Scholars during the Middle Ages kept warm on winter evenings trying to square the circle, reconcile the forces among three heavenly bodies, and prove that God exists. Squaring the circle meant finding the last digit of pi, and we do not even bother sending super computers on that errand any more. Newton discovered the laws for relating two bodies, although these laws have been repealed by quantum mechanics in the last one hundred years. In his Critique of Pure Reason of 1781, Immanuel Kant brushed aside rational arguments for God as being logically impossible to make way for his fundamentalist type of religion based on faith.
A little more than a century ago an Oxford mathematician, Charles Dodgson, pointed out a small problem in the classical syllogism we consider to be the acme of rational reasoning. Major premise: All As are B. Minor premise: X is an A. Conclusion: X is a B. In the presence of As, Bs, and Xs, anyone who refused to accept that X is a B would stand out as mentally defective.
Dodgson said the logic may not be as compelling as we think, and most logicians today agree. No one who believes both the major and minor premises is forced to accept the conclusion unless he or she also believes that syllogistic reasoning required them to. “Right,” you say. “That is easily fixed. We will just add a new rule that says those who accept the major and minor premises of a syllogism must also accept the conclusion.” No smug here. We still need one more rule that the new assumption is obligatory. I think you can see where this is going.
Today we know Dodgson better by his nom de plume, Lewis Carroll, and the problem was presented in the form of a dialogue between Achilles and the tortoise that took place shortly after Achilles beat the reptile in the race that Zeno said would never be finished. “What the tortoise said to Achilles” is a short Google read.
So far no one has died of such an infinite regress. Typically we just walk away mumbling something like “I don’t have time for this sort of thing and an approximation works fine,” although we are sometimes skeptical of others’ approximations.
But there is a deeper lesson here. There is something in human nature that wants — demands — that there be super-premises that allow us to roll up everything else that we really care about. If there is nothing that gives ultimate meaning to everything else we will make something up. I have heard some howlers, but never met anyone who did not do it. You and I may not agree on what the ultimate premise is, and will often part company over trivial cases. But who can prove that neither of us accepts the existence of a perspective that makes everything else meaningful? Who would deny that this might be called God? Who would say this is illogical?