God or Absurdity

Before getting to the crux of the master, I want to highlight a few more passages from Rebecca Goldstein's Incompleteness. 

On the one hand, I don't understand why more people don't appreciate Gödel. Then again, if a person or idea isn't helpful to the Matrix, the Matrix is adept at marginalizing or excluding them. There's a reason why logic and economics aren't mandatory in state run schools.  

As alluded to in our previous offering, postmodern proglodytes don't mind the Theorems so long as they can twist them to their own absurd ends, i.e., that there is no truth and man can't know it, which ends in power being the arbiter of truth. 

However, the existence of math alone proves that some truths are a priori. About these, Goldstein observes that

the mathematician neither resorts to any observations in arriving at his or her mathematical insights nor do these mathematical insights, in and of themselves, entail observations, so that nothing we experience can undermine the grounds we have for knowing them (emphasis mine).

Regarding the italicized passage, wouldn't it be nice if we could say the same of our ultimate theory, or of our theory of the Ultimate? 

Indeed, wouldn't it be nice if we were entitled to such an explanation? I don't mean this in any presumptuous way, rather, in the same way mouths are entitled to food, lungs to air, or male to female. 

Likewise, the intellect is entitled to truth, hence, the only philosophy worthy of man is a common sense realism that presumes the intelligibility of extra-mental being to our intellect. 

Which implies we have a God-given right to reject relativism, subjectivism, materialism, scientism, progressivism, or any other ontologically closed sub-reality.

Along these lines, a few more quick hits from Incompleteness which go to those perennial truths to which we say man is entitled. 

And by the way, when we say "entitled," perhaps we should emphasize that this only functions if it is complementary to a deep and abiding humility and even gratitude. Put conversely, deprived of its complementary aspect, our entitlement becomes a cosmically dysfunctional pride and presumption, as colorfully depicted in the events of Genesis 3.

On to the quick hits:

--Mathematicians carry all their gear in their craniums, which is another way of saying that mathematics is a priori.

--Once proved, a theorem is immune from empirical revision. 

--Gödel's conclusions are mathematical theorems that manage to escape mathematics. They speak from both inside and outside mathematics.... Our minds, in knowing mathematics, are escaping the limitations of man-made systems, grasping the independent truths of abstract reality.

--They [the theorems] are at once mathematical and metamathematical.... It is as if someone painted... a landscape or portrait that represents the general nature of beauty. 

--It is extraordinary that a mathematical result should have anything at all to say about the nature of mathematical truth in general.... mathematical reality must exceed all formal attempts to contain it (emphasis mine).

As to the latter, it is indeed extraordinary that mere quantity should reveal so much about qualities that transcend it.

But how does the seemingly closed system of math escape its own logic and break its own rules? How can 1 + 1 = 3? Or, how does a material cosmos loop around itself in the form of living systems? How does existence turn itself inside out and become experience? How does subjective experience make another loop and begin reflecting upon itself? 

How is it that the Loop is not a closed circle but an open spiral? This might be the Question of questions, ultimately coming down to whether the cosmos itself is an open or closed system.

Shifting gears back to the perennial truths of metaphysics, in an essay called Esoterism and Tradition, Laude writes that religious tradition may provide "the best possible approximation on the terrestrial level of a conformity to Reality," even if it begins to fray at the "human margin." 

This is because tradition as such involves the attempt to clothe the formless in form. God is -- by definition -- supraformal, but is, in the absence of a terrestrial form, literally unthinkable. Thus,

the form is and is not the essence. The form prolongs the essence but it may also veil it. The essence transcends the form but it also manifests itself through it.

It seems that this is precisely the dilemma Gödel resolves vis-a-vis the theorems. For just as no formal system exhausts reality, "the Divine Essence... transcends all determinations" (Laude). Thus, 

We could say, simplifying a little, that exoterism puts the form -- the credo -- above the essence -- Universal Truth -- and accepts the latter only as a function of the former; the form, through its divine origin, is here the criterion of the essence (ibid.).

For Schuon, 

Esoterism, on the contrary, puts the essence above the form and only accepts the latter as a function of the former; for esoterism... the essence is the criterion of form; the one and Universal Truth is the criterion of the various religious forms of the Truth.

Now, "Inconsistent systems are of course complete, because we can prove anything at all in them. They're overcomplete" (Goldstein). They simultaneously explain too much and not enough -- or rather, it is precisely in explaining too much that they paradoxically fall short of a complete explanation.

I cited several examples of this phenomenon in a previous post -- Marx, Freud, and Darwin, for example, in explaining everything, end up explaining nothing. But this is what any ideology does: it superimposes a limiting framework on reality, thus confining what is to what the ideology permits us to see (and prevents us from seeing). 

Now, if Genesis 3 teaches us anything, it is that man is always tempted to reject transcendent truth in favor of a pride-driven, closed system of idea-olatry. But

no validation of our rationality -- of our very sanity -- can be accomplished using our rationality itself (Goldstein).

Thus, there exist millions of people who are sane from within their ideological system, but only insane from outside it. It's not quite correct to say that such ideologues can't be reasoned with. Rather, they can only be reasoned with -- in the manner described by Chesterton in Orthodoxy:

The madman is not the man who has lost his reason. The madman is the man who has lost everything except his reason.

Similarly, Goldstein writes that "Paranoia isn't the abandonment of rationality. Rather, it is rationality run amuck, the inventive search for explanations turned relentless." Such a person is "irrationally rational," characterized by "logic run wild."

More cosmic Orthodoxy via Chesterton:

Poetry is sane because it floats easily in an infinite sea; reason seeks to cross the infinite sea, and so make it finite.... The poet only asks to get his head into the heavens. It is the logician who seeks to get the heavens into his head. And it is his head that splits.

Chesterton makes some additional observations that prefigure Gödel:

the strongest and most unmistakeable mark of madness is this combination between a logical completeness and a spiritual contraction. The lunatic's theory explains a large number of things, but it does not explain them in a large way....

His cosmos may be complete in every rivet and cog-wheel, but still his cosmos is smaller than our world (emphasis mine).

One more important observation:

As long as you have mystery you have health; when you destroy mystery you create morbidity.

The normal man "has always cared more for truth than for consistency. If he saw two truths that seemed to contradict each other, he would take the two truths and the contradiction along with them. His spiritual sight is stereoscopic, like his physical sight: he sees two different pictures at once and yet he sees all the better for that."

Note that this stereoscopy isn't so much horizontal as vertical: it requires the recognition of a hierarchy of levels. To reduce the hierarchy to a single level is to guarantee inconsistency and ultimately absurdity. To appreciate hierarchy is to situate things in their proper place. 

Contrast this with the ideologue, the man of system, the progressive lunatic. As Goldstein says, "Anything at all can be deduced within an inconsistent system, since from a contradiction any proposition can be derived." 

Where does this leave us this morning? With a binary choice: the cosmos is either open to something transcending it, or closed within itself. But if it is closed, it can't be. In other words, its presumed completeness will always generate inconsistency. Which is another way of saying God or absurdity.