Universal Logic or Logics in Resemblance Families

Abstract

It is a momentous and as yet unsolved, perhaps unsolvable, question in the philosophy of logic, as to whether there is a single universal logic. The alternative is to maintain that there are only fundamentally distinct logics, some similar to others in some but not other ways, and each reflecting another logical dimension of what for convenience can be considered an island with particular dependencies in a sea of logics. The first question this essay considers, on the event of honoring Jean-Yves Beziau for his accomplishments and contributions to the program of Universal Logic, is whether there can be a universal logic, or whether a family resemblance model for overlapping different kinds of logically irreducible similarities between putatively disparate formal logical languages provides a more plausible and explanatorily fruitful model for understanding the proliferation of logics, especially since the formalization of modal and nonclassical systems. The second question is whether it makes any difference to Beziau’s Universal Logic whether there can really be a universal logic in the sense prescribed. Here the conclusion is that Beziau’s Universal Logic research program is unaffected by the unattainability of a universal logic, construed either as an ideal of reasoning or ideal theory of reasoning. Beziau’s explanations of what he means by ‘universal logic’ are sampled from both the Preface to his 2005 edited volume Logica universalis: towards a general theory of logic, and his 2014 Synthese essay, The relativity and universality of logic. The concept of universal logic and Universal Logic are critically evaluated, with the consequence that an alternative and in many ways preferable family resemblance model of similarities of different kinds selecting different logics by virtue of different partially overlapping shared properties is not seriously challenged by Beziau’s defense of logical universalism. It is one thing to recognize that reasoning is in some sense unitary, whereas theories about reasoning are legion. It is another thing to ask why there are so many logics, and consider that the reason may be that reasoning itself, though in some sense unitary, has as many different logical dimensions as there are philosophically motivated formal systems of logic. If reasoning has the loose unity of a family rather than the tight unity of a single abstract universal entity or actual dynamic psychological occurrence, then to capture the expressive and inferential structures of a selected part of thought and discourse in the entertainment and expression of which requires its own particular kind of logical reasoning.