Logical vs. historical order

The logical order of primacy in an argument isn’t necessarily the same as the historical order of primacy. For example, Morris Cohen argued in An Introduction to Logic and Scientific Method (1934) that the axioms of a system are often discovered after the theorems. According to Cohen, many of Euclid’s theorems were already known to the Ancient Greeks for hundreds of years before Euclid did his groundbreaking work. Euclid’s contribution wasn’t as much to discover the theorems as to discover the axioms for theorems already known. His contribution was largely to systematize already-existing knowledge.

In other words: What was in the history of ideas come up with and made known before and after doesn’t necessarily match up with what’s logically precedent and antecedent.