Sentence examples for most mathematical statements from inspiring English sources

First-order logic is a mathematical language in which most mathematical statements can be formulated.

The view also holds that most mathematical statements that are deemed to be true are in fact true.5 Thus truth-value realism is clearly a metaphysical view.

The nominalistic account of mathematics that will now be discussed holds that all existential mathematical statements are false simply because there are no mathematical entities.

Frege was able to explain most mathematical notions with the help of his comprehension scheme, which asserts that, for every ϕ (formula or statement), there should exist a set X such that, for all x, x ∊ X if and only if ϕ(x) is true.

This means two things: mathematical statements are general, and they are confirmed by proof.

A mathematician friend recently explained that there is a whole class of mathematical statements that can be called independent.

Given the existence of mathematical objects, mathematical statements are true in the same way as scientific statements are true.

Mathematical platonism clearly motivates truth-value realism by providing an account of how mathematical statements get their truth-values.

As just noted, without such operators, mathematical fictionalism produces non-standard attributions of truth-values to mathematical statements.

Electrons and relations among them make certain quantum-mechanical statements true; in turn, mathematical objects and relations among them make the corresponding mathematical statements true.

In particular, there is no change in the syntax of mathematical statements.