Leftist IDs, Don't Mistake Ignorance for Wit!

2006/8/6 14:44:43

I am in a good mood these past two days, so I might as well give a basic lesson to those leftist IDs who constantly pretend to know what they don't and mistake ignorance for wit. Of course, this will not be repeated, as this ID does not have that much spare time. Setting aside that long-running math-pretending ID for now, recently one called Yuntian0460 popped up invoking the so-called "Arrow's Impossibility Theorem" to argue against voting. The logical error in this so-called theorem is the same as in the so-called "voting paradox" proposed by the 18th-century French thinker Condorcet, from which it shares a common origin—it is caused by implicitly taking the transitivity of a partial-order structure as a premise. Since the proof of "Arrow's Impossibility Theorem" is rather complex and the people here have limited level, this ID will use Condorcet's "voting paradox" as an example to illustrate the logical joke that arises from implicitly treating the transitivity of a "partial order" structure as a premise.

Of course, as is typical of leftists, Yuntian0460 and similar IDs also have problems with reading comprehension, actually thinking that this ID mistook Condorcet's "voting paradox" for one of the axiomatic premises of "Arrow's Impossibility Theorem." That is as laughable as treating the case N=4 of Fermat's theorem as the premise for the case where N is prime. The quasi-mathematical proofs by typical so-called economists generally have similar flaws. For instance, in Arrow's proof—beyond those few axioms of his—the proof itself (the specific proof can be found in any higher-level relevant textbook) uses transitivity. Just as those Western economists, when studying demand curves, arbitrarily differentiate and a priori tack on certain mathematical operations without ever knowing that these mathematical tools all have prerequisites—once you use these mathematical tools, you implicitly incorporate their hidden premises. So regardless of whether Arrow's axioms are reasonable, because his proof uses transitivity—just as with the logically isomorphic Condorcet "voting paradox"—the proof is nothing more than a laughable logical falsehood. Western economists commit such logical jokes all over their pages, and leftists actually scramble to share their trousers—how is that anything but mistaking ignorance for wit!

As for that habitual logic-joke-making math ID, they recently announced what they thought was a Columbus-like discovery: "From the standpoint of mathematical theory, dichotomy—that is, using binary numbers—can express all human thought and laws of motion, because these thoughts can all be stored in a binary computer." I have no idea what kind of "mathematical theory" this so-called math ID is referring to. Does merely claiming to be a math ID give one license to fabricate mathematics? Fine then—let us examine this so-called discovery or declaration by this math ID in a thoroughly mathematical manner:

Let us assume their claim holds: all human thought and laws of motion can be represented by binary numbers. We line up all these binary numbers representing all human thought and laws of motion. Now consider this binary number: its N-th digit differs from the N-th digit of the N-th binary number lined up above (for example, if the latter is 1, the former is 0, and vice versa). Obviously, this binary number is not among those representing all human thought and laws of motion. Yet this binary number corresponds to the following thought: "its N-th digit differs from the N-th digit of the N-th binary number lined up above." In other words, this thought is not contained within all human thought and laws of motion—a contradiction. By the simplest proof by contradiction, the assumption that "all human thought and laws of motion can be represented by binary numbers" does not hold. Not all human thought and laws of motion can be represented by binary numbers.

The proof idea above is actually not this ID's invention. It is a classical mathematical proof method with a colloquial name: the "diagonal method," first appearing in Cantor's series of proofs in set theory in the 19th century. Setting aside the mathematical developments of the 20th century, which exceeded the sum of all previous centuries, even just a certain understanding of this 19th-century mathematical knowledge would make it impossible to assert such an absurd proposition. What makes humans great is that humans can transcend all constructions. A person who can be netted by a lousy internet can only be a base person. Thoughts that can be expressed by a lousy internet and lousy binary numbers can only be the thoughts of base people!

As for the recently debated issue of so-called "one divides into two," this ID does not wish to elaborate, because this proposition fundamentally clashes with Marx's thought. In Marx's framework, "division" is a historical category—there is no a priori, eternal "division" or "divisibility." The development of modern quantum mechanics has already demonstrated this historicity of "division." The specifics I will not spell out—let it be an opportunity for leftists to go back and read more. Learn something!