On Formally Undecidable Propositions within Linguistic Systems

Wed, 21 Jul 2021 00:00:00 +0000

Abstract

Epimenides was a classical philosopher and poet. He once wrote, “all Cretans are liars.”; a line that St. Paul quotes in Titus 1:12. Now, there is no rule against quoting a classical poet but the problem is that Epimenides himself was a Cretan. Naturally, Epidemis is a liar then, and so any statement of his must be false. The statement, “All Cretans are liars” must also be false then; if so, Epimenides the Creten speaks the truth: that all Cretans are liars. If Epimenides speaks the truth, he lies and if he lies, he speaks the truth.

In 1931, a young Austrian mathematician named Kurt Goedel published a paper that shook the foundations of Mathematics. Goedel’s argument that mathematics as a system cannot be complete and consistent at the same time was a death blow to anthropocentric rationalism. Here, we intend to take Goedel’s conclusions a little further to introduce some cautious skepticism to the problem of knowledge (epistemological skepticism).

The Argument

Any language capable of expressing a Goedel Statement follows the Goedel conclusions, according to Goedel Incompleteness Theorem.
1. This is the converse of Goedel Incompleteness
2. Goedel Incompleteness refers to two conclusions arrived at by a German mathematician, Curt Goedel. It states that mathematics, as a system for explaining first order logic cannot be both complete and consistent.

As a side-note, I opine that this appears similar to the Heisenberg Uncertainty Principle, applied to the analysis of systems in motion which states that it is impossible to determine both the position and velocity of an object at the same time.

Any language that is composed of grammar (consisting of functional operations) can be mapped to arithmetic.
1. Because any language has to have an alphabet. Or rather, * letters -> words -> sentences -> paragraphs -> …* or even * letters -> nouns, verbs etc -> sentences*
2. This mapping is the same as natural numbers -> strings within the decimal system.
3. It can be any other, like hexadecimal or binary also.
4. Since there are infinitely many integers, but only a finite amount of alphabets This relation stands, and every possible string of thought that ever exists can be expressed as a mathematical statement.
From the proof of Goedel Incompleteness Theorem, we know that Mathematics (and by extension, Arithmetic) fails the Goedel test.
1. Math is either complete or consistent.
Therefore, language is also either complete or consistent.
1. We intuitively know this, through experience, objective language is often incomplete: i.e., we are never able to completely convey the complete experience of what something “feels like” even if language was advanced enough.
  1. For instance, when I testify that i see a red rose. The only relation between the word “red” and reality is our shared experience of us having seen the color red.
  2. On the contrary, if the word “red”, and an exhaustive definition of this physical property were enough to convey every aspect of its meaning about it (through the medium of language) then a person blind from birth would be able to “see” the color red without ever having to open his eyes.
The materialist claim that a mind-independent reality exists is self-referential, in that.
1. All references to the external world are always experienced through “Mind”. Therefore, it is self defeating. That a mind independent reality exists is not scientific statement, or a scientifically testable statement.
2. It can also be said, that it is not a scientific statement (it cannot be inductively deduced) that the Scientific Method is the best tool at at describing truth.
  1. At best what we have is a deductive tool.
    1. At the same time, it is the best tool we currently have at analyzing properties of the natural world.
  2. At worst, it is nothing more than evolutionary adaption. Alvin Plantinga’s Evolutionary Argument Against Naturalism seeks to show just that.
Therefore, the problem of skepticism applies to language and spans all applications of it – including but not restricted to communication, prose, poetry and speech.
1. We have to be cautious when using language to describe reality.

As for Science and the Scientific Method, these are the best tools that we have at obtaining truth about the material world. However, using them to describe the immaterial world is pointless, because that is not the function of these methods.

The Explanation

Rationalism (and its successor Critical Rationalism) is the best tool have to investigate scientific statements, however the recent elevation of these tools to a pseudo-religious status is alarming, considering that they both share a vacuous foundational tenet that has to be accepted on a purely de fide basis. The foundation of an atheo-materialist construction of reality is a false assumption, that every truth about the natural world can be constructed through grammatical systems like language.

The foundation of an atheo-materialist construction of reality is a false assumption, that every truth about the natural world can be constructed through grammatical systems (like language).

That language, even through systematic rationalist inquiry, can express all of the truths there are is a silly speculative fiction. This is but a perversion of its evolutionary purpose also, which is to get things done from a common, shared perspective in an empirical world. It is impossible for language to consistently, and completely explain my inner, subjective world and these inner experiences are as much a part of reality as any other experience. In fact, it is a simpler to defend the position that all experiences are fundamentally subjective, and are in fact inner experiences.

The Computational Argument

From the Chinese Room Experiment, we can hypothesize about an “artificially intelligent” computer that is no different from an abacus of today and works on the same principle but supplies overwhelmingly convincing evidence towards its intelligence.

Consider this: an abacus does not know what two times five is or what the number ten means. It does not, because it need not; it is a computer after all, and it computes. There is nothing more to it, than its intended purpose.

Any appearance of intelligence or anything similar is only illusory; it is a projection of our rational faculty toward non-rational entities and these lapses of agency can be forgiven, because they are unintentional. To illustrate, when a computer gamer is playing against the AI of a game, he is not playing against any actual intelligent agent but a program that traverses the graph of actions that were crawled upon from a history of intelligent agents in the past (ie, humans). We are not playing against intelligent computer simulations but rather, the entire history of actions takens by previous players of the game.

The Hard Problem

The Hard Problem of Consciousness cannot be answered, because it carries an implicit materialist frame within it, and because materialism is speculative fiction it is impossible to shine light upon it.

Consider a single container of water that can be uniquely identified depending on the configuration of its contents – an X for its empty position, a Y for any in-between position and a Z for a full position. X, Y an Z are the starting units (numbers) for a new system of (ternary) operational logic. The current system of binary logic and Von Neumann architecture (I suppose) can be completely represented using this simple contraption, it is only a matter of scaling; maybe it can even represent a qubit.

An intelligent engineer uses this bottle to devise a mechanical device that uses some streamlined fluid mechanical apparatus to perform binary operations using Tesla coils. gate valves and low-friction pumps. The first day his system has only a thousand bottles, so 3^1000 states of calculation but being the intelligent man he is, he ends up scaling it a hundred-fold giving him 3^100000 states now.

My question is this – at what point, and at how many bottles does his fluidic-computational-machine gain consciousness? Is it a million bottles, or a billion bottles? Because if the atheo-materialist conception of reality is right, then it is only a matter of adding more bottles – exactly how much, I do not know. But this operation will sure turn out to be an interesting proposition for the 97% of environmental science majors if the bottles were made out of plastic, or silicon.

Conclusion

Language is ill-suited to represent the truths of the universe, and so any attempt at doing so is ill-advised because of the limitations imposed on it. Materialists must find a new medium of communication that operates on an entirely spiritual plane that is devoid of the natural law constraints of entropy, and spacetime limits. They will run out of patience soon, and will resort to devising stranger stories to explain experimental data (or its lack thereof) to further support their positions. Likewise, there is nothing intrinsic to a computer or a CPU that makes it “smart” and any such extrapolation is mere projection. The sooner we can put away our anthropocentric god-complex, the faster we can solver the problems of our time and outrun the red-queen solving the problems of humanity for all the world, and all the generations to come.

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