - its not...?
It is common knowledge that Frege's logicist project failed. Frege 0, Godel 1. And guess what?
[quote=Rebecca Goldstein] Gödel was a mathematical realist, a Platonist. He believed that what makes mathematics true is that it's descriptive—not of empirical reality, of course, but of an abstract reality. Mathematical intuition is something analogous to a kind of sense perception. In his essay "What Is Cantor's Continuum Hypothesis?", Gödel wrote that we're not seeing things that just happen to be true, we're seeing things that must be true. The world of abstract entities is a necessary world—that's why we can deduce our descriptions of it through pure reason. 1[/quote]
Besides, the point I was illustrating from Frege is that mathematical platonism is simply assumed by many logicians and philosophers, Frege being an example, and the illustrations of why he thinks that way are germane to the argument.
Quoting Banno
Platonic objects don't exist anywhere, they're purely noumenal, they're objects of thought. It's not that any physical circle is somehow imperfect, as many people say, but that the idea of a circle is precise and determinate, and would be so, regardless of whether any physical example exists or not.
So the question 'where can I find...' denotes a failure to grasp the point at issue. The whole point is, numbers and geometric forms and the like are transcendent, they are not located in space and time. And this is why naturalism has no way of conceiving or coping with them. Hence all those hysterical rhetorics I quoted from the Smithsonian article. If you admit the reality of transcendent objects then this poses grave difficulties for the standard-issue naturalism.
I know this is a very difficult point - I've been discussing this subject since day one on this and other forums. Conceiving of anything that doesn't exist in time and space requires a kind of 'through-the-looking-glass' realisation, a type of gestalt shift regarding what is real. Added to that, as i keep saying, and you keep ignoring, it goes against the grain of all of the accepted wisdom. We're conditioned to believe that what is real exists in time and space, and empiricism continually re-inforces that by insisting that anything considered real must be sense-able. Hence your question, 'where can I find it?'
Quoting Banno
So you may think that is mere 'sentimentalism' but I don't think it does it justice.
Yep - as I said,
Quoting Banno
We might consider this alternate definition of real...
Quoting aletheist
On this account a painting is real, but it is also a construction. Our two views may not be mutually exclusive.
But i remain keen on the Austin's analysis of real as a term that gets its meaning by contrast, so again, It's a real abstract object - its not...?
It is the ontological status of real abstractions that is at issue. Empiricism has to insist that they're the product of the mind, otherwise there's no conceptual space for them to be - they're not located in time and space, yet that is the entire theatre of operations for empiricism. This is the basis of the interminable argument about whether maths is real or invented. Of course, it's both, but at least in some fundamental respect, it's real. ("God created the integers....")
(I have to sign out for some hours, I supposed to be doing a self-training course, so have to drag myself away.)
Ok - what is the conclusion that you would like us to reach from this?
Sure looks like fancified Platonism to me, if a subject must denote an object.
Quoting aletheist
I really don't understand your position. You assume that fictional characters are objects, but you deny that they are real, and you deny that they are existent. How do you validate your claim that they are objects?
Argh. You have my sympathy.
Quoting Wayfarer
Of course that is insufficient. It does not follow that they are real... and we still do not know what real is doing here.
Any argument is to be in suport of a sentiment felt by some mathematicians, that they are discovering rather than inventing. again, we need more than sentiment.
Simple--in semeiotic, anything that is denoted by a sign is, by definition, its object. Since all thought is in signs, anything that we can think about--real or fictional, existent or imaginary--is an object in this sense.
To adhere to the distinction you made for me in the other thread, in much usage of signs, probably the majority actually, the signs have significance without denoting anything. For instance in "I'm going for a walk", the only object denoted is "I". And in your example of fictional writing, there are no objects denoted. The author simply builds up images of characters without denoting any objects.
It seems clear that you are using a different definition of "object" than the one rigorously employed within the discipline of semeiotic. Again, anything that is denoted by a sign--real or fictional, existent or imaginary--is an object in that technical sense.
Quoting Metaphysician Undercover
The only signs that theoretically could signify something without denoting anything are pure icons, unembodied qualities that would only convey themselves as they are in themselves. Any sign that stands for something else denotes that other object.
Quoting Metaphysician Undercover
On the contrary, "going for" denotes a certain kind of relation as its object, and "a walk" denotes a certain kind of activity as its object. In fact, as symbols, words and phrases typically denote general concepts like these as their objects. The syntax of the sentence is what signifies the interpretant, which is the relation among the denoted objects that the corresponding proposition conveys.
Quoting Metaphysician Undercover
If this were true, then the author could not create those "images of characters" in the first place, and we could not think or talk or write about them afterwards. Again, the sign "Hamlet" denotes the fictional character in Shakespeare's play as its object.
Quoting Banno
...it's not an illusion, it's not imaginary, it's not a fiction. It's attributes are not a matter of opinion.
Ah. Is this the possibility that bothers you?
If maths were invented, do you think it might be subject to mere opinion?
Games like chess or backgammon may unequivocally be said to be invented.
Games are arbitrary, though, and lack real world applications beyond themselves.
On the other hand, was the internal combustion engine invented or discovered? It could be said that it represents a possibility that was discovered, someone else might say it was invented.
Mathematics has real world applications. I think it's fair to say that quantity and the possibility of counting is discovered, not invented; even some animals can recognize number to varying degrees.
Proofs in mathematics are said to be discovered, as they are logical possibilities that arguably would exist even if no one discovered them.
Didn't Russell rather skewer that approach? (On Denoting.)
Quoting Metaphysician Undercover
Speaking literally, yes.
Quoting Metaphysician Undercover
This needs clarifying. Produces strings of alphabetic characters? Sure. Conjures mental images of non-existent and hence undenoted people? Well, "mental" is problematic but let's park that. Or skirt it, by assuming the book is a picture book. Goodman's very neat solution is then to read "images of characters" e.g. "picture of Pickwick" not as requiring two separate denotata, a picture and a Pickwick, but as long (if only slightly) for "Pickwick-picture", a one-place predicate applying to a certain sub-class of pictures.
Quoting aletheist
If what version were true? If my suggested version, then why (could we) not?
Quoting Goodman, Languages of Art
I think it is natural to divide subjects between what is 'in the mind' and what is 'in the world'. What is 'in the world' is said to exist independently of any act of observation on the human's part - the vast universe with all of billons of galaxies, this earth and its solar system and so on.
In contrast, what is 'in the mind' is thought to comprise language, culture, reason, concepts, mathematics, science, the whole furniture of thought.
So within this mindset it is natural to presume that mathematical proofs are 'in the mind'. Where else, it is asked, could they be? They're not 'out there somewhere'. But if they're in the mind, then how could they be discovered, because they're not objectively existent? If they're in the mind, they must be a product of the mind. They are, it is said, 'mind-dependent' and so categorically different to the supposedly 'mind-independent' domain of the vast natural world.
This is where I think the conflict between mathematical platonism and empiricism lies. Many of the sources I quoted in this thread show that this is exactly how the conflict is seen by empiricists. I am not 'attacking staw men' here.
(My view is that realiity is experienced reality and that this even goes for the hard sciences. Nothing exists truly independently of any act of observation, or rather, whatever we think or say about 'what exists' implicitly implies the act of observation, which provides the conceptual framework within which any and all existence statements are made. Not seeing this is precisely the meaning of 'the blind spot' which had a very hostile reception when I mentioned it in June 2019.)
Why then did you insist on a distinction between "signification" and "denotation" in the other thread, when here you want any signification to be a denotation?
Quoting aletheist
So, you insist on a distinction between signification and denotation, then it turns out that there is no such thing as signification in common usage. All instances of signification are assumed to be denotations of objects. What's the point?
Quoting aletheist
Let's start with a clean slate then. There is no such thing as signification. Words do not have meaning, they denote objects. is that what you want?
Otherwise it's pointless for me to say that an expression has meaning (signification) and you just overrule and say no, that's not meaning, it's the denotation of an object. We will never get anywhere like that. What is your rigorous definition of "object" which allows you to claim that any instance of meaning is a denotation of an object? If you and I both read the same expression, and I interpret it as meaningful, without denoting any object, and you interpret it as denoting an object, what is your rigorous definition which makes you right, and me wrong, if you are not just assuming that anything with meaning denotes an object?
Here Russell gets Meinong wrong. Meinong does not claim that such objects exist. He claims that some objects exist, some subsist and some don't exist at all.
A popular science-math weekly used to offer challenges for readers to submit original proofs for mathematical theorems. The Pythagorean theorem received about a hundred different proofs from creative readers.
That kind of dualistic thinking does seem to be "natural". I would rather more simply say there is a distinction between what exists and is what it is independently of opinion and what doesn't exist independently of opinion and is only what it is on account of opinion.
Quoting Wayfarer
I agree that our reality is experienced reality, but we can easily enough imagine that there are realities that exist independently of our experiencing them. I know, you will say 'It is still us imagining them'; but I don't see that as a cogent objection since I don't think the purported contradiction said to be inherent in that holds.
Of course we can't experience realities which are beyond our experience, that would be a contradiction, but we can imagine them as existing, and we can (rightly, in my view) think it is likely that they do exist. On the contrary it seems absurd to say, for example, that nothing existed prior to the advent of humans.
Nice example!
This question just confirms an ongoing failure (or refusal) to understand the technical definitions of denotation and signification within semeiotic.
Quoting Metaphysician Undercover
That is not what I said. There is no such thing as pure signification (without denotation) in common usage. Likewise, there is no such thing as pure denotation (without signification) in common usage. Instead, in practice every sign both denotes its object (what it stands for) and signifies its interpretant (what it conveys about that object). This is most readily evident in a proposition, where the subjects (terms as names) denote the objects and the predicate (embodied as syntax) signifies the interpretant. The fundamental principle of semeiotic (following Peirce) as distinguished from semiology (following Saussure) is that a sign thus stands in an irreducibly triadic relation with its object and its interpretant, rather than there being only a dyadic relation between signifier and signified.
It's the theorem that's discovered/created first. Then the search for a proof. Math is not just challenging others to solve a stated problem, although for many that is a competitive aspect highly desirable.
The duality of ‘self-and-world’ develops in infancy. Interestingly, in translations of the early Buddhist texts, the expression ‘self and world’ is sometimes used in places where you would expect ‘self’ - the connotation being that self and world are mutually interdependent or in modern terms 'co-arising'. I think that since the Enlightenment, philosophy has increasingly lost sight of this interdependence. (Arguably, it was the intuition of interdependence which was the basis of Berkeley's philosophy.)
Quoting Janus
It was Plato who disparaged ‘mere opinion’ masquerading as knowledge. Scientific method is ostensibly aimed at attaining mathematical certainty with respect to its objects of analysis. The problem is, as we have discussed many times, it does so at the cost of eliminating the qualitative dimension of existence without which human life is meaningless. This is a consequence of the division of the objects of knowledge according to the primary and secondary attributes, originating with Galileo, which gave rise to what Whitehead described as the 'bifurcation of nature'.
Quoting Janus
I question that any notion of existence is coherent absent a subject to whom it is meaningful. This goes for the most rigorous scientific modelling of the Cosmos also. The units of measurement are meaningful to humans, and the human mind furnishes the perspective within which statemements about time, space, duration and distance are meaningful.
(Paul Davies, The Goldilocks Enigma: Why is the Universe Just Right for Life, p 271)
I wouldn't cal it "self and world" but rather 'self and other'. Even animals arguably have this sense. But it is this very sense and acknowledgement of existences other than our own that underpins the coherence of imagining existences that are independent of our experiencing of them, our possibility of experiencing them or even of our existence tout court.
So, I cannot agree with this:
Quoting Wayfarer
This is an ambiguous statement. Of course a notion of existence can only be coherent to a subject to whom it is meaningful; that is tautologically true on one reading. But you seem to be wanting to extend that to say that we cannot coherently imagine that there are existences that are completely independent of us; and with that I disagree.
It may be incoherent for you, on account of its not cohering with your particular presuppositions, but it presents no problem for me, because my presuppositions are consistent with it.
In fact I would say that it is incoherent to imagine that nothing existed prior to the advent of humans. I would say that it is impossible to coherently imagine that because it flies in the face of all our knowledge.
Also, I'm not convinced of the relevance of the so-called "observer problem" in QM, because there is no uncontroversial interpretation of the significance of that problem for ontology. And in any case by your own lights QM is just another human-based investigation and so can tell us nothing about anything beyond human experience.
Seems to me that proofs can neither be independently created nor discovered. Even together, creativity with serendipitous discovery aren't sufficient to make an Euler. Something is still missing. Then there is the issue of computer generated proofs. What kind of thinking is involved there?
Sure there is pure signification, in the case of any abstract use, a universal, like "temperature", "big", "good", "beauty" "green", "wet", and the list goes on and on. You just want to insist that these can only be used when describing an object, to support your special form of Platonism. But it's not true. We use all these terms as a subject when we say things like "temperature is a measurement", "big is a size", "good is desirable", beauty is what the artist seek", "green is a colour". These are phrases of pure signification, and to turn the subject into an object will most probably lead to category mistake. Because then we lose the capacity to distinguish between a physical object denoted, and a subject of study denoted. If these two are the same, as "object denoted", category mistake will prevail.
No, these words are examples of signs whose objects--that which they denote--are general concepts.
Quoting Metaphysician Undercover
No, in each of these propositions there are two or three subjects denoting two or three objects, and the interpretant conveys something about the logical relation between those objects. The interpretant of each individual word is the aggregate of all the different propositions that include it, which we attempt to summarize whenever we write a definition of it.
Quoting Metaphysician Undercover
The category mistake is conflating different definitions of "object" and "subject" that apply in different contexts. An object is not necessarily something physical, and a subject is not necessarily something that we study. In semeiotic, an object is whatever a sign denotes, and a subject is a term within a proposition that denotes one of its objects.
Intuition, instinct, imagination, et al.
Quoting magritte
I suspect ingenuity on the part of the program creator. After that a computer does what a computer does. Here's a good article: Computer Proofs
:up:
I know that's what you think, but I disagree. I think that you're way of looking at things creates ambiguity in the meaning of "object", which leads to equivocation between mental objects and physical objects, resulting in category mistake.
Quoting aletheist
Oh, come on. One cannot expect to consider all the different propositions that include a word, when interpreting that word. Many could be inconsistent or contradictory. In a logical proceeding there are stipulated propositions. But there are no objects, just subjects. The propositions make predications of subjects, not objects.
