7

I'm reading Mathematics: Its Content, Methods and Meaning. The authors make what is to me a surprising claim:

To put it briefly, truth is concrete; and it is particularly important to remember this fact with respect to mathematics, exactly because of its abstractness.

Is truth concrete? How is this claim justified?

Gavin
  • 173
  • 1
  • 5

4 Answers4

7

The context of the quote is (see page 18):

Arithmetic (and mathematics) is abstract.

Why does arithmetic have such wide applications in spite of the abstractness of its concepts ?

The answer is simple. The concepts and conclusions of arithmetic, which generalize an enormous amount of experience, reflect in abstract from those relationship in the actual world that are met with constantly and everywhere.

Thus, the "abstraction process" relies on the external reality.

Reality is concrete and mathematics is abstract: truth is concrete because it has to do with "the way the world is".

We may consider also a "more subtle" point of view: Andrey Kolmogorov was a 20th-century Russian mathematician that contributed to many area of mathematics, included the so-called Brouwer–Heyting–Kolmogorov interpretation (1925) of intuitionistic (and constructive) logic.

In a nutshell, according to this point of view, to assert the truth of a judgment amounts to have a proof of it.

Community
  • 1
Mauro ALLEGRANZA
  • 36,790
  • 3
  • 36
  • 80
  • I don't see how you infer concreteness of truth from the fact that it represents the way the world is. As I have suggested in my answer that for me implies the exact opposite, for truth to represent the world it has to be non-concrete! – infatuated Jun 28 '17 at 19:28
  • This answer has more up votes, but I'm reluctant to choose it because @jobermark seems to me to have given a better one below. Isn't truth a claim based on a comparison? (See my comment below on his answer.) I would be interested to see an argument against this. – Gavin Jul 03 '17 at 00:42
  • 1
    @Gavin - the acceptance process is not based on "polling". The answer you have to accept (if nay) is the answer to your question. Thus, you are free to choose the answer that you prefer or that helps you more than others. :-) – Mauro ALLEGRANZA Jul 03 '17 at 06:01
2

You might defend the notion that truth is concrete, but only by adopting physicalism absolutely, and by claiming that what we ordinarily consider 'truth' is only a reference to the agreement of truth to some physical instantiation.

If any abstraction that cannot be considered concrete exists, then obviously truth is not concrete. But under a physicalist mindset, one would have to claim that those do not, in fact exist. All true facts would refer to configurations of physical states, which can be considered concrete.

Still, what we generally mean when we talk about truth is not a physical state, it is the agreement of that state with an idea, and in no physical way does the state match the idea. So you would need an interpretation of truth that equates mental referents with the things they are referring to.

All this requires a lot of mapping, and the assertion of physicalism itself requires an incredible quantity of mapping and equivalence that may not, in fact be possible to pull off.

So this remains an extraordinarily contentious position, but not an indefensible one.

  • The truth of the matter can be obtained much easier. Like I said in one of our earlier discussion, the very fact that we perceive ideas as independent of physical matter is a sufficient proof that they are not physical stuff. Another proof is what I briefly mentioned in my answer. Physical entities are identical and therefore can't represent other physical entities while ideas can do this. – infatuated Jun 28 '17 at 19:30
  • @infatuated Most folks don't consider what you consider sufficient to actually be sufficient. There are still a lot of physicalists in the world. If the fact and the brain configuration that represents perception its truth are made of atoms, and appear in correlation, that is a physical configuration. Surely the magnetic areas holding the bits in an image file represent the colors in the corresponding printed image. You seem far too ready to believe very inadequate statements as facts. –  Jun 28 '17 at 21:43
  • I am not even, at base, a physicalist, and I don't accept most of the arguments you have made here about the subject. –  Jun 28 '17 at 21:48
  • Those folks just represent the limits of Western philosophy. But I'm coming from a unique civilizational domain with our own distinct philosophical heritage that is today not represented in the Western academia. You said my proof is not sufficient but didn't explain why. My proof is not based on neurology since my method is not sensual observation but rather intellectual intuition, a method that Muslim scholars of rational psychology developed into a substantial scientific discipline of its own right. I'm not dismissing natural science but that only studies what occurs on the natural level. – infatuated Jun 28 '17 at 21:57
  • @infatuated I DID SAY WHY. I directly addressed one of your central points. pointed out that physical things are used to represent other physical things. I gave two examples. Brain states representing facts and magnetic recording representing an image. Don't ignore what I am saying and claim I didn't say it. –  Jun 28 '17 at 22:12
  • With the bad slip of tongue I made in my comment and answer, I realized we've been too far from a proper communication. My pardon! But as seen in my corrected answer my point is that abstract concepts represent things that are each unique because of their specific attributes in time and place. And by representation I don't mean a causative relation as in your brain configurations thesis, but rather the ability to stand up for or represent the meaning of a multitude of things that are each distinct yet share some general shared qualities and that's what abstract things do. – infatuated Jun 29 '17 at 06:11
  • @infatuated I do not mean a causative relationship either. The brain does not cause the fact, but it does represent the fact, there is some chemical form of the memory of the fact. I don't care what you would like to redefine representation as, letters represent sounds, memories represent events, it happens. –  Jun 29 '17 at 15:54
  • Although this answer is not the most up-voted, it appears to me to be the best answer. "...truth is not a physical state, it is the agreement of that state with an idea...". Truth is a determined by comparison. "Is it true that both of these objects contain iron?" The objects may both contain iron even in the absence of comparison, but without the comparison, there is no truth established. Is it true that 2+2=4? It is, but, again, without the comparison, the issue of truth does not appear. These examples, both concrete and abstract, illustrate @jobermark's point. – Gavin Jun 30 '17 at 00:44
1

