I wonder if determinate existence is to Essential Being as formal truth is to transcendental truth. The wondering was provoked by the following passage in The Philosophy of Being: "the search for Truth is a constant process," and
much of the knowledge thus obtained can be classified and organized into unified bodies which we call "science"; but each field of science has its own limitations, and at best can give us only a portion of truth (Renard).
Now, according to Gödel, any formal system is going to contain axioms or assumptions that cannot be justified by the system, rather, "there will always be at least one true but unprovable statement," says Prof. Wiki.
I don't whether Gödel would approve my liberal use of his theorems on non-mathematical systems, but it seems self-evident to me that they apply to them as well. Of course, I could be missing something, but I can't think of a single ideology or philosophy that doesn't begin with some indefensible claim or assumption.
Except for ours, i.e., that Being Is. There are no assumptions there, only entailments. The only thing we suppose is reality, and the rest follows. The question is,
Can man know reality; does his knowledge correspond faithfully to the things that are; are objects of his knowledge what he thinks they are?
To answer in the negative is "to deny the possibility of philosophizing, of thinking, or of living." Therefore, supposing you are engaged in any one of these three, then you are affirming a philosophy of being -- that being is intelligible. To repeat:
This truth is so obvious that it cannot be demonstrated, and so necessary that it cannot be denied without the shipwreck of all knowledge (ibid.).
Back to Gödel, I wonder if his incompleteness theorems -- or at least something like them -- go to the differences between exoteric and esoteric religion? For the former is to the latter as form is to substance. In other words, every form represents a kind of limitation on the act of pure being, the latter transcending any such constraint.
For me, this solves a whole lotta problems, e.g., the inevitable inconsistencies, aporias, and fissures that result from the rigid application of any formal exoteric or dogmatic religious system.
As we know, the theorems mandate that any system can be complete or consistent, but not both; completeness is purchased at the price of consistency, and vice versa. According to Prof. Wiki,
The first incompleteness theorem states that no consistent system of axioms is capable of proving all truths about the arithmetic of natural numbers. For any such consistent formal system, there will always be statements about natural numbers that are true, but that are unprovable within the system.
The second incompleteness theorem, an extension of the first, shows that the system cannot demonstrate its own consistency.
Here again, this strikes the Raccoon as self-evident -- that no one outside of God could be wholly complete and consistent.
Physics, for example, is rigorously consistent but obviously incomplete, helpless as it is to explain (for example) the consciousness of the physicist, let alone the conformity of mind to being. To paraphrase Einstien, the most incomprehensible thing about reality is its durn comprehensibility.
Most religions take a stab at completeness, but if one pushes the doctrine too far, it will reveal inevitable inconsistencies.
But any incompleteness is down to our not being God. Somewhere Schuon has an illuminating comment about this, or at least a plausible alibi. That is to say, on the one hand,
only sapiential esoterism, total and universal -- not partial and formalistic -- can satisfy every legitimate need for logical explanations.... it alone can answer all the questions raised by religious divergences and limitations.
Nevertheless, there are inevitable limits to the expressible, and
it is no one's fault if within every enunciation of this kind there remain unanswerable questions, at least in respect of a given need for logical explanation and on the plane of dialectic.
For, just as no form can exhaust the formless, "it is all too evident that wisdom cannot start from the intention of expressing the ineffable."
Thus, wisdom can never be complete, but it is certainly more complete than any profane knowledge, reason, information, or fact. There's an incompleteness built into the nature of things, at least on this side of the rug, if only because isn't that side.
In the book Incompleteness, one of Goldstein's main objectives is to correct the common misconception that the theorems forever seal us in a closed world of subjectivity, cut off from reality.
She compares this misconstrual to the common misunderstanding of Einstein's theory of relativity, which is actually a theory of absoluteness. Yes, motion is relative, but to an absolute: the speed of light. Nevertheless, many folks apparently take it to mean that "everything is relative" or something.
Likewise, a common postmodern misinterpretation of the Theorems maintains that
the very notion of the objectively true is a socially constructed myth. Our knowing minds are not embedded in truth. Rather the entire notion of truth is embedded in our minds.... Epistemology is nothing more than the sociology of power.
And we all know where this leads: to Foucault and other metacosmic perverts and inverts. Could Gödel actually be an unwitting oddfather of these progressive oddballs? Maybe, for as Goldstein explains,
Gödel's theorems don't demonstrate the limits of the human mind, but rather, the limits of computational models of the human mind (basically, models that reduce all thinking to rule following).
Along these lines, just for some transcendental fun I re-skimmed meta-biologist Robert Rosen's Life Itself, wherein he suggests that
The celebrated Incompleteness Theorem of Gödel effectively demolished the formalist program. Basically, he showed that, no matter how one tries to formalize a particular part of mathematics, syntactic truth in the formalization does not coincide with (is narrower than) the set of truths about numbers.
In short, semantics -- i.e., meaning -- cannot in principle be reduced to syntax -- i.e., to order. This is Important, for it means that "no finite set of numerical qualities"
exhausts the set of of all numerical qualities. There is always a purely semantic residue that cannot be accommodated by that syntactical scheme.
This means that Meaning itself always persists despite our efforts to contain it via form. Which goes precisely to our larger point -- or intuition -- that esoterism can never be reduced to the exoteric formulations of dogma.
Biology may indeed appear "soft" to a hardheaded physicist, but don't confuse complexity with softness. Rather, as Rosen points out, a material system is not necessarily -- in fact, is usually not -- a simple system but a complex one, because the latter has more qualities than can be accommodated by mere syntax.
For example, this is why climate science is such a travesty. Economics too, at least the conceited kind that pretends to leap over Hayek's Wall and pretend to know the unknowable.
Now, esoteric meta-questions about this or that exoteric discipline aren't contained in the field itself -- for example, physics isn't equipped to answer metaphysical questions about itself, and to the extent that it tries to do so via its own limited stock of ideas, merely beclowns itself, insofar as it tries to magically explain the higher via the lower. Big. Mistake.
It is even the Big Mistake, because it attempts to contain what is by definition uncontainable by any formal system.
Where does this leave us? We'll explain where in the next installment.
1 comment:
Essoteric adj (arch) Of or pertaining to Standard Oil. Later superseded by Exxoteric.
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