An object is defined according to the law of identity, as unique, primary substance, but a logical subject is not unique, as secondary substance. So the relations you refer to may be applied to multiple objects, as universals, because a subject is not limited to representing one object. But in calling these subjects "objects" you imply the uniqueness of an object, as required by the law of identity, Therefore in defining "object" in this way you loose the capacity to distinguish between whether the relation referred to is a unique relation, specific to a particular situation (object in my sense), or a universal relation, common to numerous objects (in my sense), represented by a single subject. In other words, by calling the subject an object, we loose the capacity to distinguish uniqueness, due to the ambiguity and the category mistake which will prevail.
Quoting aletheist
Do you believe in the law of identity and the uniqueness of an object? If so, then how can you allow that "whatever a sign denotes" is an object, when the same sign denotes different things in the minds of different people? Do you assume an independently existing Idea, or Form, as the ideal conception, or unique object denoted, separate from the less than perfect ideas of individual human beings, which are all slightly different?
I know that you disagree, and at this point I find that comforting.
Quoting Metaphysician Undercover
There you go again, making stuff up to sound knowledgeable. That is not how "object" and "subject" are defined within semeiotic. I get it, you reject those definitions, so again we can stop wasting each other's time.
The question though, do you see that I have very good reason to reject those definitions? They increase ambiguity, leading to equivocation and category mistake. In the interest of understanding, you ought to reject them as well. Don't you think?
On the contrary, within semeiotic the definitions of terms including "object" and "subject" are unambiguous and foster greater understanding. As far as I can tell, your only reason for rejecting them is that they are different from your preferred definitions, which you want to impose on any and every context.
I am a little moody and out of sorts, so I apologize that I made no attempt to reply. I will give my brief account of Benecerraf's argument, from what I could surmise so far.
It is key that the author specifically distinguishes knowledge from theory. The first conjecture he makes is that mathematical knowledge is obtained by experiencing such situations that produce belief (causally). Assuming that I interpret the paper correctly, the belief is expressed extensionally, as the potential evidence that would be considered in agreement or disagreement with the experiencing subject. Whether the belief is justified or not in some communicated sense is not relevant, because it is defined by the circumstances that compel it. Although, this point is developed at a much higher level then what is necessary for me to expound its empirical meaning, particularly what solicits some persuasion and how it is embodied, it appears to be deliberately extensionally situated and not intensionally represented. Anyway, the argument is made, I think, that truth in abstract theories is evaluated in terms of the congruency between the conclusions and the discovered facts. In other words, we synthesize theories intensionally and then check their validity by observing situations that agree with their prerequisites and we make determination if the inferred theorems match with the states of affairs, according to some rational interpretation (i.e. Tarski's interpretation). (If the theory is logically consistent and we always observe situations that meet its prerequisites part way, we could speculate that rational logic is not good qualitative control.) If I have understood the conclusion correctly, since we have no limitations imposed on how we synthesize abstractions intensionally, and we have no analytic correspondence between our state of belief and the extension of the facts which will compel us to believe or dissuade us from believing, abstractions cannot be explained as beliefs. In other words, theoretic intensions and persuasion extensions cannot be matched apriori.
(Made an edit to express the conclusion in what I consider slightly better terms.)
Analogy,
My umbrella is designed to guard me against rain. Does it therefore rain if I have opened my umbrella? It needn't be. I might be checking to see if it works. (The object is designed as such, but my action of raising it is ultimately independent of my need for it). I run towards the visor of a building with newspaper over my head. Is it raining? The object is not designed as such, but under the present circumstances, my behavior with it indicates that I am in need of cover (my behavior is a belief indicator).
It is a rather difficult text and I am not on that same level. The author makes reference to another paper, "Platonism and the Causal Theory of Knowledge" by Mark Steiner. If someone has access to it and could elaborate its content, it might shed light.
So, there's really an obvious conflict here, between what has always been understood as 'reason', and what today's 'best epistemic theories' are. I simply conclude from all this that today's 'best epistemic theories' are deficient in some fundamental respect, in not being able to accomodate the faculty which is uniquely human, namely, reason. And that's because we're not simply physical creatures, whose capacities for learning are exhausted by our physical bodies. So if it's one or the other, I choose reason.
Set theory, and the axiom of extensionality.
Quoting aletheist
I conclude that you didn't read, or for some reason couldn't understand what I said then.
You have to account for the fact that our brain is capable of detecting isometries, similarities, etc, which is product of marriage between ourselves and our environment through long evolutionary process. In other words, there is apparent phase of alignment of the cognitive apparatus to some world qualities, which aren't purely analytic.
(We had an exchange with @Banno recently, where I presupposed observational capacity. To think of it, since I presupposed it before the conception of higher order abstractions, it may have appeared a moot point to insist that concepts in modern mathematics can be analytic, since the apparatus that performs the basic processing of the sensory information is developed in a clearly situated historical fashion.)
I will try to illustrate the empirical account of our ability to handle the aforementioned geometric mappings, from an evolutionary standpoint, by going back to the annoying umbrella analogy again.
I have never witnessed rain. I am basic reactive organism that doesn't employ universals yet, but is capable of situational memory through reproduction of rote learned responses to electromagnetic, mechanical and chemical stimuli from my surrounding environment. I have two choices for reactions. I am not very creative here. I either open my umbrella or not. My only job then is to arbitrate between those options at any time. I don't open my umbrella and it pours. I get cold, I may die. I used my umbrella, I am dry, and take no risk for my apparently fragile health. I open my umbrella when the weather is sunny, I get less sun. My vitamin D levels decrease, I may die. I close my umbrella after the rain stops, I get sunshine, good calcium absorption. Organisms that will always open their umbrella when it rains and close it when it doesn't will proliferate. The umbrella is a reaction, but in being correspondent to the elements, it also encodes the complex external phenomenon. I don't recognize this phenomenon because of its special character, but merely because I receive stimuli that map to prior experience in sustenance-positive fashion.
The concluding extrapolation is that basic cognitive faculties that allow us to ascertain certain repeating qualities of the environment from early organic history to modern day organisms can be traced back to basic reactive relations. But assuming that trial and error can explain our perceptual system, it would allows us to discover repeating features by their expression derived in our neurological structures.
Whether the material relation through chemical, electromagnetic and mechanical interaction isn't facilitated by underlying unifying causes that proliferate platonically is undecided. I don't think we could ascertain that much. For example, linearity might exist independently, in the sense that the laws in Newtonian physics are independent conceptual reality, but lines might be just token ideas that we have developed to express a set of conditions that govern the world as we see it, by whatever virtue our material sense relation happens to be, which requires speculations.
Benecerraf was probably concerned that even if we can achieve correspondence between our mental representations and the environment, which was rather glossed over, we couldn't argue the soundness of our abstractions from experience. I think that he makes the claim that belief is contingency that is formed from reasons not possible to define analytically, and abstractions cannot be given apriori empirical account. So, we believe numbers are a good model for physical aggregates. For example, counting discrete collections with numbers, every time we add one further object, we get a larger aggregate. But can we argue that this is a good argument to make use of them? I think that given the above basic cognitive capacity and some basic intuitions (rationality, induction, etc), we can. But Benecerraf would apparently disagree.
Edit: I may misunderstand the argument that he makes.
I'm afraid this is a very lame attempt. Remember Lucy, the Ramapithicus skeleton, integral to the whole story of hominid evolution, right? What was her timeframe, six million years ago, right? She would have no chance of grasping the 'concept of prime'. Fast forward 6.9 million years (and some), h. sapiens appears. H. sapiens has some ability to grasp the 'concept of prime'. H. Sapiens was the consequence of huge evolutionary leap, namely, the development of the huge hominid forebrain. But what about 'the concept of prime' has evolved or changed in those millions of years? Answer: nothing. The ability to calculate, to speak, count, imagine, and so on - these evolved, no doubt. But the subject matter of those abilities - how can that be 'explained' in terms of 'evolutionary development'? I think this is a very widespread myth concerning evolution. As if we can find some primitive antecedent of rationality, then we can see how it is made. I think that is nonsensical, I'm sorry. H. Sapiens breaks through to an ability to grasp ideas, but there is nothing in evolutionary theory to account for the nature of reason. This ability transcends the biological, which I know is a very non-PC thing to say.
Notice that excerpt from the article I quote above, which was on whether computers can be programmed to find mathematical proofs:
'We didn't evolve to do this'. And it's true. Mathematics has no evolutionary rationale. It's not a claw, tentacle, or a colorful feathered display to attract mates. It can't be 'explained' in terms of biological adaptation. Darwin was not a philosopher, but now, strangely, everything that goes under the name 'philosophy' is expected to be explicable in terms of evolutionary biology.
Please see Thomas Nagel's essay, Evolutionary Naturalism and the Fear of Religion.
I made my decision through an assessment of the results of the semeiotic (Peircian) definition of "object". You have "objects" which violate the law of excluded middle, "objects" which violate the law of non-contradiction. And, vagueness, which ought to be represented as a feature of human deficiencies, inadequate principles, and inadequate application of principles, is seen as an objective part of the universe.
This is generally the most significant negative feature of Platonic realism. When mathematical principles, and other human creations like inductive generalizations, are apprehended as objective, unchanging aspects of the universe, we have no approach toward deficiencies, falsity or other defects within these principles. When mathematical principles are apprehended as the result of human activities then we view them as fallible.
Quoting tim wood
To be "true", an axiom must correspond with reality. We can make all sorts of useful axioms which do not correspond with reality. Usefulness does not entail truth because it is determined in relation to its purpose, as means to end. The reality of deception demonstrates very conclusively that usefulness does not entail truth. So usefulness, and pragmaticism in general, must be subservient to truthfulness, in a respectable metaphysics. This means that pragmatic principles cannot take top position in the hierarchy of decision making, because usefulness is determined relative to the end, so it does not necessarily provide us with truth. The further point which Plato himself indicated, is that the end is "the good", and Aristotle outlined the need to distinguish between "apparent good" and "real good".
Quoting tim wood
When an axiom, such as the axiom of extensionality, treats numbers as objects, then if this is true, the axiom will provide us with sound conclusions. If it is not true then the axiom will provide us with unsound conclusions. To be true, such axioms require that the ontology of Platonic realism is a true ontology.
First, to talk about conceptualization, rather then instinct and notion, we need the development of language or some kind of signs. First, because otherwise we could not express definitions abstractly, and second because it appears that people started to conceptualize after they became capable of communicating their thoughts. So, assuming communication, abstract ideas are simply codification of experience attributes and behavior directives with appropriate linguistic structure. Prime numbers, specifically, are actually rather simple consequence of developing the concept of operations, which are quantity relations. They arrive at the scene when you ask, can I solve my linear equation in terms of integers. Algebraic necessity is sufficient for their introduction, but they can be observed in practice as the inability to achieve certain counts from subdivision of a rectangular area into congruent sub-rectangles. Equations themselves are regularities expressed through other regularities. They are predictive apparatus, for area estimation, for time keeping, for example. Solving equations attempts retrodiction - the estimation of conditions by their effects - which was frequently necessary. People conceptualized the problem, as something of a recurring event in their lives. It was both necessary to do so and apparent through self-reflection on their experiences.
Quoting Wayfarer
So, we agree then that, without obvious internal contradiction, we could have developed innate biological capacity to discern objects in their environment, remember objects, ascertain relations, such as distances, congruence, similarity (using continuous integration of visual and auditory, and tactile cues, present and in memory), and detect simple patterns. So, at least, I hope that we can agree, that whether it is sufficiently elaborated by science or history, according to the empirical account, this is possible?
Quoting Wayfarer
I cannot fully explain how our brain functions, because we honestly don't have enough data, but it is considered to be broadly allocated for creative and quantitative tasks, so to speak. These features are apparently unevenly distributed between the hemispheres, as was established by tests performed on people where the brain was partially surgically separated to alleviate epilepsy symptoms. Both features are embodied in billions of nodes and trillions of connections. Assuming similar structure to A.I. that synthesizes images, the brain can constantly probe for proto-ideas, trying to make new ones from variations of old ones. Simultaneously, it tries to categorize sensory experience and decompose it into basic factors, which serve as seeding ground for those new concepts to emerge and be reincorporated into the neuronal structure themselves. In other words, the environment provides us with cues, which we then use to boot our own construction of new amalgemations of these features, but in abstract linguistic terms. I say, abstract terms, because even though language also breaks down to some experience or observation pattern, it can decode layers of meaning in stages, whereas literal form associations would limit us to hybridization of direct experience. Features that are more frequently encountered or more frequently used are more likely to be revisited. Therefore, we are bringing up many candidate concepts, which are extrapolations (I speculate, literally, as synaptic input extrapolations) of their linguistically expressed relation to observed patterns, and we either fit them in the scheme of things or discard them quickly from memory. Why do you perceive our ability to generate such candidate ideas of the type 'my experience or observation 1 and similar in structure, my experience or observation 2 and similar in structure, and so forth' as insufficient?
Note that even today's A.I. can generate images that amalgamate structure and detail from different training data. (Although I have to confess that it is both aided by us in its ability to discover isometry and similarity and is much simpler. But I assume that we have decided to admit the possibility that the discovery of isometry and similarity could have developed as evolutionary contingency.. Rightfully or not.)
P.S.:
Aside from synaptic extrapolations, such as linear extrapolation, another generalizing faculty that I presume the brain is capable of is induction through recursive feedbacks, which should be essential for some indefinite concepts that generalize from finite cases/experiences by some rule application ad-infinitum. For example, the abstract "for every" (for all). I envision as its precursor the cerebral expression of "everything" (e.g., in the universe), which could be encoded by applying "more", starting from something already big like "many". In other words, a feedback loop functions analogously to mathematical schema. Language allows unification of experiences in the brain by token signs or symbols, linear or ramped extrapolation allows generalization through simple trend reproduction, and feedback allows extrapolation through induction or recursion. I also said that some ideas are rejected from long term memory. I believe that the criteria for retention of any notion, abstract or otherwise, is its effectiveness, which has two components, compactness and generality or range of applicability. Compactness depends on its own complexity as neurological structure (how much space in terms of neurons and synapses it allocates) and it follows that ideas that mesh well with previous notions will be easier to retain, because they reuse a lot of the preexisting structure of other ideas. Generality or applicability not only reinforces the concept through recall, but it also serves compactness. It may have historically developed from the need for compactness, as innate biological trait that considers the relative ability of new information to displace old information in the long term. I think that today we favor generality and simplicity consciously, because through self-reflection, we have gradually come to explicate, articulate and appraise the notions evident value.
What I'm questioning is the degree to which the designation of these capacities as 'biological' is relevant. Certainly they're relevant or useful for the study of biology but the questions philosophers ask are existential and cannot necessarily be addressed in biological or biomechanical terms. Given all the facts of evolution, existence is still an existential predicament for human beings; that is what philosophy is concerned with.
