-The Buddhist “tetralemma” of the philosopher Nāgārjuna (2nd or 3rd Century AD) : “Anything is either true, or not true, or both true and not true, or neither.”
-Boole, De Morgan, Frege, Russell (axiomatic approach), Wittgenstein (semantic approach), Emil Post (proved both axiomatic and semantic approach are complete), Peano, Godel etc
-Brouwer (rejects: formalism, law of excluded middle, proof by reductio ab absurdum, platonism. Like Kant he belived arithmetic is synthetic a priori, unlike Kant he believed geometry is analytic a priori- the opposite of Frege’s position; mathematical constructions are just mental entities)-Hilbert
The Latin phrase “ibis redibis non morieris in bello” is found in the Chronicon, a chronicle written in the 13th Century by the French Cirstercian Alberic of Trois-Fontaines. Alberic attributes that phrase to Ancient Roman oracles, who were visited by soldiers to make prophecies on their fate in the advent of a war. The interesting bit about this phrase is that, due to the peculiarities of the Latin Language, it could have two different meanings depending on the punctuation.
With the following punctuation “ibis, redibis, non morieris in bello” the phrase means “you will go, you will return, you will not die in war”. However with this other punctuation “ibis, redibis non, morieris in bello” the phrase means “You will go, you will not come back, you will die in war”. It goes without saying that in oral communication, where there is no such thing as punctuation, the oracle has a clear advantage with this ambiguous phrase: depending on the outcome of the war, he can twist the meaning of the phrase accordingly…