Shouldn't we speak of the reasonable effectiveness of math?
I think all participants here know about the statement of the unreasonable effectiveness of mathematics. Shouldn't we, rather, speak of it's reasonable effectiveness? I can't see nothing unreasonable about it and can't even imagine how else it could be.
Let's not forget though where we apply it. To dead Nature. In the human realm it seems unreasonable if effective indeed.
Let's not forget though where we apply it. To dead Nature. In the human realm it seems unreasonable if effective indeed.
Comments (134)
Why is the world describable with mathematics? Because there are regular, consistent physical relations between objects that have an inherent mathematical component (like an inverse square law).
Why are these relations present? They just are. We're they not, we would not be here to question.
Why is it more reasonable to expect an absence of such relations?
Nature is not dead.
I was with you in your first paragraph. But the fact that there is structure to the world does not mean that the world comes to our awareness packaged an ‘inherent’ way that is already mathematical. Nature became mathematizable when we contributed our own peculiar interpretive structures to it.
As you can see, I’m a mathematical constructivist, not a platonist.
Never heard of it before you.
look up Eugene Wigner.
Why?
Quoting Jackson
Why not?
Better things to do.
Name one
This is a good way of putting it.
I'm guessing that Wigner's use of "unreasonable" was ironic or tongue-in-cheek. In view of the randomness & uncertainty of its Quantum foundation, it is perhaps surprising that on the Macro level of reality, its structure & processes are predictable & consistent. In other words, there is an underlying logic to the order of reality. And mathematics is simply an abstract form of Logic.
Moreover, Logic is essential to the extraction of meaningful information by humans (Reason). Some might say that Human Logic & Natural Logic both result from the Natural Laws that caused the Big Bang to self-organize into the smoothly functioning mechanism we see today. That orderly structure of interrelationships is what allows human mathematics (logical inference) to be both Reasonable and Effective. But why should a random & accidental "explosion" (expansion) of something from almost nothing turn out to be lawful (orderly & organized)? Perhaps Wigner saw signs of design in the world, but chose to comment on it equivocally, for professional reasons. :cool:
No, it's not packaged in an inherent way, but the success of our inferred mathematical relations suggests there is an ontological basis to it.
I'm also not a Platonist. I have an Aristotelian view of immanent universals (more directly: an Armstrongian view).
The effectiveness of mathematics is neither reasonable nor unreasonable.
I observe the world. I observe that all things being equal, what happened in the past will happen in the future. This is neither reasonable nor unreasonable, it is just a fact about the world. I observe on the table in front of me my pen touching my pencil, and observe that the mere fact of touching does not cause a change of velocity of either my pen or my pencil. I discover facts about the world by observing the world. These facts are neither reasonable nor unreasonable, they are just how the world is.
"The Unreasonable Effectiveness of Mathematics in the Natural Sciences" is a 1960 article by the physicist Eugene Wigner.
A biography by Galileo's pupil Vincenzo Viviani stated that Galileo had dropped balls of the same material, but different masses, from the Leaning Tower of Pisa to demonstrate that their time of descent was independent of their mass. This was contrary to what Aristotle had taught: that heavy objects fall faster than lighter ones.
Richard Hamming reflected on and extended Wigner's Unreasonable Effectiveness in 1980. Hamming proposes that Galileo discovered the law of falling bodies not by experimenting, but by simple, though careful, thinking. Suppose that a falling body broke into two pieces. Of course the two pieces would immediately slow down to their appropriate speeds. But suppose further that one piece happened to touch the other one. Would they now be one piece and both speed up? Suppose I tie the two pieces together. How tightly must I do it to make them one piece? A light string? A rope? Glue? When are two pieces one?
Humans can invent many different mathematical systems. Those mathematical systems that are found to correspond with the world consistently through time are kept, otherwise they may be discarded. That some mathematical systems are discovered to be more effective that others is neither reasonable nor unreasonable, it is just what is.
Who is to say that the mere fact of my pen touching my pencil does not result in a change of velocity is a reasonable or unreasonable thing to happen ?
What I reject is the idea that the regularity and consistency of physical relations reduces to differences of degree that are not at the same time differences in kind. Put differently, quantitative measurement introduces qualitative change at every repetition of the counting.
I don't follow you, but I'll elaborate on my view: laws of nature are relations between kinds of things. Kinds are universals, and laws of nature are universals. This is the metaphysical theory of law realists.
Your first sentence sounds consistent with law realism. I don't know what to make of your second sentence, other than that it sounds like an interpretation of quantum mechanics. Please explain.
Are you a nominalist?
I’m a phenomenologist, but the inextricable relation between quantitative interaction and qualitative
transformation I described comes from Deleuze , whose touchstone was Nietzsche. For both orientations lawfulness , self-identity, the ability to carve out and iterate a pristine quantitative realm within a qualitative dimension are idealizations that invent rather than represent the real. A ‘kind’ is not a category, object, identity. It is a differentiation. There are no quantities within kinds. Every iteration of quantity is a change of kind.
Strange stuff from a realist perspective.
Isn't "electron" a kind? Do they not all have an electric charge of quantity -1?
Look at the period at the end of this sentence. Now keep on staring at it. We say that the period is a kind, an identity persisting in time with attributes and properties that belong to it. Mathematics begins from , and depends on , such reifications. But , most fundamentally , that is not how you are experiencing the period as you continue to gaze at it. It is not simply that your gaze or body posture subtly shifts your perspective, but that your sense of the meaning of what you are perceiving also shifts is subtle ways every moment. Each repetition of the period is a subtly new interpretation of it. This is not even including the ways in which the period , as a natural object, is not simply a system of relations among fixed kinds of physical particles. When we employ concepts like ‘kind’,property’ and ‘attribute’ so as to see electrons with numerically assigned charge, we are masking all of this underlying subtle but incessant dynamism and change for the sake of convenience. Our mathematics begins only after we have concealed what happens within ‘kinds’.
The problems with "period" aren't present for electron. I regard an electron as a type of ontic object, -specifically, objects with a certain set of properties (such as -1 electric charge, a specific rest mass, etc). I gather you disagree, so I'd like to understand your point of view.
Nature is undead.
.
Quoting Jackson
As you say, you've never heard of (Wigner's paper) "The Unreasonable Effectiveness of Mathematics in the Natural Sciences" and you should start doing your own homework so that you can contribute intelligently to the current discussion.
Quoting Joshs
:up:
As an embodied cognitionist (Lakoff, Dehaene), "the effectiveness of mathematics" seems quite reasonable to me as well.
Look into this box of apples. They are all Delicious apples, a kind of apple. Now look closely at each one after carefully counting them - there are 24. Each apple is unique, being distinguished from the others in small ways. We see this as we contemplate these apples, a particular kind of apple. After a bit each apple seems to turn its best side toward our gaze, and we begin to contemplate what may lie on their opposite sides. In so doing we drift into a meditative state in which apples prevail, even those not Delicious.
Quoting Joshs
:chin:
:up:
It's the same as being amazed that the word "apple" is so well-suited to our talk of apples...
You can't be sure they will, but just in case, here is the essay you're referring to.
Why Wigner says it is 'unreasonable' is because of the sense in which mathematical conjectures sometimes produce completely unforseeen predictions which turn out to be true - that 'mathematical concepts turn up in entirely unexpected connections', as Wigner says.
Wigner gives some examples, but admittedly they are difficult to understand unless you have some background - after all, Wigner was a Nobel laureate in mathematical physics, for discoveries derived from mathematical symettries, which I presume few here would be familiar with. But that said, one of the examples he gives is this:
[quote=Eugene Wigner, Unreasonable Effectiveness...]This (case) originated when Max Born noticed that some rules of computation, given by Heisenberg, were formally identical with the rules of computation with matrices, established a long time before by mathematicians. Born, Jordan, and Heisenberg then proposed to replace by matrices the position and momentum variables of the equations of classical mechanics. They applied the rules of matrix mechanics to a few highly idealized problems and the results were quite satisfactory.
However, there was, at that time, no rational evidence that their matrix mechanics would prove correct under more realistic conditions. Indeed, they say "if the mechanics as here proposed should already be correct in its essential traits." As a matter of fact, the first application of their mechanics to a realistic problem, that of the hydrogen atom, was given several months later, by Pauli. This application gave results in agreement with experience. This was satisfactory but still understandable because Heisenberg's rules of calculation were abstracted from problems which included the old theory of the hydrogen atom.
The miracle occurred only when matrix mechanics, or a mathematically equivalent theory, was applied to problems for which Heisenberg's calculating rules were meaningless. Heisenberg's rules presupposed that the classical equations of motion had solutions with certain periodicity properties; and the equations of motion of the two electrons of the helium atom, or of the even greater number of electrons of heavier atoms, simply do not have these properties, so that Heisenberg's rules cannot be applied to these cases. Nevertheless, the calculation of the lowest energy level of helium, as carried out a few months ago by Kinoshita at Cornell and by Bazley at the Bureau of Standards, agrees with the experimental data within the accuracy of the observations, which is one part in ten million. Surely in this case we "got something out" of the equations that we did not put in.[/quote]
I take it that this means that the equations in question made predictions which were not even contemplated in relation to the original problems they were supposed to solve. And there have been other such cases in the history of science. Take for example Paul Dirac, another Nobel laureate in physics:
Read more: https://www.newscientist.com/article/dn17111-how-dirac-predicted-antimatter/
Quoting Relativist
As soon as there are ANY differences in the world, you have a structure describable by mathematics. You can count the differences, you can make combinations of the differences, you can make combinations of those combinations, you can order the combinations (for example by size). The whole known mathematics is reducible to set theory, which is basically a theory of combinations (sets are combinations of their members).
Aristotle taught that heavy objects fall faster than lighter ones.
