AIT

There is a proto-logic, an ur-logic.

Notation is contingent.

We can symbolize numbers, for instance, both with different glyphs and/or in different bases. (And also different phonemes, of course). Still, we have same integers, all with a distance of unity between them. (A non tempered number system would be almost useless for ordinary purposes, and extremely counter intuitional.)

To consider whether a statement is true or false, we must consider it as a unity.

Indeed, thought in general is the unification of lesser unities. With math and formal logic, we see thought at its most discrete.
With a book like Finnegans Wake, we see thought/language at its least discrete. Which is presumably the point ("the abnihilisation of the etym.")

The word "transcendental" is self-canceling when followed to its logical conclusion. If experience is structured, then concepts like "unstructured experience" are one more example of structured experience.

Kronecker is a fascinating character. It's too hard to find information on the man. "God created the integers. The rest is the work of man." He was a proponent of finitism. He was quite the student of philosophy, and not just a math man. He was suspicious of the work of Cantor. He teased the man who proved pi transcendental by calling his proof elegant but also a waste of time. As pi did not exist.

Last night an amusing parallel occurred to me. As we calculate the digits of a transcendental number, each calculated digit gives us information that is one tenth as significant as the digit before. The closer we get to the limit, the slower we are moving toward it. This reminds me of acceleration towards the speed of light. As an object accelerates toward C, it gains mass, and this means an infinite amount of energy would be required to accelerate the speed of light. In the same way, an infinite number of calculations would be required to exactly calculate the digits of pi or e.

Pi does not exist, then. Only approximations of pi exists. Of course the Greek letter exists, and "pi" exists as a useful symbol, but this symbol points toward an impossibility. We cannot know a transcendental number in its fullness, no matter what integer base we use. If we calculate a trillion digits, we should think of these same trillion digits in relation to infinity, which would make them equivalent to zero digits. Any finite number divided by infinity is zero.

If I approve of finitism, then why do I speak of infinity? Infinity is an algorithm! And so is pi, and e. The notion of the infinite is where math touches Zeno and philosophy. Mathematics is a perfect zone for the examination of the so-called transcendental.

I have argued, never denying my many influences, that beings are unities. This is why math is philosophical. The notion of unity, of the One is crucial, in my opinion. We experience the world as a collection of objects. And this collection is itself an object. And by object I mean unity.

We can consider the bicycle as a unity, or zoom in and consider the chain on this bicycle as a unity. We can look at an individual animal or zoom out and consider the species. I have heard the word holon used for this Russian doll concept.

We can look at molecules, or zoom in and look at atoms. And we can zoom in even further and look at subatomic particles.

If mathematics is the grammar of nature, and mathematics is essentially discrete (despite the brilliant attempts of calculus to overcome this), we see that nature must, for human beings, be discrete, at least insofar as it is an object of thought.
This is obvious even in the fact that we unify nature with the name/concept "Nature."

Thinking is always this way.

"Science is what we can teach a computer to do." Donald Knuth.

Questions of ethics are obviously important to human life, and indeed they are associated with the philosophical tradition.

Still, I can't help feeling that ethics are philosophically off-center. Does it really require a philosopher to "do" ethics, if ethics are central to all social life? There's something questionable here. I'm suspicious of a science of ethics. Can philosophy, on the subject of ethics, transcend opinion?

Of course one can call all philosophy a matter of opinion. And philosophy is much like literature. This hasn't kept me from moving away from the obviously literary toward philosophy that addresses the "structure of structure" or, in other words, the shape of thought. (Science of science is another excellent description for the same thing.)

Mathematics has gripped me precisely because it is universal, and does transcend opinion, or at least it transcends opinion as much as this transcendence is possible. This is not to deny that their are debates in mathematics, but the core is largely not debated. The integers are there, no matter what base or glyphs or phonemes one prefers. And the primes are there. Number theory is fascinating because this is math that feeds not on nature but on itself. To use calculus to study the distribution of primes, rather than the instantaneously acceleration of rockets, is fascinating.

Mathematics is also the collision of the perfectly finite with the perfectly infinite --admitting that this "infinite" is a somewhat paradoxical concept.

