I am better understanding the “dark night of the soul” that mathematics has been for me.
I think that truth needs to involve an element of fantasy. That sounds like a paradox; but I think that our fantasies are true.
If I visualize something so vividly that it feels at least as real to me as physical reality, what grounds do I say that physical reality is real, and the visualization is unreal?
Well, one ground would be that other people can’t see the visualization; but I’ll address that issue later.
Try it. Visualize a red triangle. Visualize it so strongly that it becomes as real as your own hand. Then visualize it so strongly that it’s more real than your hand. It can be done.
People regularly achieve this sort of transcendence of physical reality on the wings of pure faith. Think of the ascetics who deprive and punish their bodies for the sake of a belief. Think of the feminists, who have managed to make widely accepted a truth that has no evidence other than what people’s hearts tell them. Think of the mathematicians, who study a vast paradise of nonexistent and impossible objects. Think of the fiction writers, who live in an imaginary world of their own creation.
Fantasy, the truth that comes from inside us, is subjective truth. The truth that comes from examining the outside world, is objective truth.
Subjective truth is considered by many to be nonexistent. And indeed, I cannot assert the existence of subjective truth in the same way that I can assert that 2+2=4. The reason is that subjective truth is subjectively true; whereas objective truth is objectively true. But subjective truth is not objectively true. Similarly, objective truth is not subjectively true.
Objective truth can only be determined through the methods of empiricism. For subjective truth, the method is this: whatever you wish to be true, is true.
The nature of our experience at this nexus places great emphasis on objective truth. We are, in the ordinary course of things, absorbed in the shuffle of the physical world and its necessities. And this same emphasis on objectivity is reflected in our intellectual climate.
Subjective truth is hard to find, hard to notice, hard to hold onto. But it is better and more important than objective truth.
People have different subjective truths. I can see my own visualizations; you cannot. My passions are not your passions. My ideals are not your ideals.
There is therefore great paradox in trying to share one’s subjective truth. Subjective truth is not objectively true. What is true for me, may not be true for you. For the most part, therefore, we must have our own truth and let others have theirs. The problem of sharing truths is a hard one.
I cannot wish to share my truth with another, if for them it is falsehood. I can only wish to share it with them, if for them it is truth.