Philosophical writings explore true contradictions in set theory, suggesting deeper metaphysical understanding.
Dialetheism is the thesis that some contradictions are true. In this paper, we explore claims to such a thesis to be found in some early philosophical writings of Newton da Costa, most notably in his book Ensaio Sobre os Fundamentos da Lógica (hereafter mentioned as the Essay). We present and explore da Costa’s claims that, in a certain sense, abstract notions such as ‘set’ and ‘truth’ may clearly involve true contradictions. Additionaly, we reconstruct da Costa’s argument to the effect that some contradictions may also be true of concrete reality. In a nutshell, da Costa suggests that some paradoxes, the aporias, are so deeply problematic that they may be pointing to reality as the source of the contradiction; i.e. aporias may ground a form of metaphysical dialetheism. This goes further than most dialetheistic claims found in the current literature. We compare these claims to a standard approach to dialetheism as Graham Priest’s, and conclude that da Costa offers a version of dialetheism too in the Essay. This opens the door for interesting explorations of some valuable yet often overlooked contributions of da Costa’s thought to the contemporary debate on dialetheism.
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Melo et al. (2025) studied this question.
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