Can we know in what realm Plato's mathematical objects exist?
Intuitionists" believe that mathematics is just a creation of the human mind. In that sense you can argue that mathematics is invented by humans. Any mathematical object exists only in our mind and doesn't as such have an existence.
"Platonists", on the other hand, argue that any mathematical object exists and we can only "see" them through our mind. Hence in some sense Platonists would vote that mathematics was discovered.
If this is what Platonists believe, then where do they think that these objectcs exist? If it's not inside our physical realm then in what realm do these objects exist and do they move inside of it?
Personally, I think math is invented by people to merely describe physical states of affairs of which some show exact correspondence with physical reality. I think Max Tegmark was on dope.
"Platonists", on the other hand, argue that any mathematical object exists and we can only "see" them through our mind. Hence in some sense Platonists would vote that mathematics was discovered.
If this is what Platonists believe, then where do they think that these objectcs exist? If it's not inside our physical realm then in what realm do these objects exist and do they move inside of it?
Personally, I think math is invented by people to merely describe physical states of affairs of which some show exact correspondence with physical reality. I think Max Tegmark was on dope.
Comments (149)
We already discussed a similar issue here: On Gödel's Philosophy of Mathematics
And the problem with saying that it’s ‘merely’ an invention of the human mind, is that it doesn’t allow for the unreasonable effectiveness of mathematics in the natural sciences. Maths is predictive, through it you can discern facts about nature which you would have no way of finding otherwise.
But what did Plato mean?
Yoou could call it as well the reasonable effectiveness. The reason being that Natural processes are patterned inherently structured.
"the unreasonable effectiveness" is also a product of human mind? which is synthetic analytic judgement?
"the unreasonable effectiveness" is also a product of human mind? "
:heart:
Good question.
I think that mathematical objects such as geometric shapes are related to Plato’s Ideas or Forms.
When we perceive something in visual cognition, for example, we really see shape, size, color, number, etc.
Therefore Shape would be something similar (though not identical) to an universal that awareness or consciousness uses to organize itself in order to generate determinate cognition.
As such, the Ideas or Forms seem to exist in latent or potential form within indeterminate forms of consciousness from where, on becoming activated, they emerge and generate particular objects of determinate cognition.
If we consider the following aspects or levels of intelligence,
1. The Good or the One;
2. Nous or "intellect" proper;
3. Logistikon, "intellectual" or "thinking" aspect;
4. Thymos or "emotional" aspect;
5. Epithymetikon or "sensual aspect" (relating to sense-perception),
then the Ideas or Forms are objects of the nous and the mathematical objects are objects of the logistikon. But the ultimate source of the Forms seems to be the Good or the One that may be described as a form of superordinate or universal consciousness.
And where does our physical realm exist? If it is embedded in a larger space, where does the larger space exist?
Space is just one of many mathematical objects and all mathematical objects exist in virtue of being logically consistent and in mutual relations, of which spatial relations are just a special kind of relation. And by the way, time is just a special kind of space, at least according to theory of relativity.
We can distinguish two kinds of mathematical objects: concrete and abstract. For example, there are concrete triangles (like concrete "give way" road signs) and one abstract triangle, which is a property instantiated in all concrete triangles. The Platonist objects are the abstract ones. Some people think that the abstract objects don't "really exist", that they are just words or ideas in our heads. Yet these words or ideas express an objective similarity between concrete objects, so the abstract objects can also be understood as being in a sense "dispersed" in concrete objects.
But mathematics is predictive only in the sense that physicists have assumed (as the Pythagoreans Heraclitus Plato Galileo had) that the unknowable natural world is mathematically orderly. This pragmatic assumption has sent mathematical physicists scouring through all maths in search of hypotheses to fit physical observations.
As of today, I doubt that there is any maths left that has not been incorporated in some physics. New maths is spurred on both from discovery-invention within pure mathematics and from mathematical physics in search of logical justification for some fanciful ideas.
One should not have to choose between these extremes. Mathematics was discovered through technological trial and error to be reasonably but not perfectly predictive of sounds coming out of musical instruments and from observations of the day and night sky. It was obvious from the first that mathematics is the guide to a hidden world that lies beneath the appearances that we take for granted as the reality of speech and action.
What 'exists' does not belong. Existence is a construct needed to describe fixed objects in a supposedly timeless reality.
Correct. But we must not forget the Forms.
There are (1) concrete or perceptible mathematical objects, (2) abstract or ideal ones, and (3) Forms.
For example, if we hand-draw a triangle on a peace of paper or in the sand, we have a perceptible triangle. But our thinking faculty tells us that this triangle is less than ideal. In doing so, we form the concept of an ideal triangle in our mind. This is the ideal object. However, we can only form an ideal object in our mind by referring to something like a universal form or pattern of which we can only have an innate intuition. This universal form or pattern is the "Form of the triangle".
The Forms are at once "dispersed in concrete (and ideal) objects" and transcendent in relation to them. This means that the Forms themselves are outside time and space, though their imperceptible properties are approximately perceptible in concrete objects like reflections of the sun in water.
I agree whole-heartedly with the Forms. All Forms can be described by math. An arbitrary periodic form can be translated (is that the right word?) into base sine forms. Like the epicylces did for planetary motion. In fact ALL FORMS can be translated or described. Not all can be reduced (important for the non-perturbative approach in quantum field theory). This idea comes closest to Plato. The math. forms are indeed not part of the physical world. But neither in an unaccessible metaphysical realm. Unless you think that the world of ideas (themselves being Forms too) IS this world. Accesible to us obviously.
Plato is a very complex writer and it is important to read him carefully and on his own terms. But I think that a first step in the right direction would be to bear in mind that the Forms are not the same as ideal objects.