Going back to the article on the indispensability of mathematics, and the problem of mathematical knowledge, why do you think the fact that we have an apparent innate ability to grasp mathematical proofs is said to be 'a challenge to our best epistemic theories'? Why do you think it was felt necessary to provide an alternative account of mathematical knowledge which sidesteps that challenge? What do you think the philosophical issue at stake is here? I'm not doubting the plausibility of the evolutionary accounts, but questioning their relevance to the philosophical issue at hand. I hope you can see that distinction.
Quoting simeonz
Consider the implication of the insertion of 'simply' in this sentence. Abstract ideas comprise practically the entire, vast, and diverse body of human culture, so that designation seems rather reductionist to me.
I mean to assume that a number is an object.
Quoting tim wood
Do you know what "true" in the sense of correspondence means? It means to correspond with reality. So take the law of identity for example, it states that a thing is identical with itself,. And this corresponds with the reality of things, as we know them. A thing cannot be different from itself. And from this we also derive the law of non-contradiction. If a thing were other than itself, then the required description of it would be contradictory, because it would correspond to a specific description, and not correspond with that description, at the same time. We see that these principles correspond with reality, i.e. that they are true. Do you agree with me on this?
However, we can state principles, laws, or axioms which are not true. And it is not required that they be true, i.e. correspond with reality, in order for them to be useful. So we can state useful axioms which are not true.
Quoting tim wood
There are two common senses of "axiom", the philosophical sense, and the mathematical sense. In philosophy an axiom is taken to be a self-evident truth, like the law of identity and the law of non-contradiction. In mathematics, an axiom is a starting point for a logical system, like a premise, but it is not necessary that the truth or falsity of the axiom (whether it corresponds with reality) be evident. I've taken this from the Wikipedia entry on "Axiom".
Worth noting here - this is something I’m saying, I don’t know if the poster you asked will agree - that a number or geometric form is a noumenal object, that being an object of ‘nous’, mind or intellect.
So it’s not an object of sense, which is what is presumably implied by many of the question about what ‘object’ means in this context. It’s not a phenomenal or corporeal object, like a hammer, nail, star, or tree. You could even argue that the word ‘object’ is a bit misleading in this context, but if it’s understood in the above sense - as something like ‘the object of an enquiry’ or ‘the object of the debate’ - then it is quite intelligible nonetheless. (See Augustine on Intelligible Objects).
The laws of biological and chemical order, may or may not have unifying underlying platonic causes. I honestly could not conjecture either way. Alternatively, nature might just have possible state configurations, with restricted transitions, or predetermined timeline of states, or even (more in tact with relativistic physics) collection of timelines for state components whose spatial ordering arises effectively by virtue of the patterns expressed in the otherwise unordered configuration components. The point is, that configurations don't need relatable logic. Aside from their combinatorial essense, which exposes codetermination in the state configuration, the relationships between the state components don't require abstract meaning. For a system inside this state to actually establish homeostasis or allostasis with the environment, the prerequisites are reproduction of the local transition patterns according to a spatial state ordering that could explain causally the chronology of each component, symmetry of the component transitions (low entropy) and change (abundant energy). Neurological, physical and physiological state can be formed by obeying correspondence with the environment into the predefined constraints on the evolution of the state space.
We could also ask about mental experience after that. As I have answered before, this could be explained in many ways, but only as speculation. I do favor the idea of emergence or compartmentalization of some innate reflection potential that applies universally to the state, by combining granular experience potentials from each component in increasing capacity for self-determination when they operate in some coherent fashion (such as in our brain), or by subdivision of the overall experience potential of the universe into smaller identities that maintain particular object constancy around components that operate coherently (such as in our brain), etc.
This departure aside. I am pushing the idea, if you will, that nothing works for simply fundamental reasons, and without elaboration of the particular context and history, there are layers on top of layers, where the puzzle is bewildering to investigate. How we expose the fundementals will depend on what we can work out about the details that were produced situationally and in consequence. Only then we can remove them from the picture and discover what is left.
For example, if the human cognitive apparatus was indeed produced in stages of increasing sophistication and it is still organized in hierarchical manner that is pivotal to efficient feature extraction and denoising of raw sensory input, we didn't simply happen to grasp our circumstances overnight, because of secretion of knowledge into us, but there was gradual accumulation of faculties in our design (whether inspired by natural forces or not) and those faculties, and not platonic forms, serve as landing pad for the knowledge that sits on top of them.
That is why I asked if you would agree that our basic cognitive functions, to pick up symmetries, patterns, etc, are articulated in our brain, i.e. visual, auditory, somatosensory cortex, and whether you allow that we may have derived those faculties from evolution. This is complex area beyond my competence that I won't fully explain, science cannot explain it exhaustively either, so if you would agree, it advances the question on faith. The same applies to stages of evolution in general. Even an unicellular organism, such as choanoflagellates, is a rather complicated biological system. It is possible to envision chemistry evolving to bacterial and later protist lifeform, but this includes many difficult stages. Self-replicating polymers, chemical encapsulation in micelle, metabolism (homeostasis by staged reactions, separation of exothermic and endothermic reactions, separation of decomposition and synthesis reactions, production of organic catalysts) for which we don't have much in the way of historical account, aside from stromatolite fossils, and which we are attempting to reenact by guessing the conditions. Or multicellular life that may have began as slime molds, and the nervous system that may have appeared as nerve nets. We discover this by phylogenetic analysis to some degree, but process of elimination that you can contest is also involved, because we lack fossils. Because lifeforms were soft tissue, depriving us from the crucial account of early morphogensis and cell differentiation, including cephalization, we cannot account for those confidently. In fact, cell and tissue differentiation is still actively studied. Language, which is crucial in my account, seems to have been driven by signalling advances, when our predecessors were forced by ecosystemic changes to move from the tree branches to the tall grass-ridden ground and to start to communicate opportunities or threats.
Quoting Wayfarer
I am reading Benecerraf's Mathematical Truth, which was referred to by the Wikipedia article you quoted. I still cannot grasp the entire argument, and the author quotes another paper that pertains to the incompatibility between platonism and rationality specifically, but to the best of my understanding, knowledge according to the text is a synthetic condition, i.e. provoked, and abstractions are analytic, i.e. applied as template. The claim is that the theory cannot be married to our knowledge in some apparent and explained sense, because their character is incompatible.
Quoting Wayfarer
The designation of some amalgamation of diverse kinds of experience and extrapolations is not that surprisingly complex in principle. The appearance of such faculty is astounding, but its operation seems to rely on crudeness itself. The brain is very ample structure, and any token word is probably encoded in a redundant fashion. Thousands of neurons and millions of synapses may be employed for a single concept (or a notion), for making associations with multitudes of sensory experiences and linguistic terms, creating significant semantic backup. So, when I said simply, I meant that the mechanism is simple. Involving human culture concerns being extended and situated in your ecological and social environment. Here, from empiricist perspective, I would consider the idea of social evolution, where experience aggregates collectively and the social dynamics evolve in parallel to the individual. The personal and the social organisms evolve together and interdependently.
P.S.; Benacerraf: Mathematical Truth
Yes, with the qualification that 'idea' in this context has determinate meaning, i.e. a real number or mathematical proof is an idea. Not simply an idea in the general sense of mental activity 'hey I've got an idea, let's go to the pub.' (Not that it's a bad idea.)
Quoting simeonz
But whether they are ‘possible state configurations’, or not, science still presumes an order. F doesn't equal MA only on certain occasions; ‘hey, that cannonball missed, the law wasn’t working today’. And if their 'configurations' couldn't be expressed in maths, then likewise, hard to see how science could get a foothold. (Your posts are hard work, although they’re worth the effort - but it’s intriguing to see how you interpret these questions, as your attitude is so different to my own. The question that occurs to me, is whether you see yourself as pursuing philosophy as distinct from science, or whether you think there is no difference and that one subsumes the other.)
Quoting simeonz
The ‘mechanism’ is not simple at all. The process by which DNA replicates, and the operation of the human brain, are two of the most complex processes known to science. The idea is simple, but I don’t think that supports your point!
The local factors of two spatio-temporal regions may be symmetric or asymmetric. By extrapolation of those conditions to the state of the entire universe, we construct the notions of complete chaos (no redundancies), or complete order (uniform, or vacant state). We ask what demands our case to be situated so particularly between them. It is epistemically reasonable to investigate, but it may be ontologically unintelligible question to ask. There is no guarantee that our understanding, from our limited experience, can be made compatible with the actual ontological perspective. It may be incommensurate with it, so to speak. We could be witnessing all the necessary phenomena that provide the meaning, but since the very meaning is unrelatable to the view and objectives that we have, our human ethics, etc, we may not appreciate it. Even if we were conveyed this meaning in explicit terms that we can interpret, we may still not appreciate it. Hence, complete disorder or order may be extrapolation that we just investigate by epistemic habit and compulsion.
Both nominalists and platonists should however agree that homomorphic and amorphic micro-state dynamics exist. I believe that their disagreement is about phenomenology, and about the implications on phenomenology on epistemic issues. That is why I turned to the philosophy of the mind initially. Because I felt that the merger of phenomenology and epistemics here is unclear. The contention seems to be between conjecture for direct disclosure of underlying design through mental experience and conjecture for representational comprehension of regularities through situated interactions. If we assume no causality from our mental state to its material vessel, or no distinction between substances of mind and matter, the same combinatorial account should be epistemically compliant with both views.
Quoting Wayfarer
I was too verbose and conflated when it came to the requirement for "reproduction of the local transition patterns ". I meant that symmetries of the micro-state transitions are necessary for the emergence of predictive systems. Representational morphisms demand it. I wanted to be relativistic as well, so I proposed that spatial structure was causally inferred by independently specified micro-state timeline dynamics. The truth is, that the state should be described in some structure, manifold, such as Minkowski space, whose symmetries have different criteria, but unfortunately, I am not qualified to elaborate them.
Quoting Wayfarer
I treated the problem in two parts, but I aimed to argue that abstract conceptual cognition, at least hypothetically, could occur without the presence of some binding agent that conveys the essence of patterns in nature directly to us, making them self-evident. First, I argued that the sophistication of our cerebral structure is sufficient for neurological processes to emergently develop conceptualization. That through the presence of linguistic skill, acquired through genetic propensity for vocal semiotics and learned behavior, along with our complex perceptual system and vast neurological capacity for processing and storage, we can encode associations, such that we can hypothetically account for abstract cognition at the level of synaptic activations.
On the other hand, the arrival of such complex nervous system naturally is much more complicated. Not just because of DNA. Self-replicating polymers are conjectured to have appeared, because organics are demonstrably chemically active and polymerize easily, and although labile in unprotected environment, the presence of solid catalytic surfaces where the matter is deposited or rock pores, could have retained them for longer durations. The process of self-replication is possible with short chained RNAs or RNA-DNA hybrids (chimeric polymer). They can form double stranded structure. The strands would then have been disassociated during particular phases of naturally occurring energy cycles in the environment (hot and cold conditions of hydrothermal vents, or high and low tides). Cellularization is a problem, but early emphaphilic compounds may have served the role of today's lipids. But how we have arrived at a metabolic cycle in the first prokaryotic cell, is a difficult question. Even if we can design metabolism that boots from prebiotic chemistry, all the fantastical stories would depend on our assumptions about special conditions and events that we can never verify. It is too complicated to arbitrate if locales of primordial earth were so very different from today's world. And we cannot magically circumvent the erosion of evidence produced from the action of entropy, that leaves us with stretches in our imagination. My objections to the hypothesis of supernatural events are, first, that they are too narrowly specified (theistically determined, etc), to the point where the details are frequently not essential for the required effect, and second, if they were indeed produced by intervention of omnipotent agency, I fail to conceive why the omnipotent agent couldn't make the regularities in nature more coercive to evolution, instead of making impromptu changes after the fact. In any case, we cannot give confident account scientifically for many stages of evolution, such as the first appearance of metabolism. morphogenesis, and partially, about language and its effects. So, any hypothesis is possible, as long as its elaboration of detail is relevant to the question being answered and is otherwise conservative (Occam's razor), and its presuppositions are also articulated.
Quoting Wayfarer
Human experience is integral part of knowledge and should not be neglected. I don't propose that there is universal formula for being correct. But people should not forego their experience. Science and philosophy need to attempt to reconcile, bilaterally.. With justified skepticism on both sides.
Edit:
I took the liberty of doing some very serious editing. So, for anyone who has read the content, if you decide, you may want to reread it, or at least I hope should not be surprised. Mostly it was for stylistic reasons - decided to rephrase some sentences, add clarifications, removed one clarification that didn't make sense.
Of course screws and bricks are objects. Why not? I take for the defining of "object", individuality, particularity, and this is described as a unique identity by the law of identity. So the conditions for being an object is to be a unique individual, and this means having an identity proper to itself.
Quoting tim wood
That's how my dictionary defines "true" and it seems to be how it is most commonly used. If you want to propose something different, I could look at that and we might hash it out, but I think you'd have a hard time changing my mind after I've spent so many years studying this.
The only other option I see as viable is to define "true" in relation to honest. Is that what you would prefer "truth" is a form of honesty or authenticity?
Quoting tim wood
How is it, that determining the truth or falsity of a mathematical axiom is not necessary, it is impossible, and irrelevant, yet axioms are "by default thought of as true". There is no honesty here. This is clearly self-deception, to think of a proposition as "true", when truth or falsity plays no role in its formulation.
Quoting tim wood
The word "members" signifies distinct and unique individuals, "objects" as per my definition. Since numbers are commonly said to be the members of sets, then numbers are objects with identity. Notice that the identity of a set is dependent on the assumption that a number, as a member, is an object with an identity.
The reason why Platonism is required is that this is the ontology which supports the assumption that numbers are objects, by designating this as true, i.e. in correspondence with reality. Here's a brief explanation. Let's assume we use the symbol "2" to refer to a group of two things, as the quantity of things there. Do you agree that this is a true description of how one would use the symbol?
In this case, "two" is what is said about the group of things, it is a predication, and the subject is the group. The group is a quantity of two. Here, it is impossible that "two" refers to an object, because it necessarily refers to a group of two objects. However, if we employ a Platonist premise, we can assume that this Idea, the quantity of two, is itself an object being referred to by the numeral "2", independently of any group of two things. Then we might use the symbol "2" to refer to this object, the quantity of two, independently of any existing groups of two. So when 2 is the member of a set, that is what the symbol "2" represents, an object, the number 2, which is independent of any group of two.
That's why Platonism is required for set theory because it provides the premise whereby the number 2, or any other number, exists independently of any quantity of things. By this ontology it is true that the symbol"2" refers to an object, the number 2. Without this premise, when "2" is used it would necessarily refer to two objects, not one object.
Quoting tim wood
That's exactly the point I was arguing when you interjected. Altheist was offering a definition of "object" from semeiotics which would dissolve the distinction between ideas and physical things, making them both "objects" as what is denoted by a symbol, under that proposed definition.
