• Wayfarer
    21.1k
    Mathematics only seems unreasonably effective because we don’t notice the sleight of hand we perform by forcing aspects of the world into idealized objects that persist identically and then apply mathematical calculations to these constructed idealities.Joshs

    I don't accept that, it's reductionist. I'm just as opposed to "scientism" as you are, but I don't buy this idea that mathematics and science is simply a projection or solely an invention. They're also discoveries, something uncovered or revealed about nature, which we are able to discern because of reason and mathematics.

    John Vervaeke is completely on-board with the 4E approach - embodied, embedded, enacted, and extended by way of extra-cranial processes and structures. I am reading up on that and trying to understand it better. But he also advocates for a kind of modernised neoplatonism, and remains committed to natural science. He's not a post-modern theorist (although I'll look out for anything he might say about that.)

    This we may call the phe­nomenal world or the self-world of the animal.

    Totally get that. Umswelt and lebenswelt. I have learned about those concepts here on this forum. But none of that detracts from or undermines the reality of mathematics and the objects of reason. Those are also very much part of the lebenswelt of h. sapiens. But they're neither 'in the world' nor 'in the mind' but are characteristic of our experience-of-the-world, which is quite different to the experience-of-the-world of spiders, birds and bats (god bless 'em.)

    when we replace one niche, paradigm, worldview for another, the old logical relations either become irrelevant or we change the sense of the concepts they refer to (Newtonian vs Relativistic).Joshs

    Totally on board with that, also. Still doesn't mean 'number is invented'.
  • Janus
    15.8k
    This perspective suggests that universals have a kind of reality that is both independent of individual human minds and intimately connected to the rational structure of the universe.Wayfarer

    I'd say universals are inherent to cognition because cognitively enabled organisms could not survive without re-cognition, which involves pattern discernment and of course memory. If any sentient being's umwelt was a play of unrelated and unrelatable particulars (James' "buzzing, blooming confusion") no orientation would be possible; the animal would not be able to recognize food, water, prey, predator, shelter, and so on.

    So, recognition is the seed of generality, of universals; an essential aspect of cognitive apprehension of anything. Symbolic language of course enables this implicit recognition to be explicitly elaborated into the conception of universals.
  • Joshs
    5.3k
    John Vervaeke is completely on-board with the 4E approach - embodied, embedded, enacted, and extended by way of extra-cranial processes and structures. I am reading up on that and trying to understand it better. But he also advocates for a kind of modernised neoplatonism, and remains committed to natural science. He's not a post-modern theorist (although I'll look out for anything he might say aboutWayfarer

    I would say that Vervaeke subscribes to what I would consider a more conservative variant of enactivism than do Gallagher, De Jaegher and Thompson. I agree that he is not a postmodernist, and that his approach is quite likely consonant with yours.
  • Wayfarer
    21.1k
    :up: I don't know yet if I'm on board with everything Vervaeke says, but I'm learning a lot listening to him, especially how to map philosophical concepts against systems science.

    recognition is the seed of generality, of universals; an essential aspect of cognitive apprehension of anything. Symbolic language of course enables this implicit recognition to be explicitly elaborated into the conception of universals.Janus

    Right. And it's a difference that makes a difference!
  • Janus
    15.8k
    Right. And it's a difference that makes a difference!Wayfarer

    Yes, I agree it most certainly is. There is no rational requirement to deny that what is real for humans in general is "really real" on the basis that we don't think it is real in itself. I'd go even further and say that what is experienced by any individual is what is most real for that individual and that what is experienced by all individuals is what is most real for humanity.

