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'.

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.

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 — Wayfarer

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.

: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!

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.

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'.

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).

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

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.

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.

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.

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 — Janus

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

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?

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.

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?

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)

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.

It comes back to the issue of identity. Same kind is not identical kind. — Joshs

Kind is an abstraction from natural regularities, and as such is a fixed or static identity. Abstractions, like number, are static, although obviously their instantiations are not.

Aristotle would thank you if he were not otherwise occupied.

]"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

I must respectfully disagree with the passage from Derrida, which I find to be 'nonsense on stilts.' Identity, or what things are, is a fundamental constituent of rational thought and cognition. Even the simplest animals must identify kinds and types to navigate their environments.

In focusing on the abstraction involved in identifying kinds and likenesses, it's an overstatement to claim there are no kinds, repetitions, or likenesses in nature. These elements are plainly evident and essential; without any similarity or repetition, there would be only chaos.

To try and focus the issue with respect to Greek philosophy, the reason arithmetical knowledge was held in high esteem by the Greeks was because of its exactitude and apodicity:

Neoplatonic mathematics is governed by a fundamental distinction which is indeed inherent in Greek science in general, but is here most strongly formulated. According to this distinction, one branch of mathematics participates in the contemplation of that which is in no way subject to change, or to becoming and passing away. This branch contemplates that which is always such as it is and which alone is capable of being known: for that which is known in the act of knowing, being a communicable and teachable possession, must be something that is once and for all fixed. — Jacob Klein, Greek Mathematical Thought and the Origin of Algebra.

(Emphasis added.)

Arithmetical proofs are not contingent - they are, as it were, perfectly intelligible to reason. Whereas empirical truths, or sensory knowledge, was held to be of a lower order - because the senses may deceive, because things may not be as they appear. That is the sense in which arithmetical and logical knowledge is regarded as 'higher' or more trustworthy than sensory data. Ultimately, this was because arithmetical proofs and logical laws are nearer to 'the unconditioned' (hence the italicized phrase above). To put that in the context of traditional philosophy, generally, rational principles and universals are nearer to the One than are sensible particulars. That even survived until the 17th C:

In contrast to contemporary philosophers, most 17th century philosophers held that reality comes in degrees—that some things that exist are more or less real than other things that exist. At least part of what dictates a being’s reality, according to these philosophers, is the extent to which its existence is dependent on other things: the less dependent a thing is on other things for its existence, the more real it is. — 17th Century Theories of Substance, IEP

I think that is what has been lost to the mainstream of Western philosophy, due to the decline of Platonic realism and the ascendancy of nominalism and empiricism.

I think where abstraction and quantification becomes pernicious is precisely in draining the world of the fleeting qualities of immediacy, now-ness, presence- of being, in fact. That's what I think the sources you mention ultimately have in their sights, isn't it? But I think that, if only the respect for arithmetical and logical principles that traditional philosophy had are retained, but the aesthetic and ethical principles that animated it are abandoned, that's what leads to 'the reign of quantity'. Which is precisely the 'cultural impact of empiricism'. That's what culminates in eliminative materialism and the idea that mind is the product of physical principles. It is the hallmark of a secular age.

I think what has really gotten lost in modern philosophy of all schools, is any orientation towards the unconditioned. And how to talk about it without falling back into tired religious tropes or metaphysical dogma. There is nothing that maps against it in the current lexicon, and it's not generally discussed, and if it is, it's couched in the lumbering verbiage of a 'philosophical absolute' or something similar. This, I think, is one of the major underlying themes of Vervaeke's Awakening from the Meaning Crisis.

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. — Janus

I'd say this abductive shift is key in these sorts of arguments. "Which is more rational or plausible? To say that kinds do exist, or to say that they do not exist?"

:lol: :cool:

:up:

I must respectfully disagree with the passage from Derrida, which I find to be 'nonsense on stilts.' Identity, or what things are, is a fundamental constituent of rational thought and cognition. Even the simplest animals must identify kinds and types to navigate their environments. — Wayfarer

:up:

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

Derrida wants to say here that the old ontological metaphysics, built around the notion of ‘presence’, is over. It means that the present that eludes our consciousness is the other, always unknown side of what sustains ‘pure repetition’. The significant part of whatever we are doing now, at this present time, is completely absent from what we can see or feel. Yet, it is not clear how the absolute break, ‘pure repetition’ is related to iterability. But what is the process of the production of the same? It should not be simply attributed to iterability, mark, or differance. The identical is not the ultimate gap designating one of these, but the structure of operative recursive connections, maintaining temporal stability of persistent self-reference.

