A proposition is the (homotopy) type of its proofs
نویسنده
چکیده
There are, at first blush, two kinds of construction involved: constructions of proofs of some proposition and constructions of objects of some type. But I will argue that, from the point of view of foundations of mathematics, there is no difference between the two notions. A proposition may be regarded as a type of object, namely, the type of its proofs. Conversely, a type Amay be regarded as a proposition, namely, the proposition whose proofs are the objects of type A. So a proposition A is true just in case there is an object of type A.
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