In his 1941 Ph.D. thesis, written at Yale under Frederick Fitch, the logician and analytic philosopher Richard Milton Martin (1916–85) discovered virtual sets before Quine, and was possibly the first non-Pole other than Woodger to employ a mereological system. From these and other devices, he gradually forged a first order theory capable of expressing its own syntax as well as some semantics and pragmatics (via an event logic), all while abstaining from set and model theory (consistent with his nominalist principles) and from modality and other intensional notions. Between 1943 and 1992, Martin published 16 books and about 240 papers (of which 179 were included in his books) on logic, linguistics, mathematics, metaphysics, the semiotic triad, science, phenomenology, theology, Frege, Peirce, and Whitehead. The young Chomsky took every course Martin taught at Penn, and Quine’s Word and Object (1960) cites Martin with approval. Yet no reference work on twentieth century philosophy has an entry under his name—hence this paper.

We show methods to construct, and give examples of, consistent intuitionistic theories that admit quantifier elimination. The examples are very intuitionistic in the sense that they prove the negation of the schema of linearity.