I'm happy to clarify. Please read Digital Time in Analog Space, as I have went into details there.
Transcendentally intuited space (and time) is continuous. This is where perfect triangles live, and the only place they live.
Spacetime and physics time in general (despite Newton's ambiguity) is an imposition of number upon the continuous. Zeno's paradoxes are a perfect example of this. Also, consider calculus. Which is a brilliant cheat....
Despite possible misunderstandings, I am utterly anti-mystical. "Positronic" theology is just a ironic twist on negative theology....which happens to connect to transcendentally intuited number. Keep in mind that "transcendental" is not "transcendent." (Except that it's related to ideal beauty...)
How does this idea approach isolation? Can there be isolation from the universal mind?
But where is that part about numbers being tautologies. I am really eager to see that! (I don't think he thought Kierkegaard or Schopenhauer wrote nonsense. However, he did not particularly like them for their metaphysics either, but for something quite different).
6.022 The concept of number is simply what is common to all numbers, the
general form of a number. The concept of number is the variable number.
And the concept of numerical equality is the general form of all
particular cases of numerical equality.
Everyone will read philosophy through their individual perspective, so interpretations vary, but I feel that it is quite clear that no mind can exist in isolation.
Everyone will read philosophy through their individual perspective, so interpretations vary, but I feel that it is quite clear that no mind can exist in isolation.
Community is essential for each individual to develop, and as has been shown in cases where children are not allowed proper social development, those that are separated from the community early on suffer debilitating cognitive problems for the rest of their lives.
The first few years in particular are especially important, as it is during this time that language develops, and early language development has been shown to be a key indicator future cognitive ability.
The Ancients understood this concept, which is why they worshiped Logos (the Word) and focused their Pedagogy on the development of dialectic. For them to master the world you must first master the word.
The TLP was only wrong concerning logos. Wittgenstein realized eventually that logos was related to something that number was not. Logos is context-bound, continuous. Meaning is a spectrum, which is the opposite of a tautology.
Witt did not despise "nonsense, etc." You don't understand him. Sorry. He loved Kierkegaard and Schopenhauer. You're going to have to face it that your boy was a German, and quite concerned with the trancendental. It's just that logos cannot be reduced to that. As Hegel knew. You're a sophist in denial, methinks.
Zeno's spatial paradoxes have been solved, as far as my understanding of the matter goes. I can solve the first two on my own: 1) space is not infinitely divisible in reality, and in ideal conditions calculus solves the paradox 2) Space is not infinitely divisible by two in reality, and in ideal conditions calculus solves the paradox.
Calculus is usually developed by manipulating very small quantities. Historically, the first method of doing so was by infinitesimals. These are objects which can be treated like numbers but which are, in some sense, "infinitely small". An infinitesimal number dxArchimedean property. From this point of view, calculus is a collection of techniques for manipulating infinitesimals. This approach fell out of favor in the 19th century because it was difficult to make the notion of an infinitesimal precise. However, the concept was revived in the 20th century with the introduction of non-standard analysis and smooth infinitesimal analysis, which provided solid foundations for the manipulation of infinitesimals.
In the 19th century, infinitesimals were replaced by limits. Limits describe the value of a function at a certain input in terms of its values at nearby input. They capture small-scale behavior, just like infinitesimals, but use the ordinary real number system. In this treatment, calculus is a collection of techniques for manipulating certain limits. Infinitesimals get replaced by very small numbers, and the infinitely small behavior of the function is found by taking the limiting behavior for smaller and smaller numbers. Limits are the easiest way to provide rigorous foundations for calculus, and for this reason they are the standard approach.
Its kind of funny you know, many Positive Philosophers read Tractatus as a form of Linguistic Positivism, which was a claim Wittgenstein vehemently denied to his death. Many, including I, feel this is why he seems to confront transcendence head on in PI.
So it is only "continuous" in the form of transcendental intuition?
Yes I was thinking along the same lines, but how about after development? Is there still a connection or is the universal mind a "shadow" for the hermit? I can see how in a sense logos shaped the person, making it a part of what defines them, so they would be dependent on it for that reason. Perhaps another useful question is whether or not higher level language is what makes us 'special', or does it just allow for more complicated levels of interactions that other animals also experience?
What do you mean "in reality"? You forget that number is also, at least to me, just as transcendental as continuous space. We don't know, in my opinion, reality-in-itself.
We just apply our universal human faculties, both continuous and digital, and do what we can. Calculus doesn't solve Zeno's paradoxes. It's just a brilliant dodge. ....
We can only think in pieces. Infinity and the infinitesimal are both paradoxical, or mere negations. In-finite = non-number. For number is essentially finite. Don't get me wrong. I'm quite impressed by calculus. But utility is not Truth. (Calculus is pragmatism-by-numbers...:bigsmile:
Yes, but we can only understand space as continuous or digital, both of which are transcendental.
It is the result of an infinite calculation, without having to do the infinite calculation.
What makes our digital understanding transcendental?
Examine those sentences together. By the way, I salute you for engaging me on this.
Why wouldn't number be transcendental? Why should nature-in-itself be numerical?
My best answer to your question is that it is utterly impossible to think in continuities. However, nature seems to agree with our transcendental number, or it used to, until we zoomed way in. So nature may also be digital. But it doesn't matter much, for we can't help but think of it that way. To speak metaphorically, there is only one number. This isn't mystical. No sir. This is just the result of hard thinking. Equations and tautologies.