Truth whether as in statements that employ general abstract concepts to describe reality or as a meaning itself, is not concrete even though it is abstracted from concrete reality. For if it were concrete we could not use it to describe and represent other concrete things, just as you can't use concrete water to represent concrete fire or even another concrete water because concrete stuff are all unique and don't match.

This is one way abstract concepts distinguish themselves from concrete sensible things. This thesis also forms the cornerstone of Theist philosophers' argument for immateriality of human consciousness. The modern consensus though assumes that such rational metaphysics was undermined by Kant's critique of pure reason however Kantian philosophy itself is highly problematic.

infatuated
  • 1,665
  • 10
  • 15
  • There is no sense in which concrete things are all identical and don't match. Words on a page represent ideas. They match, to some degree. –  Jun 28 '17 at 22:19
  • @jobermark, You're right I realized I have used the wrong word and fully falsified my point. I meant that all concrete things are unique rather than identical which means the exact opposite of what I meant. I edited my post. – infatuated Jun 29 '17 at 05:59
  • the printed words only considered separate from their unique time and place can albeit imperfectly represent other similar words but then they would no longer be physical entities but rather images in our imagination. And there's no way for the physical representation of the general shapeless, colorless idea of 'word' that can represent all particular words regardless of their specifics physical properties in the external world. – infatuated Jun 29 '17 at 06:16
  • I guessed that, it is still false when the vocabulary is corrected. The uniqueness of physical entities does not imply they don't represent things. The physical letter 'A' on a page can both be itself and represent many things in different contexts. A physical thing does not have to be a material object at a given time and place. Warmth is physical, so is light. –  Jun 29 '17 at 16:03
  • All your arguments are just begging the question -- you think the idea of ideas means real physical representation is impossible, but your proofs are just references back to this unproven assumption. Words may be considered complex patterns of behavior. That would make them physical things. –  Jun 29 '17 at 16:04
  • @jobermark. You're still not getting my notion of representation and I think it's my fault. So let me clarify by example: an abstract concept of human being represents the meaning of all individual humans despite all their specific physical/material attributes, a function unique to ideas. (And note that I ever use material in the traditional sense not modern, synonymous to physical and natural). Other notions of representation you bring up either point to our subjective association of ideas with sensations or bodily processes that accompany our mental/lingual functions. Wholly different! – infatuated Jun 29 '17 at 17:33
  • @infatuation Not wholly different -- grounded in observation. You are convinced that physicalism is false, that means you get to make definitions that assume physicalism is false, and use them to supposedly prove that physicalism is false. But there are problems with these assumptions. If you will not consider anyone else's interpretation of the same word, you can refuse to take them seriously, and just assume your assumptions, but they don't have to take you seriously either. The result is not an argument, it is two arrogant groups not talking. –  Jun 29 '17 at 17:40
  • There is no way that you know that meaning is independent of behavior. And if meaning is just an aspect of behavior, it is physical. Your internal impression of what ideas are is just a feeling, and it is far more subjective than the things you are dismissing as subjective. –  Jun 29 '17 at 17:45
  • @jobermark Let me again clarify. When I say subjective association of ideas with sensations I'm referring to your example of how letter A can represent different things in different contexts. I guess one way of that would be through different meanings that we would read in words that employ letter A. This form of representation is though based on our lingual conventions of how letter A and other letters are written and pronounced and conventions about meaning that words represent. – infatuated Jun 29 '17 at 19:05
  • This is what I meant with saying subjective association of ideas with sensations because letter A considered as some ink on paper will only cause sensations in us. But all the ideas that it seems to represent are in fact generated by our our human subjective conventions. But all of these have just been unrelated to the notion of representation that I'm arguing from here, or maybe just a corroboration of all that I mean to argue along: that only ideas because of their abstract nature can represent multitude of distinct concrete stuff. – infatuated Jun 29 '17 at 19:09