Quoting Wayfarer
I don't mind using the same word "object" to refer to a sensible object, and also an intelligible object, as an approach to these categories, so long as we maintain the separation between what it means to be an intelligible object and what it means to be sensible object. What I objected to was altheist's proposed definition of "object" which would dissolve this distinction, making sensible objects and intelligible objects all the same type of "object" under one definition of "object".
However, I find that when I employ adherence to the law of identity as the defining feature of an object, then it's difficult to maintain the status of intelligible objects as true "objects" under this principle. This presents the difference between the phenomenal and the noumenal. The human intellect apprehends the phenomenal, but we assume a perfection, or Ideal, which is beyond the grasp of the human intellect, like God is. This is where we derive the idea of the individual unity, and why it is impossible for the human intellect to grasp the completeness, or perfection, of the unique individual. And "object" is generally used to refer to a unique individual.
Quoting Wayfarer
Here's a problem to think about. At what point does an idea manifest as a full fledged "intelligible object"? What would be the criteria to distinguish a simple idea in the general sense, from an "Idea" or "Form" in the sense of a mathematical object?
Let's say there are two extremes, the bad idea and the good idea, with countless cases in between. The good ideas, like mathematical objects get designated as "Ideas", or "Forms", Platonic objects of eternal truth. The bad ideas are human mistakes. But what about all the things in between which are not so easy to judge? What about a human idea which gets accepted and becomes an object, like Euclid's postulates? Or on the other hand a proposed mathematical axiom which gets rejected as insufficient? Doesn't the distinction between a Platonic object, as eternal truth, and a human idea which may be mistaken, seem somewhat arbitrary?
The whole point of what was to become form-matter dualism, is that the forms of things can be identical, or rather, particular things can ‘participate’ in a form. So the ‘idea of a screw’ or ‘the idea of a brick’ can be turned out in many individual shapes and sizes, but the form is the same for each - a screw is a screw, not a nail. So the identity, the what-it-is-ness, is imparted by the form it embodies (‘I asked for a screw not a nail!’) And also by the function it is intended to perform (form follows function.)
Quoting Metaphysician Undercover
Sure. The difference seems much more obvious to us moderns, though. I can imagine in the classical period, that the concept of the form was much crisper and easier to imagine.
Quoting Metaphysician Undercover
Now wait just a minute. Isn’t the idea, in form-matter dualism, that ‘the mind perceives the Form, and the eye the Shape?’ Go back to the original metaphor of hylomorphism - a wax seal. The wax is the matter - it could be any wax, or another kind of matter, provided it can receive an impression. The seal itself is the form - when you look at the seal, you can tell whose seal it is (that being the purpose of a seal). That is the original metaphor for hylomorphism.
So this principle was extended and elaborated in later hylomorphic dualism - the intellect, nous, ‘receives’ the form, the eye ‘perceives’ it. That is explicated at length in this passage from a text on Thomistic psychology:
Hence the relationship between ‘forms’ and ‘universals’. It seems clear as crystal to me, but apparently not to everyone.
In this matter the proposition ‘results from chance’ is itself self-contradictory. That something ‘just happens’ is not an explanation. Why is it that in every branch of science, causal relations are sought, but in respect of the formation of life, the absence of a causal explanation is the desired outcome? I don’t think the answer to that question lies within science.
I don't buy this, because you and I are different, just like two bricks are different. If two bricks are different why would you think that any one property that one brick has would be identical to the property of another brick. And if ideas are properties of human beings, why would you think that an idea which I have would be identical to your idea?
Do you know what identity is, according to the law of identity? It means the very same as, one and the same. Identity is proper to the thing itself, and it is shared with nothing else, because if something else had the same identity it would not be something else, but the same thing. So I don't buy the idea that the very same idea could be in your mind, and my mind. I think the evidence indicates that this is not true.
Idealism might propose independent "Ideas", as Ideals, which are independent from any human ideas. These Ideals are supposed to be the true immaterial objects. This is what Plato describes in The Republic. There is the divine Idea of a bed, the perfect bed. The carpenter attempts to replicate this Ideal with one's own idea of a bed, then builds a replication of that idea. Notice the two layers of representation between the artificial material object and the independent "Idea", as an object. The human idea does not obtain to the level of "object" with independent existence, because it is only a representation of that supposed independent, divine Ideal.
Quoting Wayfarer
The theory of participation comes from Pythagorean Idealism. It can be argued that Plato actually refuted this theory. Through his analysis of this type of Idealism, he actually exposed its weaknesses. Although Aristotle is given credit for the actual refutation, he simply synthesized, in a more formal argument, the information provided by Plato's analysis.
A very good example of the theory of participation is fount in The Symposium. Beautiful things obtain their beauty by partaking in the Idea of beauty. What is evident here is that there is an independent Idea, also sensible things which partake in that Idea, and then human ideas which are produced from observation of the sensible things. Notice how the sensible world is a medium between the independent Ideas, and human ideas, because it is the sensible things which partake of the independent Idea, not the human ideas themselves. The human ideas are derived from the sensible things
Plato wanted to understand how the sensible particulars partake in the separate Ideas. The issue is that the Ideas must be prior to the sensible particulars in order to account for numerous particulars being part of the same Idea. This means the Ideas must be in some sense a cause. But from the human perspective, we get our ideas from the sensible things, so we see them as the cause of ideas. So from our perspective we see sensible things as active, and the ancient view was that sensible things actively participated in the separate Ideas. This makes the separate Ideas appear as passive (eternal, unchanging), and denies them causal capacity.
The key to turning this around is revealed in The Republic, as "the good". The good is the motivation for action, as the ground for intent. When we assign causal capacity to intent then we see the reality of human actions, and the fact that the sensible objects follow from the human ideas, necessitating that the idea of the artificial thing is prior to its sensible existence. Both Plato and Aristotle assign this order to natural things as well, making the independent or separate "Forms" the cause of natural sensible objects.
In The Republic, Plato removes the sensible object as necessarily the medium between the human idea and the divine Ideas. This is contrary to Kant, who makes all human ideas dependent on sensation. But for Plato, it appears like the good, in the sense of what is morally proper, cannot be derived from sensible existence, it is only apprehended by the mind. Therefore the human mind must have the capacity to be guided directly toward the divine Ideas, without the intervention of sensation.
Quoting Wayfarer
I don't see the point in distinguishing shape from form. The shape is a part of the form, the part perceived by the eyes. But the eye cannot interpret the meaning in the shape.
Remember, in Aristotelean hylomorphism there is two distinct senses of "form". There is the form of the object which inheres within the object itself, combined with its matter, constituting its identity as the thing which it is, and there is the form which the human mind abstracts. These two are not the same, as the abstraction does not contain the accidents.
If by chance, you mean, improbable event, then this is not what is involved. The hypotheses are not presupposing extraordinary occurrences. That wouldn't methodologically agree with conventional empiricism. If you mean that the we rely on ideas whose historical accuracy cannot be firmly supported, then you are correct. We cannot fight the effects of irreversible erosion of remnant evidence for proto-organics whose active proliferation would not have survived the climactic and ecosystemic changes that have transpired henceforth. Science is forced to speculate, and appeal to reason. There is no internal contradiction in doing that, just methodological hermeticism. The same applies to conjectures in morphogenesis, because soft tissue organism do not fossilize in a manner that confers their organ structure. Some ideas can only be hypothesized. Not because science is in contradiction, but because the effects of time and entropy preclude us from recovering the historical account necessary for inspection of scientific consistency. This forces abiogensis to rely on scientific retrodiction (since this is the only form of prediction we have), fossils, sediments, phylogenetic analysis of organisms, and as a last resort, conclusions by elimination. We also need time. Not to create fiction, but to figure out arguments for or against claims. On the other hand, you might mean that the conditions, as hypothesized, even if true, are very particular to earth. That is arguably true. While this may support a theistic argument, it does not necessarily contradict science and support revelation in the sense of incident miracle. I will explain this as it ties into a discussion trend on this forum.
When I am discussing physics and natural sciences, I am not intently contrasting them with theism, just with scientifically incompatible theism. Science is not an overall world view for me, but just a fraction of my world view. Namely, faith in the virtue of experience and its reconciliation with reason. Physics is not in a privileged position over experience and reason to establish rules and maintain them, because it favors a particular mindset. This is what mainstream religion used to do, and this is why I am not instituionally religious. The laws of science evolve constantly. What it tries to do is very narrowly defined and has comparatively little bearing on the condition of the universe. Physics tries to infer from experience predictive ways to reason about state patterns which appear to reproducibly apply to all spatio-temporal vicinities. In other words, it deals with universal constraints that can be observed anywhere, in close proximity around a location. It does not account for the global affairs altogether, aside from those local constraints that apply everywhere.
There are caveats, naturally. Since the universe, by scientific retrodiction is conjectured to have been concentrated, it is pertinent to ask, how the known limitations of local state dynamics would transitively confine, through their consistent following application, the development of matter after it dispersed. This will either confirm or refine our conception of the natural law. The second issue is, that since we know that we cant make the laws fully predictive, at least locally (QM asserts it), the question is whether the present day celestial variety lies within the realm of that cognitive gap we can account for, or are there initial varieties that have spawned it. Without any physically contradicting explanation, we could concur that they were present, either as a starting feature, or because time may protrude back beyond the concentrated stage in additional historical cycles. Another caveat is that laws are now mostly probabilistic, which makes them implicitly global in some sense. The second law of thermodynamics applies to all vicinities, but its strength depends on the size and the volume under consideration. And even then, the result is inclined, not strict, so the pattern that the law postulates makes local sense, but from a global vantage point. The same is true for QM, which applies rather weakly for singular events, but matches much more strongly for spans of time and at greater scales.
From this, I think it is apparent that whether something is a miracle is not dependent on being in agreement with a known physical law, but whether it is in agreement with reproducible pattern of sensory experience. If newly uncovered state dynamic is consistent, the situation would provoke amendment of the scientific expressions that convey the predictive implications. On the other hand, claims for hypothetical material events whose probability for occurring is extraordinarily small according to our prior experience, and whose sensory realization (such as described) cannot be demonstrated, are unlikely to be treated in agreement with science. As I have mentioned before, persuasion in the effectiveness of the scientific methodology is ultimately spontaneous, but I agree much of it. I agree that minimalism when conjecturing from evidence is warranted. That patterns of experience should be interpreted as simply as we can (by cognitive ability) without rendering the power of the interpretation too limited to be useful. The only vindication for detail is how it extrapolates to generalization. This is the methodological convention for science, and I agree with it.
We claim that certain studies are natural, because they investigate the relationship between events using physical law. They trace the connection between initial conditions and particular outcome, trying to establish how the constraints we know derive the typical result with reasonable certainty. Science does not explain how the particular global context was formed. It does not therefore explain the root cause of the initial conditions. Even when sciences seek deeply rooted causes, they only end up in other apriori features. The present day state of affairs may easily fall within the predictive gap of our physical law. Either way, there is scientific contradiction to admit that the initial state of the universe can be supreme design, but any conjecture about the quality and nature of the designer is opposed to scientific minimalism.
Some examples of natural sciences that we talked about. Neurology tries to figure out how the admissible transitions postulated by physics conclude at the biological outcomes that we typically observe with reasonable certainty. (It is far from succeeding.) Morphogenetic studies try to establish how the physical law traces the path of development of life from fertilized egg cell to a developed human being. Abiogenetic studies try to explain the arrival of contemporary organisms from early prebiotic chemistry. In contrast, revelation theism attacks the lack of evidence and criticizes the use of conjectural latitude to reaffirm naturalism and conventional science. The fact is that the early factors and events are obscured. Abiogenesis therefore has to rely on plausibility as argument, of events that are admissible considering the evidence present, but unpoven. Theism considers lack of hard evidence and confident reason scientific impotence, but does not require it of itself, because proof and reason are inessential to its central faith. They even consider its lack vindication of their ontology. In other words, theists start epistemically satisfied without reliance on detailed knowledge of the world and consider themselves in a better position, because their opponents are obviously challenged by their harder epistemic requirements.
I am tentatively theistic, possibilian, misotheistic. I conjecture things like telepathy, or zodiac influences, good and bad energies in the world, etc. But my ideas are tentative, reevaluated, doubted, and if they survive the test of experience and contemplation, increase in detail and confidence. My conjectures aim to become more articulate from detail that I accumulate. I am not looking to gain fundamental wisdom that refrains from elaboration of my world view by facts. I call this epistemically positive attitude. I employ fixed set of persuasions, indeed, but all my ideas are under constant attack, and my experiences are given time to convince me or dissuade me. In contrast, conventional mainstream theism can argue in a manner that appears epistemically satisfied, prior to experience, and experience appears to be gained mostly introspectively. The knowledge of material relations is considered antithetic to the ideal proposed. I consider this attitude epistemically negative. I am sorry if I come off antagonistic, but this is how I see things about most theistic proposals.
I will again try to articulate, to the best of my knowledge (which is not very ample), why RNA may have formed naturally over time. Its arrival is currently conjectured to have happened in stages. Such stages of increasing complexity can be synthesized in laboratory conditions, but one problem that exists is that the chemical concentrations supplied, the thermal and mechanical conditions are not naturally present today. The hypothesis is, that because the intense geothermal activity, the frequent moon cycles, the carbon dioxide concentration in the air and water, and the stronger sun radiation, those conditions may have existed for a while. Linking the stages is another challenge, as the retention of the intermediates, i.e. nucleobases, nucleotides, pre-RNA compounds, short RNA or RNA-DNA hybrid chains, is not natural in unprotected aqueous environment. Several hypotheses exist. My understanding here is shallow, and I will advise you to double check, but apparently the properties of certain solids, particularly clays or crystals, identify them as bonding agents of carbon compounds, which become retained on such surfaces, a sort of locale for the emergence of organic film. Those newly formed prebiotic organic substances, being protected from dissolution in the surrounding water by their solid host, are compelled to react with each other and polymerize over time. It was a staged process of attainment of structure. While chance was involved at each stage individually, those surfaces show in laboratories that they are sufficiently conducive to polymerization, thus would be able to effect a starting point for primitive self-replicating compounds over time. Another not so different hypothesis is that the pores of rocks served as areas, which concentrated and retained intermediate organic substances together, prevented them from diluting in the surrounding environment, and partially protected them from reacting with other proliferate chemical agents. This may have provided early substitute for cellularization, and hence fostered the appearance of longer polymers (which are less stable) and eventually metabolic cycles (which is indeed thornier topic). And a hypothesis exists that isolation was provided by same phase separation. This is possible in emulsions, or coacervates, which are substances that form droplets in other liquids. Those droplets might have recombined through fussion and fission, which would allow them to exchange reactants over time, allowing for early form of natural selection. It is also possible that cellularization existed before self-replicating polymers, offered by simple organic amphiphilic compounds. This could have provided a stage for the arrival of RNA-like polymers later, either distributed by vesicle or possibly as a kind of viroid.
