When one properly makes the analytic versus synthetic distinction one realizes that

**the entire body of conceptual knowledge**

is entirely comprised of stipulated relations between expressions of language.

This explicitly includes

**but is not limited to**every single detail about every aspect of every mathematical system along with the semantics of every mathematical expression of any of these systems.

The only possible rebuttal to the above claim is to find a valid counter-example of a pure concept that is not entirely defined using language. As long as we stay on the analytic side of the analytic/synthetic distinction this is impossible.

To formalize the body of conceptual knowledge merely requires expressing the stipulated relations between expressions of language as relations between finite strings.

So we end up with the simplest possible notion of a formal system that can express every element of the entire body of conceptual knowledge as simply a set of stipulated relations between finite strings.

The notion of True(x) is simply the satisfaction of the stipulated relations in the body of conceptual knowledge and the notion of False(x) is the satisfaction of the negation of x in this same body of knowledge.

**To understand this idea think of this simplification of Curry/Howard Correspondence.**

A software function is named according to the Relation that it represents and returns Boolean.

Finite strings are always Unicode characters. Arguments to this function are finite strings.

">"("5","3") returns true

">"("3","5") returns false

">"("orange","apple") returns false // type mismatch error

">"("apple","orange") returns false // type mismatch error

"◁" is a type of operator

"◁"("cats", "animals") // returns true

Copyright 2019 Pete Olcott