A thought came to me yesterday about what kinds of actual (as opposed to potential) infinities could exist, and it struck me that any ‘infinite’ whose members are ‘reduced’ from something ‘simple’ (meaning non-composite, seem-less and whole). For example, there are an actually infinite number of true propositions, but there is no set of all true propositions, and perhaps we should think that all such propositions are derivable from one simple true proposition (a maximally specific proposition). Thus, there is no problem, since propositions are only the way we present bits and parts of this one ‘truth’ to ourselves as finite cognizers (perhaps it is a potential infinite). Perhaps what is distinctive about such sets is precisely that there cannot be any single set which contains all the members of that description (for instance, there is no set of all true propositions, nor is there a set of all numbers).
This kind of solution would make numbers and propositions easy to deal with, since there are infinitely many of them and they do, I think, exist. However, what of monads (atoms of substance) in which I am more and more inclined to believe. Leibniz would say that there is an infinite aggregate of monads – but must this be so? Why couldn’t we have something similar to the monadology with a finite aggregate of monads? It seems to me that we could.