Quoting RussellA However, Richard Hamming's thought experiment gives a powerful reason why heavy objects should fall at the same speed as lighter ones. This thought experiment allows us to predict that universally a heavy object should fall at the same speed as a lighter one, not only on Earth today, but on the far side of the universe and millions of years from now. Such thought experiments can predict both what cannot be seen and what cannot be experimentally foreseen.
Personally, I have consistently observed across space and time that the mere fact of my pen touching my pencil does not result in a change of velocity of either of them, from which I may reasonably agree with Hamming that it follows that there is a universal law that heavy objects should fall at the same speed as lighter ones.
Does not such a prediction show the "unreasonable" power of reason, and by extension logic and mathematics ?
Beliefs are always self-referential, and therefore always well-suited to the world and always "unreasonably" effective
For example, a table is the relation between a table top and table legs. The same applies to apples, governments, unicorns, houses, ethics, etc. As relations don't ontologically exist in the world (FH Bradly) but only in the mind (the Binding Problem), tables don't ontologically exist in the world but only in the mind. As the concept of tables only exists in our thoughts and talk, it should be no surprise about the "unreasonable" effectiveness of our thoughts and talk about tables, as thoughts about tables and tables are one and the same thing.
The question is, are our laws of nature comparable with the situation as regarding the table? As tables only exist in the mind, perhaps our laws of nature only exist in our mind, and consequently, as both self-referential, obviously both well-suited to the world and "unreasonable" effective.
My deduction of the universal law that heavy objects should fall at the same speed as lighter ones is only valid as long as there is a condition of satisfaction between my beliefs and the state of affairs that obtains in the world. My belief clearly does not determine the state of affairs in the world, but as my belief is self-referential, my belief is both well-suited and "unreasonably" effective as to what I believe to be the state of affairs in the world.
Paradigm shifts in my beliefs does not alter the self-referential nature of belief
However, my belief in such a law of nature, my belief in how the world is structured, is no guarantee that what I observe will continue to comply with my present beliefs, in which case I may be forced through the same kind of paradigm shift as described by Thomas Kuhn and be forced to develop a new set of beliefs that correspond with my new experiences and observations.
The point remains that even this new set of beliefs will also be self-referential, in that even my new beliefs will be well-suited and "unreasonably" effective as to what I believe to be the state of affairs in the world.
Our self-referential belief in reason, logic and mathematics can only ever be well-suited to the world and "unreasonably" effective
IE, regardless of what beliefs I may have, what reasoning. logic or mathematics I use, my beliefs will always be well-suited and "unreasonably" effective to my understanding of the world around me because of the self-referential nature of belief.
Quoting jgill
In this example , the category ‘apple’ subsumes the particularities of the individual apples. The parts
can vary ( kinds of apples) without altering the whole ( the category apple). But does this logical subsumption bear any resemblance to how we actually construct and experience the relation between parts and wholes? Or is it the case, as the Gestaltists say, that the whole precedes its parts and the parts redefine the whole?
Wittgenstein analyzed the issue of the meaning of parts and wholes.
“There is a tendency rooted in our usual forms of expres- sion to think that the man who has learned to understand a general term, say, the term "leaf', has thereby come to possess a kind of general picture of a leaf, as opposed to pictures of particular leaves. He was shown different leaves when he learned the meaning of the word 'leaf'; and showing him the particular leaves was only a means to the end of producing 'in him' an idea which we imagine to be some kind of general image. We say that he sees what is common to all these leaves; and this is true if we mean that he can on being asked tell us certain features or properties which they have in common. But we are inclined to think that the general idea of a leaf is something like a visual image, but one which contains what is common to all leaves. This again is connected with the idea that the meaning of a word is an image, or a thing correlated to the word. (This roughly means, we are looking at words as though they all were proper names, and we then confuse the bearer of a name with the meaning of the name).
(d) Our craving for generality has another main source: our preoccupation with the method of science.I mean the method of reducing the explanation of natural phenomena to the smallest possible number of primitive natural laws; and, in mathematics, of unifying the treatment of different topics by using a generalization. Philosophers constantly see the method of science before their eyes, and are irresistibly tempted to ask and answer questions in the way science does. This tendency is the real source of meta- physics, and leads the philosopher into complete darkness.”
(The Blue Book, pp. 17)
The whole is a set of parts, but even a part is a set of parts. For the sake of argument, treat the parts as elementary and logical rather than real. As relations have no ontological existence in the world, but only in the mind, the parts may exist in the world, but the whole only exists in the mind.
From particular observations to general laws
From my particular observations in different locations over a period of time that the mere fact that my pen touches my pencil does not result in a change of velocity of either, I can make the general assumption that two objects in contact does not result in the change of velocity of either. I can also make the general assumption about the regularity of the laws of nature. This confirms Richard Hamming"s thought experiment that universally, heavy bodies fall at the same speed as lighter ones, contrary to Aristotle's teaching.
That I can predict a heavy object and a lighter one will fall at the same speed not only on Earth today but on the far side of the universe millions of years from now does initially seem to illustrate the unreasonable power of reason, and by extension logic and mathematics.
General laws only exist in the mind
As general laws, such as the law of nature that two objects when touching does not cause a change of velocity of either require relations between parts, a relation between object A and object B, then general laws can only exist in the mind and not the external world.
We have a whole concept of a universal table (apples, government, ethics, etc) in our minds, which is based on the observation of the relationship of particular parts in our external world. We have the whole concept of a universal law of nature in our minds, which is based on the observation of the relationship of particular parts in our external world. Both the concept of universal table and universal law of nature extend to the far side of the universe. Does our ability to extend the law of nature to the far side of the universe show the unreasonable power of reason ? No, no more than our extending the concept of a table to the far side of the universe shows the unreasonable power of reason.
Concepts such as tables and the law of nature remain in the mind. It does not follow that our projection of these concepts onto the external world makes them states of affairs that obtain in the external world. The fact that we can project our concept of tables and laws of nature onto the far side of the universe cannot be said to show the unreasonable power of reason, as neither of these concepts actually obtain as states of affairs.
As reason, logic and mathematics are self-referential, they cannot be said to be either reasonably or unreasonably effective
Our beliefs are self-referential, in that my concept of a table or a law of nature is of necessity well-suited to what I observe in the external world. IE, on the one hand I have a belief in my mind of a table or law of nature existing in the external world. On the other hand a table or law of nature is a belief that exists only in the mind and not the external world.
It was Eugene Wigner who spoke of the "unreasonable effectiveness of math". Nature has dead and alive elements. Many deed phenomena (which doesn't mean they don't contain at least the seeds of life) behave in fixed patterns, contrary to living phenomena. For example, the principle of least action applies to dead matter but not to life.
I still don't see why that's unreasonable. It seems only reasonable if What's so unreasonable about getting things out you didn't put in, as the anti-particle?
Astute observation. But how would you describe my face changing from neutral to laughing in math? The principle of least action applies to falling stones but does it apply to a bacteria?
"Dead" matter means it was once alive, yes?
From Wigner's paper: , and he goes on to observe that we would run out of interesting theorems were it not for the creation or discovery of new concepts.
What would you had asked Him? To give back your wife? Just kidding! : :joke:
Good question. I was much younger and I think an associate professor at the time, and my interests then might not have been my interests now - hard to recall. But probably I would have discussed the origins of mathematical concepts, those ideas that seem to pop out of nowhere and can become so important. Without such breakthroughs math would stagnate. An example is the notion of metric spaces, an abstraction or generalization of Euclidean distance.
:smile:
Mozart has some tasty chocolate balls!
If you don't see the point of Wigner's essay, there's not a lot of purpose me trying to explain it again.
Mathematical systems are invented and then discarded if discovered to be ineffective
(I hope @jgill agrees)
As Wigner wrote: "I would say that mathematics is the science of skilful operations with concepts and rules invented just for this purpose. The principal emphasis is on the invention of concepts".
I can invent the elementary mathematical system such that 1 + 1 = 3. Many mathematical systems can be invented. The mathematical system whereby 1 + 1 = 2 has also been invented.
As it has been discovered through observation of the external world that the mathematical system 1 + 1 = 2 is more useful than the mathematical system 1 + 1 = 3, the former has been kept and the latter discarded.
IE, Wigner was correct when he wrote about "the unreasonable effectiveness of mathematics in the natural sciences", because any mathematics that has been shown not to be unreasonably effective has been discarded
Reason, logic and mathematics require regularities in the external world
Wigner wrote - The laws of invariance of physical theories.........regularities in the events in the world around us which can be formulated in terms of mathematical concepts with an uncanny accuracy"
If there were not inherent regularities in the world, we could not predict that two rocks dropped at the same time from the same height reach the ground at the same time, regardless on whether on the Earth or the far side of the Universe.
"Laws of nature" exist only in the mind and not the external world
Wigner wrote "It is not at all natural that "laws of nature" exist, much less that man is able to discover them"
As concepts such a tables, apples, governments, ethics, laws of nature, etc require relationships between their parts, and relations have no ontological existence in the external world (see FH Bradley) but only in the mind (see the Binding Problem and Kant's Apperception and its Unity), such concepts exist only in the mind and not the external world.
Our beliefs are always "unreasonably effective"
Wigner wrote: We are in a position similar to that of a man who was provided with a bunch of keys and who, having to open several doors in succession, always hit on the right key on the first or second trial. He became sceptical concerning the uniqueness of the coordination between keys and doors".
In general, our beliefs in tables, apples, governments, ethics, laws of nature, mathematics, etc are always "unreasonably effective" and well suited to our understanding because beliefs are self-referential.
On the one hand, I have a concept of or a belief about a law of nature existing in the external world, and on the other hand, a law of nature is a concept or belief that only exists in the mind and not the external world.
