Abstract

A non-classical logic is proposed that extends classical logic and set theory as conservatively as possible with respect to three domains: the logic of natural language, the logcal foundations of mathematics, and the logical-philosophical paradoxes. A universal mechanics of consciousness connects these domains, and its best witness is the liar paradox. Its solution rests formally on a subject-object partition, mentally arising and disappearing perpetually. All deep paradoxes are paradoxes of consciousness. There are two kinds, solvable ones and unsolvable ones. The solvable ones disappear by proper partitions, the unsolvable ones arise by inevitably improper partitions enforced by the natural worldview. The categorial distinctions of subject and object, certainty and truth, consciousness and being, inner freedom and outer constraint, psyche and physis, mental practice and formal theory indicate an immemorial mystical monism of consciousness without which mathematical Platonism could not survive