On Hell and Forgiveness

[Amarok]

How is the number 4 different in mathematics?  Are you saying that if their are 4 trees in reality, that is subjective?  Do you believe in the basic principle; the law of identity?

I'd suggest reading some Frege or Russell. That will get you started.

There is a difference between saying 'there are four trees' is objective (which I will agree to: it is a publicly observable situation) and saying the number 4 is objective (no publicly observable situation exists for this).

Once again, the use of 4 is a language construct. The number itself doesn't exist as something separate.

And, in math, there are several different mutually exclusive *models* for the natural numbers. Russell proposed one (so four would be the class of all sets with four elements--which can be defined in terms of logic and equality). But there are other definitions that don't have the logical issues that Russell's definition does (being a proper class is problematic--see Russell's paradox).

Von Neumann gave a different definition that is often used in set theory today, but it is far from being the only possible one: see discussions of the difficulty by Hillary Putnam.

When you say the number 4 is 'objective', I think you are missing any number of subtleties concerning how that concept is, or can be, defined. At best, it is an equivalence class of concepts, but that also fails to capture the intuitions many have.

And that is part of the point: we have intuitions, but those intuitions are self-contradictory. The upshot is that '4' is a *language* construct, not something that exists out of a language.

I have also found that people that emphasize the 'law of identity' tend to have not thought very much about these things. Might I suggest a bit of modern model theory as a subject of utility?

Indeed 4 is a description of a quantity not a separate magic thing in it's own right .