  • But letter A considered only as ink on paper can't represent anything else by its own virtue. If it invokes other things in our mind, it is because of our subjective associations. So as you see unlike your assumption we can distinguish nature of abstract ideas among our other mental entities and how they work by introspective and analytic insights which I have seen to clearly demonstrate their immaterial nature. I know this thesis has to still answer endless questions by science but good news Islamic rational psychology has encountered and survived these modern scientific objections! – infatuated Jun 29 '17 at 19:20
  • You don't seem to realize that computers exist, or that animals and other physical systems use information. Representation does not necessarily involve a human. If a scent makes a dog think about another specific dog, the urine has represented something. Not all the meanings things 'seem' to represent can then be 'generated by our human subjective conventions.' This is an outdated notion from late Aristotelians, it has been challenged, and you are ignoring a long history of people rejecting this logic. What you need to do is not repeatedly 'clarify', it is take the objections seriously. –  Jun 29 '17 at 21:04
  • Part of the point you are missing is that subjective thought is to some degree biologically recorded. You emotionally respond to something because it causes biological changes. So declaring those all not to be concrete doesn't really pass muster. You can declare yourself superior to the scientific worldview, but without engaging the actual issues, that is just arrogance. –  Jun 29 '17 at 21:09
  • @jobermark Believe me I'm not heedless of all ur supposedly counter arguments/examples. I've already said I don't deny that all of our mental activities and thoughts have biological effects. But if there is some additional immaterial agency running along all those observable biological effects, one can never know a thing about them via sensual methods. No doubt animals also associate thoughts with sensations. But since we are not animals we can not study their subjectivity neither that of computers. But u readily dismiss things our intuition reveal to us about some aspects of our existence. – infatuated Jun 30 '17 at 14:11
  • As for computers to avoid more misconception. Obviously computers don't have subjectivity yet I have been convinced by philosophical proofs from my own tradition that for all worldly phenomena there is corresponding immaterial agency. And the proofs come from intuitive contemplation. And I'm talking about a tradition far more advanced and sophisticated than its counterparts in the Western tradition such as Neoplatonism or Cartesianism, and one that also responds to questions by modern biology and physics. – infatuated Jun 30 '17 at 14:29
1

Truth about Truth, whether it is about mathematics or any other sciences must be the same always. So I didn't consider mathematics here. If we verify mathematics closely we can understand that it deals with abstract ideas though it seems to be concrete.

From a very lower level we can say truth is concrete. They (most facts) exist for a short time; our senses help to perceive so. But truth is/must be immutable.

Since these concrete 'things' undergo changes, we cannot treat them as truth. So the only thing we can do is to imagine that. That means, we can only say that truth is abstract.

But when in the case of the Ultimate Truth, it is beyond these two. The Ultimate Truth transcends concreteness and abstractness. It can't exclude your self/our self. The proof is, Truth can be realized. And there were/are many living examples who realized the Truth.

Sometimes we say 'Now I understand the truth'. Since understanding is a mental process only, we can't say so actually. The greatest wonder is, we (most men) are ignorant about that--the thing that is beyond concreteness and abstractness. We can think only of a concrete thing or an abstract thing.

If Truth is abstract,

'Concreteness produced from Abstractness'....There is something illogical. Then we will be compelled to say every thing is abstract.

You will get some explanations from this article.

SonOfThought
  • 3,743
  • 1
  • 9
  • 18
  • That was a good step towards full truth! Neoplatonism argues for existing of non-material simple wholes from which both abstract and concrete stuff emanate forth! What is decidedly more significant is that Muslim Neoplatonists have explained how this thesis can be empirically realized via intuition and introspection! – infatuated Jun 28 '17 at 19:34