What do paradoxes suggest about human logic?
What they suggest to me is the limitation of human language [philosophical or otherwise] in establishing with any degree of precision the truth about certain relationships.
There are a number of paradoxes [antinomies] philosophers have been debating for centuries—infinite time and space, free will, solipsism, dualism, cause and effect. And we are no closer to resolving them now then ever before.
There may be places logic can’t go. You can’t make the assumption the human brain is fully capable of grasping everything. There may be “realities” it is simply not hard-wired to grasp.
But some of these paradoxes are really just “relationships” invented in the human mind out of the whole cloth that language can be.
Take, for instance, the “arrow paradox” from Aristotle:
If everything when it occupies an equal space is at rest, and if that which is in locomotion is always occupying such a space at any moment, the flying arrow is therefore motionless.
This is, for all pratical purposes, absurd. That is not the way motion unfolds out in the world. It is the way it is made to unfold in Aristotle’s mind.
Or a variation of this is the speculation that between the arrow and its target is a distance. And there is always a precise half way point between them. But when the arrow reaches that point, there is yet another half way point to be reached. And this goes on indefinately. Therefore the arrow never reaches the target.
Purely an intellectual contraption.
We could do the same thing with time. Between now and the day a man is to be executed in prison there is a precise half-way point. And when that point is reached there is another one. And this goes on and on and on. And, therefore, the man is never executed.
What is this but a sleight of mind? The syllogistic logic of going around and around in circles.