Page "Non-Aristotelian logic" Paragraph 2

While Łukasiewicz seems to have spent more time on three-valued logic than any other system, he said that one could keep increasing the number of truth values indefinitely.

Thus, he wrote: " if 0 is interpreted as falsehood, 1 as truth, and other numbers in the interval 0-1 as the degrees of probability corresponding to various possibilities, a many-valued logic is obtained which is expansion of three-valued logic and differs from the latter in certain details.

" Richard Threlkeld Cox later showed in Cox's theorem that any extension of Aristotelian logic to incorporate truth values between 0 and 1, in order to be consistent, must be equivalent to Bayesian probability.