Gottlob Frege (1848-1925) was German philosopher and mathematician noted for his achievements in logic and considered by some to be the father of Analytic Philosophy. His work was posthumously popularized by Giuseppe Peano and Bertrand Russell.
The name and content of Begriffsschrift ("Concept-script"), published in 1879, refer to Gottfried Leibniz' project to create a "lingua characterica", expressing "content through written signs in a more precise and clear way than it is possible to do through words." Frege introduces the substitution of the mathematical concepts of functions and arguments for the traditional logical concepts of predicates and subjects, as well as the idea of using a quantifier to bind a variable which ranges over a domain of discourse, laying the foundations for First Order Predicate Logic.
Sense and Reference
Sense and Reference is an 1892 paper introducing a conceptual distinction between what he called "sense" ("Sinn") and "reference" ("Bedeutung") in linguistic expression. To illustrate the difference, he cited the example of the terms "morning star" and "evening star". They have different senses, which is to say "modes of presentation", but they have the same reference, which is to say, they both "mean" or "indicate" ("bedeuten") the planet Venus. Analogously, the mathematical terms "2 x 2" and "3 + 1" differ in sense, but have the same reference, "4".
Frege suggested that the sense of a proposition is composed of the sense of its terms: He called this composite a "thought" ("Gedanke"). The reference of a proposition is then understood to be its truth value. "The morning star is identical to the evening star," is thus understood to be true, i.e. refer to truth, because the terms, despite differing in sense, have an identical reference. Accordingly, a proposition which contains terms that have no reference (i.e. "empty names") cannot itself have a reference: It has no truth value. "Odysseus was set ashore at Ithaca while sound asleep" can only be true or false in so far as "Odysseus" has a reference.
Sense and Reference (as On Sense and Nominatum) is cited in the bibliography of Loglan 1.