There is a familiar clash between the scientific image offered by science and the manifest image emerging from common sense. This dichotomy is typically put forward at a metaphysical level, but it can be extended to logic by distinguishing between the formal logic of the scientific image and the informal logic of the manifest image. At the commonsensical level of the manifest image, we seem to take for granted logical laws and rules of all sorts, which taken together could be seen as constituting a logical system, which we may call the Global Deductive System, or GDS in short (following Orilia 2014). This presumably includes classical logic (CL), as well as naive principles of truth and predication (TP). However, as it is well known, CL and TP taken together generate logical paradoxes such as the liar, Russell’s paradox and Curry’s paradox. Russell’s paradox and the liar generate contradictions, and, by assuming CL and its Ex Falso Quodlibet rule, explosion, i.e., that every proposition whatsoever can be proven. Curry’s paradox, on the other hand, generate…
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