In my mind math and numbers are a form of logic, logic is a form of reason, and reason (logos) is a product of intelligence (nous).
I salute your engagement of this issue.
In my opinion, Logos is not only logic
but related to the continuous.
For two reasons: first, it organizes qualia, which are experienced continuously and
digitally. Second, logos is metaphorical, and metaphor is not tautology. So the logos is partially like number, but partially something else, that number is not.
In fact, I suggest that number is created by subtracting or negating this analog element of logos. Hegel goes into this. Also, I attack this in my "Truth is Triangular" thread. Logos is synthetic, or temporal. Number is equation or eternity.
---------- Post added 03-01-2010 at 11:56 PM ----------
Reality itself I would maintain is also discrete, digital and quantitized and the impression of continuity in space and time is a product of the conceptual constructs of the human mind. (Much as we can digitize any medium and experience it as continuous). Continuity is a feature of human conception not independent reality. This would make number even more foundational to reality.
I have to disagree w/ you here. Reality is experience both digitally and continuously. Do you know Zeno's paradoxes? The thing is, we can't
perfectly digitize the continuous. Pi is an example of this. So are infinitesimals. Calculus is a cheat, not a true digitalization of continuity.
I do agree that continuity is a transcendental intuition. But I also think that number
is. I do agree that the world seems amazingly compatible with our numbers. But I feel that Kant's noumena is a necessary limiting concept. For me, the transcendental is what we can know w/ certainty, and nothing else. Of course scientific pragmatic truth is plenty good enough to work with. We don't need
tautological certainty. It's just beautiful.
---------- Post added 03-02-2010 at 12:01 AM ----------
Ours ideas of such continuous perfect forms as circles, spheres, etc. can only be represented in mathematical form not in reality. The calculus the discrete representation of the continuous is thus a major breakthrough in the ability to provide a mathematical model of reality.
I think we must distinguish between perfect geometrical forms and numbers. Perfect geometry, in my view, is possible only because
our transcendental intuition of space is continuous. This is why I think that pi is significant: it's the irrational collision of transcendental number (digital) with transcendental space(continuous). In my opinion, calculus is a brilliant bluff. I'm not saying it doesn't work. It's ingenious.
I don't think that the continuous can
be represented by the discrete. I think there is only one number, for one thing, and that this primary number is the base of all our usual numbers and also of our words. But our words are also immersed in a continuum of qualia and social practice, including metaphor, and conversations like this. Number is essentially identity. Word is something that morphs, something essentially temporal.
---------- Post added 03-02-2010 at 12:05 AM ----------
Well anyway just a sketch of number, reason, quanta, and process and the ways in which they correlate. Is number then transcendent or transcendental? I am not sure how you use the term but in theology transcendental means beyond the material realm, or separate from the material realm and so number I would maintain along with reason exists prior to "creation". Number is a form of truth, of beauty, and a transcendental reality not at all a construction of the human mind imposed on reality but Truth discovered not invented.
I'm coming from a Kantian use of the word "transcendental." For me, the the "transcendent" is just an adjective for the beauty
of truth. So number, in my view, as well as Euclidean space and continuous time, is transcendental. I do think that the number transcendental was a prime mover of human evolution. I suggest that number is at the core pure negation, and that pure negation is numinous, or attractive. Negation is the source of concept. It slices the world into meaningful unities(concepts), by excluding/negating what is not-concept.
I differ w/ you in thinking that number is possibility just an imposition of the human mind. But I can't be sure.