04 January 2011

Computational Proof that Reality Trumps Stories, Rules, & Theories

This post by Psychologist Mark Changizi explains how vagueness is inherent to all concepts. The direct implication of this observation is that all abstract ideas can be rendered impractical, which provides the opponents of any proposal an opening to criticize it.

[V]agueness is intimately related to the ancient sorites paradox, where from seemingly true premises that (i) a thousand grains of sand makes a heap, and (ii) if n+1 grains of sand make a heap, then n make a heap, one can derive the false conclusion that one grain of sand makes a heap.

When you or I judge whether or not a word applies to an object, we are (in some abstract sense) running a program in the head.

The job of each of these programs (one for each word) is to output YES when input with an object to which the word applies, and to output NO when input with an object to which the word does not apply.

That sounds simple enough! But why, then, do we have vagueness? With programs like this in our head, we’d always get a clear YES or NO answer.

But it isn’t quite so simple.

Some of these “meaning” programs, when asked about some object, will refuse to respond. Instead of responding with a YES or NO, the program will just keep running on and on, until eventually you must give up on it and conclude that the object does not seem to clearly fit, nor clearly not fit.

Our programs in the head for telling us what words mean have “holes” in them. Our concepts have holes. And when a program for some word fails to respond with an answer — when the hole is “hit” — we see that the concept is actually vague.

Your ability to see the boundary of the borderline region [of the holes] is itself fuzzy.

Our concepts not only have holes in them, but unseeable holes. …in the sense that exactly where the borders of the holes are is unclear.

And these aren’t quirks of our brains, but necessary consequences of any computational creature — man or machine — having concepts.

The discussion below the original posting of this article includes Changizi's responses to basic criticisms of the computational premise of the argument.

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