Mystery and Order; the right and left hemispheres

Mystery 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

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[1] 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?”[2] In German this is called Entscheidungsproblem – the decision problem.[3]

Turing found that he could answer this question by framing it in terms of a Turing machine[4] – 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.”[5]

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The Subsidiaritan Criterion of Just Coercion

How can we tell whether a given sort of government coercion is just?

Government just is coercive control. But coercion eo ipso traduces a man’s dignity – which is to say, his status as an image of the Most High, and therefore in his very being a thing worthy of all honor and respect; a King, indeed, within his own small domain. Men ought then to be coerced as little as possible. So the basic problem of just government is to discover where coercion is justified nonetheless; and the moral hazard of all government is that it will coerce where it ought not to. The probability that government will err is obviously very high; so then is the probability that it will coerce unjustly.

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The Gödelian Limit of Political Formalism

It is a straightforward corollary of Gödel’s Incompleteness Theorem that no strict formalization of political theory can possibly adequate to the multifarity of human reality, either in the most general terms or, a fortiori, in the particular and peculiar. Only a very informal formalism respecting genera, types or sorts of political order – as democracy, monarchy, etc. – is practical. When it comes to the formulation of concrete policy for a particular concrete polity, then, only the most general recommendations can make good general sense. And even a good general recommendation based on the eternal verities of human society must be tweaked if it is to fit a particular society in its given historical condition.

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The Proper Terminus of Any Science

Explanations, and the understandings they mediate, must all terminate (at least in principle) upon *some singularity or other* if they are to hang together – if they are to succeed as explanations by satisfying our urge to understand. This is as true for explanations of singular phenomena as it is for explanations of regularities. Science then, of any sort, has no alternative but to adduce some singularity or other as the original fact or truth at the basis of all others. The terminus ad quem of the scientific project must be an account of the terminus a quo of all things: a terminal singularity. This, whether the posited singularity be a historical event such as the Big Bang, or a fundamental equation that can work as a Theory of Everything, or what have you.

But only one sort of terminal singularity can ultimately succeed – not at completing inquiry, for (per Gödel) that completion is not possible to finite beings, but rather at satisfying them that things cohere intelligibly. Only one sort of terminal singularity can set the scientist’s mind finally and fully at ease.

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Immergence

When a complex orderly phenomenon such as consciousness arises in matter, it is these days often ascribed to a mysterious emergence of properties implicit in those of its material substrates. But really it goes the other way. Consciousness – ordered form in general – does not emerge from the material substrate of our world. It rather immerges thereto, from elsewhere. Novelty of all sorts is added to history from without.

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Credo: Resurrexit

Except for a couple years when I was in the wilderness, I have partaken each Easter in at least one liturgical celebration of the Resurrection of Jesus Christ from the dead. As a cathedral chorister, I have often assisted in the celebration of four or five in the year, beginning at 9 PM on Easter Eve and stretching to 5 PM the next day. So I have heard about – let’s see – about 114 Easter sermons. Never once, in any of those homilies, was the fact of the Resurrection ever directly addressed. They generally spoke instead about God’s love, and his power – working in us, of course – to make things in the world all nice and fair, and to heal broken relationships. At most, preachers refer to the Resurrection as the context for their message of hope for renewed worldly life, as if it were a literary device or a metaphor. They never grapple with it directly.*

This has always amazed me. On Easter morning, preachers have their best opportunity of the year, after Christmas, to tackle head on one of the biggest stumbling blocks to faith, before a large audience of unbelievers, or proto-believers, or quasi-believers, or wannabe-but-don’t-know-how-believers, or those who have fallen away from the faith but remember their homeland with nostalgic affection, and would like to return if they could see a way to do so. It is, i.e., a fantastic opportunity for evangelization – not to swell the attendance rolls, but to save souls. Yet they all seem to shy away from the main thing that Easter is about: a dead man come to life again. To a typical modern, the story of the Resurrection looks like – well, it looks like sheer nonsense, crazy talk about an impossibility. And that apparent insanity at the heart of Christianity makes the whole religion incredible, empty, vain, as St. Paul knew (I Corinthians 15:17). Credence in the Resurrection is crucial to conversion; without it, there is no such thing.

But preachers never talk about this difficulty. I cannot resist the conclusion that – perhaps because they are themselves typical moderns – most preachers simply don’t know how to think about the Resurrection, any more than their skeptical auditors on Easter morning. They may believe in it, but they don’t know how to talk about it.

This is a sad state of affairs, because there is nothing especially difficult about the Resurrection.

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Nature Cannot Explain Itself

In his brilliant, aphoristic demolition of the modern, Pure: Modernity, Philosophy and the One, philosopher Mark Anderson explains in a few short paragraphs why nature cannot explain nature:

A particle of matter is because of an act of existence for which it itself is not responsible. It is what it is because of its microstructure, the specific and stable organization of its constitutive elements – in a word, its form, which it itself does not produce. The same is true, mutatis mutandis, of forces and laws of nature, which neither bring themselves into being nor cause their specific and essential character.

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