A thought on Existence versus Substance

I’ve spent a significant amount of time thinking about how it is that the mind can consider objects that don’t seem to be obviously physically real. For example, Cantor’s cardinals don’t have any convenient corporeal form, yet there are theorems that rigorously govern their notion, that we can discern from other statements that are false about that very same topic. This, in my opinion, leads to the question of how it is that the mind, which science says should be entirely physical, can consider objects that don’t appear to be a part of 3-space, and derive apparently true statements about those objects. I think I have a sensible answer, which is that all true statements govern reality, and in that sense, they exist, even if they don’t have a location. For example, the rules of combinatorics govern at all points in space in time, and therefore exist in that sense. However, the rules of combinatorics are not embedded in some cosmic ledger, and instead, exist through the effects that they have on objects. We’re still in a bit of trouble with Cantor, because nothing within the human purview is infinite. So then we’re resigned to considering ideas that govern other ideas, under the assumption those latter ideas exist, and I’m fine with that, and perhaps that’s the right answer. But all of this points to the possibility that the human mind, distinct from the brain, is similarly without a location, and instead governs the behavior of a sentient person, including their brain. Perhaps this is a leap, but we need something to explain the fact that the mind can consider objects outside 3-space that have no finite expression, that we instead understand through reference. That is, when I write \aleph_0, I’m not encoding or representing anything, and I am instead referencing something that is in your memory as a reader, thereby conjuring a concept with which you’re already familiar, that cannot be expressed physically in finite time.


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