IE, even if our belief is wrong, we still believe it.
Amazing that inventions work so well, then. Or maybe they're all in the mind as well?
What do you make of the phenomenologist's position, articulated so well by Joshs?
Quoting Joshs
In philosophy there seems to be a constant game of 'did we discover it or invent it?' - whether we are talking math or morality. I know how you feel about Platonism, but what do you make of the view from phenomenology?
Take the wheel as an example. As with all inventions they were invented in the mind, and then made into a physical thing of perhaps wood and steel, a circular rim supported by spokes revolving around an axle.
The parts of the wheel physically exist in the world, and once created, exist independently of whether anyone is thinking of them or not. This is compatible with Realism, in that there is a mind-independent world of matter and forces.
For the Naive Realist, our sense provide us with a direct awareness of the wheel as it really is.
For the Indirect Realist, we do not perceive the external world as it really is, but are only aware of a representation of the external world. Our awareness is of the concept of the wheel, not the "wheel" itself.
The concept of a wheel definitely exists in the mind, otherwise we would not be having this conversation. The question is, do wheels ontologically exist in the external world ? A wheel is a spatial relation between its rim, spokes and axle. Whether wheels ontologically exist in the external world depends on whether relations ontologically exist in the external world.
I am persuaded by FH Bradley's Regress Argument that relations don't ontologically exist in the external world, meaning that wheels don't ontologically exist in the external world.
If one is going to argue that wheels do ontologically exist in the external world, then this will require a justification that relations also ontologically exist in the external world.
Is there any reasoned argument that relations do ontologically exist in the external world ?
https://thephilosophyforum.com/discussion/comment/650566
You wrote:
We have to show that relations exist.
Glasgow is west of Edinburgh - so we are told.
It could mean that if we turn over the whole universe item by item we will find at least one thing that is to the west of another thing.
There is a case - at least one case - of something being to the west of something else.
From which if finally follows that relations exist...........we can see that relations have ontological existence.
As regards the ontological existence of relations, there are two possibilities - either i) relations don't exist and after turning over the whole universe item by item we won't find at least one thing that is to the west of another - or ii) relations do exist and after turning over the whole universe item by item we will find at least one thing that is to the west of another
However, the problem with your statement "There is a case - at least one case - of something being to the west of something else" is that the statement can only be made on the assumption that relations do exist.
It is equivalent to saying that if relations exist then relations exist.
It is.
It's not I don't understand his irony. I think it's unreasonable. Why should it be unreasonable that math predicts anti particles? It's a logical, so reasonable, consequence of the Dirac equation.
But you don't know that. It's quite feasible that the wheel was invented because some Cro-Magnon discovered that you could roll a big rock on logs. Basic empiricism.
Quoting RussellA
I'm not familiar with Bradley's Regress Argument, nor with the meaning of 'ontologically exist'. But at least you're prepared to discuss universals, which few here are, so I will persist.
Quoting RussellA
I think that you're saying that statements about what exists can only be validated against instances that might be encountered in the sensable universe. That for something to exist, it has to be 'out there somewhere' - you have to find an instance of it in order for it to 'ontologically exist'. I'm guessing that's what you mean by that rather awkward phrase.
Bertrand Russell provides an example in Problems of Philosophy, which I'm guessing you're familiar with, given the particular example that you've cited involving Glasgow. The way he puts it is like this (and please forgive the lengthy quotation):
[quote=Bertrand Russell, The World of Universals; https://www.gutenberg.org/files/5827/5827-h/5827-h.htm#link2HCH0009]Consider such a proposition as 'Edinburgh is north of London'. Here we have a relation between two places, and it seems plain that the relation subsists independently of our knowledge of it. When we come to know that Edinburgh is north of London, we come to know something which has to do only with Edinburgh and London: we do not cause the truth of the proposition by coming to know it, on the contrary we merely apprehend a fact which was there before we knew it. The part of the earth's surface where Edinburgh stands would be north of the part where London stands, even if there were no human being to know about north and south, and even if there were no minds at all in the universe. ...We may therefore now assume it to be true that nothing mental is presupposed in the fact that Edinburgh is north of London. But this fact involves the relation 'north of', which is a universal; and it would be impossible for the whole fact to involve nothing mental if the relation 'north of', which is a constituent part of the fact, did involve anything mental. Hence we must admit that the relation, like the terms it relates, is not dependent upon thought, but belongs to the independent world which thought apprehends but does not create.
This conclusion, however, is met by the difficulty that the relation 'north of' does not seem to exist in the same sense in which Edinburgh and London exist. If we ask 'Where and when does this relation exist?' the answer must be 'Nowhere and nowhen'. There is no place or time where we can find the relation 'north of'. It does not exist in Edinburgh any more than in London, for it relates the two and is neutral as between them. Nor can we say that it exists at any particular time. Now everything that can be apprehended by the senses or by introspection exists at some particular time. Hence the relation 'north of' is radically different from such things. It is neither in space nor in time, neither material nor mental; yet it is something. ...
It is largely the very peculiar kind of being that belongs to universals which has led many people to suppose that they are really mental. We can think of a universal, and our thinking then exists in a perfectly ordinary sense, like any other mental act. Suppose, for example, that we are thinking of whiteness. Then in one sense it may be said that whiteness is 'in our mind'. ... In the strict sense, it is not "whiteness" that is in our mind, but "the act of thinking of whiteness". The connected ambiguity in the word 'idea', which we noted at the same time, also causes confusion here. In one sense of this word, namely the sense in which it denotes the object of an act of thought, whiteness is an 'idea'. Hence, if the ambiguity is not guarded against, we may come to think that whiteness is an 'idea' in the other sense, i.e. an act of thought; and thus we come to think that whiteness is mental. But in so thinking, we rob it of its essential quality of universality. One man's act of thought is necessarily a different thing from another man's; one man's act of thought at one time is necessarily a different thing from the same man's act of thought at another time. Hence, if whiteness were the thought as opposed to its object, no two different men could think of it, and no one man could think of it twice. That which many different thoughts of whiteness have in common is their object, and this object is different from all of them. Thus universals are not thoughts, though when known they are the objects of thoughts.
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. [/quote]
There are very many crucial points made in this passage, of which I'll point to a few. One is the distinction between the existence of universals and of sensable objects. As Russell says, neither 'north of' nor 'whiteness' exist - rather they subsist or 'have being' - rather an awkward expression, but it's rather a difficult point. The second, and crucial, point, is that such qualities or relations or whatever they are, are not dependent on thought, but they can only be perceived by thought. Both of which point to what I regard as an absence or lack in the current philosophical lexicon, with respect to the distinction between 'being' and 'existence'. It's the tip of a very large iceberg.
It's not "so what". That's how you interpret it. It's "that's how it is". If matter behaves regularly it comes as no surprise that math describes it well. Math is about quantitative regularities and interdependences. The Dirac equation is an example. If you work with the equation you work with a naturally occurring regularity. So you bump into the positron.
No, that's what you've said. You say in your OP, you can't imagine it being any different. That's because you live in a society that has made these discoveries. If you lived a hundred years ago you couldn't even imagine such a discovery. But, yeah, so what.
No, of course not. That's stating the obvious. But a 100 years ago I could have used general relativity to predict unobserved phenomena. That's how it works. You make predictions with math. Like the Higgs boson was inferred 60 years ago. Like many other phenomena are calculated before discovery. How else could it function? If this wasn't the case, physics would have abandoned .math long ago. The eight-fold way.
Concepts are invented not discovered
One day, a Cro-Magnon on a walk through the forest happened to observe a big flat rock that had fallen from the side of a mountain rolling along on some logs on the ground. Let us call the Cro-Magnon George.
George had made a particular empirical observation and discovered something in the world, in that a flat rock can continue to move freely along the ground as long as it is supported by round logs.
George was able to make the intellectual leap from the particular to the general, and reason that any flat object may move more freely along the ground as long as it is supported by round objects. George using reason was able to use a particular observation to arrive at a universal concept, the concept of the wheel.
If concepts existed in a mind-independent world then they would be "out there somewhere"
and discoverable. However, if that were the case, two people independently observing an object, for example a rock, should be able to write down all concepts discoverable within the object, in which case, when compared, their lists should be the same. Concepts in objects cannot be discovered by observation alone, but require the inventive power of reasoning using the intellect.
IE, because the concept of the wheel does not exist in either a mind-independent rock, log or relation between the two, George could not have discovered the concept from an empirical observation. But as the concept of the wheel exists in George's mind, and because it cannot have been discovered from an empirical observation, it must have originated in George's mind, been invented in the mind of George.
Quoting Bertrand Russell, The World of Universals
"North of" and London exist in exactly the same way
The object Edinburghlondon has the related parts i) Edinburgh and ii) London
London has the related parts i) north of the Thames and ii) south of the Thames
South of the Thames has the related parts i) built up areas and ii) trees and grasslands
Built up areas have the related parts i) buildings and ii) roads
Roads have the related parts i) paving and ii) junctions
Paving has the related parts - etc
Russell writes that " the relation 'north of' is radically different from such things" as London, in that "north of" subsists whilst London exists. Yet London only exists as a relation between its parts north of the Thames and south of the Thames.
IE, the object London depends on its existence on relations between parts - the area north of the Thames and the area south of the Thames. If, according to Russell, relations don't exist in a mind-independent world, then it follows from Russell's own argument that neither can London exist as a mind-independent object.
Quoting Bertrand Russell, The World of Universals
Universals are thoughts
A group of people may agree to share a common language. It may be agreed within the group that white objects are linked with the word "white". In the world being observed by the group, not only do white objects physically exist, but also and the word "white" physically exists as an object.
