Logic and Faith II

Bill Vallicella, the Maverick Philosopher, has commented here on my previous “Logic and Faith” post, with his usual thoughtfulness and insight. He has also expatiated further on the general question of faith and intuition.

I feel the need to add a few more thoughts of my own.

Dr. Vallicella quite rightly corrects my assertion that every logical chain must begin with an act of faith. He points out that one may derive some axioms directly from outer sensory experience, and indeed the example I gave in my post, in which I suggested that we all could agree that there is a large statue standing in New York Harbor, is a representative instance of that sort of derivation. Included, also, in this class of axiom-finding is inner sensory experience, such as the knowledge that I feel tired, or even, I suppose, that I feel sad or angry. The degree of objectivity of such inner sensory experiences, by the way, is an open question; it is quite possible that given the right equipment and understanding an outside observer might one day to be as certain that I feel sad or tired as I am. This may in fact be an important point as regards the source of intuition, but I’ll come back to that in a moment.

Vallicella goes on to suggest other ways in which we may arrive at trustable postulates. For one, he mentions the testimony of reliable witnesses. Such witnesses, though, essentially serve as our sensory proxies; the extent to which we are willing to grant them “power of attorney” as regards our own beliefs is a calculus we make based on previous experiences we have had with them, and the stakes we put at risk by believing them. I think that in an important sense believing a witness is not really a new type of axiom-derivation; we are simply extending the chain that we use when we trust our own senses, and adding a link of a somewhat elastic nature.

Finally, there is intuition. When I spoke of faith in my previous post, this is really what I meant to examine. Dr. Vallicella has quite correctly parsed several other sources of belief and knowledge that I had carelessly lumped together, and I hope that I have now managed to trim them away.

Vallicella gives as an example of intellectual intuition our ability to see the truth of the law of non-contradiction (the assertion that no contradiction can be true). I will add that we are also capable of sensory intuition, in which we are able to discern patterns and regularities in the world even when they are suggested by only the merest hints (or sometimes, even when we are presented with truly ambiguous sensory data), and emotional intuition, in which we assign valuation to plans, ideas, people based not on logic or reason, but just on a “gut feeling”. Very often, much more often than mere chance, these intuitions are a good bet, but they can indeed be wrong. As an example of a misguided intellectual intuition that bedeviled logicians and geometers for millennia, there is Euclid’s notorious Parallel Postulate of plane geometry, which can be expressed in many equivalent ways, one of which is to say that “given any line L, and a point P not on that line, that there is only one line through P that will not intersect L.” The truth of this seemed intuitively obvious to Euclid, sufficiently so at least that he included it in his list of five axioms. It turns out instead that this assumption is neither necessarily true, nor derivable from the other axioms, and in fact a geometry based on a denial of this axiom is the geometry that underpins Einstein’s relativistic description of the spacetime we live in. As for sensory intuition, its unreliability is easily illustrated by optical illusions such as this, and of course lapses in our emotional intuition are, alas, demonstrated again and again by con artists, unfaithful lovers, crooked politicians, and so forth.

Despite all of this, most of the time our intuitions are indeed quite trustworthy. Why? I think it is important to remember that much of the information processing that we do is completely unconscious, and that a great deal of it is done “behind the curtain” by cognitive modules that are the result of our long evolutionary history. As Steven Pinker has gone to great lengths to point out, we are very far from being “Blank Slates”, and we have a tremendous amount of hard-won design built into our skulls. The point is that we are able to do an awful lot of cognitive work without the need to represent either the raw data or the processing itself in our conscious awareness. Such things as number and spatial geometry are such useful abstractions even to a rudimentary human mind that they have long ago been wired into our genome, and we need no longer be distracted by their machinery. Pinker makes a lovely example of the usefulness to early man of counting: if three bears go into a cave, and two come out, is it safe to go in? Obviously this is of significant adaptive value, and by now these categories are wired right in. What Kant saw as a priori can in this light be viewed as our evolutionary inheritance, the result of our biological history.

The next question is: how does faith differ from trusted intuition? Is there a useful distinction to be made?

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