Definition of proposition in a constructive setting

Question

In a typical discrete math course, we are taught that a proposition is something that is either true or false but not both, which seems to be based on a classical interpretation.

How would one go about defining a proposition in a constructive setting?

Maybe "something that we may attempt to provide evidence for"?

Answer 1

Useful references:

• A.Heyting, Intuitionism: An Introduction (3rd ed. 1971), page 24:

We only assert a proposition if we can prove it; so we only assert that either $a=0$ or $b=0$ if we can prove one of these propositions.

See also Errett Bishop, Foundations of constructive analysis (McGraw-Hill, 1967), Preface, page viii, dealing with the "pragmatic content" of mathematical statements:

It appears that there are certain mathematical statements that are merely evocative, which make assertions without empirical validity.

In a nutshell, according to Intuitionsim (and most constructivists):

knowing [asserting] that a statement $A$ is true means having a proof of it.