Sentence examples for mathematical sentences from inspiring English sources

Thus, to say that philosophers of mathematics are interested in figuring out how to interpret mathematical sentences is just to say that they want to provide a semantic theory for the language of mathematics.

In sum, then, the idea here is that fictionalists about pure mathematics can endorse a paraphrase nominalist view of mixed mathematical sentences.

There is no evidence, however, that people use mathematical sentences nonliterally.

Fictionalists then argue that it is not a bad thing that mathematical sentences are not literally true.

The first is a straightforward question of interpretation: What is the best way to interpret standard mathematical sentences and theories?

Perhaps the simplest and most straightforward is metamathematical formalism, which holds that ordinary mathematical sentences that seem to be about things such as numbers are really about mathematical sentences and theories.

"They're a single mathematical sentence that is capable of describing the miraculously beautiful and diverse behaviour of almost all of Earth's fluids," she says.

For it is easier to assess whether a mathematical sentence is true than whether a mathematical intuition is veridical.

Thus, on this view, a mathematical sentence is fictionalistically correct if and only if it would have been true if there had actually existed abstract mathematical objects of the kinds that platonists have in mind.

Where classical platonism says that a mathematical sentence S is true just in case the objects that S talks about have the properties that S ascribes to them, the present form of intuitionism says that S is true (in some suitably lightweight sense) just in case S is provable.

How exactly acceptance should be defined is a matter of some controversy, but one obvious way to proceed here is to claim that fictionalists accept a pure mathematical sentence S if and only if they believe that S is true in the story of mathematics.