Dear Joseph Quinn,
I apologize for my failed attempt at chiasmus. I fear it was about as unShakespearean in its command of language as writing ever gets. However, I do hope it got my point across–Truth is infinite, and the infinite is Truth. It’s based off of something you said during one of your mathematics lectures, when you were explaining how infinity can only ever be defined in a higher dimension. In other words, infinity on a number line (one dimension) can only be defined using a plane (two dimensions), and infinity on a plane can only be defined in three dimensions. The actual explanation behind that was a bit longer, and certainly you remember why. So let’s not get into that.
What I do want to focus on is the part where you said that infinity is like Truth. You drew an analogy there–Truth is like infinity because Truth in one language can only defined using another language, another dimension. I looked up this claim, and it turns out that the guy who said this was Tarski. It also turns out that that claim only applies to formal (not natural) languages.
Regardless, I think it was a brilliant analogy.
The Truth of our world is impossible to define within the confines of our world. After all, Truth encompasses everything; it is infinite. Physicists have already realized that the four dimensions (three spacial and one temporal) that we perceive cannot be explained in only four dimensions. It’s like how in the story of the blind men and the elephant, the Truth would be that they were all feeling an elephant–not a snake, pipe, tree branch, or anything else. In that way, I disagree with anekāntavāda, the Jainist concept of multiple truths. Just because you have a piece of the Truth does not mean that it is Truth. Truth is all-encompassing; it is infinite. But infinity is itself not just a number. It can be treated as one (I got lost partway through your explanation of transfinite numbers), but it is really just an incredibly complicated concept.
So what is Truth? Could I redefine Truth as a single answer? A single value, like 42? Perhaps it would require the defining of transfalsehood (get it? transfinite -> transfalsehood?). Or maybe it’s that Truth is infinitely more complicated than the concept of infinity, because the infinity which exists within our universe would have to be defined by Truth. Perhaps there must be another universe in order for our universe to be defined. Is Truth truly infinite?
Maybe I’ll be able to attend another one of your lectures, and maybe then I’ll be able to ask you these questions. Good luck on getting your PhD!