Philosophical Skeleton Keys: Archetypes, Forms, & Angels

Ockham comes in for a lot of criticism around these parts, the poor honest earnest man. And not unrightly, perhaps, given his (largely innocent and inadvertent) role in the incipience of the prevalent modern nominalism that has gutted the West (he was not really much of a nominalist, as we think of nominalism these days). But in most things he was on target (this is true of all heretics, scoundrels, sinners, and fools (or else they’d die before they could do much damage, understood by their contemporaries as mere silly kooks)). Most of all, he was right in respect to his famous Razor, which more than any of his other immense contributions to human thought will surely warrant his everlasting renown – his status, shared with only five or six other philosophers, as a household name (at least among those who consider themselves somewhat educated). Even men who know nothing else whatever of epistemology or philosophy of science have some notion of Ockham’s Razor. His Principle of Parsimony is perhaps the most important operational, practical principle of thought (the Principle of Sufficient Reason, e.g., is by contrast ontological; or again e.g., the Principle of Noncontradiction is logical; and so forth). It is the whole basis of American Pragmatism, which is to say, of the philosophy of science universally presupposed in the practice of professional scientists. It is followed in its pragmatic importance – opinions differ about their proper order – by the Principle of Elegance (the more beautiful theory is more likely to be true) and the Principle of Adequacy (theories must adequate to the entirety of their proper domain). I would add also the Principle of Serendipity – as I here now decide to name it, not knowing how other thinkers might have done so: the principle, i.e., that a true theory is likely to explain more things, and they unsuspected things, than we had looked for it to explain – things that, i.e., are outside its (expected) proper domain (huge swathes of mathematics, e.g., turn out to exemplify the Principle of Serendipity).

Ockham, then, God Bless him: All else equal, that theory is best which is simplest – which postulates the fewest types of concrete entities.

So then: what about the Platonic Forms? Ockham’s Razor – a native, chthonic tendency in my thinking from infancy – bugged me about them from the first moment I read of them. What the heck are they? Are they a different sort of thing than the things of this world? What’s the Platonic Realm, for Heaven’s sake? Where is it? How does it interact with our own? If it does interact with our own, then isn’t it really integral with our own? If so, then what sets the Forms apart from their contingent instantiations here below? What does eternity have to do with creaturity?

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Chaos and Order; the right and left hemispheres

Chaos and Order; the right and left hemispheres

In The Master and His Emissary, Iain McGilchrist writes that a creature like a bird needs two types of consciousness simultaneously. It needs to be able to focus on something specific, such as pecking at food, while it also needs to keep an eye out for predators which requires a more general awareness of environment.

These are quite different activities. The Left Hemisphere (LH) is adapted for a narrow focus. The Right Hemisphere (RH) for the broad. The brains of human beings have the same division of function.

The LH governs the right side of the body, the RH, the left side. With birds, the left eye (RH) looks for predators, the right eye (LH) focuses on food and specifics. Since danger can take many forms and is unpredictable, the RH has to be very open-minded. Continue reading

The rationale of a brittle Church

Why it may be good for the Church to be brittle

Bruce Charlton comments on the “brittleness” of the Catholic Church.

I feel that with the RCC it is all or nothing – to be viable it needs to be authoritarian, heavy-handed, and anti-individual; and any attempt to reform the undesirable aspects will just smash it.

I agree, although I used the word “fragility” instead.

I do think we should be careful in deciding what is and is not “desirable”.  Vulnerability is per se bad, of course.  Then again, falsifiability is a virtue in a belief system; we don’t want our theories to be “flexible”.  That the Catholic Church can hypothetically lose or sabotage its credibility is a testament to its current clarity.

A Catholic apologist could say that Christ wants the Church to have one particular teaching and to operate in one particular way and that He arranged things so that the Church will fall apart if either is modified.  An institution with more social capital, more sociological attractiveness, could presumably turn that capital to other purposes and still function.  I’ve said before that it is a credit to Christianity that it dies so quickly when it is liberalized.  That the universities have–at least on the surface–prospered so well under political correctness says something uncomplimentary about academia’s real driving force, or that of we its denizens.

Lastly, we could entertain the possibility that the truth is not what we humans would prefer it to be, that popular belief systems have been “optimized” to human wishes to such a point that the truth, whose attractiveness is constrained in ways falsehoods’ are not, is quite unpalatable to modern men given the alternatives, and can only be imposed as dogma during our impressionable years.  Not that an authoritarian religion is particularly likely to be true, but rather that only an authoritarian religion might be true.  After all, Catholicism is predestination without assurance of salvation, moral rigor without the compensating pleasures of self-righteousness, being “deep in history” but always on the losing side, and who wants that?

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Gödel’s Theorem (revised)

Kurt Gödel[1] was a Platonist,[2] logician and mathematician who developed the intention of making a profound and lasting impact on philosophical mathematics. His next task was to think of something! Amazingly, at the age of twenty five, he achieved his goal, publishing his incompleteness theorem.

Godel and Einstein

Kurt Gödel and Einstein

A good friend of Albert Einstein’s, Einstein once said that late in life when his own work was not amounting to much, the only reason he bothered going to his office at the Institute for Advanced Study at Princeton was for the pleasure of walking home with Gödel.