An ideal object, e.g., an ideal triangle, is something that I form in my mind. But my ideal triangle is not the same as your ideal triangle; it is multiple as it exists in many minds; it is subject to time as it is not permanently fixed in the mind, etc.
In contrast, the Form of Triangle is one, unchanging, and eternal. It is beyond space and time and cannot be expressed in language.
The other peculiarity of the Forms is that they are at once (1) present in particulars through their properties and, therefore, immanent and (2) other than each and all particulars and, therefore, transcendent to them.
Acquainting ourselves with the concept of ideal objects is a necessary step toward understanding the Forms. But, eventually, we must go beyond the level of ideal objects in order to “attain to the knowledge of reality” as Socrates puts it in the Phaedo (66a).
Seems more complex than at first sight! Like many first sights. It sounds even religious. Though the Greek had a mountain full already. Damned! this is how a forum should be!
If something is beyond space and time, then where could it be?
It may sound "religious" to the modern mind. But Plato's primary concern is never religion per se which is based on belief (pistis), but knowledge (noesis or gnosis) which is based on experience.
Religion, in so far as it plays a role in the acquisition of knowledge, is just an intellectual framework or ladder that leads to an actual experience that transcends both belief and reason.
Somewhere beyond space and time? I.e., within a form of awareness or consciousness where experience of time and space has not yet emerged.
You need to have some cognitive elements, visual or auditory, etc. in order to perceive space and time. Prior to this, there is no time and space. The Forms being unchanging, eternal, etc., cannot be anywhere else.
All determinate experience, including time and space, begins with the Forms. This is why Plato is actually serious about the Forms. It isn't just literary licence.
Plato's Forms and their corresponding Name are similar to the nama-rupa ("name and form") concept of Indian philosophy.
But for Plato, this isn't exhaustive, he routinely distinguished between:
- the object in which a property is instantiated (the apple, the yield sign)
- the property concrete instantiations share (the redness of an apple, the triangle-ness of a yield sign)
- the Form in which these objects participate by sharing a given property (the Form of Apple, the Form of Triangle)
most later and certainly contemporary realists dispense with the 3rd one, which was sort of Plato's signature, and may have been more motivated by other concerns (aesthetic, religious, cultural, etc) than strictly philosophical or logical ones
Other scholars—especially those working in other branches of science—view Platonism with skepticism. Scientists tend to be empiricists; they imagine the universe to be made up of things we can touch and taste and so on; things we can learn about through observation and experiment. The idea of something existing “outside of space and time” makes empiricists nervous: It sounds embarrassingly like the way religious believers talk about God, and God was banished from respectable scientific discourse a long time ago.[/quote]
[quote=Many have asked]Is God A Mathematician?[/quote]
[quote=Galileo Galilei]Mathematics is the language in which God has written the universe.[/quote]
I think the idea that there is a Form for every conceivable thing under the sun is unwarranted. Different Forms would be perfectly capable to combine to form virtually any perceptible object.
Some of Plato's statements cannot be taken literally and are simply presented to make a point or illustrate an argument in order to make it easier for the reader to understand certain concepts. At the end of the day, readers need to exercise their own judgement. Plato simply shows the way ....
Yeah but for the materialist, these mental objects are located in the brain. There is a model for explaining how concepts like God or math can spread across billions of human minds, memes, parasitic reproducing bits of idea. They have a physical being in the neurons of their hosts. God is just a very effective meme.
For memes undergoing natural selection pressures as they reproduce in their hosts it only makes sense that ones that explain the world well and have predictive power would come out on top. Mathematical ideas are memes they are successful because they have utility for their host.
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To get back to the original post, from an idealist perspective , Hegel, you have the universal (forms) producing the specific, since we can only understand the world through ideas (universals). Since the true is the actual, and the truth is the whole, it follows that it is these ideas that give rise to the world of experience, the only world we can speak of directly. It also develops that world to become more complete, to reach a higher stage of truth.
It's a take I find appealing. More than I do Neoplatonist or Gnostic versions, which have the forms living in a kind of magical soul dimension of pure mind and pure ideas. The problem there, is that, as Aristotle showed, and Plato acknowledged in the Parmenides, the world would be filled with various infinitely regressing forms- a whole dimension of reductio ad absurdum infinities.
Plato agreed. In the Parmenides, he disavows the idea that there are Forms for low or gross things (I forget the specifics examples, but iirc "dirt" or "mud" may have been given), he tended to think that there were only forms for things like Truth, Beauty, Justice and so on. The problem is, his theory didn't really provide any basis for such a distinction (once again this seemed more motivated by non-logical or philosophical considerations, like aesthetic or religious ones), and so this certainly was a problem/inconsistency with his picture.
And as far as the reducibility/redundancy of certain Forms, I thinks that's also a very valid objection- where do we draw the line? Is there a Form for Square apart from the Form of Rectangle? Maybe Forms for geometrical shapes or objects all reduce to more fundamental concepts like the Form of Line Segment or Angle? This seems somewhat arbitrary and subjective, and contingent on our particular purposes or context or what sort of conceptual schema we happen to be using, which undermines the notion of a separate, independent, objective realm wherein these Forms exist/are located.
The physicality of the mind isn't as cut-and-dried as is necessary to matter. Too, God being material is absolutely fine by me.
Petitio principii.
Not really. I'm not saying it's the case, it's just a model that explains the forms and how they could arise from material processes.
Yes, I get that.
That may be one way of looking at it. Plato certainly follows the reductivist tendency already found in Greek philosophy, and in natural science in general, that sought to reduce the number of fundamental principles of explanation to the absolute minimum, hence the “first principle” or arche of the earliest Greek philosophers.