Each individual may develop their private concept of "whiteness" by observing white objects in the world. But also each individual may also link their private concept of "whiteness" with the associated public word "whiteness"
It is true as Russell writes "One man's act of thought is necessarily a different thing from another man's" - in that my concept of "whiteness" is of necessity not identical to yours.
But it is not true as Russell wrote that "if whiteness were the thought as opposed to its object, no two different men could think of it", as one person's private concept of "whiteness" is linked to everyone else's private concept of "whiteness" through the public linguistic object "whiteness".
IE, universals, such as the concept of "whiteness" not only exist in the mind as a private thought, but also are universally understood by a group sharing a common public language.
Quoting Wayfarer
Universals and sensables are of the same kind
There are sensable objects such as Edinburgh and London and universals such as "north of" and "whiteness".
IE, a sensable object such as London is no more that a relation between its parts, and if relations are universals, then sensable objects cannot be argued to be of a different kind to the universals from which they are comprised.
Quoting Wayfarer
Universals are dependant on thought
It has been well-argued that universals such as whiteness, apples, houses, governments can not be explained as Platonic Forms that exist in a mind-independent world.
Universals can be perceived by thought, in that we can discuss them.
If universals don't exist in a mind-independent world, yet we can perceive them in our minds, then they must have been created in the mind. As universals have been created by thoughts in the mind, they must be dependent for their existence on thoughts in the mind.
IE, universals are dependent on thought and can be perceived by thought.
There is one step in between. It's this:
If relations do not exist, then it is not the case that something is to the west of something else.
Glasgow is to the west of Edinburgh.
Therefore (at least one) relation exists.
The first premiss does not assume that relations exist. It suggests a criterion for finding out whether they exist or not. The suggested criterion is to go and look at the world to see whether anything is to the west of anything else. I cannot think of a better criterion, but perhaps there is. So it's a challenge - if that's not what it is for a relation to exist, what should the criterion be?
This leads to:
Statement 1 = If relations do not exist, then it is not the case that Glasgow is to the west of Edinburgh
Statement 2 = Relations exist, and It is the case that Glasgow is to the west of Edinburgh.
The conclusion that "therefore (at least one) relation exists" of necessity follows from statement 2 rather than prove anything about the ontological existence or not of relations.
Why is math's utility "unreasonable"? I guess the answer has to do with scope (cross-domain applicability) and strength (the certainty that it guarantees).
What should worry us:
1. Maslow's hammer
2. The Streetlight Effect
You're defending the empiricist view that all concepts are derived from experience. (Some of the following is cribbed from Edward Feser)
Your initial example of a wheel was poorly chosen, the universal concept that is nearest is actually the circle. A circle is 'a round plane figure whose boundary (the circumference) consists of points equidistant from a fixed point (the centre)' as a matter of definition. As such, that is a concept which is discoverable by any mind capable of understanding such concepts. Something similar can be said of other geometrical primitives (squares, triangles and so on.) And these are concepts, not mental images - any mental image you can form of a triangle will be an image of an isosceles , scalene, or equilateral triangle, of a black, blue, or green triangle, etc, whereas the abstract concept "triangularity" applies to all triangles without exception. The concepts that are the objects of intellectual activity are universal, while mental images and sensations are essentially particular. Any mental image you can form of a man is always going to be of a particular man - tall, short, fat, thin, blonde, redheaded, bald, or whatever. But the concept "man" applies to every man.
Second, mental images are always to some extent vague or indeterminate, while concepts are at least often precise and determinate. To use Descartes’ famous example, a mental image of a chiliagon (a 1,000-sided figure) cannot be clearly distinguished from a mental image of a 1,002-sided figure, or even from a mental image of a circle. But the concept of a chiliagon is clearly distinct from the concept of a 1,002-sided figure or the concept of a circle.
Third, we have many concepts that are so abstract that they do not have even the loose sort of connection with mental imagery that concepts like man, triangle, and crowd have. You cannot visualize triangularity or humanness per se, but you can at least visualize a particular triangle or a particular human being. But we also have concepts -- such as the concepts law, square root, logical consistency, collapse of the wave function, and innumerably many others -- that can strictly be associated with no mental image at all. You might form a visual or auditory image of the English word “law” when you think about law, but the concept "law" obviously has no essential connection whatsoever with that word, since ancient Greeks, Chinese, and Indians had the concept without using that specific word to name it.
Quoting RussellA
Quite right! That is the point at issue, which here you appear to be conceding.
Quoting RussellA
The 'law of the excluded middle' didn't come into existence when it was discovered by h. sapiens; it would be true in all possible worlds, and would remain so, even if h. sapiens were to become extinct. This is the point of the a priori nature of the pure concepts of reason in Kant. So universal concepts are not created by thought, but can only be discerned by a rational intellect. And that is quite in keeping with the mainstream of Western philosophical thought, even if not with today's empiricism - so much the worse for it!
"A couple of years later, I read a theoretical paper that predicted the effect that I had seen in my data. It wasn’t a monumental thing at all - just an unexpected result buried in the mathematical description. I scoured my old research notebooks, saw the effect in those preliminary data sets - but only in those incomplete experiments that were essentially feasibility studies for my real project. There was nothing complete enough to publish"
An unexpected result buried in the mathematical description.
[quote=Ms. Marple]Most interesting![/quote]
Conceptually distinguishable (rationalism) but perceptually not (empiricism).
I wonder about the extent of the conflation among distinct objects that occur due to the low-resolution of our senses?
Perception smoothes the grainy world structure. The water feels like a continuous stuff.
Like how AI is used to "correct" images on telescopes here on earth and in outer space?
What if we are AI? we just don't know it (yet)! Vide creationism, simulation hypothesis.
Correct. One of your sporadically insightful observations. :wink:
Then we're fucked! Do you really think consciousness can be programmed?
No. Concept and percept are not separable or even two really existing categories. The distiction is purely theoretical.
As regards the unreasonable effectiveness of mathematics, it is initially truly amazing that from sitting on a train using Richard Hamming's thought experiment, I can disagree with Aristotle and agree with Galileo that heavy objects should fall at the same speed at lighter ones, not only on the train but universally on the far side of the universe.
However, the starting position is the amazing regularity and invariance of what we call "the laws of nature". Given such regularity, the "laws of nature" applicable on the train will also be applicable on the far side of the universe.
The fact that I can codify and quantify using reason, logic and mathematics the "laws of nature" that I observe on the train, and still be applicable on the far side of the universe, is not a measure of success of my reasoning, logic and mathematics, but rather is a measure of the regularity and invariance of the "laws of nature".
Without such regularity and invariance in "the laws of nature", our reasoning, logic and mathematics would count for nothing.
IE, mathematics is only effective because of the unreasonable regularity in the "laws of nature"
An associated issue is the question as to whether universal concepts such as "north of" and "whiteness" are or are not dependent on thought. Are they discovered in the external world or invented in the mind ?
Wayfarer - page 2 - The second, and crucial, point, is that such qualities or relations or whatever they are, (Bertrand Russell's "north of", "whiteness") are not dependent on thought, but they can only be perceived by thought.
RussellA - page 2 - If universals don't exist in a mind-independent world, yet we can perceive them in our minds, then they must have been created in the mind. As universals have been created by thoughts in the mind, they must be dependent for their existence on thoughts in the mind.
IE, not agreed yet.
Quoting Wayfarer
Yes. In the sense that concepts are created in the mind based on observations of the external world, not that concepts ontologically exist in a mind-independent world.
Quoting Wayfarer
I agree that the mind uses the inventive power of intellectual reasoning, and part of its inventive power is in the invention of universal concepts, such as "north of".
Quoting Wayfarer
SEP - Disjunction - The law of excluded middle (LEM) states that any proposition of the form (??¬?) is logically valid. The semantic principle of bivalence states that every proposition is either true or false (and not both).
SEP - Structured Propositions - For example, when a German speaker utters the sentence ‘Schnee ist weiss’ and an English speaker utters the sentence ‘Snow is white’, they have said the same thing by uttering the sentences they did.
The proposition is taken to be the thing that is in the first instance true or false
IE, as propositions don't exist in a mind-independent world, and as the "law of excluded middle" is based on propositions, the "law of excluded middle" doesn't exist in a mind-independent world.
Quoting Wayfarer
Exactly, a priori in the mind.
Quoting Wayfarer
If universal concepts were not created by thought, then the universal concepts of love and hate could be discovered in a mind-independent world.
Which can be discovered indeed
My point is that dead matter seems to obey many mathematical structure. If this wasn't the case, chaos would rule supreme. In experiments, reality is arranged to fit the formula.
I think before going further, you should explain further what you mean by your term 'ontologically exist'.
Mathematics obeys matter, rather than matter obeys mathematics
From observations of the world, we arrive at the belief that there is a regularity in what we call "the laws of nature". We are able to justify such a belief through further experimentation.
In order to model what we believe to be the intrinsic regularity discovered within the "laws of nature", we invent mathematical systems also having intrinsic regularity.
If our intrinsically regular mathematical systems prove to be effective in predicting future states of affairs, then we can infer that the "laws of nature" are also intrinsically regular. We can never prove that the "laws of nature" are intrinsically regular, as this leads into Hume's problem with inductive reasoning. We can never know that the "laws of nature" are intrinsically regular, as knowledge requires a justified true belief, and the truth is beyond what we can inductively reason.
The "unreasonable" effectiveness of mathematics is a strong indication that within the "laws of nature" there is an inherent regularity.
Which renders math reasonably effective.
The mind is of a different kind to the mind-independent world
Realism is the belief that the world comprises the mind and a mind-independent world.
Although the mind is part of the world, my belief is that the the nature of the mind is different to the nature of the mind-independent world. FH Bradley's Regress Argument persuades me that relations don't ontologically exist in the mind-independent world, whilst the Binding Problem and Kant's Unity of Perception do persuade me that relations do ontologically exist in the mind.