I am not the person to answer questions about this topic. But to me, it appears that there are semi-plausible conjectures. As I explained, they depend on the hypothetical initial conditions. If I wanted to emphasize a weakness, I would attack the appearance of enzymic metabolism. Even though, as I said, any attack without a known historical account is proof by your opponent's ignorance, which I do not condone. But, still, it appears to be a weak link, or at least I haven't encountered plausible natural explanations. Attacking morphogensis is similar, but even if the detail is not clear, there is reasonable expectation of growth in complexity under the proliferation of forms during the Cambrian era. Language is maybe insufficiently explained, as a phenomenon that evolved quickly, under presumed environmental stress, but in just single species.
I don't see your point. Your ones and fives, and my tens and twenties are physical objects like bricks. And each one of your ones is different from every other one of your ones, just like each brick is a different brick, despite the fact that they may all look the same to you. So why would you assume that there is some type of a one, which is the very same one as every other one, despite occurring in distinct situations?
Quoting tim wood
They are proposed as Divine, therefore not from human minds.
Quoting tim wood
If you read what I said, you'd understand it as saying that the separate Ideals, which are the property of a Divine Mind, are not found by human minds. Human minds are lacking in the perfection required for such Ideals.
Quoting tim wood
Clearly, despite the fact that I have two things both of which I call a brick, and I have a similar brick in my right hand to the one in my left hand, they are not both the same thing. The fact that the two things, called bricks, each have a different identity, is what the law of identity is meant to express. Do you agree with this?
I take your general point about a distinction between some things being invented and discovered. Nice.
Curious how modality seems to be the big background issue on the forums at present - it comes up repeatedly in various discussions, and now shows itself here. That logical possibilities exist is just to say that there are patterns in logical space, that there are patterns in the way we can string symbols together. We might indeed describe the process of identifying these patterns as making a discovery. That's not strong enough to support the contention of platonic realism in the OP.
@Banno drew my attention to your response, so I would like to suggest that while we discover separate instances of logical relations in objects and situations, and in us, through the intellectual predisposition to operate our decisions effectively under logical premises, this doesn't seem to change the fact that we are persuaded by instinct to extrapolate those cases to universal laws, without some reliable providential certainty. So, instances of logic are evident (empirically or introspectively, which is still a form of observation of nature), and logical laws are taken on faith. I support reason and science, because I believe in them, having observed their predictions so far, but the emphasis here remains on believe.
P.S.: I also believe in the scientific methodology, as I have previously stated. That is, to learn from experience and to rectify beliefs when confronted with reproducible and reliable contradicting evidence.
Well said, and quite to the point. (I'm not institutionally Christian but have attended Buddhist services so I guess that makes me 'religious' in some sense.) But the point here is philosophical rather than religious. As you observe, physics proceeds by strictly excluding anything which cannot be accounted for in physical theory. In the context of modern science, this manifests as the consideration of only that which can be made the object of quantitative analysis, and represented and expressed in mathematics (which a point made in the OP.) But as you're no doubt aware, physics has become paradigmatic for science generally, and is associated with the philosophical outlook of physicalism and, more broadly, naturalism. That's what is at issue as far as I'm concerned. And my contention is that the nature of life and mind cannot be reduced to, or explained solely in terms of, physics or physical laws. If that make me a dualist, so be it, I'm quite happy to wear that moniker.
The skeptical challenge to the dualist position is: well, you say there is this 'spooky mind-stuff', so where is it? This is where the limitations of the method of objectification need to be made clear. The attributes of the intellect (nous) appear by way of what the mind is able to grasp, in other words, in the operations of reason. They are themselves not an object of scientific analysis, although without the use of reason, scientific analysis could not even start. But as the empiricist instinct is always to proceed in terms of what can be objectively grasped and quantified, then the operations of reason, although assumed by it, are not visible to it.
[quote=Jacques Maritain]what the Empiricist speaks of and describes as sense-knowledge is not exactly sense-knowledge, but sense-knowledge plus unconsciously-introduced intellective ingredients, -- sense-knowledge in which he has made room for reason without recognizing it. 1 [/quote]
Quoting Banno
Ongoing. I'm learning SalesForce. They have an entire training environment online. The training is free, but it costs US$200.00 to sit the certification exam. There's a lot of demand for SalesForce administrators, I'm hoping to add it as a string to the bow (as technical writer). That's what I'm supposedly working towards, but I'm endlessly distractable, especially by this forum. There's a lot of detail, much of it tedious. Anyway, today's Sunday (although that said at this minute I supposed to be vacuuming the swimming pool.)
Quoting tim wood
I contend that it is because of Platonism that the West was able to realise the scientific revolution, where the Orient was not. The separation of form and substance, the analysis of the relationship of ideas and matter - all of these were essential to the formation of science. The fact that science has now forgotten its own origins is symptom of degeneration, not of progress. Maybe the current crises in cosmology and physics vindicate Plato's original contention that matter itself is unintelligible.
I'm in broad agreement with this. I just don't think it entails platonic realism, nor that The Unreasonable Effectiveness of Mathematics in the Natural Sciences helps the case much.
Now the realist will object - wait a minute, you're saying the whole world exists inside the mind? (which is just what @Janus asked.) When you ask that question, you're projecting a perspective from outside the mind; you're imagining a universe with no-one in it, which was, of course, empirically the case prior to the evolution of h.sapiens [sup]1[/sup]. But the point is, scientific realism tries always to assume 'the view from nowhere', a perspective which brackets out the subjective elements of judgement altogether, to arrive at a rigorously objective understanding which is the same for all observers. Within that framework, humanity is one amongst all other phenomena. But that 'construction' of a world devoid of any subject, is a methodological step, it's not a metaphysical truth. It too is a construction, albeit not something in the individual mind, but a collective construct. But what happens in modern thinking is that the methodological step is interpreted as a metaphysical truth, which overlooks or forgets what the human mind brings to this whole picture, the sense in which the mind 'holds it together'. Again that is the argument of the article on the blind spot of science.
But even within this framework, mathematical proofs are valid because they are indeed 'common to all who think'. They're part of the structure of reason - which is Frege's view. But because they're not an aspect of empirical reality (out there somewhere) then they can't be regarded as empirically real - which is Benacareff's view. And if they're not empirically real, they're not real, because there ain't no other kind of 'real'.
That's where I've gotten so far. Now, back to the swimming pool.
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1. This point is why Kant said he was 'an empirical realist but a transcendental idealist'. Things can be true from an empirical perspective, but that doesn't mean the empirical perspective is the final truth about things. This also has parallels in Buddhist philosophy as the 'doctrine of two truths, conventional and ultimate'.
2={0,{0}} , 3={2,0,{0}}={0,{0},{0,{0}}} , etc. from the Peano Axioms through set theory. But there are other ways. Just a passing comment.
That's the way Aristotle designed his system of logic, from the premise that matter is unintelligible. Part of the physical reality is intelligible, form, and part is unintelligible, matter. It was evident that there are aspects of reality which cannot be understood because they appear to defy the three fundamental laws of logic. What Aristotle did was insist that we uphold the law of identity, and insist that we uphold the law of non-contradiction, but for that aspect of reality which appears unintelligible he allowed that the law of excluded middle to be violated under certain circumstance. So for example, in the case of future occurrences which have not yet been determined (the sea battle tomorrow for example), propositions concerning them are neither true nor false. And even after the event occurs, if it does, it is deemed incorrect to think that the proposition stating that it would occur was true prior to it occurring. In his Physics and Metaphysics, "matter" is assigned to this position of accounting for the real ontological existence of potential, that which may or may not be.
Thanks for the example --- not that I understand it.
I agree. The problem I see with Platonic realism is that if it is not taken to be claiming that there is a separate realm where the Ideas, universals and numbers live, then I can't see what it is claiming other than that (at least some) ideas and generalities have a conceptual or logical existence which is independent of human opinion.
It's all a matter of belief, as I see it, since there seems to be no possibility of any context-independent certainty.
We differ here in our perspective, about what is reasonable and unreasonable explanation. Because I admit the hypotheses of panpsychism and pantheism, which are very distinct from dualism in spirit. I also admit dualism, but I always find it the most encumbered with detail of those positions. Not to mention, that it is sometimes linked directly to theism and spirituality, which are nothing bad in principle, but are is extremely loosely implied.
I will argue from the point of panpsychism and pantheism. The brain could be capable of experiencing itself not by sensory perception, but as self-reflection. For the panpsychist position, the constituents of nature might have innate ability to self perceive, which elaborates into collective experience under certain circumstances, and for pantheism , the starting point would be omniscient consciousness that is compartmentalized into epistemically isolated portions (the deity is the ultimately extended mind). In both cases, the qualia is realized by the physical domain. This is not outwards pointing experience, just self-experience, but the state has subsumed both the mental and the physical role, and contentions (forces of interaction) arise natively between the mental parts, not conveyed through transduction from some envelope medium.
For panpsychism, the extent to which a physical process expresses a cognitively viable transaction (producing retention and manipulation of information) determines how much the local awareness coheres and produces collective experience. For pantheism, the global awareness is split from the divine awareness on boundaries that do not belong to the same sentient process. But in both cases, the experience is fragmented and nested in layers. It breaks into vantage points, each one incomplete. Each part can self-reflect, but larger parts subsume smaller ones in a manner, which articulates self-reflection in a qualitatively different way.
The totality is omniscient, but incoherent. It does not entail regard for the constituents. Personality arises as property of self-determination, to whatever extent possible, whose identity becomes specific to each vantage point. It is not aggregated. The awareness of constituents is limited in quantity and quality from the point of view of the aggregates, even if they are not coherent enough to understand that. And the aggregates behave in ways whose motivations might be unrelatable in terms of focus and character to the vantage points below it. For illustration, the blood cells spilled during shaving become subject to destruction that their natural programming objects to, but the individual (with the clumsy hand) cannot understand that significance - instead he sees a potential for a scar. For both pantheism and panpsychism, dullness of the structure results in less self-awareness. This time, not because it is not cohesive after splitting on information processing boundary, but because it is not articulate. It does not secrete as much collective experience, or allocate as much supreme awareness. While those structures may be still aware, it is a poor, inexpressive awareness.
Back to your question, matter experiences itself, but partly in fragments and only partly collectively. That is why, it cannot be aware of itself in detail at the aggregate level, even though it is aware of itself at the individual level. Those conditions that are experienced by our constituents on their own are lost to us, as to the person that we identify as. But the interactions between constituents allow communication (metaphorically), such that a vantage point can receive second hand image of its own state, by virtue of being compelled by the surrounding forces to representation of (parts of) its recent configuration, but possibly through expression that varies based on the manner in which the information was acquired. Hence, we are capable of receiving our state image from surrounding material constituents, which provides the detail of our self-experience that we would otherwise be lacking, but in a manner that realizes itself differently then if we were truly able to self-reflect in full detail.
My brain experiences itself, but not the specialized regions and biological redundancies. It conceives a foggy image of its complete configuration that only figures the high level detail. This includes the information processing aspects, which are captured as collective qualia. And while this qualia does not realize the image of its micro-states, the content that is absorbed as the collective self-awareness uses the sensory organs and material surroundings as additional loopback through which to refine its self-reflection. Piggybacking on devices, such as a recording of fMRI made earlier, played on a monitor, it receives neurological image of its recent state. It still does not have full perception of its constituents, which presently are capturing this image, but since the sensory image now traces physical interaction pathways that constitute information transaction, those are experienced at the collective level in sufficient detail to articulate mental experience and reflection.
Earlier I proposed monistic intersubjectve idealism. Particularly, a form of what I would call unconstrained pantheism, where the creation is fictional. It could shed and gain parts, and the story and rules can change. Merely the epistemic completion suggests that it will be explored with consistency, until the principal content has been extracted. The point here is that the universe is not guided by law, but by motivation to explore it. It doesn't have to be coherent, just provide useful experience for supreme vantage point.
Edit - This is work of pure fiction. Not a strongly supported conjecture.
Damn. I could write several posts on the errors in the first paragraph alone.
But I don't think such direct criticism will be useful here. Instead, I might try to describe back to you the picture I have of your view, and see where it differs from my own.
You mention a natural division between objective and subjective, but reject this as a construction. You then posit a realist objection. So you think along lines such that objective explanations are somehow subjective explanations; that primacy must be given to individual experience and so forth.
I think the subject-object distinction causes more confusion than clarity. It's just an overburdening of the simple grammatical distinction between first and third person. What can be said in the first person can be said in the third person salva veritate. "The construction of a world devoid of any subject" is a misunderstanding of what saying something in the third person consists in. Saying something in the third person does not remove the individuals involved so much as translate them. It's not a voice form nowhere, but a voice from anywhere.
Thanks. I start with the notion of a concise response, and end up with a lot of words. There are usually no paragraphs in what I write. A monolithic chunk of text with a few empty lines, to throw off the reader. I'll try to rectify the last post, at least mechanically.
I don't like to belabor myself, but it doesn't come easily. Even after several edits, I usually remain verbose. I sometimes end up summarizing in a finishing paragraph. The problem is, in very long posts, I become spent and may give up. Sorry. The truth is, as I have said before, the forum format, for which I am very grateful also, is mostly for exchange of sketch ideas. But when the perspectives differ, suggestive communication is insufficient, and both parties either have to make things concrete or give up.
Quoting jgill
Well, I haven't. Nothing as noble. My occupation is in the technological sector (software developer).
Agree with @jgill - your posts are very hard to parse. I think it’s worth the effort, but the longer your posts become, the less inclined I am to keep trying.
If you read my posts fairly, you will actually realise I’m quite a conventional philosopher. In fact most of what I say, I hope, could be contained within the bounds of Aristotelianism, albeit with a somewhat porous border with Buddhism. What makes me a minority report in the context of this forum is that I don’t subscribe to philosophical or scientific materialism. But I try and validate the points I’m making against sources. Now I understand you might have a very different perspective, but I think it would help you a lot to map what you’re saying against some of the literature. Preferably, popular sources, rather than peer-reviewed science journals. Use them to illustrate the point - where you agree with them, and where you disagree. I’m sure you have many such sources. One of the things I really get from this forum is finding out about what others are reading.
We’re clearly on a different wavelength in some respects, but I think your posts and ideas have a lot of potential, hopefully the back-and-forth of this medium will help you sharpen that up a bit.
I make the effort to the extent, which my ability and energy afford me. I admit that it is not as good as it could be.