It seems to follow the inner logic of Plato’s explanatory framework which is hierarchical and necessarily leads from the many to the One.
In any case, all objects of knowledge and, in particular, the Forms need to be considered in the light of the Good (= the One) which is their ultimate source. The Forms merely serve as a ladder to ultimate reality. They can be reached only by transcending reason and they in turn need to be transcended in order to reach the highest.
The Platonic method is the Upward Way, Ano Odos, a process of vertical progress that takes the philosopher through a hierarchy of realities ranging from human experience to ultimate truth,
I think this to mean that bits of matter somehow represent ideas, in the same way that codes represent objects in, say, computer systems. It seems natural, even obvious.
The problem is that even very simple mental operations can generate enormously divergent patterns of neural activity. Very simple stimulus and response patterns in mice are subject to what is called 'representational drift' - the same stimulus evokes responses in very different regions in the brain over time. Same thing happens with humans, albeit even more complicated. I read that long neurological studies attempted to trace characteristic patterns of activity in human brains when learning simple tasks, like memorising a new word, but that the activities were so divergent that researchers could detect no consistent pattern despite years of studies (see Why Us?, James le Fanu.)
Furthermore, consider the way in which a divergence of symbolic forms can be used to convey the same idea. A number can be represented by a variety of symbols, but they all specify the same idea. So the meaning of the idea is in some sense separable from its physical form. The mind, of course, can recognise such equivalences and translate one form to another - but again, can that be understood as a physical process? I think rather that it's a pretty cogent argument for dualism.
Quoting Count Timothy von Icarus
Forms are not shapes, or necessarily even entities or things. They are more like principles.
[quote=Joshua Hothschild, 'What's Wrong with Ockham?']...Among all the kinds of forms which can be signified by terms, according to Aquinas, there is no one uniform way in which they exist. The existence of the form “sight,” by which the eye sees, may be some positive presence in the nature of things (which biologists can describe in terms of the qualities of a healthy eye that gives it the power to see), but the existence of the form 'blindness' in the blind eye need be nothing more than the nonexistence of sight ? the 'form' of blindness is just the privation of the form of sight and so not really an additional form at all.
In general, distinguishing and qualifying the different ways there can “be” a form present in a thing goes a long way toward alleviating the apparent profligacy of the realist account of words signifying forms. ....
Aquinas’s famous thesis of the unicity of substantial forms is an example of another strategy: linguistically I may posit diverse forms (humanity, animality, bodiliness) to account for Socrates being a man, an animal, and a body, but according to Aquinas there is in reality just one substantial form (Socrates’ soul) which is responsible for causing Socrates to be a man, an animal, and a body. In this and other cases, ontological commitment can be reduced by identifying in reality what, on the semantic level, are treated as diverse forms. As Boethius had seen, what the mind is capable of logically distinguishing need not be actually distinct in the nature of things.
In principle, any number of strategies for reducing overall ontological commitment are available within the framework of realist semantics, so that in general, the kind of form that fulfills the required semantic function did not need to be the kind of form that has a distinct and positive metaphysical presence in the nature of things.[/quote]
Quoting Prishon
Inventiveness in the subject has gone far beyond this; abstractions and generalizations move way beyond physical applications. But there is some truth in your statement. Babylonians measuring fields and Egyptians designing pyramids, etc. The jury is out on Tegmark. Some take him seriously. I don't.
Quoting magritte
ArXiv.org receives hundreds of mathematics research papers each day. I would guess relatively few make it into physics.
Quoting Smithsonian Magazine, What is Math?
Creating relevant questions is an art form. Like a lawyer never asking a question they do not know the answer to. My observations are that working math people pay little attention to these issues. As for discoveries, when a mathematician conjures up definitions and relationships from wherever, perhaps as mere speculation or like a game, if there is a consistency to what is done then a slew of logical results may suddenly pop into existence, to be discovered by investigators. But there is that touch of creativity at the beginning.
If anyone CAN tell its a mathematician. Thanks for this great answer!
That's nothing. Try this on for size.
1 X is within space & time. No!
2. X is beyond space & time. No!
3. X is within space & time AND X is beyond space & time. No!
4. Neither X is within space & time nor X is beyond space & time. No!
Where could X be?
As usual almostly: :heart: (dont get me wrong though... ? ).
Only God knows, I guess.
Nowhere
Since Descartes, there is the apparent division between physical and mental - but I think there's something deeply the matter with that. Maybe it's a consequence of taking something that was originally a kind of explanatory metaphor - almost like an economic model, you might say - too literally. I question whether anything is 'purely' physical, or 'purely' mental - that view is a consequence of taking the model introduced by Descartes as if it is literally true, but it's an abstraction. A 'rogue metaphor'.
As regards the truth of 'mathematical platonism' - what interested me in the idea of mathematical platonism was the realisation that numbers don't come into or go out of existence (i.e. they're not temporally de-limited) and they're not composed of parts. But they're real, in that they're the same for all who can count, and they're among the elementary components of rational thought. When I hit on this idea, I thought I had seen why the ancients believed that numbers and geometric forms existed on a higher plane than ordinary things, which are always temporally delimited and composed of parts. At the time, that struck me as an epiphany, a significant Aha! moment. I don't know if I'm right in thinking that.
What struck me as interesting about the question is the sense in which numbers can be said to exist. Take any number - 7 will do. That is something that exists, you might say. But what you're looking at when you say that is a symbol. 7 can also be represented by VII, by 'seven', or in binary code, but what is being represented is always the same. The quantity that is represented by the symbol is a purely intelligible concept - it is only recognisable to an intelligence capable of counting.