Set theory is math that concentrates on unification pure and simple. The grouping of groups. Badiou fascinates me, but I have not bought his book. There are too many good books out there. This is why libraries are such a great idea. Rather than each of us buying 100 of the same books, 100 of us can each buy 1 percent of a hundred different books. But the library in my city is lazy about buying recent philosophy books. How it annoys me that so few read philosophy! That so few care! I do feel a certain rage at the general thoughtlessness ....

Wittgenstein was right to focus where he focused. It doesn't matter whether one agrees with each of his statements. He saw that philosophy can easily be absorbed in a bad way by psychology. Philosophy in the ideal sense is more central than a "science" like psychology. If philosophy is the science of science, it must keep to the center. Empirical specialists have different concerns the philosopher. The politician is applied ethics, for instance. The physicists aren't looking to Aristotle. But the philosopher does still have a use for Aristotle. The accident and essence distinction is the presentation of a "law" of thought. We do think in terms of accident and essence. And this is a contingent revelation of the proto-logic. Accident is simply that which is not part of the abstract unity of an abstract class. Accident and essence have everything to do with set theory.

I blog for the few who might be interested in this aspect of philosophy. I would be happy to discuss these ideas with those who have a real interest and not just an aggressive vanity. I don't mind sincere disagreement. I simply despise a trait that I myself have been a carrier of, which is a tendency to contradict from a motive of vanity. Vanity and envy are always with us. Except when the beauty of the universal makes us utterly forget them.













Infinity is a direction. Positive infinity is a direction down the number line, which has a potential infinity.



If we consider a word like "if," we see we are dealing with a word that is not so easy to define.

Does this not also apply to a word like "not"?

And the question mark: does not this too say something strange?

This leaves us with "and" and "or" which are used in everyday speech in several ways. But of course they do also have a strict logical use which identical to one, in each case, of their everyday uses.

All is this is well known to a student of logic. We also could mention words like "some, " "all," or "none."

Words like this have a meaning entirely different from the meaning of a word like "dog" or "run."

We can use these words to get a peek at the proto-logic.

But remember, it is the opinion of this guy that notation is contingent. And phonemes too are contingent. Or in other words accidental. The word "if" has an essence that has nothing to do with the roman letters that represent it or the way these letters are pronounced in English. I feel that it's safe to assume that any human language must have a word that functions like "if" does in English.

If we examine computer programming language, we see a few basic necessary concepts, and if is one of these, and perhaps, w/ "goto" (the basic ingredient of loops), the most crucial programming concept. I suppose variables are also a contender for this spot. With variables and "goto" statements alone we can create significant and productive loops. This I admit. But without "if" statements, a program has ZERO flexibility. With "if" statements, one program can do anything than programs in general are capable of.

Structured program makes "goto" statements taboo not because they are unnecessary but only because these same structured programming languages provide one with more sophisticated looping structures. The do-while structure is a loop with taste, a loop with restraint. The goto statement is the all purpose tool of the anarchist. The goto statement is the teenage boy of looping structures, and in more complicated programs is often the cause of spaghetti algorithms.

Algorithms are a crucial modern concept, as the modern world is currently guided by algorithms. But not one in ten humans are clear as to the nature of algorithms. What are they? Systems of precise instructions, that include the manipulation of variables within conditional loops. Of course we cannot exclude the input and output procedures that make them useful in the first place.

A number like e can only be approximated. This same number e is also known as the exponential function. It's amusing that the approximation of the such of number is achieved, digit by digit, with an exponentially decreasing amount of precision. In base-10, the 5th digit is only a tenth as precise or significant as the 4th.

We use base ten. Can we imagine base infinity? We would need an infinite number of glyphs. And this would require an infinite memory. So base infinity is a thought experiment. Base 1000 is certainly possible, if absurd.

The advantage of smaller bases is that they provide for the possibility of algorithms. When we multiply large numbers, for instance, we use an algorithm. We break multiplication down to small multiplications, to the kind we memorize in grade school. 7 times 9, and so on. We then "carry," move the decimal point, etc.
To double any binary number requires only the addition of a zero. This is similar to taking any number in base-10 times ten.


AIG, or algorithmic information theory, is something special. I read Chaitin's Meta-math again and was more impressed this time than last, as I was more prepared.

Comprehension is compression. A natural "law" is useful to the degree that it compresses information. We need only look at computers to see this idea in its full potency. The compression of picture and music files is only possible because of repetitions within the constituent bits of these files. A program that calculated the digits of pi could be infinitely shorter than an "algorithm" that presented omega.