Even though the model referred to satisfies the theory, etc., it is 'unintended'; and we recognize that it is unintended from the description through… - Hilary Putnam

Analytic philosophers - both in the 'constructivist' camp and in the camp that studies 'the ordinary use of words' - are disturbingly unanimous in regarding 2-valued logic as having a privileged position: privileged, not just in the sense of corresponding to the way we do speak, but in the sense of having no serious rival for logical reasons. If the foregoing analysis is correct, this is a prejudice of the same kind as the famous prejudice in favor of a privileged status for Euclidean geometry (a prejudice that survives in the tendency to cite 'space has three dimensions' as some kind of 'necessary' truth). One can go over from a 2-valued to a 3-valued logic without totally changing the meaning of 'true' and 'false'; and not just in silly ways, like the ones usually cited (e.g. equating truth with high probability, falsity with low probability, and middlehood with 'in between' probability).

Carnap was driven from Germany by Hitler, and his position has been condemned in the Soviet Union as 'subjective idealism*. Even in the United States, there have been a great many who could not understand this attempt to turn philosophy into a scientific discipline with substantive scientific results, and who have been led to extreme and absurd misinterpretations of the work I have been reporting to you here. Few, perhaps, would have expected traditional empiricism to lead to the development of a speculative theory of ' universal learning machines'; and yet, in retrospect, a concern with systematizing inductive logic has been the oldest concern of empiricist philosophers from Bacon on. No one can yet predict the outcome of this speculative scientific venture. But it is amply clear, whether this particular venture succeeds or fails, that the toleration of philosophical and scientific speculation brings rich rewards and that its suppression leads to sterility.

[Oddly enough, Putnam believes part of the attraction of some of these formalisms is their obscurity]. "I think part of the appeal of mathematical logic is that the formulas look mysterious - you write backward Es!"