The way I parsed that distinction, is to say that numbers (as universals) are real, but they don't exist.
There's some support for this distinction in Russell's discussion of the Problem of Universals, where he says:
[quote=Russell, The World of Universals; https://www.gutenberg.org/files/5827/5827-h/5827-h.htm#link2HCH0009]We shall find it convenient only to speak of things 'existing' when they are in time, that is to say, when we can point to some time at which they exist (not excluding the possibility of their existing at all times). Thus thoughts and feelings, minds and physical objects exist. But universals do not exist in this sense; we shall say that they subsist or have being, where 'being' is opposed to 'existence' as being timeless. The world of universals, therefore, may also be described as the world of being.[/quote]
So - the sense in which numbers and universal are not physical, is that they reside in a realm of abstraction - but they're nevertheless real, in that they're not arbitrary or 'made up' (not that you can't invent imaginary numbers and systems, given the ability to recognise numbers.) It's important to realise the sense in which this relates to the meaning of 'transcendent' - not being 'spooky woo stuff', but truths that transcend time and space.
That is the 'formal realm' (i.e. the domain of numbers, shapes, and forms). But don't make the mistake of thinking it must be 'out there somewhere' - it does not literally exist. The urge to identify what is real with only what exists is one of the vices of modernity.
In the earlier matter-form (hylomorphic) dualism of the classical tradition, matter (hyle) receives form (morphe), and particulars are the combination of matter and form. So matter doesn't exist in its own right; in that view, the idea of something 'purely physical' is not intelligible. Maybe you could say that individual things are only real to the degree that they are an instance of a form. So it's not as if 'the physicall' is one thing, and 'form' another - they generally only exist together as a combination of form and matter. That's where it's very different to Cartesian dualism. (See this post on hylomorphic dualism in Aquinas.)
In that Smithsonian article I linked to on the nature of maths, it's said that empiricists will generally reject platonism. As the essay says, in today's culture, only what is physical is thought to exist. So obviously, that is incompatible with the platonist attitude. And this hails back to a titanic struggle in the history of ideas, in my view. That was how materialism became the dominant view. It has huge ramifications.
From the SEP article:
[quote=SEP, Platonism in Mathematics; https://plato.stanford.edu/entries/platonism-mathematics/]Mathematical platonism has considerable philosophical significance. If the view is true, it will put great pressure on the physicalist idea that reality is exhausted by the physical. For platonism entails that reality extends far beyond the physical world and includes objects which aren’t part of the causal and spatiotemporal order studied by the physical sciences. Mathematical platonism, if true, will also put great pressure on many naturalistic theories of knowledge. For there is little doubt that we possess mathematical knowledge. The truth of mathematical platonism would therefore establish that we have knowledge of abstract (and thus causally inefficacious) objects. This would be an important discovery, which many naturalistic theories of knowledge would struggle to accommodate.[/quote]
Not to contradict you but the number 1 is defined as the pattern (abstraction) in the following sets: {ghost}, {&}, {R}, {9}, {John}, you get the idea. What's common (the repeating pattern) is the one-ness.
:ok: Much obliged.
It doesnt indeed contradict. Its simply wrong.
From the link you provided:
Sensible Form and Intelligible Form
[i]“EVERYTHING in the cosmic universe is composed of matter and form. Everything is concrete and individual. Hence the forms of cosmic entities must also be concrete and individual. Now, the process of knowledge is immediately concerned with the separation of form from matter, since a thing is known precisely because its form is received in the knower. But, whatever is received is in the recipient according to the mode of being that the recipient possesses. If, then, the senses are material powers, they receive the forms of objects in a material manner; and if the intellect is an immaterial power, it receives the forms of objects in an immaterial manner. This means that in the case of sense knowledge, the form is still encompassed with the concrete characters which make it particular; and that, in the case of intellectual knowledge, the form is disengaged from all such characters. To understand is to free form completely from matter.
“Moreover, if the proper knowledge of the senses is of accidents, through forms that are individualized, the proper knowledge of intellect is of essences, through forms that are universalized. Intellectual knowledge is analogous to sense knowledge inasmuch as it demands the reception of the form of the thing which is known. But it differs from sense knowledge so far forth as it consists in the apprehension of things, not in their individuality, but in their universality.
“The separation of form from matter requires two stages if the idea is to be elaborated: first, the sensitive stage, wherein the external and internal senses operate upon the material object, accepting its form without matter, but not without the appendages of matter; second the intellectual stage, wherein agent intellect operates upon the phantasmal datum, divesting the form of every character that marks and indentifies it as a particular something.
“Abstraction, which is the proper task of active intellect, is essentially a liberating function in which the essence of the sensible object, potentially understandable as it lies beneath its accidents, is liberated from the elements that individualize it and is thus made actually understandable. The product of abstraction is a species of an intelligible order. Now possible intellect is supplied with an adequate stimulus to which it responds by producing a concept.”[/i]
So, the form (universals) individuates in objects (particulars). The senses, it seems, can't see past the particulars but the mind grasps the essences, another name for universals. :up:
:ok:
No. The senses can look at ALL forms. There simply are no universals. The essence is no name for universals. The essence simply cant be defined.
:ok:
Dont put a thump up for a definition of the essence, please. You are playing God.
Intuition? or the pure reason?
I think I do. I am seeing clouds in the sky, and a hill below it. I am also seeing this text as I am typing.
I hear the sound of the cars passing outside on the road. But cannot find any forms. Well the only forms I normally see are in the junk mail for placing orders for clothing from the mail order companies.
No matter where I looked, the platonic forms were not found. Now I am guessing, they could be my intuition or pure reason.