Although everything in the mind-independent world exists in the mind, such as matter and the forces between them, there are some things that exist in the mind but not the mind-independent world, such as concepts, unicorns, apples, numbers, universals, abstracts, love and hate, ethics, pain and pleasure, fictional characters, ghosts, gods, relations, etc.
Therefore, there is a set of things that ontologically exist in the mind, and a different set of things that ontologically exist in the mind-independent world, though the sets do overlap.
IE, in the mind-independent world, quarks and the weak nuclear force do ontologically exist, but love and hate don't.
I hope not! Consciousness has, to my reckoning, many facets to it; the logic has been replicated (on computers) but not duplicated, if you catch my drift.
:chin: :snicker:
:lol: I wouldn't want to cause an outbreak!
I question the coherence of the idea of a 'mind-independent world', but I don't think I'll pursue it. (I have some familiarity with F. H. Bradley whom as I understand it was one of the last of the British Idealists, in other words, he did not subscribe to the doctrine that reality comprises a plurality of really existing mind-independent objects, as can be seen here.)
Thank you for your service.
First time reading the essay, myself. A handful of quotes from it:
The language he uses is deeply religious throughout. These were moments where I thought the religious nature of his appeals were apparent -- it may not be a Christian religion, but the religion of the philosophers -- in the God that thinks itself and brings order to nature, or whatever formulation he may prefer.
Which isn't to say he is wrong, I think. What I would say is that religious appeals are only effective among believers. His is the wonder of a scientist with a passion for something I don't think even exists -- "ultimate truth" or "foundations" as he is also often reasoning within. He's sort of pulling a couple of transcendental moves along the way, really -- without the empirical law of epistemology, no physics is possible. Physics exists, therefore....
But for myself I prefer to focus on the multiplicity of science. And there I think I'd actually wend a path between yourself and Wigner. For where you say:
I wouldn't put any caveats on the usage of mathematics to understand human beings just because it is "alive" whereas matter is "dead" -- we have a theory of evolution, after all, and we use mathematics in biology, so there's no need to think math can't help in understanding life (not that you said this, but you are asserting that nature is dead, so "life" naturally springs to my mind as the antipode). Humans are just the animal that talks too much and thinks such talking is really special, so we could -- with effort -- come to understand the human animal in more precise terms than that.
And further, I think there is something curious about math. I just don't think it's religious, or tied to ultimate truth, or the scientists' quest for the One Pure Description.
I think "Why does mathematics help human beings?" a reasonable and interesting question that seems to me to be a pretty close approximation to what Wigner is mentally ogling in his essay -- I often wonder about the nature of math in relation to nature, I just don't think placing that question in the realm of the mystical or religious to really get me going. I'm not religious.
It's funny you say that - his Wikipedia page says he was a convinced atheist. Maybe the fact that it reads as 'religious' is because the kind of mathematical Platonism he seems to be suggesting goes against the grain of philosophical naturalism. There's a remark in another essay about philosophy of maths that I've read, saying '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” (i.e. like numbers) 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.'
Anyone have an idea why?
Is this a case of the nonmathematical nature of reality or is it just that we aren't smart enough?
There is no indication in the article that Wigner proposes the mystical or religious to explain why our theories work so well.
Wigner wrote - "The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve".
Metaphors are commonly used in science, such as: evolution by natural selection, F = ma, the wave theory of light, DNA is the code of life, the genome is the book of life, gravity, dendritic branches, Maxwell's Demon, Schrödinger’s cat, Einstein’s twins, greenhouse gas, the battle against cancer, faith in a hypothesis, the miracle of consciousness, the gift of understanding, the laws of physics, the language of mathematics, deserving an effective mathematics, etc.
IE, it would be more true to say that the language he uses is deeply metaphorical rather than religious.
I'd say that the reason it reads religiously is that it reminds me of the God of the philosophers -- so he may think he was an atheist, but in the essay he admits that these are articles of faith. "Religious", after all, is much wider than a/theism.
Quoting RussellA
Quoting RussellA
If you prefer metaphorical, then that's fine. My point remains -- the metaphor works for believers in ultimate truth.
I agree that as a metaphor, the "ultimate truth" works for atheists in their belief of an "ultimate truth".
Interesting observations. My ex-wife's father, a friend of Wigners, was an architect and intellectual in Hungarian society. He had no use for organized religion, but was something of a disciple of Tielhard de Chardin, an intellectual and Catholic priest who advanced the idea of an Omega Point, toward which the world moves and reaches in its final days. A curious blend of science and something like religion.
that is indeed interesting. I think overall that what has happened is that religion has 'burst its banks', i.e. overflowed the boundaries that had been set up for it by the Church. All of the Biblical symbolism of tares and wheat and flocks and blood sacrifice which are natural to an early agrarian culture make no sense in the post-industrial landscape, but there's a deeper level of meaning which flows on regardless.
Kurt Godel apparently developed a rationalist 'proof of God' argument towards the end of his life (ref). He too was religiously unaffiliated, but also a mathematical Platonist, as many physicists are.
Ever since I began to think about it, I've held that numbers and basic geometrical principles and the like are real, in that they're the same for anyone who can grasp them. So they're not dependent on your or my mind, but can only be grasped by a rational mind. Secondly, that because reason uses these to interpret and organise experience, then they are fundamental elements of lived reality, not in the way that objects and energy are, but as fundamental constituents of the human 'life-world'.
Not all of those are metaphorical. I can't see how Newton's equations of motion are metaphorical, although I agree that many of the other examples are. There are also such things as 'rogue metaphors' that have become deeply embedded in cultural discourse but have assumed many meanings that they may not have originally carried. I think evolutionary biology is rife with 'em.
That sounds right. If nature were more chaotic, we might still have a rich 'science of formal systems,' but this would probably have little interest or prestige apart away from its specialists.
Newton's second law F=ma is a metaphor, not a literal fact.
Andrew May makes a strong point that even Newton's second law is a metaphor, in that that when a body is acted upon by a force, the time rate of change of its momentum equals the force, in that F=ma,
Andrew May Metaphors in Science 2000
"In his article on the use of metaphors in physics (November issue, page 17), Robert P Crease describes several interesting trees but fails to notice the wood all around him. What is a scientific theory if not a grand metaphor for the real world it aims to describe? Theories are generally formulated in mathematical terms, and it is difficult to see how it could be argued that, for example, F = ma "is" the motion of an object in any literal sense. Scientific metaphors possess uniquely powerful descriptive and predictive potential, but they are metaphors nonetheless. If scientific theories were as real as the world they describe, they would not change with time (which they do, occasionally). I would even go so far as to suggest that an equation like F = ma is a culturally specific metaphor, in that it can only have meaning in a society that practices mathematical quantification in the way that ours does. Before I'm dismissed as a loopy radical, I should point out that I'm a professional physicist who has been using mathematical metaphors to describe the real world for the last twenty years!"
The equation F=ma cannot be literal because of Hume's problem of induction. Through logic and reason and the empirical observation of constantly conjoined events, we hypothesise that F=ma. Through further empirical observation we discover that this equation proves to be effective in the prediction of future states of affairs. We believe the equation to be literal, but this belief is only a hypothesis.
We believe, we hypothesise, that there is a regularity in what we call the "laws of nature", and accordingly create a mathematics also founded on regularity in the expectation that the regularities in our mathematics will correspond with the regularities in the "laws of nature". That our mathematics are effective in predicting future states of affairs in the world infers that our hypothesis that there are regularities in the laws of nature is correct, is true. But, this is not knowledge, as our hypothesis can never be proved, only a justified belief.
A metaphor may be defined as i) a figure of speech in which a word or phrase is applied to an object or action to which it is not literally applicable and ii) a thing regarded as representative or symbolic of something else.
IE, as the equation F=ma can never be proved to be a literal description of states of affairs in the world, and must always remain a hypothesised representation, it falls within the definition of metaphor.
Aren’t you the one supposed to be defending realism? :smile:
Luckily, my livelihood is not dependent on my selling.
I believe in Realism
Idealism is the view that things exist only as ideas, with no reality of material objects outside of the mind. Realism is the view that objects exist in themselves, independently of our consciousness of them. My position is not that of Idealism, as I believe objects exist in themselves, independently of our consciousness of them. It comes down to exactly what "objects" are. My belief that elementary particles and elementary forces do ontologically exist in a mind-independent world, though relations don't, is consistent with Realism.
Do you believe in Realism or Idealism ?
As you wrote on page 3: "Ever since I began to think about it, I've held that numbers and basic geometrical principles and the like are real, in that they're the same for anyone who can grasp them. So they're not dependent on your or my mind, but can only be grasped by a rational mind." It would follow from your position that if numbers are real and not dependent on your or my mind, then there must be a mind-independent world." This is a belief in Realism.
Yet you also wrote on page 3: "I question the coherence of the idea of a 'mind-independent world'. This is a belief in Idealism."
Are these positions compatible ?
Like a spider! :chin:
It's a rather simplistic description. Philosophical idealism can accept that material objects and forces have a degree of reality, and that they're not mere phantasms or delusions. In that sense, they're not 'in the mind' in the way that expression would usually be understood. An idealist philosopher will understand that she will be scalded by hot water or cut by a razor. So she may not hold that things only exist 'in the mind' in a simplistic or obvious sense, but that the constructive activities of the mind are foundational to our knowledge of the world, and that we can't go beyond that to see things 'as they are in themselves'. That was nearer to Kant's view.
Quoting RussellA
But numbers and logical principles can only be understood by a mind capable of counting and reasoning. So they're real, but they're not material objects like rocks or trees.
The view that abstract objects are real is generally associated with Platonism or scholastic realism. But you've already indicated that you reject this with reference to F H Bradley's argument.