Derrida wants to say here that the old ontological metaphysics, built around the notion of ‘presence’, is over. It means that the present that eludes our consciousness is the other, always unknown side of what sustains ‘pure repetition’. The primary part of whatever we are doing now, at this present time, is completely absent from what we can see or feel. Yet, it is not clear how the absolute break, ‘pure repetition’ is related to iterability. What is the process of production? The identical is not the ultimate gap, but the structure of operative recursive connections, maintaining temporal stability and persistent self-reference — Number2018

Consciousness for Derrida and Heidegger implies self-affection, a selfless turning back to itself to reflect on itself.
To be conscious is always to be self-conscious. This is the origin of identity, A=A. To say that experience is not conscious to itself does not mean that ‘the primary part of whatever we are doing now, at this present time, is completely absent from what we can see or feel’. On the contrary, differance, as the in-between of transit, is precisely what we see and feel.

Derrida famously wrote:

“The iterability of an element divides its own identity a priori, even without taking into account that this identity can only determine or delimit itself through differential relations to other elements and hence that it bears the mark of this difference. It is because this iterability is differential, within each individual "element" as well as between "elements", because it splits each element while constituting it, because it marks it with an articulatory break, that the remainder, although indispensable, is never that of a full or fulfilling
presence; it is a differential structure escaping the logic of presence..(Limited Inc)

His thinking about identity was strongly influenced by Heidegger’s notion of Being as event. Heidegger introduced us to a beginning for thinking that is ontologically prior to the overt distinction between the present and the absent, the same and the other, familiarity and subversion, schemes and their dislocation, something and nothing, the relevant and the strange, binding and separating, identity and difference, being and becoming, good and evil. What Heidegger elaborated in the guise of the ‘as' structure, temporality and the making of the work of art marries these gestures within the same paradoxical moment. Heidegger constantly struggled to come up with an adequate way of articulating a notion of transit, othering and difference that the grammatical structure of language mitigates against, an essencing which is neither simply present nor absent, neither something nor nothing, neither future, now nor past.

Kind is an abstraction from natural regularities, and as such is a fixed or static identity. Abstractions, like number, are static, although obviously their instantiations are not. — Janus

I agree.

I must respectfully disagree with the passage from Derrida, which I find to be 'nonsense on stilts.' Identity, or what things are, is a fundamental constituent of rational thought and cognition — Wayfarer

I agree that identity is a fundamental constituent of rational thought. My argument, shared by Varela, Thompson and other enactivists that Vervaeke claims to be influenced by,
is that rationality is secondary and derivative of a more fundamental form of sense-making, mindful skilled coping, which places relation and difference as prior to identity.

In focusing on the abstraction involved in identifying kinds and likenesses, it's an overstatement to claim there are no kinds, repetitions, or likenesses in nature. These elements are plainly evident and essential; without any similarity or repetition, there would be only chaos — Wayfarer

If we abandon the abstraction, or more precisely, see the variation within the abstraction that we employ to turn similarities and likenesses into fixed kinds, we not only do not lose what we are aiming for , the intimate relationality, harmony , compatibility and meaningfulness between events, but we gain a richer and more robust sense of the radical interconnectedness of events than we do when we smother phenomena with the stifling templates of self-identical kinds.

I'd say this abductive shift is key in these sorts of arguments. "Which is more rational or plausible? To say that kinds do exist, or to say that they do not exist? — Leontiskos

Not only is saying kinds exist more rational, I would say that the notion of categorical identity is essential to most definitions of rationality. But then, there are more rigorous, more fundamental ways of grounding truth and meaning than by means of identity and rationality.

But then, there are more rigorous, more fundamental ways of grounding truth and meaning than by means of identity and rationality. — Joshs

I don't think so, and I don't think it's a coincidence that your sentence reads like a necessary falsehood. Apart from very odd and idiosyncratic definitions of "rational," something less rational or less plausible is not more robust.