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Mathematics 2016, 4(4), 69; doi:10.3390/math4040069

Proposal for the Formalization of Dialectical Logic

1
Department of Applied Mathematics, University of Alicante, Alicante 03690, Spain
2
Department of Mathematics, University of Alicante, Alicante 03690, Spain
*
Author to whom correspondence should be addressed.
Academic Editor: Indranil SenGupta
Received: 18 August 2016 / Revised: 27 November 2016 / Accepted: 6 December 2016 / Published: 11 December 2016
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Abstract

Classical logic is typically concerned with abstract analysis. The problem for a synthetic logic is to transcend and unify available data to reconstruct the object as a totality. Three rules are proposed to pass from classic logic to synthetic logic. We present the category logic of qualitative opposition using examples from various sciences. This logic has been defined to include the neuter as part of qualitative opposition. The application of these rules to qualitative opposition, and, in particular, its neuter, demonstrated that a synthetic logic allows the truth of some contradictions. This synthetic logic is dialectical with a multi-valued logic, which gives every proposition a truth value in the interval [0,1] that is the square of the modulus of a complex number. In this dialectical logic, contradictions of the neuter of an opposition may be true. View Full-Text
Keywords: analysis; contradiction; dialectics; neuter; opposition; quality; quantity; synthesis analysis; contradiction; dialectics; neuter; opposition; quality; quantity; synthesis
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Usó-Doménech, J.L.; Nescolarde-Selva, J.A.; Segura-Abad, L. Proposal for the Formalization of Dialectical Logic. Mathematics 2016, 4, 69.

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