Risto

This past weekend while reading Descartes' Meditations on First Philosophy I was struck by the similarities between Descartes' descriptions of human finitude and natural infinitude, and the maxims of Kurt Gödel's Incompleteness Theorem. I'm no expert (or amateur) on Gödel's Incompleteness Theorem, however it seems as though Gödel's Theorem is a formal expression and proof of aspects of Descartes' philosophy.

For example, Descartes states that "[f]or although the idea of substance is in me by virtue of the fact that I am a substance, that fact is not sufficient to explain my having the idea of an infinite substance, since I am finite, unless this idea proceeded from some substance which really was infinite." Unfortunately for humans, "the nature of the infinite is such that it is not comprehended by a being such as I, who am finite," and "it is the essence of a finite intellect not to understand many things." Tying this back to Gödel; in the book Incompleteness: The Proof and Paradox of Kurt Gödel by Rebecca Goldstein, the author describes some of the conclusions we can draw from the Incompleteness Theorem, and notes that "[t]he limits of formalization, of our attempt to reduce all ... knowledge to the specified rules of a system, are not congruent with the limits of our knowledge. Our ... knowledge exceeds our systems." In other words, "aspects of ... reality ... escape our formal systematizing (although not our knowledge)"; "[w]hereof we cannot formalize, thereof we can still know." Hence the human ability to possess knowledge about nature exceeds the human ability to explain and understand the legitimacy of that knowledge, but nonetheless our (finite) knowledge proceeds by legitimate processes from (the infinity that is) nature.

What's important to note here is that while incompleteness validates the logic of inductive inferences, it also invalidates the idea that humans can be objectively certain about their empirical beliefs. As Descartes notes in his reply to the second set of objections, "there is more objective reality in the idea of an infinite substance than there is in the idea of a finite substance." This is what Bronowski was getting at in The Origins of Knowledge and Imagination when he noted that "[n]ature is not a gigantic formalizable system. In order to formalize it, we have to make some assumptions which cut out some parts. We then lose the total connectivity. And what we get is a superb metaphor, but it is not a system which can embrace the whole of nature ... [because] no formal system embraces all the questions that can be asked." Therefore, because "the reach of all formal systems is limited," "[w]hen you axiomatize an arithmetical or mathematical system, you automatically impose a limit on it," and conceptually speaking, "you cut the universe in half." Axiomatization is of course inescapable, and as a result of this human communications will always be ambivalent to some degree. Quite simply; "[t]here is no way of exchanging information that does not demand an act of judgment." Thus humans may legitimately claim to understand aspects of nature, but only insofar as their finite physiology (and it seems to me that in particular their limited capacity for humility) permits. Humans exist as formal systems, and formalization necessitates natural incompleteness. Human incompleteness means the species has an innate inability to achieve total connectivity, and although humans possess the ability to contemplate the Cartesian infinity that is nature, they are forever blocked from fully apprehending it, regardless of scientific advancements.

The implications of this are manifold. Consider for example the most recent disagreement or misunderstanding you had when dealing with a friend or family member. Now, consider the mathematical certainty of the fact that incompleteness is your permanent lot in life. Finally, reflect on the ramifications of incompleteness for our most cherished mathematical models, as applied for example in economics and politics. Externalities and collateral damage anyone?

Self-fulfillment? Bounded by what limitations? Valid achievement? Defined by what context? Material gain? Supported by whose loss?

What's most astounding is not the lack of possibilities, but that you continue forth in full recognition of your own discontent, and with at least partial recognition for the discomfort of others.

Of course, one finds comfort in uncomfortable ignorance; "The more perfect race memory is, the more strictly confined will be the organism to [its] environment." However, the question you face is not "what should I do?" No, that's not the question at all.

You're quite intelligent, and you're quite aware that isn't the question.

In fact, you're so intelligent you almost know that question is disingenuous, and you're so aware you almost know that there are only two choices: what you want to do, and what you should do.

Progressing from almost to honest is easy, simply answer the following: why is want not compatible with should?

What is not so simple is also what is most disturbing; the possibility that you may never even try to answer. The answer is that it's never easy to administer elaborate hatreds and highly polished superfluities, bodily or mentally.

Mental complexity alone does not indicate validity, doctor. Obstruction arises from and is perpetuated by efforts that require commitment regardless of outcomes, and outcomes that require commitment regardless of discontent.

Discontent emerges as discomfort, and choice arises.

Will you permit discomfort to embellish itself by administrative degrees; to what extent must you extend in order to satisfy what definition? Will bodily awareness become mental unawareness; to what extent does unawareness satisfy? Ex aliquid nihil fit; ex nihilo nihil fit.

"Nature is not a charitable institution. She is always inimical to life." You on the other hand need not be.

Every word is polyvalent; all speech is metaphoric. Every utterance in every context is a metaphor that is grounded at best to a shared set of core concepts, where foundational concepts are contextually dependent on the overall beliefs and belief system of the individual speaking, and where high level concepts need not be congruent in any way beyond the physical boundaries of any individual participant.

Simply because we believe a thing, that does not imply that others believe or understand that thing in a way that even remotely resembles our own conception of that thing. Consider for example the word "communication."

In this particular case, the only thing any individual participant can be certain of is that there exists a severe disconnect between what Colborne Street residents regard as communication, and what they have been told communication consists of. It's quite disheartening really; for "they who have put out the peoples eyes reproach them of their blindness."

"There was an artist in the city of Kouroo who was disposed to strive after perfection. One day it came into his mind to make a staff. Having considered that in an imperfect work time is an ingredient, but into a perfect work time does not enter, he said to himself, It shall be perfect in all respects, though I should do nothing else in my life. He proceeded instantly to the forest for wood, being resolved that it should not be made of unsuitable material; and as he searched for and rejected stick after stick, his friends gradually deserted him, for they grew old in their works and died, but he grew not older by a moment. His singleness of purpose and resolution, and his elevated piety, endowed him, without his knowledge, with perennial youth. As he made no compromise with Time, Time kept out of his way, and only sighed at a distance because he could not overcome him."

This past December the American House of Representatives "approved a ... bill to fund the Pentagon through the remaining 10 months of fiscal 2010." The amount? $636 billion.

On a related note, militaryindustrialcomplex.com claims that the total value of all publicly reported American defense contracts since October 30th, 2006 is $875,486,950,134 (up from $874,063,722,549 on January 3rd, 2010, which is an increase of $1,423,227,585 -- note that I include mention of this increase in order to suggest that this is an interesting site to keep an eye on). While the summations on militaryindustrialcomplex.com should not be considered "100% accurate," what's most important here is the sheer size of the numbers involved, and the "significance of such a relationship between ... government and business."

To give these numbers some context consider global military spending for the year 2008, during which American military spending comprised 48% of all military spending.

"From my standpoint, I think numbers almost are distracting." Which is to say: numbers like this might almost be distracting to the observer who is untrained in the ways of bureaucracy, and perhaps cause that observer's thoughts to stray beyond the boundaries of bureaucratic truth, and perhaps even cause that observer to mistakenly hazard a question about the foundations of these numbers. Almost.

It's good though. "One important reason we have a Defense Department is that when we give it money, it spends it, which creates jobs, whereas if we left the money in the hands of civilians, we don't know what they'd do with it. Probably put it in open trenches and set it on fire." Stupid civilians.