My claim that numbers and logical principles are real independently of our minds, but can only be grasped by a mind, is closer to traditional realism than to scientific realism.
But:
Quoting RussellA
This is just what has been called into question by 20th Century physics, specifically the Bohr-Einstein debates. Now obviously that is a deep issue - in fact this whole issue is deep - but the thrust of the 'quantum revolution' was succinctly expressed by Werner Heisenberg, when he said:
[quote=The Physicists Conception of Nature]We can no longer speak of the behaviour of the particle independently of the process of observation. As a final consequence, the natural laws formulated mathematically in quantum theory no longer deal with the elementary particles themselves but with our knowledge of them. Nor is it any longer possible to ask whether or not these particles exist in space and time objectively … When we speak of the picture of nature in the exact science of our age, we do not mean a picture of nature so much as a picture of our relationships with nature. …Science no longer confronts nature as an objective observer, but sees itself as an actor in this interplay between man and nature. The scientific method of analysing, explaining and classifying has become conscious of its limitations, which arise out of the fact that by its intervention science alters and refashions the object of investigation...[/quote]
So, this questioning of the 'mind-independent' nature of the supposed fundamental constituents of existence - namely, atomic particles - really has undermined many forms of realism. It was this which was at the heart of Einstein's discomfort - as a staunch scientific realist he could never accept the so-called 'observer dependent' nature of quantum physics. But I believe, as has been discussed in various other threads, that experimental evidence has confirmed Heisenberg's approach - 'the Copenhagen interpretation' - over the realist view.
For this reason, there is actually a kind of idealist streak in a lot of modern scientists. Not all, by any means, and a long way from unanimously, but it's there to be found.
"The doctrine that the world is made up of objects whose existence is independent of human consciousness turns out to be in conflict with quantum mechanics and with facts established by experiment." ? Bernard d'Espagnat
"We have to give up the idea of realism to a far greater extent than most physicists believe today." ? Anton Zeilinger
“The atoms or elementary particles themselves are not real; they form a world of potentialities or possibilities rather than one of things or facts. ? Werner Heisenberg
and so on.
Some have said that "definitions are not all that helpful", but it has also been said about Ordinary Language Philosophy that traditional philosophical problems are rooted in misunderstandings philosophers make by distorting or forgetting how words are ordinarily used to convey meaning in non-philosophical contexts. Such philosophical use of language creates the very philosophical problems they are employed to solve.
Idealism may be simply defined as a belief that there is no mind-independent external world. Realism that there is a mind-independent external world. Within Realism is Direct Realism and Indirect Realism. Direct Realism may be simply defined as the belief that we directly observe objects in the external world as they really are. Indirect Realism may be simply defined as the belief that we only observe representations of objects we believe to be in the external world. Kant was an Indirect Realist.
IE, it is true that Idealism accepts that material objects and forces have a degree of reality, but that reality is in the mind, not in a mind-independent world.
Quoting Wayfarer
The Platonist believes in the existence of abstract objects, where abstract objects exist outside time and space, are not causal and are necessary. The Nominalist believes in concrete objects, where concrete objects exist in time and space, are causal and are contingent.
It is still possible for the Nominalist to reject the Platonism of abstracts while still believing in the ontological existence of relations.
I personally reject the Platonism of abstracts because I find the idea of objects existing in the external world outside of time and space incomprehensible.
For a similar reason, I also reject the ontological existence of relations, as they also exist in the external world outside of time and space.
Quoting RussellA
Quoting Wayfarer
The age of the universe is about 13.8 billion years, and human intelligence has been on the Earth for about 7 million years. That a mind-independent world existing 13,793 billion years before the arrival of human observers has been called into question makes no sense to me. It brings to mind the belief of Young Earth Creationism, whereby lifeforms were created in a supernatural act about 6,000 to 10,000 years ago.
I am also sure that most contemporary philosophical interest in the quantum world is comparable to that of medieval discussion about the philosopher's stone and its relevance to alchemy.
Not so. His philosophy is described as transcendental idealism although I daresay your simplistic definitions would render the distinction unintelligible.
Quoting RussellA
That's because you're trying to imagine an external world outside space and time, as 'a place', where 'things' never change. But the subject of the analysis are purely intelligible in nature, i.e. they can only be grasped by a mind, so they don't exist in the way that sensory objects exist. They are inherent in the scheme of things, rather than existing as manifest phenomena. But because our culture is so deeply indoctrinated to think only in phenomenalist terms, it's an impossible distinction to grasp.
Quoting RussellA
I can see you're not educated about the philosophical implications of physics. And I can also see why you believe it doesn't make sense, but then, that is why some of the greatest minds of the last century have been perplexed, and still are perplexed, by these very same issues. (See [url=https://www.discovermagazine.com/the-sciences/does-the-universe-exist-if-were-not-looking]Does the Universe Exist if We're Not Looking?, Discover Magazine.)
Sounds like you are not hopeful then.
[quote=Arthur Schopenhauer, World as Will and Representation]The fundamental absurdity of materialism is that it starts from the objective and takes as the ultimate ground of explanation something objective , whether it be matter in the abstract, simply as it is thought, or after it has taken form, is empirically given—that is to say, is substance, the chemical element with its primary relations. Some such thing it takes, as existing absolutely and in itself, in order that it may evolve organic nature and finally the knowing subject from it, and explain them adequately by means of it; whereas in truth all that is objective is already determined as such in manifold ways by the knowing subject through its forms of knowing, and presupposes them; and consequently it entirely disappears if we think the subject away. Thus materialism is the attempt to explain what is immediately given us by what is given us indirectly. All that is objective, extended, active—that is to say, all that is material—is regarded by materialism as affording so solid a basis for its explanation, that a reduction of everything to this can leave nothing to be desired (especially if in ultimate analysis this reduction should resolve itself into action and reaction). But we have shown that all this is given indirectly and in the highest degree determined, and is therefore merely a relatively present object, for it has passed through the machinery and manufactory of the brain, and has thus come under the forms of space, time and causality, by means of which it is first presented to us as extended in space and ever active in time. From such an indirectly given object, materialism seeks to explain what is immediately given, the Idea (in which alone the object that materialism starts with exists), and finally even the will from which all those fundamental forces, that manifest themselves, under the guidance of causes, and therefore according to law, are in truth to be explained.[/quote]
Quoting Rebecca Goldstein
I understand entirely. I think there's room for some quality prompts on the subject, especially common fallacies or misrepresentations. Sometimes 3 or 4 key ideas highlighted with some recommended readings are helpful to others. And it could be done rolled out over several posts.
I am fascinated that one of the key aspects of the Western philosophical tradition is often poorly understood or abandoned and I say this as someone who is not an idealist. Frankly, I couldn't say how one could ascertain whether idealism is the case or not. Nevertheless I am very interested in basic delineations of this approach.
Quoting Wayfarer
Yes - it's a great quote.
Good idea. I had started something but side-tracked myself. Now that I have that book, I might use it as a base.
The term "Transcendental Idealism" is more metaphorical than literal
A better description than "transcendental idealism" could be "justified belief within Indirect Realism" in that we hypothese the cause of representations discovered in phenomena from the senses using justified belief.
A wave function collapses when a wave function reduces to a single eigenstate due to an interaction with the external world. The fact that this interaction is called an "observation" does not mean the observer has to be a conscious being. It can be a particle of light, a molecule of air, a wall, a ceiling, a window, etc.
"Observation" is being used as a metaphor in that only conscious beings can observe. A rock cannot observe the air, the tree cannot observe the wind, etc. That wind howls does not mean that wind is in anguish. That a wave of terror washed over him does not mean that terror is a wave. That to say that Jess is dynamite does not mean she is made of dynamite.
It is true that Kant as an Indirect Realist believed in Epistemological Idealism, but it is certainly not true that he believed in Ontological Idealism.
IE, the fact that Kant's philosophy is called "transcendental idealism" does not of necessity mean that it can be described as either transcendental or Idealism.
Quoting Wayfarer
I agree that abstracts can only be grasped by the mind.
The question that remains to be answered is how can something exist in a mind-independent world outside of time and space ?
Quoting Wayfarer
Can anyone make a valid argument that a mind-independent world did not exist in the 13 billion years before the arrival of human observers ?
There is an interview with John Wheeler Does the Universe Exist if We're Not Looking
We inhabit a cosmos made real by our own observation
John Wheeler has a gut feeling that we inhabit a cosmos made real by our own observation.
The article notes that "When physicists look at the basic constituents of reality— atoms and their innards, or the particles of light called photons— what they see depends on how they have set up their experiment."
In addition "Our observations, he suggests, might actually contribute to the creation of physical reality. To Wheeler we are not simply bystanders on a cosmic stage; we are shapers and creators living in a participatory universe."
IE, from the standpoint of Epistemological Idealism within Indirect Realism, I agree with the above, and I am sure that not only Kant but also Schopenhauer would as well.
Are humans necessary for the existence of the universe
The article also asks "Does this mean humans are necessary to the existence of the universe? While conscious observers certainly partake in the creation of the participatory universe envisioned by Wheeler, they are not the only, or even primary, way by which quantum potentials become real. Ordinary matter and radiation play the dominant roles.........In this case the mica, not a conscious being, is the object that transforms what might happen into what does happen."
IE, the article raises the question "Does the Universe exist if we're not looking", and its answer is yes.