Quoting Wayfarer
I have my philosophy textbook, wikipedia, random articles, Stanford E. P., and this forum. My commitment is rather shallow in this regard. I am authentically curious, but the articulation frequently strikes me much more conjectural and personal then evidential. I usually read hypotheses as a sketch, and gradually piece them together, rather then focus in depth. ( Edit: In principle, the starting points for my ideas are Leibniz and Spinoza, but theirs are theistically or spiritually inclined, whereas mine are rather void in that regard and are predominantly phenomenological.)
But I confess that I am illiterate, by the forum's standards. I always try to emphasize how unremarkable my purview of philosophy is, but it doesn't get across. Maybe because I express myself with overconfidence. For abiogenesis, I could provide some articles, which might be interesting to you, but they are not official sources either. They are found as random reads off the internet as well.
Quoting Wayfarer
If you would like to elaborate, do you perceive the differences between us as rooted in the technical or the ethical side of things. Is it a matter of innate persuasion, which I have also stated that science is, or experiential conviction? That is, do you consider my proposals too vague, which would be a fair point, or unsound, or ethically inadmissible.
This is obviously not true. Your posts are sometimes a bit awkwardly written but you’re by no means illiterate. You ought to ask yourself why you say that. Your posts are quite sophisticated (although could use editing.)
Quoting simeonz
I have an intuition that ‘philosophy requires no apparatus’. What I mean by that is that the fundamental questions of philosophy remain the same, no matter what our period of history or scientific discoveries. The figure of Socrates is fundamental in that regard. He had access to no specialised knowledge and obviously none of the instruments and theories which characterise the modern world. Nevertheless his quest for an authentic state of being is still the archetype for the philosophical endeavour, in my opinion. 'Man, know thyself' is the most general, yet most important, command in philosophy. It is notoriously difficult.
I do find your proposals a little vague, but that’s OK, as exploring these ideas is why we have forums. As to my objections to scientific naturalism generally, they are not aimed at you in particular. I understand that scientific naturalism is the predominant attitude in today’s world, so I'm swimming against the tide in that respect.
In some ways my philosophy is motivated by religious ideas, but I have to qualify that by saying that I have a broad view of what religion means. The classical Christian view is that Christianity is the only religion, and that other religious conceptions, although admirable in some ways, are all ultimately flawed and doomed. Whereas I tend towards a pluralist view. Philosopher John Hick says of the relation of different religions:
(Another philosopher of religion whose work I have found very useful in this 'universalist' sense is Karen Armstrong.)
More specifically, the particular genre or milieu that this OP is motivated by is Christian Platonism, which is one of the three main schools of traditional philosophy that have motivated me (the others being Vedanta and Mah?y?na). The cultural issue in the West is that the rejection of religion, which was caused by the way religion was framed in Western culture, culminates in a 'culture of unbelief', as it were. There is a deep and generally unstated prohibition - a taboo, in fact - on certain ways of thinking that has become deeply embedded in Western thought since the Enlightenment. Calling attention to that is my theatre of operations.
If I may take a rain check for a while. I need a few days to compose my thoughts.
On a different note, I didn't actually mean illiterate, as in functionally illiterate. When I use words, I sometimes misuse them by intending some non-default meaning, even without qualification, assuming reinterpretation from context. I meant a person rather uneducated, namely for the topic of philosophy.
Ironically, this does imply that my command of English needs some polish. And, so does my command of my native language.
I think that the majority of posters on this forum would naturally assume that the mind is the product of the evolved brain. This is the issue I'm wanting to home in on. This means that, before h. sapiens evolved, there were no intelligent minds in the universe (leaving aside any similar types of intelligent species, or more advanced types of species, that we don't know about.) It is, I think, taken as a truism, that in the absence of a divine intelligence or higher intelligence, which I will likewise presume is the majority view, that the Universe is in an important sense mindless - not the product of a mind, and not the theatre of any mind, save the minds of evolved species, such as ourselves, but that our mind, the human mind, is a product of that essentially mindless process.
That is the sense in which I think common-sense realism pictures the mind as a product of, and therefore dependent on, the brain, and the evolutionary processes that gave rise to it. It seems obviously true. So when I venture an idealist/constructivist opinion, the objection is - and we've seen it again in this thread - 'hang on, surely the Universe existed before humanity evolved to see it.' It is taken as an affront to common sense to see it any other way (I've had this very reaction from your good self in times past.)
My response is to acknowledge that this timeline is empirically true, and that I concur with the evidence in respect of the timeline of human evolution. But I also point out - and this is the crucial point - that 'before' is itself a human construct. The mind furnishes the sequential order within which 'before' and 'since' exist. In itself the Universe has no sense of 'before' or 'since' or anything of the kind. (This, I take to be the meaning of Kant's insistence that space and time are 'intuitions' rather than objective realities. See the passage from Magee's book on Schopenhauer in this post which I've posted a number of times previously).
The other line of argument starts from the scientific realisation that there's a strong sense in which 'mind creates world'. I think the modern version of this idea starts with Eddington and Jean's idealism which emerged around WWII. It's continued to develop, almost in an underground way. They're the dots I'm wanting to join, so I'm reading up on that area.
Quoting Wayfarer
Well, that's not right. We can be pretty sure that there is no frame of reference in which this conversation takes place before the Earth was formed, for example. Or if you want an example without any sentient beings, there is no frame of reference in which the sun becomes a red dwarf before it forms. Also, the entropy of the universe is higher now than it was a few billion years ago.
Kant's notions of space and time are dated.
Further I don't see what this has to do with the OP, with Platonic Realism & Scientific Method.
I think the dots you want to join are too estranged.
BTW I’ve just discovered an exceptional science writer by the name of Timothy Ferris, who’s book The Mind’s Sky explores just these kinds of things.
Mathematics is just another language and is therefore invented and arbitrary. It uses scribbles to represent some state if affairs, just like other languages. You can even translate the scribbles into English or some other language. What you can say with mathematics you can say in English.
Quoting Wayfarer
Words are like numbers in that they allow you to make quantitative predictions, too. Words represent how we view the world as quantified objects. The mind is a measuring device.
This is well said, and I will extend this to point out that the whole concept of "the Universe" is just a human construct as well. So it makes no sense to argue from the premise that "the Universe existed before humanity evolved to see it". This is because, as "the Universe", is simply how we see things (as per Kant, phenomena). Therefore it assumes that our conception of "the Universe" correctly represents what existed before humanity, and this requires that temporal extrapolation which is doubtful.
This proposition, that "the Universe existed before humanity evolved to see it" is only justified if our conception of "the Universe" truly correlates with what existed before humanity, otherwise it's similar to the often quoted expression "have you stopped beating your wife", where you start by assuming something unjustified, likely a falsity, and say something about it. It's nonsensical.
Therefore, as philosophical skeptics, we ought to call into question, all the mathematical constructs, and the premises employed by the theories of physics, to determine their justification to assess our conception of "the Universe". And this is why platonic realism needs to be rejected. Platonic realism leads to the idea that mathematics provides us with eternal unchanging truths, and this supports the idea that "the Universe", as we conceive of it is a true conception, based in the eternal truths of mathematics. Then when the relationship between what is theorized about "the Universe" through mathematics, and what is actually observed empirically, becomes completely disjointed, (as in quantum mechanics wave/particle duality), platonic realism pushes us into this notion that mathematics (which is really a human construct), is the underlying fabric of the Universe which existed before humanity evolved to see it. This is because the underlying fabric or "substance" of the new conception of "the Universe" is no longer consistent with empirical observation. Therefore if "the Universe" is to represent something real, the mathematics must be real, because that's all that's there, mathematics with nothing empirically observable.
Thanks. I don't agree with your rejection of platonic realism, however. As far as I know, Plato never placed dianoia - mathematical and discursive knowledge - at the top of the hierarchy of knowledge. It was higher than mere opinion, but didn't provide the same degree of certainty as noesis.
Have you heard of Sabine Hossenfelder's book Lost in Math? She too agrees that mathematicism in physics, if we can call it that, is leading physics drastically astray, but that has nothing really to do with Platonism, as such. It is the consequence of speculative mathematics extended beyond the possibility of empirical validation.
The aspect of platonism I focus on is the simple argument that 'number is real but incorporeal' and that recognising this shows the deficiencies of materialism, and also something fundamental about the nature of reason. How to think about the question is also important. I think there's huge confusion about the notion of platonic 'entities' and 'objects' and the nature of their existence. Most of that confusion comes from reification, which is treating numbers as actual objects when they're not 'objects' at all except for metaphorically.
As Aristotle said, we're 'creatures of reason' (iusually 'the rational animal') - so we live in 'the space of reasons' as naturally as fish live in the sea. I'm interested in exploring that idea.
Yeah makes wonder why phycisists went to all the trouble of devising new form of mathematics and symbolic forms to express concepts that literally could not be described in English. You should join the Physics Forum and let them all know, it would probably save them heaps of time and effort.
The strongest case for realism is that we can't do science without some kind of abstract entities, whether they're mathematical or other kind of operators quantifying over particulars. I recently listened to a Sean Carol podcast with a philosopher arguing for a kind of mathematical realism who makes that point. An even stronger case which he defended is that arithmetic is strongly related to consistency, and you can't do away with it unless you're willing to ditch giving consistent accounts of the world.
Now maybe that must means our cognition requires us to have some sort of consistent abstraction to make sense of the world. But that raises the question of why the world would be that creatures would find it advantageous to evolve such a cognition, if there are no real abstract entities whatsoever.
Of course Carol himself thinks that the world does have a mathematical structure to it described by the wavefunction, but that's a separate matter.
So then give us the English account of QM without any math.
What Plato placed at the top of the hierarchy is the study or knowledge of ideas and forms. But I do not think that "certainty" is the proper descriptive term for the higher levels of knowledge. Aristotle followed a similar division, and named the highest as intuition. You can see that there might be something amiss with describing this as certainty. The higher forms of knowledge lead us to higher levels of correctness, or good in Plato's world, but this is not really based in certainty.
Modern epistemology places too much emphasis on certainty, but certainty is just a form of certitude, which is an attitude. And this attitude is more properly associated with the lower levels of knowledge like opinion. We become certain of our opinions, but the true knowledge seeker always keeps an open mind.
Quoting Wayfarer
I haven't heard of that book, maybe I'll check it out when I get a chance. I believe the problem referred to is related to Platonism, because a misunderstood Platonic perspective is what validates the separation of logic (such as speculative mathematics) from empirical validation. When Forms are allowed completely separate existence, then a coherent logical structure need not be grounded in empirical fact. So we might construct an elaborate and very eloquent logical structure, which is even very useful for the purpose (good) that it serves, without having any real substance. That in itself is not bad, but amateur philosophers, and many common people will come to believe that it is saying something real and true about the universe, when in reality the whole structure is just designed to make predictions based on statistics, or something like that, and it's not saying anything real or true about the universe.
Quoting Wayfarer
Recognizing the reality of the incorporeal is a very important step. The way I see it is that if anyone has any formal training in the discipline of philosophy, this recognition cannot be avoided. There are many self-professed philosophers who will not make the effort to properly train themselves, and will simply deny the reality of the incorporeal. For whatever reason, I don't know, they tend to deny the reality of what they have not educated themselves about. Perhaps it is simplicity sake, monism provides a nice simple approach to reality, and whatever aspects of reality it cannot explain, they can be ignored as unimportant to those materialistically minded people. But unless a person is ready to take on the task of informing oneself about the immaterial, having a personal reason to do so, some sort of interest, it seems unlikely that the deficiencies of materialism will ever become evident to such a person. It's like morality, unless a person has the attitude, the desire to be morally responsible, the person will never see the benefits of morality.
Yes, you’re right.
Never read a layman's book on QM?
If math was the only language that could be used to explain QM then what need would there be for an interpretation?
You can say your numbers in English, you can say the function symbols in English, so I don't see the problem you guys are having here. The numbers and symbols represent something. What do they represent - more math?
So are you saying that the mathematical symbols don't refer to anything that isn't just more math? What does the math say about reality?
That's what mathematicians claim, so I would think there is some truth to it. If there is anything more than math, being referred to, this is dependent on application.
And prime numbers would have never been discovered without math.
They typically describe the history of some important experiments and physicists leading to the development of QM along with the various interpretations and the authors opinion. But they also include a few equations, with a note that QM is describing a world of the microphysical we don't experience.
I'll revise my question. Can you replace the equations in QM with English making no reference to mathematical concepts?
I should add that the difficulties of interpretation that are presented by quantum mechanics, is that while the mathematics are clear cut, the implications are bewildering - such as non-locality, super-position, the wave-particle duality and so on. The early pioneers of quantum physics leaned towards realism and believed that they would track down the ultimate constituents of reality, but instead opened a Pandora’s box. The maths still makes incredibly accurate predictions - the famous aphorism of ‘measuring the distance from New York to Los Angeles to within a fraction of the width of a human hair.’ But nevertheless, the same scientist who mastered that mathematics, Richard Feynman, also said ‘I think it’s safe to say that no-one understands quantum mechanics’.
I’m aware there’s a lot of bogus philosophy written on the basis of dodgy interpretations of physics, but even the mainstream, commonly-accepted interpretations are pretty far out.
So when you look at reality you see numbers and mathematical function symbols, not objects and their processes? F=ma refers to a state of affairs that isn't just more math.
So you agree that language is necessary for math?
Quoting Marchesk
Sure, because the mathematical concepts refer to states of affairs that isn't just more math. What is a mathematical concept, if not words in a language? Are you saying that it's mathematical concepts all the way down? Are you an idealist? The universe isn't made of numbers and function symbols. It is composed of objects and their processes. The scribbles on paper refer to those objects and their processes. Are electrons numbers or objects or processes? Are tables and chairs composed of numbers or electrons?
When I look around, I do not see force, nor does "f=ma" refer to a state of affairs, it is a universal, which is a generalization. Force is a concept. And I do not think we can adequately differentiate between mathematical concepts and non-mathematical. Is "large" a mathematical concept? Are shapes mathematical?
When you look at the world what do you see?
Is it concepts all the way down?
Do objects and their behaviors symbolize mathematical concepts or do mathematical concepts symbolize objects and their behaviors?
No, I'm dualist, I apprehend both, with a fundamental incompatibility between the objects which I see, and the concepts which I understand.
Quoting Harry Hindu
It goes both ways. Some scientists try model the behaviour of natural things using concepts, but artificial things are representations of concepts. Fundamentally, symbols always represent something mental.
The realist argument is that those numbers and symbols are about something which exists independent of us.
Quoting Harry Hindu
For us to do the math. Does that mean prime numbers only came to exist when mathematical language was created? I'm not so sure about that.
