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
This we may call the phenomenal world or the self-world of the animal.
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
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
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
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! — Wayfarer
Still doesn't mean 'number is invented'. — Wayfarer
—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
“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
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 — Janus
Exactly. We invented the concept of ‘same kind’ in order to count, but same kind doesn’t exist in nature. — Joshs
Exactly. 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? — Wayfarer
"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 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.”
]"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
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.
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
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 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
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 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
“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)
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
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
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
But then, there are more rigorous, more fundamental ways of grounding truth and meaning than by means of identity and rationality. — Joshs
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