On Hell and Forgiveness

[Angrboda]

Yeah, I don't see how resurrecting Frege's failed project adds any light to the discussion.

Of particular note, Steve, you apparently didn't read far enough, the Wikipedia article you quote states, "Although Bertrand Russell later found a major flaw in Frege's work (this flaw is known as Russell's paradox, which is resolved by axiomatic set theory), the book was influential in subsequent developments, such as Principia Mathematica." So the problems with Frege's concepts was resolved by appeal to set theory.  Even ignoring that for the moment, unless you can argue Frege's point independently of Frege, all you're doing is making an appeal to authority which, for various reasons, is unsuccessful.  But if you want to argue Frege on his own terms, knowing that he was ultimately unsuccessful, I'm more than happy to listen.

I stand by my prior arguments.

Wait a minute. I did read to the bottom. The actual article was on his entire work: The Foundations of Arithmetic. It is irrelevant that some of his theories had problems. It says nowhere that his concept of numbers is wrong (the subject at hand). You left off the second half of that paragraph: "The book [Frege's Foundation of Arithmetic] can also be considered the starting point in analytic philosophy, since it revolves mainly around the analysis of language, with the goal of clarifying the concept of number. Frege's views on mathematics are also a starting point on the philosophy of mathematics, since it introduces an innovative account on the epistemology of numbers and math in general, known as logicism."

Now since this is not my area of expertise, perhaps if you explained why Frege's concept of numbers is wrong or has been supplanted...

Not my argument to make, Steve. If you can't carry your own water, I'm not going to carry it for you.

You're attempting to shift the burden of proof fallaciously so that you can rely upon an empty argument from authority. Not gonna fly, Steve.

Your point about the concept of numbers being parts of a whole seem refuted when we consider that numbers at their root are a one-to-one correspondence--not assembled by some addition.

Correspondance is no less dependent on parts and wholes than sets are (e.g. the example of the set being simultaneously a one and a many), so this objection leads nowhere. (And I've not suggested that numbers are "assembled by some addition" so that is a straw man which won't feed the bulldog, either.) You've simply substituted one dependent construct for an equally dependent construct. So we have two problems here. First, you haven't really gotten under the issue and are simply making surface motions which don't address the deeper issues. Second, that you're struggling with my argument abets my initial point that your claim that no one considers numbers subjective, which Neo amended to, no rational person does, was simply hot air. People, serious philosophers and mathematicians, do consider the viewpoint, even if they ultimately conclude against it. I don't know what your original point to Poly was that you were supporting with that statement, but whatever it was, your support for it, at least on this point, appears to have collapsed.

Why don't you reframe whatever point you had been making towards Poly without the bankrupt appeal to what "everybody knows to be the case."