According to the source document:
[quote=CPR A369]I understand by the transcendental idealism of all appearances the doctrine that they are all together to be regarded as mere representations and not things in themselves, and accordingly that space and time are only sensible forms of our intuition, but not determinations given for themselves or conditions of objects as things in themselves. To this idealism is opposed transcendental realism, which regards space and time as something given in themselves (independent of our sensiblity). The transcendental realist therefore represents outer appearances (if their reality is conceded) as things in themselves, which would exist independently of us and our sensibility and thus would also be outside us according to pure concepts of the understanding.[/quote]
However, Kant then grants that you can be both a transcendental AND an empirical realist:
[quote=CPR A370]The transcendental idealist, on the contrary, can be an empirical realist, hence, as he is called, a dualist, i.e., he can concede the existence of matter without going beyond mere self-consciousness and assuming something more than the certainty of representations in me, hence the cogito ergo sum. For because he allows this matter and even its inner possibility to be valid only for appearance – which, separated from our sensibility, is nothing – matter for him is only a species of representations (intuition), which are call external, not as if they related to objects that are external in themselves but because they relate perceptions to space, where all things are external to one another, but that space itself is in us. [/quote]
So, Kant is not denying the apparent reality of the empirical domain, but that it has intrinsic or inherent reality.
Quoting RussellA
The problem is philosophical, not scientific. You're taking the scientific realist view as an absolute description. In other words, you're not seeing the role that the mind plays in constructing the picture of the world - even of the world prior to the advent of human consciousness. In that sense, even the most apparently-obvious scientific hypotheses are mental constructions. They may be accurate mental constructions, which can be tested against all manner of observations, but the mind has an inextricable role in their construction. Have a look again at this quote.
Quoting RussellA
It's more than a 'gut feeling'. Wheeler was one of the giants of theoretical physics. In terms of popular science, he is known for this theory of the 'participatory universe'. It's about a lot more than simply what happens in an experiment.
Quoting RussellA
That's because you have in your mind the firm belief in an external reality. I understand that questioning that belief is difficult.
As you wrote about Kant's theory of "Transcendental Idealism": "you can be both a transcendental AND an empirical realist", this indicates the phrase "Transcendental Idealism" should be treated as a figure of speech rather than something to be taken literally.
In my terms, Kant's phrase "Transcendental Idealism" includes both Epistemological Idealism and Ontological Realism. The problem is, how to link them ?
For the Ontological Idealist, ie for those not believing in the ontological existence of a mind-independent world, this is not a problem, as there is no "Ontological Realism".
However, for the Ontological Realist, it does remain problematic.
We can only ever have knowledge of representations in our mind. The belief that something mind-independent caused them we can justify in various ways. However, if we can never have knowledge of what caused these representations, we can never know that our belief is true.
For example, I have subjective knowledge of the colour red. I believe it was caused by a wavelength of 700nm. I can justify this using scientific procedures, but as science itself is founded on representation, a science founded on representation is incapable of getting behind the representations themselves.
David Stove's Discovery of the Worst Argument in the World addressed this problem, raising the inevitable conclusion that there is no way to get out.
IE, many justifications can be made for our belief in a mind-independent world, but none
as far as I know beyond doubt. One can only say that from the weight of evidence there is most likely a mind-independent world, and perhaps pragmatically that is all one needs.
Quoting Wayfarer
As my belief is that of Indirect Realism, I agree.
Quoting Wayfarer
It is true that I find it impossible to question the ontological existence of a mind-independent world.
Otherwise I would find it difficult to fill the kettle with water, switch on the kettle and put a tea bag into my cup if I didn't think these things were real and not a figment of my imagination.
Otherwise I would be diagnosing myself as schizophrenic, hallucinating about things that are not really there.
Otherwise, I would be diagnosing myself as having Dissociative Identity Disorder, in having long conversations about science and philosophy with myself, between two distinct personalities both existing in my mind.
IE, my sanity requires me to believe that I am interacting with a world that is mind-independent.
All due respect, you're misunderstanding what idealism means. Idealists do not think that the world is a figment of the imagination, although if you believe that is what they think, then I'm probably unable to set you straight on that.
I studied David Hume under David Stove as an undergrad. I liked Stove and respected him, but I'm afraid that his 'Gem' is rather a caricature. I mean, yes, there are those who abuse the kinds of arguments that Stove has in his sights, but there is a genuine philosophical insight that I think Stove is somehow missing. See this critique of 'Stove's Gem' (and I knew that writer, too - he's known for his writings on Aristotelian philosophy of maths).
Quoting RussellA
That's really not the case, but I grant, it is a very hard idea to fathom. See this primer.
There are different kinds of Idealism.
For example, as described by the SEP - Idealism, there is Berkeley's "Ontological Idealism", where the mind is the ultimate foundation of all reality, or even exhaustive of reality, and there is Kant's "Epistemological Idealism", where Idealism is not about any existence of things but only our representation of them.
IE, some Idealists think the world is a figment of the imagination.
Quoting Wayfarer
Berkeley's argument "the mind....is deluded to think it can and does conceive of bodies existing unthought of, or without the mind, though at the same time they are apprehended by, or exist in, itself" may be countered by common sense justifications.
Quoting Wayfarer
"Transcendental Idealism" does not address Stove's problem
Kant's "transcendental" is about a priori pure and empirical intuitions. Kant's "Epistemological Idealism" is not about any existence of things but only our representation of them.
The expression "transcendental idealism" can only be a figure of speech as it is about more than the transcendental and idealism, in that it does not include any reference to the world of the noumena, an important part of Kant's theory.
Experiencing certain phenomena through my senses, I have subjective knowledge of the colour red. I was born with the innate ability to perceive the colour red. "Transcendental idealism" is the combination of my innate ability to perceive red and my perceiving the colour red.
Using reason, understanding and imagination, I arrive at the belief that my perception of red was caused by light in the external world having a wavelength of 700nm. This light having a wavelength of 700nm is Kant's noumena.
IE, Kant's "Transcendental Idealism" does not address the problem of how we are able to know what precedes, if anything, our phenomena.
I'm with you in spirit, but perhaps we dream up those essences and only later learn to check if they or their implications are compatible with observations.
This might be truish but seems like 'bachelors are unmarried men.' There's also the problematic issue of 'private knowledge' (Cartesian baggage). I suggest, inspired by Robert Brandom, that to 'know' something is to take responsibility for a judgment. We are always already within the space of reasons. If you disagree, please make a case. (And there's the rub. )
Quoting RussellA
As I see it, the idea of the self always already includes the idea of the other. Your 'I' or 'self' is the bearer of responsibilities and entitlements, the 'virtual' source of deeds and claims, and the target of rewards and sanctions. It's absurd to rationally question the very framework of rationality. It's literally anti-social madness.
Berkeley's 'esse is percipi' principle wasn't meant in the sense of a speculative truth-apt empirical proposition, but as a grammatical norm for eliminating i) Cartesian doubt regarding the existence of the external world that inevitably arises when the world is thought of as being only knowable indirectly via intermediate mental representations and ii) Lockean doubt regarding the existence of either primary or secondary qualities, that arises when the 'subjective' content of perception is believed to be ontologically separate from 'objective' mathematical structure.
It is ironic that Berkeley's 'realist' critics misunderstand him by projecting their own deeply entrenched representationalism onto his remarks and then attributing to him the corollaries of their own positions.
Understood correctly, Berkeley was a defender of common-sense who cannot be interpreted as saying that the world is a 'figment of the imagination', unless the concept of 'imagination' is generalised to such an extent that it includes the content of all involuntary perceptions, to the point that the phrase "figment of the imagination" no longer says anything.
Private knowledge of representations
I observe an object in the world and have subjective knowledge of the colour red in my mind. As the object in fact emitted light of a wavelength of 700nm, my perception of the colour red can only be a representation of a wavelength of 700nm. My perception of red is private, in that no-one else will be able to perceive what I perceived. It is private knowledge and will forever remain private knowledge. And yet there is a public word "red" that allows me to discuss publicly what I have privately perceived.
My understanding of how this is achieved I wrote hereQuoting RussellA
Inferentialism and Representationalism are both required within language
For Brandom, the meaning of a sentence comes from its relationship with other sentences using inferential logic. This is along the lines of Wittgenstein's "meaning is use" in Philosophical Investigations.
As I see it, both Inferentialism and Representationalism are required within language.
Inferentialism is about coherence within a given language, and Representationalism is about correspondence between the language and the world. Inferentialism allows new ideas to be discovered by finding new relationships between existing ideas and Representationalism allows new ideas to be discovered in the world.
Reason and judgement are needed by both Inferentialism and Representationalism, whether the inferential logic of Inferentialism or the discovering of concepts in the constant conjunction of events in the world. As reason and judgement are attributes of the mind, they can only be the responsibility of the individual making that reasoning and judgement.
Inferentialism uses inferential logic within language itself, but as language exists publicly within the world, there is no difference in the way in which we perceive objects in the world within Representationalism and language as an object in the world within Inferentialism.
IE, our knowledge is always of representations of objects in the world, whether the subjective colour red in the mind representing the object 700nm in the world or the subjective concept red in the mind representing the public word-object red in the world.
Quoting igjugarjuk
I agree
The mind cannot change without a corresponding change in the brain
I am arguing from a position of Reductive Physicalism rather than Non-Reductive Physicalism, where mental states are nothing over and above physical states, and are reducible to physical states. For every actually instantiated property F, there is some physical property G such that F=G.
The mind exists within the brain. The brain is a physical structure and is the framework. The mind is the content. What is in the mind corresponds to what is in the brain. What is expressed in the mind must be in some way be expressed in the brain, in that the mind doesn't have a soul outside of time and space allowing it to act independently of the brain. The mind cannot change without a corresponding change in the brain.
The Self cannot inspect itself
Hume’s denial that there is an inner perception of the self as the owner of experience is one that is echoed in Kant’s discussion in both the Transcendental Deduction and the Paralogisms, where he writes that there is no intuition of the self “through which it is given as object”
On the nature of self-awareness, for example, in an unpublished manuscript Schopenhauer concurs with Kant, asserting that, “that the subject should become an object for itself is the most monstrous contradiction ever thought of”
The same can be said of the Wittgenstein of the Tractatus, who famously likens the self to the eye which sees but does not see itself.