Maybe one needs to do transcendental leap to be able to see them?
Would it be same as pure reason?
Wiki on Nous is excellent actually.
It sounds nous is being suggested as equating part with pure reason in Wiki.
"As in Xenophon, Plato's Socrates frequently describes the soul in a political way, with ruling parts, and parts that are by nature meant to be ruled. Nous is associated with the rational (logistikon) part of the individual human soul, which by nature should rule. In his Republic, in the so-called "analogy of the divided line", it has a special function within this rational part. "
That basically is what I believe. Probably because of my Western memes. [Comments in brackets mine.]
What could be "this cosmic nous"?
But let's go back to the question in the OP. Why is it that the human ability to grasp mathematical relationships is so effective in respect of discovery? For that matter, consider the word 'discovery' - something previously concealed becomes revealed or clear. And mathematics has played a central role in that, as far as mastery of nature is concerned. A classic case in point I often refer to, is Paul Dirac's discovery of anti-matter. He predicted it, long before it could be detected, because it 'fell out of the equations'. And years later, lo! there it was. That's why I can't buy into this idea that it's simply something humans thought up, it's the discovery of something deep about nature herself. When Galileo said the book of nature is written in mathematics, he wasn't simply employing poetic allegory..
That's the 'romance of mathematics'. Actually it's very unpopular in mainstream academic circles today, because it's very hard to reconcile against Darwinian evolution. The fashion is always to rationalise such abilities in terms of adaptation, when it seems to be so much more than that.
But, on that note, take a geez at one of my favourite online essays on this theme, A Fabulous Evolutionary Defense of Dualism, Clay Farris Naff.
I never really bought the idea that reducing the number of forms and making actualities be the product of mixtures of a smaller set of forms solved the Third Man problem. Plato himself gets at this in the Parmenides when he says there aren't forms for dirt and mud, but that there might be for more essential items. However, you still have the problem of infinite regress with the form of the large or small. The only solution I find particularly appealing there is to boot out the forms that are necissarily comparisons (e.g. small, large, bright, etc.), but then you still have to deal with them in some way.
Aristotle's categories seem to get around this issue in a much better way. I mentioned Hegel before because I think the synthesis there provides an explanation of how the universal and the particular can interact in being in a "circle of circles," while avoiding the Third Man Problem, through rejecting epistemological realism entirely.
Right, when memes are said to live in the host, it isn't in a particular set of synapses we're talking about, it's a set of processes that give rise to a corresponding, similar-enough, set of mental phenomenon. Memes are abstractions that live as part of the emergent system of conciousness in their hosts. However, I think memes can still be understood as physical processes. The evidence for this is that people with damaged brains stop being able to understand ideas. If there is a powerful idea in a society, one that dominates their conciousness, and that society and its texts are destroyed, the meme vanishes until some lost text is found and translated by archeologists. It doesn't hang out in the ether, or if it does, no empirical evidence for it can be produced. So maybe it is the case that the idea lives on in an eternal realm, but the eternal realm is not necissary to explain ideas.
That you can't pinpoint the physical location of an idea, and that the activity that makes up the idea changes from moment to moment isn't at all incompatible with the findings of neuroscience, it's what we should expect. If ideas corresponded to hardwired structures then we'd have a finite memory capacity and would loose very specific bits of information with age and neuronal death, which isn't what we see. I would also disagree with the code analogy. I think brains as computers analogies generally do more harm than good in explaining things. When you write code, the meaning of your operations doesn't shift over time. Individual strings remain constant. That's not how brains work. The pattern of neuronal activity associated with something as simple as a smell varies over time, eventually corresponding to entirely different sets of neuronal activity. Since the subjective mental phenomena don't appear to change over time, this appears to suggest that the process, not the medium in which it occurs, creates the mental phenomena.
It's like how ecosystems exist but aren't located in a singular location as well. The movement of ideas works the same way that a terraforming operation could recreate an ecosystem in any physical space using none of the same material.
So I don't think you need non-material ideas to make sense of ideas. You just need a model where there are myriad ways to represent the same idea. The other problem for eternal ideas is that, if they are not material, how do they interact with our material brains? It seems like you'd need some version of Decartes pineal gland in place for that.
Which is not to address that the "material world" is itself a subjective abstraction made up of ideas, and that, in every sense, our understanding is the product of ideas. I find valid arguments for forms of idealism or dualism in that direction, just not in Plato's original direction of pointing to seemingly eternal ideas.
I think that "God", if he exists at all, could be anything.
The point is not to decide in advance what ultimate reality is. The point is to have an experience of it.
In the meantime, there can be nothing wrong with referring to it as "the unfathomable, ineffable, One".
I think "intellect" can be misleading. To understand Plato we need to understand the Greek terms he is using.
The word nous comes from the root gno- (PIE *gneh, “to know”) from which gnoos > noos, and it signifies the knower, i.e., that within us that is aware, knows, and understands.
Therefore:
A. The nous is the knower.
B. The nous is our true self.
C. Being a knower is our natural or true self.
D. Knowledge is of two kinds, of oneself and of things other than oneself.
E. Knowledge of other things is impossible without reference to the knowing self.
F. The highest form of knowledge is self-knowledge.
G. To attain self-knowledge we must rise from objectivity to pure subjectivity.
There are the following levels of awareness:
1. Perceptible object “out there”.
2. Mental image of object.
3. Thought about object.
4. Ideal object conceived in the mind.
5. Form of the object or combination of Forms (Size, Shape, etc.) constituting the ideal object, intuitively grasped by the nous or subject.
