[StJacques]

I wrote:

". . . they rely upon axiomatic reasoning rooted in mathematics that establishes a construct which is basically Nominalist in its form (its utility follows from its definitions). . . ."

You wrote:

". . . Nominalism is the position in metaphysics that there exist no universals outside of the mind. . . ."

Yes; exactly. If no universals exist outside of the mind then the truth or falsity of a proposition follows from the definitions and/or assumptions upon which it is based.

[Alamo-Girl]

Thank you for your reply!

Yes; exactly. If no universals exist outside of the mind then the truth or falsity of a proposition follows from the definitions and/or assumptions upon which it is based.

Since I am not a Nominalist, the universals I have used (in this case, mathematical structures such as pi) exist outside of anyone's mind.

It seems to me a Nominalist's propositions would have to be based on his own mental abstractions. Your original statement and its rephrasing would apply in either case (Nomalist or Realist):

1. its utility follows from its definitions

2. the truth or falsity of a proposition follows from the definitions and/or assumptions upon which it is based

IMHO, if the definitions or assumptions are personal imaginings (such as an extreme, a man thinking he's Napoleon) any conclusions therefrom are likely imaginings as well.