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Expert(s) for : Logic
My research in formal logic and philosophy of science essentially focuses on the foundations of mathematics and the foundations of physics from technical, critical, historical and philosophical points of view. From a strictly philosophical viewpoint, I support a radical constructivist thesis that consists of showing that arithmetic or number theory and its internal logic are the building blocks of mathematical theories.
In philosophy of physics, my antirealist viewpoint emphasizes the internal logic of physical theories and of mathematical physics in the same constructivist spirit.
Lastly, I have also carried out parallel research into Hegel's dialectical logic and have been able to show that it is a traditional syllogistic logic coupled with the dynamic process of sublation or sursumption (Aufhebung) with the help of a double negation operation.
My recent work addresses the probabilistic interpretations of logic where validity is defined in terms of probability, in particular the interpretation of intuitionistic logic with strong negation where the probability of the conditional is the conditional probability. Also in intuitionistic logic, I am working on developing a mixed direct method (Quine substitution and normal forms) to test intuitionist validity in propositional calculus. I am also developing a similar method for intuitionistic logic with strong negation. I have also worked recently on Lesniewski's ontology and its relations with set theory.