Quoting Harry Hindu
I don't know what a fundamental particle is. I do know that its properties are described mathematically. Tegmark's point is that all physical properties are mathematical. I don't know whether that just means we have to understand them that way, or that there is real mathematical structure.
The challenge to the anti-realist here is to come up with a way of describing electrons that doesn't use math but is still faithful to the experimental results and predictions.
Quoting Harry Hindu
You’re working within the representative realist notion where ideas stand for, or represent, things.
Physicists went out to explore just those ‘objects and their processes’, confident that they existed independently of anything said about them. But that was just what was called into question by what they discovered. They discovered that the answer to the question 'is an electron a wave or particle' depended on how you asked the question, and that it was impossible to say that an electron 'really is' either of them.
It was the paradoxical nature of quantum theory that Einstein could not accept. He too was a staunch scientific realist, who believed that the world existed independently of all and any scientific theory. That's why he posed the question 'does the moon still exist when nobody is looking at it?' I think this was, in his mind, a rhetorical question, the implication being: of course it does. But the point is, he still had to ask the question.
This became the subject of the famous Bohr-Einstein debates, which went from around 1927 until Einstein's residency at Princeton.
For an in-depth discussion of the debate, it's protagonists and issues, check out the following:
Uncertainty: Einstein, Heisenberg, Bohr, and the Struggle for the Soul of Science, David Lindley
Quantum: Einstein, Bohr, and the Great Debate about the Nature of Reality, Manjit Kumar.
But, be aware that Bohr himself says that the implications of quantum physics are 'shocking'. They're shocking precisely because they call into question our instinctive sense of the reality of the physical universe.
I don't understand. You apprehend both what? What is incompatible?
Quoting Metaphysician Undercover
It don't see how fundamentally, symbols always represent something mental when you just said that concepts can represent natural things, unless you're saying that natural things are mental, but then that would make you an idealist/pansychist, not a dualist.
Do tree rings represent the age if the tree independent of someone looking at the tree rings?
Right. So is math the numbers and symbols, or the thing the the numbers and symbols are about, or the relationship between the numbers and symbols and what they are about?
Quoting Marchesk
Are you asking if the actual scribble, 19, came to exist when mathematical language was created or what it represents came to exist when mathematical language came to exist? What is the scribble, 19? What does it represent? Is not, "prime number" a word in a language?
Quoting Marchesk
To describe something is to use symbols to represent that thing. Does it really matter if we use math, English or Spanish? Claiming that all physical properties are mathematical is akin to claiming that physical properties is information, or that physical properties are measurable. Math makes use of measurements. That's what the numbers represent. Being that languge precedes math, therefore is more fundamental than math, then isn't it more accurate to just say that physical properties be represented using symbols?
Not just ideas, but everything. Effects stand for, or represent, their preceding causes. The scribbles in your post represent your idea yesterday that you intended to communicate to me.Your idea represents an actual state-of-affairs that exist independent of you and I talking about it. At least, that is what you are asserting. If that is not what you are asserting, then what are you talking and thinking about?
Quoting Wayfarer
But what about the physicists themselves? What are they composed of - waves or particles? You seem confident that these physicists and their discoveries exist independent of your observation of them. I assume that the physicists you are talking about aren't scribbles on a screen, but human beings, which are objects just like everything else that we observe. This idea that you're asserting that these physicists have contradicts the very thing that they are trying to show.
Whether or not an electron is a wave or particle is dependent upon the view you are taking and the causal sequence that lead to that particular observation. The observer is part of the very universe that the physicist is describing and part of the causal sequence that manifests as the effect in the mind.
You asked me:
Quoting Harry Hindu
It is not concepts all the way down, I am dualist, so I see (apprehend with my mind), that there are aspects of the sensible world which cannot be conceptualized. That is the incompatibility between the intelligible and the sensible, which gives the need for dualism.
Quoting Harry Hindu
A concept is not a symbol. So a symbol can represent a concept which can represent a natural thing. But a symbol cannot represent a natural thing directly because it is required that a mind establishes the relation required in order that something can be a symbol. Therefore, it is necessary that a mind acts as a medium, between the symbol and the thing, in order that the symbol can be a symbol. This is what it means to be a "symbol" to be related to soemthing by a mind.
Quoting Harry Hindu
No, that's nonsensical. A symbol must be interpreted to represent anything, and what it represents is a function of the interpretation.
This makes no sense. How can you apprehend something which cannot be conceptualized? Apprehend and conceptualize are synonyms. Both are akin to "grasping" something mentally.
Quoting Metaphysician Undercover
Are not concepts natural things?? You seem to be making a special case for human minds, as if human minds are seperate from nature, when minds are just another causal relationship, like everything else.
Quoting Metaphysician Undercover
What if it's interpreted wrong? Is it still a symbol? It seems more accurate, and less religious, to say effects represent/symbolize their causes.
You're clearly not trying, if it makes no sense to you. Have you ever "grasped" the idea that you do not understand something? That's what I mean. When someone speaks a foreign language for instance, you might apprehend that you do not understand what the person is saying.
Quoting Harry Hindu
In the ontology which I respect, concepts are artificial. Do you not respect the difference between natural and artificial? "Artificial" is commonly defined as produced by human act or effort rather than originating naturally.
Quoting Harry Hindu
I don't see any principle, other than 'what was intended by the author', whereby we'd distinguish a wrong interpretation from a right interpretation of a symbol. Therefore your claim that a natural effect symbolizes its cause (without an appeal to intention), is just as likely to be incorrect as correct. So it's a worthless assertion.
Or you're clearly not trying if it makes no sense to me. Someone speaking a different language to me clearly does not understand that I don't understand that language. Speaking and writing requires an understanding of your audiences understanding of the words you are using. It requires two or more following the same protocols to communicate. How you might communicate with a child or a person just learning English will be different than how you communicate with an adult that speaks English fluently.
So you're saying that your dualism isn't one of mind vs. body, rather one of understanding vs mis-understanding? I still don't get it.
Quoting Metaphysician Undercover
And humans and their actions are outcomes of natural processes. The only reason you'd want to distinguish between what humans do and what everything else does is because you believe in the antiquated idea that humans are specially created or created separate from nature.
Quoting Metaphysician Undercover
I haven't excluded intent. As a matter of fact I told Wayfarer that their posts symbolize their idea and their intent to communicate it, which are causes for there being scribbles on the screen that we can observe. Tree rings symbolize the age of the tree because of how the tree grows throughout the year, not anything to do with the intent of some human. Humans come along and observe the tree rings and their intent is to understand what the tree rings are. The human attempts to grasp what is already there and the processes that produced the tree rings. This is how the human comes to understand what the tree rings are, which is what they mean. This is what humans do, we attempt to understand what exists by explaining the causal processes involved in producing what we observe.
The question you asked me was how can I apprehend that there is something which I cannot conceptualize. The example was, when someone speaks a foreign language to me, I can apprehend that the person is speaking to me but I cannot conceptualize what the person is saying. Therefore it is an example of what I said, there are aspects of what I am hearing, which I cannot conceptualize.
Quoting Harry Hindu
Don't fret, it's not a big deal if you do not understand dualism. But if you want to, I suggest studying some classical philosophy to get a grasp of the concepts.
Quoting Harry Hindu
No, my reason for separating intentionally constructed things (artificial) from natural things, is to help me understand reality. Clearly we haven't yet obtained a firm grasp on reality, so I don't know why you would think that this is an antiquated approach.
Quoting Harry Hindu
Obviously, the intent to determine the age of the tree is implied in this description. Otherwise you simply have a growing tree with the form that it grows into, nothing symbolized by that tree without the intent to determine something about it. Therefore you have not separated this relationship from intent, as you claim.
Quoting Harry Hindu
Right, you seem to understand here. The relationship between the tree rings and the age of the tree is something determined by human beings through their intent to understand. It is a form of measurement. Do you agree? And do you see that measurement is an act of comparison carried out by human beings, relating one thing to another, rings to a time scale in this case? This comparison, act of relating one to the other, does not occur without those human beings.
Obviously I'm not talking about the symbol. It's the number it references, not whatever we use to denote it. 19 is just a symbol. It represents a quantity which is also prime.
Quoting Harry Hindu
Math is about the mathematical objects the symbols represent. Numbers, sets, proofs, functions, graphs, whatever. Realism is asking whether any of those objects are real, not the symbols. The symbols we came up with to represent the objects.
Quoting Harry Hindu
It matters for this debate. If we can't use a non-abstract language to describe the world, then the realists about abstract arguments have a good argument for something abstract being part of the world.
I'm way late to your most excellent post. I think Bertrand Russell is exactly right about mathematics and ignorance. There are elements in Platonism which are very appealing to some, in particular me. The thing is, or one of the problems it faces, is that we have to posit almost an infinite amount of mental objects to account for what we see in the world. The general line of thinking here is not so much that for example, all "trees" fall under our concept or Platonic notion of Tree and likewise for "apples" and "horses" and many of the classical objects of thought. The issue is, what do we do about new objects? What do we say about, say, laptops or plastic or anything else that did not exist previously? Are we going to have to postulate ideas for all these objects?
Maybe I'm misunderstanding you final point, but, even though I agree that we need some kind of Platonism to make sense of manifest reality, I'm not convinced that most of these objects can fall under the scope of science, in any deep theoretically illuminating type of inquiry.
Thanks for your interest, and a very good point. There's an essay I often cite, 'What's Wrong with Ockham', by Joshua Hothschild, which unfortunately is no longer published online (although downloadable here.). It's a critical review of the baleful consequences of the nominalism of Ockham (and others) on the Western intellectual tradition. Aquinas is presented as the exemplar of scholastic realism, i.e. defending the notion of forms. Ockham made a similar criticism of scholastic realism to yours, saying that it implied 'a highly populated domain of discourse'. But Hothschild points out that:
I think there's an irresistible tendency to conceive of the forms as shapes - that the form of a cat is a feline shape, and so on. And many school book examples of the forms are given as triangles and circles, which reinforces that tendendy. Nevertheless I think it's a mistaken apprehension of what the forms are, although understanding what they are, is obviously one of the key issues!
There's another useful essay, Meaning and the Problem of Universals, Kelly Ross. It's a revisionist interpretation of the meaning of the forms, where he remarks:
That's interesting and it seems to follow from the general argument. But then the concept of form seems to become extremely elastic, as in we'd have to speak of the Form, and not forms in the plural. It seems to dissolve our notion of an object as a particular entity, as in a television and a book are different objects.
But then do we do away with objects all-together? The problem for me is that I can't think of form in the abstract absent initial instantiation. And I am no nominalist, I tend to side with Scotus, Peirce and Haack, existence and real are different, I believe universals to be necessary to make the world intelligible. So if we think of form in the abstract, I'm not left with any positive notion that I can use, outside its application.
If you find something interesting let me know. I don't have a clue either.
The key dialogue is Plato's Parmenides.
On a very general note, this lecture, Lloyd Gerson on Platonism vs Naturalism, is well worth listening to. The standout passage for me is around 38:00 with discussion of Aristotle's doctrine of universals, but take the time to listen to the whole thing when you have an hour or so.
Will watch it for sure. Thanks for sharing.
But numbers are just symbols. Where in reality is there a number that the symbol points to? Quantities are always OF something, not something that can exist on its own. Math is merely a comparison of measurements.
Where is the number/quantity 19 in relation to the symbol 19?
The issue is in mathematical physics, that discoveries are made BECAUSE of the maths, not made first by observation, and then described mathematically. A case in point was Dirac's discovery of anti-matter. According to the equations he developed or discovered that described electrons, there ought to be positive counterparts to the negatively-charged electrons. At the time no such things were known but lo and behold some years later they were discovered [sup] 1[/sup]. There are many other such examples in the history of physics, which is why Eugene Wigner felt compelled to write the essay On the Unreasonable Effectiveness of Mathematics in the Natural Sciences.
Quoting Harry Hindu
A number is a symbol denoting a count. And the count is nowhere but in the mind of the counter, it is a purely intellectual act. Yet all who can count will agree that 19=19 so it is not the property of a single observer.
If that's true, then it should be possible to do physics without numbers.
Quoting Harry Hindu
In the world somehow? I don't know, but the symbol 19 is arbitrary. There are other symbols that also denote 19, such as its binary representation or the word nineteen. A mathematical object is not its symbol, since the symbol can be anything we want it to be.
Anyway, the mass of an electron is the same value before our evolutionary ancestors could count. We understand that value numerically.
When we speak of real, the gold standard seems to be real in a physical sense - touchable, visible, audible, tasteable, in short detectable by some physical method i.e. real is defined in terms of the physical. My last conversation with you in this thread ended on that note. If it's all the same to you, I wish to explore this a bit more.
To my reckoning, there are two distinct worlds we humans and probably some non-human animals experience and they are: 1. the physical world and 2. the mental world. The former is the world we can bodily bump into like chairs, tables, rocks, etc. and the latter is populated by what are basically abstractions.
It's evidently clear that what all of us are aiming for is an agreement between the physical and the mental - when the two are in sync, we feel good and when they're not, it's disconcerting. My theory is that the reason why we seek a convergence between the two worlds is that it's absolutely necessary for our well-being and survival. If we have the wrong mental impression of the physical, it has unpleasant, even fatal, consequences. Just ask the person who mistook a venomous snake for a coil of rope.
Since, as can be inferred from the previous paragraph, making a mistake in matters physical can lead to injury and death, the physical becomes our top priority and, on any given day, we'd rather side with the physical than the mental. In other words, given an inconsistency concerning the physical and mental world, e.g. that unicorns and demons aren't physical, we're, in the case of the former, disappointed and, in the case of the latter, relieved. These responses reveal the privileged status the physical world enjoys over the mental world. Our conception of real as physical is reflected in this.
Yet, if we ask for a reason as to why the physical should be treated in such a special manner, a reason other than concern for our own welfare as physical bodies, we find none. Too, if well-being is a priority and if that's the reason, it seems to be so, why our idea of the real is grounded in the physical, then what do you make of this short clip,
of people who die inside which, the way I see it, is mental death. We do, on many occasions, go through mental death and such experiences are, by all standards, equivalent to physical injury and death - the pain and suffering of dying inside is at par with the pain and suffering of physical injury and death.
In conclusion, the mental world, since it too has its own version of injury and death just like the physical world, shouldn't be treated as less real than the physical world. It must be mentioned though that most cases of dying inside happen when our mental impressions are shot to pieces by physical facts i.e. when our mental world fails to line up with our physical world. Despite this it can't be denied that there's something nonphysical about mental injury and death (dying inside); after all, why does our body not respond in the way it does to physical assaults.
To wind up, the mental world has all the features of the physical world even though they differ qualitatively. If so, we're not justified in treating them differently and if that's the case, mental objects in the mental world are as real as physical objects in the physical world.
