Sentence examples for mathematical proposition from inspiring English sources
The phrase "mathematical proposition" is correct and usable in written English
It can be used when referring to a statement or assertion in mathematics that can be proven true or false. Example: "The Pythagorean theorem is a well-known mathematical proposition that relates the sides of a right triangle."
There cannot be "undecidable propositions," Wittgenstein argues (PR §173), because an expression that is not decidable in some actual calculus is simply not a mathematical proposition, since "every proposition in mathematics must belong to a calculus of mathematics" (PG 376).
Whether or not it is ultimately defensible and this is an absolutely crucial question for Wittgenstein's Philosophy of Mathematics this strongly counter-intuitive aspect of Wittgenstein's account of algorithmic decidability, proof, and the sense of a mathematical proposition is a piece with his rejection of predeterminacy in mathematics.
What could it mean to say that a mathematical proposition was true if there was no possibility of proving it?
Mathematicians once believed that the truth or falsity of any mathematical proposition could be decided by applying the rules of mathematical logic.
There is no guarantee, for example, that for an arbitrary mathematical proposition p, either p or not-p can be proved.
In this sense of conversion, the passage from a proposition to its converse is not, in general, a valid inference; and though often a mathematical proposition and its converse may both hold, separate proofs must be given for each case.
It was for this reason that Kant regarded mathematical propositions as synthetic, since he was convinced rightly that mathematics advances our knowledge.
Philosophers have a tendency to step outside the framework of mathematics and ask "from the outside" whether mathematical objects really exist and whether mathematical propositions are really true.
Gödel showed that no such language can formalize proofs of all true mathematical propositions.
Euclid, like geometers in the generation before him, divided mathematical propositions into two kinds: "theorems" and "problems".
At least one of them has been shown to be insoluble in principle; it falls into Gödel's category of formally undecidable mathematical propositions.