John von Neumann wrote: “Kurt Gödel’s achievement in modern logic is singular and monumental – indeed it is more than a monument, it is a landmark which will remain visible far in space and time. … The subject of logic has certainly completely changed its nature and possibilities with Gödel’s achievement.”[3]

While at university, Gödel attended a seminar run by David Hilbert who posed the problem of completeness: Are the axioms of a formal system sufficient to derive every statement that is true in all models of the system? Continue reading

The Halting Problem – there is, definitively, more to thinking than computation

Alan Turing

Alan Turing

Kurt Gödel’s Incompleteness Theorem was inspired by David Hilbert’s question “Are the axioms of a formal system sufficient to derive every statement that is true in all models of the system?” Hilbert played the same role regarding Alan Turing’s proof of the halting problem. Hilbert had asked: “Is there some mechanical procedure [an algorithm] for answering all mathematical problems, belonging to some broad, but well-defined class?”[1] In German this is called Entscheidungsproblem – the decision problem.[2]

Turing found that he could answer this question by framing it in terms of a Turing machine[3] – could there be a program that could determine whether any other arbitrary computer program and input would eventually stop or just loop forever? This was called the halting problem.

“Alan Turing proved in 1936 that a general algorithm to solve the halting problem for all possible program-input pairs cannot exist.”[4]

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The Form of Forms is Itself Formless

That which has no form cannot be conceived – and vice versa. It’s easy to see that this is so when we try to think of what a square circle is like, or a four-sided triangle.

But, let’s talk about God.

To put the same thing another way: that than which no greater can be conceived by any mind cannot be conceived by any mind. If that than which no greater can be conceived could be conceived by any mind, then that mind would insofarforth understand how its conception of that thing could be surpassed, and would realize that in conceiving of it he had not yet quite conceived of that than which no greater can be conceived. He would realize that he had not been thinking of the unsurpassable. He would, i.e., realize that he had been thinking, not of God, but rather of something like Gaunilo’s Island, than which always some greater island might be conceived.

So, here’s the shocking consequence of these considerations: Not even God can conceive himself.

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Happy Valentine’s Day! Now Get Over Yourself & On to a Holy Lent

One of the oddities I have noticed in my time as a dour dire Orthospherean is that we seem to get quite a few followers who are into self-actualization, somehow or other.

It’s odd. Self-actualization is so very *modern,* after all, and we are … not. It is, we might then say, somewhat heterospherean.

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Incarnation & Transubstantiation are Formally Analogous

Transubstantiation stymies us in the same way, and for the same reason, as the Incarnation. In both cases, God takes embodiment in a finite creaturely vessel. The Logos takes the form of man and of bread (and likewise of Church, and Word – but tace re them for the nonce). These forms remain what they were. Jesus the man is still a man – Good News for us, since only qua man could he make strictly human reparation to God for the sins of Man, thus healing the cosmic wounds particularly inflicted by men – and the bread is still just as bready as ever – again, good, or we could not eat him, and so partake his Body and its sacrificial redemption of all our predicaments. The human nature is not driven out of the man by the divine nature, and the breadiness of the bread is not driven out by the divinity of it. On the contrary, they are each perfected. When God becomes man, a man – and, so, Man in general – becomes the God, so that men (can) become gods. Likewise, when God becomes bread, the bread becomes the supersubstantial Bread of Heaven: it becomes the God, who is the manna that feeds the angels, and the other members of God’s Body. Us.

We are what we eat, deo gracias.

In both cases, the soma remains soma; and, so, as soma, divine participant and influence in this world – a solid, as heavy as any stone, and so therefore scandalous to any who would pass by.

The true question is this: why should either Incarnation or Transubstantiation so scandalize us? Is it not only, merely, that these Incorporations of the divine into his creation are difficult for us to comprehend?

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Plato’s Cave

Plato’s Cave

Plato’s allegory of the cave appears in Book VII of Plato’s most famous and longest dialog, The Republic. Plato’s dialogs frequently star Plato’s teacher Socrates as a character. The dialogs involved discussions and philosophical arguments between various characters, some of whom were based on real people. Plato particularly disliked the sophists who were professional rhetoricians and who seemed to care more about money and social success than truth. In fact, Plato accused them of teaching their students how to make the worse argument appear better – enabling their students to convict the innocent and set free the guilty.

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Established Sacerdotal Hierarchy Controls for Competitive Holiness Spirals

Holiness spirals are not first a search for status, although once they have got going, they do result in an arms race to see who is holiest among the Pharisees, thus of the highest moral and political rank, and thus least suitable as a scapegoat.

They are, first, a search for the proper constraints of true holiness upon conduct. Men are Fallen, and live in a Fallen, corrupt world; and they know it. They want to get holy; they want desperately to get ritually pure. Until they can honestly feel that they have done so, they will feel terrific anxiety, and thrash about in their predicaments like a bear in a trap.

Trapped bears are very dangerous.

When there is no established sacerdotal hierarchy that can authoritatively define the unquestionable constraints of holiness, and then offer men a way to get back within those constraints when they have strayed beyond their pale – that can give them a way to know that they have reached safe harbor – then men are going to push and push toward holiness however they can discern it according to their own best lights, without let or correction, and without possibility of any satisfactory completion of the search (because a forecondition of success for any search is a clear definition of success – such as can be authoritatively furnished to the searcher only by an incontrovertible authority). Anyone who disagrees with the notions of those who find that as a result of their personal quest for holiness they themselves are of the holiest sort then becomes a legitimate scapegoat in their eyes, and so a social enemy. There is then mutual repudiation and scapegoating of adversarial sectarians; mutual excommunication; schism; and, with the ensuing conflict of irreconcilable cults, civil war either hot or cold.

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