Sorry for the long post, What say you?
Would it be possible to do meaningful math without the numbers referring to things that are not mathematical? When Farmer Joe counts the chickens in the pen and there is one less than there was yesterday, is he counting numbers, or counting chickens? Are chickens math or organisms?
Quoting Marchesk
What is the mass of an electron? Wouldnt you be providing an arbitrary measurement? Does an object weigh 19 pounds or 8.6 kg?
Quoting bongo fury
My question would be that if you ditched numbers, how can talk about the properties of electrons, such as their mass and charge, since the value is the same for all electrons? Another way to ask the question is what are physical properties if they're not mathematical (que Tegmark)?
Those are just different units for the same value.
Quoting Harry Hindu
Yes, math is done in abstraction all the time. It's not like there are prime chickens.
The value of what - another number - something mathematical, or feature of some object?
19 = 8.6
or
19 pounds = 8.6 kiolograms?
It's not the numbers that are equal, but the weight, right? When we talk about weight, are we talking about measurements, or something else? Aren't measurements OF something? Isn't a measurement simply a comparison of objects and their features?
Quoting Marchesk
Right, so unless you are saying abstractions exist independent of minds, then math doesn't exist independent of minds. But don't think that doesn't mean that abstractions aren't real, or that they don't have causal power. My point is to watch where you are pointing with your words. When talking about ten chickens, are you talking about a number or chickens?
Both. Were there not 10 chickens before humans were around to count them? The example I always heard was 2 dinosaurs were in a pond, and then a third joined. Did 1 + 2 = 3 not exist in the Jurassic?
Quoting Harry Hindu
Sure, but the measurement always gives us a numerical value of some kind, and we decide on the units.
I guess the question is, when is a discovery made - when it is observed in the math, or when it is observed in nature? Either way, it was observed.
Quoting Wayfarer
But why does 19 = 19? Is it because 19 is the same scribble as 19?
There were a quantity of chickens before humans were around to count them. What we call that is arbitrary. Aliens could use a different scribble to refer to the quantity, or use a totally different number-system for all we know.
Can numbers exist on their own without being attributed to things? Can things exist without being counted, or having numbers attributed to them?
Quoting Marchesk
When comparing an apple to an orange, are all the words that we use to compare them numerical? Is color numerical, what about taste or smell?
It's hard to see how aliens would come up with a different arithmetic for discrete entities and it have the same usefulness.
Quoting Harry Hindu
I don't know, but they seem to have an objectivity which goes beyond our arbitrary choice of words and symbols.
Quoting Harry Hindu
Sure, but can they be understood to exist without any mathematical properties?
Quoting Harry Hindu
No, I don't think math is all there is to existing.
I don't know what reality fundamentally is, but the question is whether reality includes some sort of abstraction, which would mean nominalism is wrong. If it does, math is the best candidate. At least the maths that are applicable to the world.
... That would be a cheek, indeed.
Quoting Marchesk
Ah but they aren't necessarily abstract, they are roughly like general terms, concrete syntactic elements (words) saying things about particulars... in effect, sorting them. They are predicates pointed at things, held true of them, sorting them; not themselves among the things predicated of and sorted. No reifying, then, of the ways of sorting by quantifying over them like chickens or other space-time regions. (Let me count the ways... No, we shan't let you, if you have to reify them as abstract entities!)
The book is (I gather) about proving the principle that physics can be expressed on that relatively non-commital basis.
Quoting Marchesk
Ways of sorting, which physics asserts are the right ways.
Hello my old friend.
I think the larger question that informs your inquiry is that of the intelligible order and the intelligence that is its author.
I am going to offer a very different view, that of self-organization, bottom up rather than top down. The observed order is accidental in that things could have developed differently and nothing prevents further development in very different directions. Intelligence is a contingent and emergent feature. The laws of nature are not fixed, their stability temporal.
Sorry for interrupting your conversation here.
I have to leave soon, it's way too late where I'm at. Nevertheless, I'd really like to continue talking about your ideas on this type of philosophy: it's the most interesting to me. I think, despite some differences we may have, they're insignificant given on what we agree.
I've got to pick your mind on many topics. So I guess I'll try to be around on one day that you'll be here for an hour or so - not that I need an hour to talk, but enough time to clear some things up.
Have a good one.
The way I put it is that, in respect to formal ideas such as math and logic, that the ability to grasp such ideas evolves, but the ideas themselves [s]do not[/s] - no, that's wrong, obviously there is huge development in some areas of maths. But there's a major element which is discovered not invented - although, having discovered, one can then invent.
When I was first introduced to philosophy I was enamored by the idea of Forms. Some years later I came to see them as images themselves, part of Plato's poetry that was intended to replace the myths of the gods.
The key point for me is that the so-called intelligibles are not existents in the same way that objects of sensory perception are. They are more like, on the one hand, the rules of logic, and on the other hand, the laws of form, in that they act as constraints on the realm of the possible.
Have a read of Meaning and the Problem of Universals by Kelly Ross, which is a kind of revisionist history of the idea.
This is highlighted to some extent by Colin McGinn in his Inborn Knowledge: The Mystery Within.
I was wondering, which contemporary philosophers speak of this kind of thing, that is a-priori knowledge. Math and logic surely are a-priori, but I suspect even more may be a-priori than what we initially may think to be the case. Sure, we need contact with the world to activate our or nourish our innate capacities, but our exposure to the world is too brief to account for concepts based on learning.
How do you think about these things?
The last book my dear departed mother gave me, as a Christmas present, almost 20 years ago, was Steve Pinker's The Blank Slate. I'm not at all disposed towards Pinker's philosophical attitude, but he has many interesting things to say about linguistics and evolution. And this book was an argument against the 'tabula rasa' of empiricism, that humans begin life as a blank slate, in favour of the idea of evolutionary inheritance giving rise to innate abilities.
Myself, I feel that evolutionary explanations are only part of the picture. It seems obvious to me that infants are born with all kinds of proclivities, talents, dispositions, inclinations, and so on, and I don't know how much of a grasp science has on all that, or whether it all can be explained solely in terms of evolution and genetics.
Case in point is musical prodigies. I'm a jazz fan, and about 6-7 years ago, this young pianist suddenly exploded on the scence, Joey Alexander. At the time of his first album he was a young teen, of Indonesian parentage, and looked about 10. But played and improvised with a maturity well beyond his years - jazz legend Herbie Hancock was completely blown away by him. Mozart was another example, penned his first symphonies as a child. I don't think there's a scientific account of why those kinds of talents ought to exist, not even to mention that musical genius has no obvious connection to biological adaptation. Not that I'm saying I have a better theory, other than some vague sense of there being a collective consciousness of some kind, that takes birth in such forms. But I would never try and persuade anyone of the truth of such an idea.
I suppose in the philosophical literature, the grandfather of such notions is in the Meno, with the slave boy whom, by questioning, is shown to know abstruse mathematical principles, innate in him, due to the knowledge imprinted on the soul prior to birth. Again I feel as though this is an analogical or mythical depiction to allow for the uncanny ability that humans generally have to acquire learning - namely, talent. Indeed the whole idea of anamnesis, 'unforgetting', suggests this kind of idea. Perhaps it's a mythological depiction of the notion of cultural inheritance - that would be a naturalistic account, although I do feel that it's something which current naturalism would find it hard to accomodate. There's a lot that's uncanny about it.
On a more prosaic note, I was introduced to the notion of the a priori in my class on Hume. It seemed to me that Hume, and philosophy generally, rather took for granted the notion of the a priori. The standard example of 'bachelor being an unmarried man' made the point, but it also sells it short. Why should the Universe be such that there are things we know a priori? That's the question that occured to me. I think it is Kant who really appreciates that question, whereas Hume, as I say, simply took it for granted. Kant also explored the synthetic a priori, the significance of which I feel is even more taken for granted. How is it that, given two pieces of information, we can reliably infer a third, which is not directly given by the first two, but is nevertheless apodictically true? That too is uncanny, but also mainly taken for granted.
Harking back to Pinker, the taken-for-granted approach is that the requirements of biological adaption are sufficient to explain our apparently-innate linguistic and intellectual abilities. But again, I'm rather skeptical that it is only a matter of biology. Actually Chomsky has also written on this, Why Only Us? co-authored with Robert Berwick. I'm meaning to read that, but there's about ten thousand books I'm meaning to read. At least Chomsky approaches it with a satisfactorily awed appreciation, in my view.
I read part of that a while ago, I forgot much of it, but the little I remember was suggestive and I think proves the point of the title of the book. I have read The Language Instinct and The Stuff of Thought. I'll have to go back to that one. The chapter in The Stuff of Thought called Cleaving the Air is quite interesting: showing language in a quasi-Kantian perspective. How correct this is in terms of scientific evidence, I can't judge, but it sounds persuasive.
Quoting Wayfarer
Yes, I share those exact same intuitions. This is very likely imbedded in our genetic code, though how it happens so far is kind of mysterious. Of course, if you take it that "this happens because of genes and evolution", that's not saying too much, I don't think.
Quoting Wayfarer
Hume thought that human creativity was beyond our scope of understanding. I've been learning the hard way that these types of "rationalistic idealisms" look like total hand-waving and maybe even irrational. Oh well.
Quoting Wayfarer
Yes. I'm in the same boat in terms of reading. Chomsky thought Ralph Cudworth had more interesting things to say about cognitive structure than Kant. Cudworth's an interesting case. He speaks of "native and domestic" ideas. But he is not well known at all.
So Plato's meno, Kant - anything else come to mind? This type of tradition is sadly not as active as I would like.
Hmm. I can't say I can definitively explain great talent but it seems to me that some forms of autism (for instance) come with exceptional gifts and I don't think this necessitates access to a special realm of ideas. Some brains are odd. The critic, Harold Bloom, was able to read and process 1000 pages in little over an hour with almost total recall. He could read the entire novel Don Quixote during lunch and provide insightful analysis. I don't think this involved archetypes either but I do think it fits into the general realm of remarkable capacity. People with musical ability have a great knack for mimicking or reproducing and embroidering on patterns and formulas (which is essentially how music works - having studied the violin and learned to memorise songs after one or two hearings, I have some idea of this although I was no Mozart) I suspect some brains are just abnormally fecund.
I've seen this claim before and I really doubt it is even possible (I know this is irrelevant to the rest or your post, sorry).
I took a look at what was available to read on Amazon. The only thing "Look Inside" reveals is the forward by Hedley on the legacy of the Parmenides. There is an introductory essay of readers and interpreters. I wonder what he has to say about the problem of interpreting Plato. Hedley sees the dialogue as the legacy of Parmenides as interpreted by Plato. That legacy includes the influence on Socrates and Plato. And this raises the question of why Plato's Socrates continued to talk about Forms after this encounter with Parmenides when he was young.
I think it has something to do with Socrates "second sailing" (Phaedo 99d). After the criticisms of the Forms Parmenides says that one who does not “allow that for each thing there is a character that is always the same" will “destroy the power of dialectic entirely” (135b8–c2). In his search for the causes of all things he undertakes a second sailing, a turning away from what the eye sees and toward speech, logos. In other words, contrary to the myth of Forms in the Republic, the Forms are not discovered through transcendent mystical experience. They are that which for each thing must remain the same if there is to be dialectical speech.
It seems impossible, right? I've heard Bloom interviewed on this claim. Before he died he said that in old age he slowed down to 500 pages an hour.
He was probably cheating and just reading the Bloom's Notes summaries...:grin:
That's all I can come up with at the moment, sorry.
Quoting Tom Storm
There was a savant, Kim Peek, the basis of the Rain Man character, who could read two books simultaneously and perform other astounding feats. Savants are a whole other area of mystifying capacity.
Quoting Tom Storm
I suspect the brain is analogous to a receiver~transmitter in some basic respect, rather than an originator of information.
Quoting Fooloso4
(This is in reference to a book on Plato and Parmenides.) I'm of the view that the Western metaphysical tradition starts with Parmenides and that I have to get a better understanding of him. The standard text is Cornford, I am looking for something more contemporary. I found a publishing company called Parmenides Publishing, which lead me to Arnold Hermann and read some of the views. I'm warily eyeing the kindle edition of his Plato and Parmenides, but it's an expensive purchase and a difficult topic.
Could be. What I tend to see is the human capacity for imitation. We are magnificent copyists. Sometimes we copy better than the originals and then riff.
Peter Kingsley has some interesting things to say.
I read it some years ago. He pays careful attention to the details of the dialogue, which is to say he does not treat it like a discourse or doctrine. It is a Socratic dialogue. Socrates called himself a physician of the soul. At the heart of the discussion of Forms in the Republic there is a turning of the soul.
He also wrote on Parmenides proem. I just found this. https://philarchive.org/archive/MILPAT-4v1
Miller's interpretations do not suffer from the anachronisms often found in modern interpretations.
[Edit: I read the paper. Given the complexity of the subject matter I thought it was very clearly written. I don't know if this is the kind of thing you are looking for though. Unlike Hedley it does not address Parmenides' legacy.
Quoting Fooloso4
That is a reference to 'metanoia' is it not?
It is not, as or as I know, a term used by Plato. Here is the passage.
" ... the power to learn is present in everyone's soul and that the instrument with which each learns is like an eye that cannot be turned around from darkness to light without turning the whole body. This instrument cannot be turned around from that which is coming into being without turning the whole soul until it is
able to study that which is and the brightest thing that is, namely, the one we call the good." (518c)
[quote=Wikipedia]Mathematical realism, like realism in general, holds that mathematical entities exist independently of the human mind.[/quote]
You might wanna take a look at Synesthesia and grapheme color synesthesia
Some excerpts below for your consideration:
[quote=Wikipedia]Grapheme–color synaesthesia or colored grapheme synesthesia is a form of synesthesia in which an individual's perception of numerals and letters is associated with the experience of colors[/quote]
[quote=Wikipedia]Reports include feeling sensations in the hands or feet, coupled with visualizations of shapes or objects when analyzing mathematical equations, physical systems, or music. In another case, a person described seeing interactions between physical shapes causing sensations in the feet when solving a math problem.[/quote]
The point is, for (some) synesthetes, numbers have colors like an apple or a banana has and some math problems can give you the sensation of being physically touched! Are numbers real like apples, bananas and the hands of a masseur on your feet?
Hey only kidding. What impresses me about platonic realism is that numbers and fundamental concepts are not the product of your mind or mine, but can only be grasped by a mind. Whereas the tendency of empiricism is to attribute reality only to things that exist in space and time - the expression is ‘out there somewhere’. So they’re real in a way that sense objects are not.
:up: It looked like a good lead to follow and I thought you might be interested. Like they say somewhere in a little town in America, don't forget to be awesome! G'day.