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Gottlob Frege (1848 - 1925) is one of the major founders of modern formal logic (symbolic logic, mathematical logic). His Begriffschrift is the first complete system of modern logic, running all the way through set theory. Alas, Russell found a contradiction in it (the set of all sets not containing itself both does and does not contain itself). This led to a revision of the whole project of logic and eventually to separating set theory off.

For Lojban, Frege's main contribution is the distinction between Sinn (sense, designation) and Bedeutung (reference, denotation). For a given predicate, the denotation is simply the set of all the things to which the predicate refers ("cow" refers to cows, say). The designation is that by which the reference takes place -- what it is about cows that make then the denotation of the word "cow." The same applies to names and sentences. Frege held that e.g. properties were things with holes in them, to be filled by things to make propositions. This led eventually to devises like the lambda calculus, that represented properties explicitly in this way.

Because "Hesperos is Phosphoros" is newsworthy (or was a couple thousand years ago) and "Hesperos is Hesperos" is not, Frege set out to examine the role of sense -- as opposed to reference -- in language and logic, thereby beginning the development of intentional logic, as well as being a leader of the normal, extentional form. The main points that come up from this in Lojban (all of them already in Frege) are

  1. In oblique contexts, the reference of a word is its normal sense.
  1. Therefore, in oblique contexts a word may have a reference even if it does not in the non-oblique context or it may have a different reference.
  1. Consequently, names may not be moved from oblique to non-oblique context
  1. nor quantified over outside of context
  1. nor may identicals be exchanged outside the context in which the identity is asserted.

Frege taught Carnap logic, Carnap taught Broadbeck,and Broadbeck taught James Cooke Brown. Frege (and Carnap) were active in the constructed language movements at the end of the 19th century and between the world wars.