Rodrigo Defends Infinity with Existential Overlapping

Actually written JANUARY 21, 2024

A philosophy cohort of mine, Rodrigo Vanegas, presented me with an interesting argument in defense of intrinsic/objective/metaphysically real infinity. So I’ve been thinking about it.

Having presented Rodrigo with the problem of how infinity creates self-contradictory gaps in existence, i.e., the problem of metaphysical adjacency, he offered what I here call the “existential overlapping” idea as a way to achieve gapless adjacency and thus “defend” metaphysically real infinity.

Rodrigo proposed that two things can be adjacent, without gaps, if we understand the two things as if they occupied ranges on a number-line, wherein Thing-A would occupy locations 0 through 1, and Thing-B would occupy locations 1 through 2. The Things would be adjacent at location-1, and there would be no gaps of self-contradictory nothingness.

While I have already considered this idea, Rodrigo’s presentation of the idea prompted me to think about it deeper and to target the idea for written analysis. So here goes.

The idea tries to get rid of any existential gap between Thing-A and Thing-B by making them overlap where they meet. The overlap is at location 1. We therefore acknowledge that Thing-A and Thing-B must be comprised of parts. For example, the whole idea presumes that there is a part of Thing-A that does not overlap with Thing-B (e.g. 0 - .99999…) and a part of Thing-A that does intersect with Thing-B (e.g. 1).

But now the parts must also have gapless adjacency. So now we need to apply the overlapping idea to all the parts. Each of the adjacent parts must in turn have parts so that they can share the parts at the locations where they are adjacent. Each level of parts needs more parts to achieve gapless adjacency, and the needed parts in turn need more parts, that need more parts, that need more parts … And now we’ve got logical infinite regress. The overlapping idea fails to solve the problem of gapless adjacency; it just repeats the problem infinitely.

This being the case, the metaphysical reality of infinity remains problematic. My inner Zeno remains un-answered.

But there’s more here, for me anyway.

Rodrigo and I were actually supposed to be talking about mereology, because I was trying to explain a conundrum I was having with mereology. I never got a chance to fully explain the conundrum because I was cut off by circumstances.

But you can see a hint of the conundrum I was having in terms of the infinite regress of parts written above. That was where I was going with this. How can parts have gapless adjacency? And maybe they don’t. Maybe there’s actually no adjacency between parts – meaning that all parts are mereological simples that have no size and that space-time does not exist objectively, as an intrinsic feature of existence.

I speculate on such a sizeless existence in my writing “Against Metaphysical Continua”.

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