    Still doesn't mean 'number is invented'.Wayfarer

    I agree—recognition and thus the workability of cognition itself entails difference and similarity, which in turn entails diversity and kind and thus generalities and number.
  • Wayfarer
    21.1k
    Philosophically, though, the point of difference I want to establish against evolutionary naturalism, is that such abstractions are not necessarily the product of evolution. While evolutionary naturalism provides a pretty comprehensive account of the development of cognitive capacities, it does not necessarily account for the nature of the abstract entities these capacities enable us to apprehend. The ability to cognize abstractions, such as mathematical truths, may be an evolved trait; however, the abstractions themselves are not products of evolution. Instead, they represent cases of exaptation, where a cognitive capacity evolved for one function is repurposed to engage with another: in this case, the realm of objective (or 'transjective') truths that transcend biological adaptation. (This is what I mean by 'transcending biology'.) It challenges the reductionist view that everything about us can be fully explained through the lens of biological adaptation. The argument relies on the inherent capacity of the human mind to grasp transjective truths uch as mathematical proofs and logical principles, which exist independently of our evolutionary history, but which are able to be discerned by h. sapiens. This approach does not appeal to religious revelation but instead emphasizes the autonomy of reason, so is in line with the approach of Greek rationalism. And there's nothing in it which relies on falsifying the empirical records of evolutionary history, but I think it corrects the reductionist tendencies which often result from 'popular Darwinism'.
  • Janus
    15.8k
    I don't see the question you are asking— that is, simply put, "how is abstraction possible" as being capable of an answer. I tend to think that questions that cannot be answered are, discursively speaking, non-questions. however interesting or inspiring they may otherwise be.

    So, I agree with you that science cannot answer such a question, however I don't think there is any other way to answer it either (which is not to say there are not various ways to think about it).
  • Joshs
    5.3k


    —recognition and thus the workability of cognition itself entails difference and similarity, which in turn entails diversity and kind and thus generalities and numberJanus

    Recognition does involve difference and similarity, but number requires the concept of identity , the repetition of the exact same. We look at an aspect of the world and construe that aspect on the basis of ways in which it appears similar to previous events and differs from others. When we count 1,2,3 instances of a ‘this’, we assume that the categorical whole , the ‘this’ , of which we are counting instances ( apples, people, trees) , remains identical in its meaning for the duration of the counting. If the ‘this’ changes its meaning and became a new ‘this’ every increment of the counting we could only ever count one instance of it before having to start the count over. What allows us to enumerate is a convenient ignoring of the fact that similarity in the real world never means identity. So we invent the device of numeric identity, the exact same, which is very useful but at the same time covers over intricate changes in what is being counted.

    As Heidegger expressed it:

    “The same never coincides with the equal, not even in the empty indifferent oneness of what is merely identical...The same…is the belonging together of what differs, through a gathering by way of the difference. We can only say "the same" if we think difference.
    “The most insidious manner of forgetting is the progressive "repetition" of the same. One says the same with a constantly new indifference; the mode of saying and interpreting changes.
  • Joshs
    5.3k
    The ability to cognize abstractions, such as mathematical truths, may be an evolved trait; however, the abstractions themselves are not products of evolution. Instead, they represent cases of exaptation, where a cognitive capacity evolved for one function is repurposed to engage with another: in this case, the realm of objective (or 'transjective') truths that transcend biological adaptation. (This is what I mean by 'transcending biology'.) It challenges the reductionist view that everything about us can be fully explained through the lens of biological adaptation.Wayfarer

    The most valuable idea buried within the biological concept of exaptation is that meanings , purposes and other living patterns of organization can be re-invented in ways that are not logically derivable from the previous schemes of organization. The limitation of the concept as it is usually employed is that it makes such inventiveness secondary to and derived from deterministic causal mechanisms. I think people slip into reductive determinism to ground process of change for the same reason that you want to ground human rationality in something that transcends or precedes exaptation. That is, if I were to propose a notion of exaltation not based on mechanisms of efficient causation, you would find it not grounded enough. Becoming, untethered from any conception of the right path, the true source, the objectively real, is just meaningless chaotic drift.

    But not all relativistic philosophies of becoming see historical change as directionless from an ethical or empirical point of view. The direction is always toward the most intimate engagement with contextual circumstance that is possible via mindful skilled coping. The use of propositional, logical, mathematical axioms and conceptual abstractions flattens and conceals the intimacy of change in our perceived world , which reinvents itself just as continually as humans invent understandings to anticipate and cope with it. Our mathematical abstractions appear to ‘slow down’ the creative becoming of the world enough to make us convince ourselves that the world gives itself to us ‘naturally’ as transjective universals. The price we pay for such illusions is a world that is alternatively self-identical and arbitrary.