6. Nous or subject being aware of itself (pure subjectivity).
As subjectivity refers to the knowing self, we may use the question “Who am I?” which can be answered as follows:
1. (Gazing at the external object): “I am the knower or perceiver of the object”.
2. (Closing the eyes): “I am the knower or perceiver of the image of the object”.
3. (Thinking): “I am the knower of the thoughts about the image”.
4. (Conceiving the ideal object): “I am the knower of the ideal object”.
5. (Contemplating the Forms): “I am the knower of the Forms”.
6. (Contemplating the consciousness from which the Forms arise): “I am that”; “I am myself”; “I am”; “I”, etc.
In this way, we progress from the distant perceptible object "out there" to increasingly closer layers of awareness until awareness itself (or something as close to it as possible) is reached.
Clearly, this requires systematic mental training, that can be a life-long endeavor, in order to reach the final goal. However, a few hours or days of practice should at least give us an idea or intuition of what it is about.
At any rate, if Plato is right about the soul, Forms, the One, etc., then I think this would be one way of testing it for oneself.
Aristotle claims that Plato regarded them as intermediates, between Forms and sensible things.
One issue of contention is the ontological status of these intermediates. Another is the relationship of intermediates to Forms. An insightful discussion of this and the importance of mathematical objects and the limits of logos for Plato's philosophy can be found here:
https://pdfs.semanticscholar.org/9a77/b70f6a93af7cc665bbac3fc64e5bfaffd1c6.pdf
From the article:
What Mary Didn't Know.
There are experiences we can't put into words: Qualia, allegedly.
There are words we can't experience: Engage the warp drive Lt. Worf. Definitely.
The knife, it seems, cuts both ways. My question is if the reach of language exceeds experience (2nd case above), doesn't this mean experience, all manners of experience, is, for that simple reason, always effable?
How did you come to that thought? Do you have any explanation for that belief or thought or conviction? Just a feeling? Guess? Personal experience? Inductive or deductive reasoning? If there were such things as general mind, then again where is it? Who is owning the mind? Having a mind means the haver can perceive, feel, think, and act. Does the owner of the mind exist in physical form?
That isn't an entirely bad question. And, of course, we could call the Good, the One, or God a "Quale" if we really wanted to. :smile:
However, my point is that what matters is not to name the object of experience but to experience it. And if we choose to name it, we may equally go for one of the names used by Plato himself (or by later Platonists). "The One" seems fairly neutral (as opposed to "God", for example) and would fit an object of experience of this nature IMO.
Hmmm I am not sure if I could agree with that point.
Who can only write the book of nature in mathematics? Humans. (I don't believe God or the aliens or cats can do this.)
Who discovered the antimatter? Paul Dirac. What was he? A human. (I don't believe he was a God or the aliens).
If you woke up on the earth 20000 years back, and were standing on a field with no one around you.
Just field, sky and yourself. Would you have been able to imagine the antimatter? The book of nature? Calculus or the Relative Theory? :) I think they are all in human mind, and the maths, the laws, scientific knowledge and all the facts have been discovered, and manifested into information by humans. Well, the ancient Greeks started the ball rolling.
Well, Socrates says:
You hunt something down by following its tracks until you see it. The tracks of the Forms are the universals, the things whose properties can be perceived in particulars ....
The universals and particulars ring a bell. Yes, it was in the Introduction to Metaphysics book. I can remember vaguely.
I will read up it again, and the Phaedo too. The Form was always very tricky part in Plato.
Thanks for the info.
Very tricky indeed. But nevertheless essential, I think.
I feel that the only way minds can be universal is sharing knowledge and truths discovered by reason and logic, and keep passing them onto other minds.
:ok:
In Rome Total War, a recommended formation for infantry is to keep veteran men on the right flank of your army - the experience making up for the fact that shields offer no protection, being as they are held in the left hand.
Right! Damned! Why don't you write things once in a while with which I don't agree?
It was Xenophanes who started the view of an objective unique reality, to be known by ratio. The scientific ratio, back then of course still primitive, though who knows what some Greeks were thinking. Archimedes found "his" law in bath, so... It was still the time of the gods and Xenophanes expressed this view of a human-independent unique reality by means of a horrible kind of god.The one and only. All knowing, all seeing, super in anything. It didnt posses a list of qualities as qualities are subjective. Plato beleived in a mathematical heaven of unchanging forms. I think it was this kind of thinking, together with Xenophanes' view became to be the reality that only science can adress or at least approximately komen. Falsificationalism is based on this. Popper "expanded" endless falsification as the real thing will never get reached; tiring indeed. Why not saying that after falsifying, criticizing, falsifying, criticizing, ...ad inf. that you theory is "it"?
Rather clever them Romans, weren't they? :grin:
The Forms are hypothetical. In the Phaedo Socrates says:
The Forms are an attempt to make sense of the world. In the Republic Socrates will tell a tale of the philosopher who escapes the cave and ascends to the sight of the Forms. But Socrates also indicates that he has had no such experience. Here too the Forms are hypothetical not things known. In the Republic we also find the promise of dialectic being able to move beyond hypothesis by the use of hypothesis. But nowhere in any of Plato's dialogues does he identify anyone, either an historical individual or a fictional character, whose journey ends in knowledge of the Forms. The journey always ends in aporia.
Indeed!
Plato's tetrahaeder, octohaeder, icosahaeder, an attempt to make sense of the world?
First, although there is some disagreement, mathematical objects, including Platonic solids, are not Forms. See above: https://thephilosophyforum.com/discussion/comment/585928 Second. they are, literally, fundamental to the cosmogony of the Timaeus. They are the mathematical or eidetic models of the elements fire, water, air, and earth.
