# On what logic is all of classical mathematics true but undecidable statements are neither true nor false?

## Are all mathematical statements either true or false?

Brielfy a mathematical statement is a sentence which is either true or false. It may contain words and symbols. For example “The square root of 4 is 5″ is a mathematical statement (which is, of course, false).

## Is every statement true or false?

every statement is either true or false; these two possibilities are called truth values. An argument in which it is claimed that the conclusion follows necessarily from the premises. In other words, it is claimed that under the assumption that the premises are true it is impossible for the conclusion to be false.

## Are all true statements provable?

We can ask whether a given statement is true in a given model. This is really the only notion of “truth” that makes sense. If all models agree that a statement is true, then that statement is provable in ZFC. If they all agree that it’s false, then there is a proof that it is false.

## Are there true statements that Cannot be proven?

But more crucially, the is no “absolutely unprovable” true statement, since that statement itself could be used as a (true) axiom. A statement can only be provable or unprovable relative to a given, fixed set of axioms; it can’t be unprovable in and of itself.

## Is a mathematical statement true or false?

In math, a certain statement is true if it’s a correct statement, while it’s considered false if it is incorrect. And if the truth of the statement depends on an unknown value, then the statement is open. Being able to determine whether statements are true, false, or open will help you in your math adventures.