And what lay beyond the limits?

In this case it was the realization that what you had long suspected was in fact true. That mathematics had no limits. That it was inexhaustible. There was no longer any question about that. And now you had to sit down and think about the universe.

And what did you think? About the universe.

You thought that your inquiry was going to labor under a shrinking availability of the empirical. Even while you worked the universe was receding.

So what would you bring to bear on the inquiry?

I suppose the only thing that you had. Your mind.

And why would you think that your mind was up to the task?

Because we’re here. We’re not someplace else. And there is nothing else to know. Some of Gödel’s notions were beyond questionable. I thought about his platonism but then I thought that it was not so different from Frege’s. Take another look? Not much help. I thought that perhaps the same daring that had led them to their foundational ideas might very well produce other inquiries indistinguishable from gibberish. I put all that away for a while. But it wouldnt stay away. I disagreed more and more with Aristotle. He came to seem more like this blank slate guy. I knew that it was just not so that at birth we were not human beings. I get it that he understood that the mind has a form but he didnt seem to understand what that meant. The mind has to be capable of its own existence.

I dont understand what that means.

I know. I just dont know some other way to put it. I understood that if you allowed yourself to become totally entangled you might not find your way out again. Worse, you might not want to.

Yes. Abidement. Is that a word?

No. The noun would be abidance. But abidance is a general state to abidement’s specific. There is no answer to the question of unanimity among mathematicians. My new friend Chihara—perhaps a fan of Gödel but certainly not of his intuitions—says that mathematicians regarded as biological organisms are basically quite similar.

Is this how he explains their agreement about mathematics? By saying that they are all alike?

I think that most mathematicians would miss the humor in that statement. And it would hardly explain our disagreement about almost everything else. I suppose too that you could say that mathematical intuition only explains an access to mathematics and not to its existence.

So how do you explain its existence?

Maybe the best you can do is point at it. After Wittgenstein. It’s the problems that constitute the body of mathematics, not the answers. Which the problems assume.

Is that true?

I dont know what’s true. But maybe that would account for the sense of discovery.

Are we circling the notion of tautology in mathematics?

Rather nice that. Circling the tautology.

But you’re still an admirer of Gödel.

Very much.

And your new friend?