The Platonic forms are materializations of the corresponding eternal forms in Platonic heaven. But they are approximations. Math describes them exactly but it doesn't privide an image of the forms. The forms are unknowable in principle. Seems reasonable that they correspond to the real elements used in the cosmogenesis. It would be nice if the Platonic solid were made from the five elements. There would be a bigger arsenal of real forms to chosen from in the construction of the solar system. Even better than atoms. ?
I don't know what this means. The Platonic forms are eternal forms, or so the hypothesis states.
Quoting Prishon
According to Plato, it is not the objects themselves with which the mathematician deals but their images, that is, drawings or diagrams.
Prishon must correct. With forms he probably meant solids.
Indeed. The forms can never be known. Like the elements of heaven. The images are not the forms, which have no form.
Perhaps you could ask.
Prison, did you mean "Platonic solids"?
Prishon says: "Yes! How the f. did you know?"
I would say that they are not known. That they are is not known. What they are is not known. To ask what they are is problematic because they are supposed to be the answer to the question "what?". This amount to asking "what is what" as John Sallis has pointed out.
Prishon must know himself/herself. Way ahead of the rest of us on his Socratic quest.
:heart:
How about "We never agree on anything."
We will have some disagreements for sure, but that's just natural. :D
Quoting Prishon
I think your elaboration is excellent. I remembered my teen time reading Archimedes shouting out "Eureka '' coming out of the bath after finding out how to measure mass of any matter no matter how odd shaped they are, just immersing them into water, and measuring the overflown water from the tub. Popper's Logic of Scientific Discovery is still in my reading list. :roll:
Plato was also a dualist I gather. The material world we live now is a shadow of the true world of Idea. Maybe in the world of Idea, is where the Forms belong? Some books says that Plato thinks that we are all born with the Forms from the past life. We never learn new things. The knowledge is all in the mind and forms already with us, and we just retrieve them.
We live in the shadow of our images, the results of our attempts to imagine what is happening. Noticing that is happening doesn't put the "material world" in a place. That would be pretty arrogant after just saying you didn't know what things are.
That all of our individual minds also form part of a collective consciousness. Jung's idea of a collective unconscious. The Buddhist doctrine of ?l?yavijñ?na, the 'storehouse consciousness'. That there is a kind of 'species consciousness' - a form of consciousness common to h. sapiens, mediated by culture and history. Unity of mankind. That kind of thing. But it's very important not to reify it as 'the One Mind', as something objectively real. It's not something we can objectify. (There was a popular 1960's book about Tibetan Buddhism 'liberation through knowing the One Mind', but it was by a Californian theosophist who never set foot in Tibet. Such ideas are very easily misconstrued.)
Good summary but there's a point that it doesn't pick up on.
[quote=Lloyd Gerson, Platonism V Naturalism]when you think, you see - mentally see - a form which could not, in principle, be identical with a particular - including a particular neurological element, a circuit, or a state of a circuit, or a synapse, and so on. This is so because the object of thinking is universal, or the mind is operating universally.
….the fact that in thinking, your mind is identical with the form that it thinks, means (for Aristotle and for all Platonists) that since the form 'thought' is detached from matter, 'mind' is immaterial too. [/quote]
That is something brought out in Aquinas' epistemology also.
Correct. This is Plato's Theory of Recollection (anamnesis) according to which souls having lived before and having experienced the Forms, have latent knowledge of them, which knowledge can be retrieved through recollection.
Plato introduces this in the Meno and Phaedo:
Yes, if Platonism believes in eternal truths like the Forms, then it is incompatible with materialism and naturalism.
Quoting Wayfarer
I think Theosophy was responsible for a lot of confusion which is not surprising as it was invented by Blavatsky and promoted by subversive elements like Annie Besant for their own agendas. When genuine spirituality is in decline, it creates a vacuum that impostors rush to fill ....
This in turn gave rise to "Transcendental Meditation" and other fraudulent New Age projects promoted by the hippy movement that developed around the belief in drug-induced "shortcuts to enlightenment".
Quoting Corvus
:grin:
Ha! Good one! I have to day that I'm a bit biased in my attitude towards Popper. At university I took philosophy as one of the teachhings to choose from. Physics is nice but one wants a bit more! At least, if I''m that one. A professor gave me some copied papers of some books of Feyerabend. Well, the papers weren't copied but Feyerabend's writings were on them. I dunno if I wouldn't have met Feyerabend if he hadn't give those copies (I'm sure I would) but I'm thankful he did. Feyerabend is something else and in strong disaggreement (talking of which!) with Popper. So... I have read that book of Popper you have on your shell. It's on my shell to, but to say I wipe the dust off...No. He should himself be falsified!
Anyhow, suppose I have a theory about the origin of the universe. What took place around the big bang (inflation) and before (and after). How long should I go on criticizing or trying to falsify it ( which would be a bit problematic...)?
Always nice writing with you! :smile:
How is the term 'memes' not simply a metaphor or an idiomatic expression? They can be physical, mental, objective, subjective - however you want to define them! I think it was coined by Dawkins as a counterpart to genes, but that is not a particularly favourable provenance. And granted, it's a useful word, and I sometimes use it myself. But I don't think it refers to anything real.
Plato's dualistic world view must had been opposed by many, even one of his pupil Aristotle. Aristotle seemingly had his own worldview (monistic), and his own theory of form.
But wouldn't that view of mind is a mythology rather than philosophy or science?
Physics is cool, but Metaphysics is even more cool. :grin:
Quoting Prishon
I have a couple more Popper - Self and Brain(??), Open Society and Its enemies.
Quoting Prishon
All theories with weakness deserved to be criticised and falsified.
:up: :smile:
Thanks for your confirmation.