    An inherent violence attaches to the becoming of the world in the extent to which change is construed as arbitrary. The perceived arbitrariness and externality of change is in turn a function of how we understand beings to BE in themselves as mathematically self-present.
  • Janus
    15.8k
    Recognition does involve difference and similarity, but number requires the concept of identity , the repetition of the exact same.Joshs

    Kind and generality consist in identity. Each particular is unique, so there is no identicality of particulars. Things are counted as being of the same kind, so there is identicality of kind.
  • Joshs
    5.3k
    Kind and generality consist in identity. Each particular is unique, so there is no identicality of particulars. Things are counted as being of the same kind, so there is identicality of kindJanus

    Exactly. We invented the concept of ‘same kind’ in order to count, but same kind doesn’t exist in nature.
  • Paine
    2.1k
    Exactly. We invented the concept of ‘same kind’ in order to count, but same kind doesn’t exist in nature.Joshs

    I get the argument that the concept serves a purpose in how we talk. The claims about what exists in nature seems to contradict the limits presented regarding such description. But how does that let us say what exists in nature?
  • Janus
    15.8k
    Exactly. We invented the concept of ‘same kind’ in order to count, but same kind doesn’t exist in nature.Joshs

    Something must exist in nature that would support the judgement of 'kind' otherwise how would we have arrived at the idea? Animals generally associate with their own kinds, and for that matter 'animal' is a different kind than 'plant', and 'human' is a kind of animal. Then we have the biological and non-biological kinds of substances and even the different kinds of microphysical "particles".

    So, I am not convinced we are entitled to say that kind does not exist in nature, I think the evidence points rather to the conclusion that kind does exist in nature, on every level of being.
  • Wayfarer
    21.1k
    We invented the concept of ‘same kind’ in order to count, but same kind doesn’t exist in nature.Joshs

    Flocks of birds, schools of fish, all comprise collections of ‘the same kind’. There are repetitions and patterns and instances of ‘the same kind’ in nature. How is that not so?
  • Joshs
    5.3k
    Flocks of birds, schools of fish, all comprise collections of ‘the same kind’. There are repetitions and patterns and instances of ‘the same kind’ in nature. How is that not so?Wayfarer

    It comes back to the issue of identity. Same kind is not identical kind. The same only continues to be itself slightly differently from one moment to the next. Iterability produces
    "an imperceptible difference. This exit from the identical into the same remains very slight, weighs nothing itself...". “It is not necessary to imagine the death of the sender or of the receiver, to put the shopping list in one's pocket, or even to raise the pen above the paper in order to interrupt oneself for a moment. The break intervenes from the moment that there is a mark, at once. It is iterability itself, ..passing between the re- of the repeated and the re- of the repeating, traversing and transforming repetition.”“Pure repetition, were it to change neither thing nor sign, carries with it an unlimited power of perversion and subversion. (Derrida)
  • Joshs
    5.3k
    I get the argument that the concept serves a purpose in how we talk. The claims about what exists in nature seems to contradict the limits presented regarding such description. But how does that let us say what exists in nature?Paine

    I should have said that it is the nature of a meaning intention that contextual change intervenes in the repetition of the same ‘identity’. For Husserl, number in itself is not tied to anything but itself. Enumeration, as an empty ' how much', abstracts away all considerations that pertain to the nature of the substrate of the counting, including whether that substrate offers itself up for measurement in qualitatively or quantitatively changing increments. Enumeration represents what Husserl calls a free ideality. Derrida characterizes this feature of number in the following way;
    “I can manipulate symbols without animating them, in an active and actual manner, with the attention and intention of signification(crisis of mathematical symbolism, according to Husserl) .”

    “Now, Numbers, as numbers, have no meaning; they can squarely be said to have no meaning, not even plural meaning. …Numbers have no present or signified content. And, afortiori, no absolute referent. This is why they don't show anything, don't tell anything, don't represent anything, aren't trying to say anything. Or more precisely, the moment of present meaning, of “content,” is only a surface effect.”

    Numeric idealization is unbound (within the strict limits of its own repetition); no contextual effects intervene such as was the case in the attempt to repeat the same word meaningfully.
12345Next
bold
italic
underline
strike
code
quote
ulist
image
url
mention
reveal
youtube
tweet
Add a Comment

Welcome to The Philosophy Forum!

Get involved in philosophical discussions about knowledge, truth, language, consciousness, science, politics, religion, logic and mathematics, art, history, and lots more. No ads, no clutter, and very little agreement — just fascinating conversations.