[vehemenz]

Coding is not mathematics. If you'll recall from your philosophy courses (irony of ironies), Russell's project in the Principia Mathematica failed. Mathematics is not just logic, and vice-versa.

Also, the "p exists because of q" form of argument puts philosophy causally "before" these other disciplines.

[holowoodman]

No, you should re-read and understand what exactly failed in the Principia Mathematica. Goedel-Incompleteness only means that either the Principia is short an axiom, or it will produce a contradiction because it already has an axiom too many. Nothing there separates mathematics from logic in any way. Nothing separates coding from mathematics in any way. The only failure the incompleteness proof gives us is that we now know that the Principia will either be found contradictory or incomplete. But that doesn't make it useless at all, our mathematics, coding and logic is still based on the axioms from the Principia and derived proofs. Science works very well with this, our physical description of nature by principia-derived mathematics also didn't turn up any kinds of problems there. The only real failure is the philosophical expectation of being able to generate all mathematical truth from that one set of axioms.

Yes, if you go back to antiquity, there were only philosophy and religion. Science and mathematics were once sub-branches of philosophy. But that's a few thousand years before the internet, and the renaissance at the latest was where philosophy was fully separate from sciences and mathematics.

[baerrie]

Coding does not equal logic. Language precedes every discipline and even the concept of rational rigor. The study of language, and the stabilization of its form, is what laid the groundwork for every discipline after including religion, math, philosophy, etc

[TimorousBestie]

In addition to these points we also have a handful of weaker-than-arithmetic but provably-decidable theories, which jointly encompass almost everything done on a finite computer.