A Concrete Exemplification of the Inexorable Internal Logic of the Fall

To my recent post on the internal logic of the Fall, in which I argued that under that logic the Fall was liberation from a cruel delusion that YHWH is anyone special, and so a turn toward hard good solid real truth, in which its advocates, both human and demonic, as basically nice guys, could not but do their best to convince us to follow them in their rebellion against YHWH and his Father El Elyon, our loyal leftist atheist commenter and friend a.morphous had this to say, God bless and keep and save the poor man:

Maybe we differ [about the Fall] because you think it would be better for it not to have happened. I disagree that this is desirable, but I don’t really have an argument, it’s more a matter of esthetics. Sinless and perfect humans would not be very interesting, and would be less than fully human.

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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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Kwagunt: Creek and Canyon

When I was 18 I was fascinated with American Pragmatism and its theory of truth. I devoured the works of William James and Charles Peirce, the founders of that epistemological school (most of them, anyway; when it comes to scholarship, I’m a hopeless dilettante). They are two of the most amiable minds I have ever encountered. They argued that we come to believe that propositions are true, not so much because they really are, as because they are expedient for us to believe. So, what we call truth is what it is expedient for us to believe – whether or not what we believe really is true.

This notion raised a firestorm when it was proposed in the late 19th century. James and Peirce both expressed themselves strongly, so it was not perhaps unnatural that they were widely understood to mean that truth is nothing but what it is expedient for us to believe. They did not; they meant only that we are so made as to feel that a proposition is true, or likely to be true, or “close enough for government work,” when it works out well in practice – in mundane life, or in scientific experiment, or when tested by logic, or when fitted to our other well-tested beliefs. So, Pragmatism is not so much an epistemological theory, properly speaking, as it is psychological. This has not stopped later generations of Pragmatists from insisting that there is no final Truth, no terminus ad quem of intellectual inquiry, but rather only one waypoint after another in an endless process of searching that is designed only to get us through life, from one approximation of a good understanding to the next.

I was thinking about all this one day as I hiked along the slick muddy bed of Kwagunt Creek, which flows down a canyon to meet the Colorado River in the Grand Canyon, where I was then sojourning as a whitewater boatman. Pragmatism’s insights into our intellectual operations – or mine, anyway – seemed undeniably accurate. How then could I ever know that I had understood a real truth? I mean, there would be nothing to prevent me from such a veridical discovery, but absent any objective criterion of truth – such as, you know, whether or not a notion was true *in fact* – nothing to show me that I had ever achieved it, either.

It was then that I slipped in the mud, very nearly falling on a small boulder and hurting myself quite badly. I thought first, chuckling, about Dr. Johnson’s retort to Bishop Berkeley’s Idealism, which was to kick a stone and demand whether the pain that resulted were merely ideal. I thought then about pain, and what it tells us about our relation to the world. It occurred to me suddenly that pain would be totally useless, indeed worse than useless, unless it conveyed veracious information. There would be no reason for an animal to be equipped with pain, and good reason for it to be insensible thereto, unless the pain conveyed knowledge. Indeed, if an animal’s perceptions of any sort were not at least mostly veridical, its survival prospects would be terrible. So, there can be no way that animals – including man – that have survived millions of years of testing by nature can be poorly set up to apprehend those aspects of the environment that are really important to their lives, to their prosperity, survival, and reproduction. On the contrary.

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