ABSTRACT
This chapter focuses on the elements from distinct, philosophical disciplines, following L. Wittgenstein, that truth in the standard models of Arithmetic, Geometry, Set Theory and Linguistics consists in operations on physical paradigms. It shows that some historical facts about Hilbert’s Finitism with some logical truths about Intensional Operators, and well known points about the general character of Wittgenstein’s Philosophy of Mathematics. Professional interest in the foundations of mathematics has focused on meta-mathematics, and the results of K. Godel, but the chapter suggests that both are largely irrelevant to proofs in standard models. It is concerned with their central character being mathematical rather than meta-mathematical, and finitistic, as Wittgenstein claimed, since they are all to do with things we deal with in this world. Wittgenstein used an aesthetic metaphor, drawing on that fact, to characterize the formalists’ ‘useless’ enterprise: they produce pure wallpaper pattern that is decorative designs with no reference, or only a vague reference beyond themselves.
