Kant turns to the algebraic function to provide the necessary connexion to counter Hume. This relation is different from material implication, the “hypothetic judgment form” of general logic.

If p, then q. What is this? A reflection in language of some definite and hard structure, which we express and codify as material implication, itself possibly reducible by truth-functional definition to “not-p or q.”

Truth is close to being, but truth functional

A “connexion” of input and output

A function is a process or a relation that associates each element x of a set X, the domain of the function, to a single element y of another set Y (possibly the same set), the codomain of the function. If the function is called ƒ, this relation is denoted

y = ƒ (x)

and is read “ƒ of x”.

The element x is the argument or input of the function, and y is the value of the function, the output, or the image of x by ƒ. The symbol that is used for representing the input is the variable of the function (one often says that ƒ is a function of the variable x).