We can think of the number 10 as one quantity or as ten unities. It's same with all number. Our positional number system, including the decimal point, obscures this. On the other hand, irrational numbers reveal this.....(irrational means continuous, upon careful consideration....)
The problem here is that we have so far observed things as quantized, so the idea of continuity may turn out to be the fabrication.
I think "one quantity" is an abstraction of "ten unities". They both mean basically the same thing, its just that "ten" is more specific, unless "unities" means something different from "units".
6.022 The concept of number is simply what is common to all numbers, the
general form of a number. The concept of number is the variable number.
And the concept of numerical equality is the general form of all
particular cases of numerical equality.
That's just it, man. We can only think in quanta. But Zeno's paradoxes show the collision of transcendentals. So does pi. Yes, number mirrors nature so well that its hard to think that number is transcendental, or imposed by the human mind(exact same meaning). But because we cannot think outside it (try!), it does seem to be transcendental...
---------- Post added 03-02-2010 at 01:36 AM ----------
You're on the right track. Abstraction is always unification, as thought is always digital. This is what words have in common with numbers. We can zoom in our out. Look at that the pieces (also unities) or zoom out and see the pieces as another unity.
The one number theory is not exactly mine, as it was inspired by Parmenides and negative theology, but it's largely mind, as far as I can tell. I just noticed that Wittgenstein hinted in that direction.....
It's a strange and beautiful idea.....(I think James Joyce was aware of it, but it's hard to tell, as Finnegans Wake is the most difficult book in English---probably intentionally, to force us to see that words aren't numbers, although that have a numerical core....
Notice that he says "equality." Equality is unification. And so is tautology. But dialectical synthesis is something else. (I tackle this in Truth is Triangular..)
Don't be put off, my scientific friend, by my "positronic theology" label. My religion is pure pure science, on the root & transcendental level.....my god is the structure of the human mind.....
Hmm, that is a lot of different ideas to take in. I can only think to respond with how I view infinities. I see them as a result of forming a frame of reference. An infinity is a representation of all possibilities, or a "scrunching" of a frame of reference's possibilities, like trying to fit every number on one number line.
I think we can conceive of things in terms of continuity, but I think the math for that is more complex, so it might be harder to grasp.
So the "one number" represents the ultimate abstraction? Something like that?
It sounds to me like you view infinity as a continuum. For instance, how many number are there twixt 0 and 1? (An infinite amount, right? But this requires transcendental continuity. We can use positional notation to zoom in as much as we want, but there is always as much more as we want. It's the same with pi. Take all the pi you want: there's the same amount left, and it's not amount...but a continuity..)
Pi helps show my point I think. If your frame of reference is a circle, then your frame is infinite.
"how many number are there twixt 0 and 1?"
That is using 0 and 1 as a frame of reference, those are the limits you are setting on the system.
0 and 1 are ambiguous, but infinity seems to marry that ambiguity (the ability to zoom in and out) to continuity. Perhaps infinity is the "only number" you are speaking of, the ultimate reference frame?
No, that would be a paradox. Anything framed is the opposite of in-finite, which means unframed...
The tiniest amount of space contains an infinite amount of space.....transcendental intuitive space is freaky, man....No wonder we imposed our number....
---------- Post added 03-02-2010 at 02:08 AM ----------
Exactly! Like I said, we impose transcendental number on transcendental space. That's why we get an infinity twixt any two numbers. (excluding of course identical numbers..)
I am not sure how that is a paradox. Maybe "frame of reference" is a bad term to use, but rather "coordinate system".
The reason that "infinity" can be presented as the pure number is because any and every word is built on this only number, for every word is digital, including words like "infinity."
But what infinity refers to is not at all digital, but the exact antonym of digital.
I'm trying to grasp this by replacing "only number" with "abstraction", I think I am going to need you to elaborate on "only number" before I grasp your meaning.
Let's take any chunk of intuitive space you like. Is it not endlessly dividable?
So it's infinite! But it's the space that's infinite......Our divisions are not only finite but finitude...
Abstraction is synthetic. Differences are negated in order to synthesize similarities. For instance, a dog and a cat are both animals. The word animal transcends and includes both dog and cat, but loses information.....that information is what is negated in order to synthesize...All synthesis requires this...
But we can synthesize to the limit. And that would be something like the only number, or pure number. Basically it's the number one, except we know that it could have been named something else. It's English name is not of its essence. Neither is it's graphical representation. But only language using humans can abstract it in the first place. We are transcendentally digital so it was bound to happen. And the cultures who learned to manipulate this abstraction would have an edge...
With words it's something similar. Basically negative theology wanted to make god as "transcendental/transcendent" or "infinite" as possible. He wasn't this and he wasn't that. He wasn't any thing. But we can only think in terms of things. So god is just negation. hence negative theology. Concept is never completely continuous, but has always a digital core.
Heidegger asked "what is the Being of beings"? What does it mean to exist, apart from any other quality? So he was steering word toward this same pure negativity. Being isn't a being. But that's impossible. For we only think in beings or unities, or digitally. So the best he could do was cross it out. That's why negation and the only number are the two transcendentals of thought, as far as I can tell.
Check out "truth is triangular" if you want more on synthesis. I know this is a strange subject. i was always warned away from hegel. But this book by Kojeve made clear the obscure. Hegel is all about synthesis, which is the essence of man's temporal existence....(negating all that he shares with mere animals, who do not culturally evolve...)