Change cannot be spontaneous
A physical structure can be changed by something exterior but cannot spontaneously change itself, in that a snooker ball can start to move when hit by a snooker cue, but a snooker ball at rest cannot spontaneously start to move.
The brain is a set of physical parts. Each part may be changed by something exterior to the part, but each part cannot spontaneously change itself.
Even if there is nothing external acting on the brain, the brain may change because of the interaction between the parts that make it up. The brain as a whole is changed by its parts, not by the set of parts acting as a whole. The brain as a whole cannot be changed by the brain as a whole, meaning that the brain cannot change itself.
A framework consisting of a set of parts may change by the interaction between its parts, but not by the set of parts as a whole, ie, a framework cannot change itself.
IE, our rationality, our self, is not the content of the framework of the brain. Our rationality, our self, is the framework of the brain. As a framework cannot question itself, as you say, "It's absurd to rationally question the very framework of rationality."
I'm on a Brandom kick, so I'll mention his take. Representings are responsible to the represented thing, which functions like a target. Gadamer may come into play here. A kind of unspecified completeness is imagined from the beginning.
Quoting RussellA
From a certain perspective, reason and judgement and the mind are abstractions or fictions, just like the self, just like responsibility. It looks to me that we have an entire system here of inherited concepts, which only make sense together.
Imagine practical animals who start with a limited cognitive vocabulary, which they use relatively rationally to thrive together in their environment. Now imagine the slow development of a metacognitive vocabulary, with words like 'judgment' and 'epistemology' and 'responsibility. ' As I see it, one accomplishment of philosophy has been to make the sociality of reason explicit to itself.
I think this is fairly reasonable but still a little problematic. As long as the mind is (understood as) a factory of stuff that will "forever remain private knowledge," it's hard to see how anything comprehensive can established about it. The lurking assumption is that there is just one 'forever private' experience of red (for instance.) But 'forever private experience' opens up an abyss of possibility. It's outside the space of reasons. At the minimum we need claims, entry into the symbolic realm, such as 'The square looks red to me.' (Or a recorded measurement of a change in heart-rate, etc.)
The 'self' I'm talking about is the persona or reputation. A rough analog is your LinkedIn profile. The metaphysical subject, on the other hand, is a hot mess. I agree with Kant and Hume that no such subject is available (or not one worth bothering with.)
I like Brandom because to me he's just describing the philosophical situation itself ( the interpersonal structure of rationality. ) For instance, you mention Hume's denial. A 'scorekeeping' conception of rationality will emphasize how we'll contextualize this denial against Hume's other claims. Hume is like an actor on a stage among other actors. His speeches are unified as his speeches..and interpreted as such a unity. As are we. This social situation seems basic to rationality.
Nice post on Berkeley. I'm glad to hear he's more sensible than the cartoon version of him.
In all my years as a mathematician, however, I must confess that I have never worked in applied mathematics. Like most in my profession, I explored an intriguing abstract concept. Still do.
If you start with a logical system, it shouldn't be a surprise that you end up with something logical.
Not only do we use logical. I would make the bold declaration that animals use logic, even if they don't understand they are using logic.
I guess I was just emphasizing what Popper also emphasized. Theory creation ('projecting' a pattern on reality) can itself be 'irrational' or mysterious without science failing to be science. This is because the science consists in the way we treat such theories, independent of their source. Another common point is that theory guides observation in the first place (tells us what to look for, frames the situation.)
I think this makes sense, though folks can fuss over the ideal application of 'use.' Along these lines we can picture a distinctly human metacognition laid on top of an inherited and more common animal cognition.
Did Berkeley believe that the world is a "figment of the imagination"
Bertrand Russell The Problems of Philosophy - 1912
He then proceeds to consider common objects, such as a tree, for instance. He shows that all we know immediately when we "perceive" the tree consists of ideas in his sense of the word, and he argues that there is not the slightest ground for supposing that there is anything real about the tree except what is perceived. Its being, he says, consists in being perceived: in the Latin of the schoolmen its "esse" is "percipi." He fully admits that the tree must continue to exist even when we shut our eyes or when no human being is near it. But this continued existence, he says, is due to the fact that God continues to perceive it; the "real" tree, which corresponds to what we called the physical object, consists of ideas in the mind of God, ideas more or less like those we have when we see the tree, but differing in the fact that they are permanent in God's mind so long as the tree continues to exist. All our perceptions, according to him, consist in a partial participation in God's perceptions, and it is because of this participation that different people see more or less the same tree. Thus apart from minds and their ideas there is nothing in the world, nor is it possible that anything else should ever be known, since whatever is known is necessarily an idea.
IEP - George Berkeley
Berkeley’s famous principle is esse is percipi, to be is to be perceived. Berkeley was an idealist. He held that ordinary objects are only collections of ideas, which are mind-dependent. Berkeley was an immaterialist. He held that there are no material substances. There are only finite mental substances and an infinite mental substance, namely, God.
AC Grayling - Berkeley's Argument for Immaterialism
Berkeley's philosophical view is often described as an argument for "immaterialism", by which is meant a denial of the existence of matter (or more precisely, material substance.) But he also, famously, argued in support of three further theses. He argued for idealism, the thesis that mind constitutes the ultimate reality. He argued that the existence of things consists in their being perceived. And he argued that the mind which is the substance of the world is a single infinite mind – in short, God.
Blake Winter - Berkeley's Arguments on Realism and Idealism
Bertrand Russell credited Berkeley with being the first philosopher to show that the position of idealism may be held without contradiction (Russell, 1997). However, in addition to this, Berkeley also attempted to show that realism was absurd, because it required concepts which could not in fact be conceptualized (1977). From this, Berkeley concluded that idealism was not merely possible but necessary, or at least necessarily the only theory we could understand. That is, he concluded that we are epistemologically forced to renounce realism in favour of idealism.
We will take realism to mean the ontological position that there are things which exist that are neither minds nor ideas in minds. We will take idealism to mean the ontological position that everything that exists is either a mind or an idea in a mind.
If Realism is the belief in a mind-independent world, and Idealism is also a belief in a mind-independent world, then how do Realism and Idealism differ ?
Realism may be defined as the ontological position that there are things which exist that are neither minds nor ideas in minds. Idealism may be defined as the ontological position that everything that exists is either a mind or an idea in a mind.
From the above texts, Berkeley's position was that of Idealism, believing Realism to be absurd. Berkeley was also an Immaterialist, in that there are no material substances but only ideas in the mind and ideas in the mind of God. Berkeley may admit that the tree continues to exist when we shut our eyes, but this continued existence is due to the fact that it remains as an idea in the mind of God.
Imagination is defined as the faculty or action of forming new ideas, or images or concepts of external objects not present to the senses.
IE, as Berkeley's position is that all that exists in either in our minds or the mind of God, and as something that exists as an idea is part of an imaginative rather than real world, I stick by my statement that "some Idealists think the world is a figment of the imagination", including Berkeley.
Yes, as with Kant's a priori pure and empirical intuitions, people have a historically-effected consciousness and they are embedded in the particular history and culture that shaped them. Given this, our interpretation of the world is a matter of "the give-and-take of question and answer, and our understanding of the world changes with the questions we ask of the world and the answers we get back.
Quoting igjugarjuk
Yes, as with Kant's a priori pure and empirical intuitions, which provides the framework of the mind, as you say: "we have an entire system here of inherited concepts". Through millions of years of evolution we have an inherited framework of the brain, and consequently the mind and self, which of necessity sets limits to what we are able to reason and judge.
Quoting igjugarjuk
However, even if I may never know your particular subjective experience when observing a wavelength of 700nm, through reason, judgment and imagination, I am able to gain an extensive understanding about it.
The tool we use is language, allowing private sensations to be publicly discussed.
For example, the start of the Universe may forever remain private to us, yet through reason scientists have developed a cosmological model explaining the existence of the observable universe from the earliest known periods through its subsequent large-scale evolution. They have understood how the universe expanded from an initial state of high density and temperature, and have offered a comprehensive explanation for a broad range of observed phenomena, including the abundance of light elements, the cosmic microwave background (CMB) radiation, and large-scale structure.
IE, even private experiences are not outside the space of reason, if the tool we use to understand them is language.
Quoting igjugarjuk
Yes, in the world is the mind and the mind-independent. Yet the mind is part of the world, so the mind must share characteristics with what is mind-independent, giving us a link between the mind and what is mind-independent.
In a sense, the mind and the mind-independent make up one unity, giving the mind the possibility of being able to understand the mind-independent, because the mind has evolved in synergy over millions of years within the world. The mind is a product of the world, as is that which is mind-independent.
IE, the mind and mind-independent are part of one greater unity, the world.
That is to say, take the matryoshka doll for example. You have two in front of you. Any able-visioned person not familiar with the item would conclude you have two dolls. However, if you know more than what can be currently seen (modern science) you would there is in fact much more than two. Same can be implied with half-life and various chemical reactions not yet understood.
Say you know every chemical reaction with 99.99% of possible elements except for one unknown combination never tried before. Due to not properly understanding the nature of it's reactivity you may reach an unexpected result. This is how medicine and chemistry works. The math is not wrong, per se (that is to say, yes, 1 understood value and 1 understood value will equal 2 or it's expected value), simply that there are additional variables that are unknown.
I speculate my specialty (infinite compositions of complex functions) is a solution awaiting a problem. :cool:
I hope something comes along and make your work suddenly practical. That'd be exciting. I know it's happened for some mathematicians. (I'm a lesser angel in the field myself, working more in programming languages these days, though, for better or worse.)