MSC 03 · Logic & foundations

Mathematical logic & foundations

Model theory, proof theory, recursion theory: formal systems, provability, computability.

Founded: 1879 — Frege's Begriffsschrift, the first fully formal logical system

The claim

Henri Poincaré, 1905: La Logique reste donc stérile, à moins d'être fécondée par l'intuition (“Logic remains sterile unless fertilized by intuition”); after Russell's paradox: “Logistic is no longer sterile — it engenders the antinomy.”

Source: Poincaré, essays collected in Science et méthode, c. 1905–06 (primary French text).

Aimed at the Peano–Russell logicist program specifically, not at the later technical subfields (model theory, recursion theory) that didn't exist yet.

What happened

Model checking (1981) — Clarke, Emerson & Sifakis — 2007 Turing Award; industry-standard hardware/protocol verification.
Formally verified software (seL4) (2009) — Curry–Howard-based proof assistants; seL4's machine-checked correctness proof is deployed in Qualcomm chipsets and DARPA's HACMS drone program.

102 years — founding (1879) to first real-world technique (model checking, 1981)

Verdict: Named dismissal, later applied.

Confidence: medium-high.