:smile: Morning (at least, here it is). I havent read that book. Is it relevant maybe for another discourse currently taking place on this forum?
Morning to you. :) Yup sure, I haven't even read it yet.
But you firstly have to learn the meaning.
You have learned to count. There are peoples who cant count to ten or even four.
They’re not objects, except in the metaphorical sense of being ‘objects of thought’. But they’re common to all who think. That’s the point. That’s what I mean by ‘structures in mind’ although I’ve only just come up with that expression, don’t know if it’s going to work.
Quoting Prishon
Humans can be educated to count. Crows and monkeys can count very small numbers, up to about 4, or at least recognise the difference between a collection of 3 and 4. But beyond that, they can’t count. It’s that ability that makes homo, sapiens.
Numbers are not objects themselves. That's clear. Though the number seven candle put on top of the birthday cake of my child neighbor seemed pretty real and objective. Numbers have the habit of embracing equals. The equals being objects or mental whatevers. You have to look for equals first. Whats the difference between 5 and 6 apples? One apple. Whats the difference between 356 apples and 357 apples? Still 1. But what if you cant count? Is there still a difference? How would you know the difference? By laying all apples side by side? How many apples are sqrt(-1) apples? How many are -1 apoles?
Some people seem to think the numbers, data, and information are objects in the universe. I think mathematics objects and all information are in the human mind. You just apply to the real world for practicality.
It is not about how you learnt to do mathematics. The point is that once you learned it, you apply it to do all further counting / maths by yourself without recourse to observation like the Science must do. In that respect mathematics is a priori.
But that doesn’t do justice to the predictive ability of maths, to make discoveries about reality that could otherwise never be made. It sells it short. It’s a cop-out.
Left and right of the = there are different things.
You need to use intuition and imagination too. It is ample for any prediction.
New predictions can be made indeed. But whats the quality of these prediction?
Yet somehow the same! What recognizes that? It would be nous, right?
It's the numbers equalizing.
It is the great intellectual event of the late 20th century: new discoveries in neuroscience are challenging our established ideas about morality, free will and human nature. But can science really tell the whole story?
Read that essay, it’s a beauty. Signing out for the night my time.
Ah, youre on the other side. G'night!
Math -> Physics -> Chemistry -> Biology -> Brain/Mind.
If math doesn't exist in some kind of Platonic realm and is all in the head as it were, we have a problem:
Math -> Physics -> Chemistry -> Biology -> Brain/Mind -> Math. It's circular! All of reality is, in a sense, mind-generated. :chin:
But not vice versa. What does it indicate apart from its mindful process and acts of reason.
Quoting TheMadFool
But the whereabout of Platonic realm is not conclusive is it? It does not preclude possibility of its locus in the human mind, does it?
:ok:
This is a pretty common view, but not one I share. Socrates says the Forms are hypotheticals, the way in which his mind organizes the world according to kinds. They are, literally, what is placed under the unstable objects of the world, in order to understand the world as stable and unchanging. There is, however, no methodological transition from dialectic to knowledge of the Forms. (Republic 511b). The myth of recollection requires acceptance or rebirth. One problem is just when one is supposed to have gained such knowledge, in which past life, and how was it possible then?
The Forms are said to be what sensible things are images of, but they are themselves images, what Socrates imagines knowledge must be:
This sounds like Kant.
Quoting Fooloso4
Would it be because the mind cannot see itself? Reason cannot reason reason itself. :)
Quoting Fooloso4
:100: :up:
No it does not but if math is invented, Platonic realm missing, then we have a major issue because of the circularity I mentioned earlier which I will reiterate for those interested:
Supervenience-like relationship exists between the sciences which can be represented in the following way:
Math -> Physics -> Chemistry -> Biology -> Mind (Brain) -> ?
Legend: The mind supervenes on biology, biology on chemistry, chemistry on physics, physics on math.
The ? = Math if math is invented. That would close the loop as it were and we have on our hands a rather vexing circularity: Everything we know, including the mind as per physicalists, is math but math, if Platonism is false, is mind (it's in our head). So, everything is mind then or everything is math. It's quite confusing.
But who said math is invented? Why do you want invent math? Math is already there in your mind from your previous life and soul according to Plato. You just need to retrieve it.
No, we are not saying everything is mind. We are saying that the math knowledge and ability is in mind, and we apply it to the real world objects.
I don't see why anyone has to loop with the subjects. If you count 10 apples from one tree, and 20 apples from the other tree, then you come to total 30 apples. The mission completed.
We're not talking about knowledge and ability. What we're concerned with is the reality of math. Is it discovered, in which case Platonism would be true, or is it invented, Platonism false? The rest of my argument follows from that.
The knowledge and ability were mentioned, because you said that everything is mind. Just to say that, everything is not mind. Never said that we were talking about knowledge and ability.
:ok:
If it's already there in the mind (which I dont think, but the inner world could be the Platonic realm) we only have to look in there with the mind's eye to discover it. We can then apply it to the outer world. It depends on you willing to find this math. Does math exist in the physical world, as that dopey Tegmark conjectures (and even an infinity of "Parallel level-4 universes" full of it!)? Then where can I see Einsteins equations, supposedly written in Nature, only to be read by us? Galileo talked anout the book of Nature, Hawing said that God is a mathematician, math is thought to be "unreasonably effective" (hinting to its objective existence). But maybe the book of Nature is written in the language of freedom, is math reasonably effective, and is God a freedom fighter.
It is because the Forms cannot be grasped by reason. They are not objects of reason.
:lol: Keep saying funny things like that and I'll never argue with you.
:lol:
Sure, I think I said it too in one of the posts. It makes sense, and very much inline with Kant's epistemology.