Some finitisms

I’m thinking about the kinds of finitisms there are. Here are some:

1. Ontic finitism: There can only be finitely many entities.

2. Concrete finitism: There can only be finitely many concrete entities.

3. Generic finitism: There are only finitely many possible kinds of substances.

4. Weak species finitism: No world contains infinitely many substances of a single species.

5. Strong species finitism: No species contains infinitely many possible individuals.

6. Strong human finitism: There are only finitely many possible human individuals.

7. Causal finitism: Nothing can have infinitely many items in its causal history.

8. Explanatory finitism: Nothing can have infinitely many items in its explanatory history.

I think (1) and (2) are false, because eternalism is true and it is possible to have an infinite future with a new chicken coming into existence every day.

I’ve defended (7) at length. I would love to be able to defend (8), but for reasons discussed in that book, I fear it can’t

I don’t know any reason to believe (3) other than as an implication of (1) together with realism about species. I don’t know any reason to believe (4) other than as an implication of (2) or (5).

I can imagine a combination of metaphysical views on which (6) is defensible. For instance, it might turn out that humans are made out of stuff all of whose qualities are discribable with discrete mathematics, and that there are limits on the discrete quantities (e.g., a minimum and a maximum mass of a human being) in such a way that for any finite segment of human life, there are only finitely many possibilities. If one adds to that the Principle of the Identity of Indiscernibles, in a transworld form, one will have an argument that there can only be finitely many humans. And I suppose some version of this view that applies to species more generally would give (5). That said, I doubt (6) is true.