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C9: Pathways to Falsity
Organised by Heinrich Wansing (Ruhr University Bochum)
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According to W.V. Quine (Methods of Logic, 1950), “Logic … has as its business the pursuit of truth ... and the pursuit of truth is the endeavor to sort out the true statements from the others, which are false.“ Under this Boolean conception, pathways to truth are already pathways to falsity. However, once the idea of the totality of all false statements as the set-theoretic complement of the totality of all true statements is given up, truth and falsity emerge as separate notions that are on a par semantically as well as epistemologically. Identifying the true statements, then, does not necessarily mean that the false statements are also identified, and sorting out the false statements is just as important as sorting out the true statements. In a paper from 1991, titled “n reasons for choosing N”, David Pearce, complements Quine’s conception of logic by characterizing “negative reasoning” as “that which involves an inference to the falsity of a proposition … .. We can then distinguish a special case of negative reasoning, which we might call /inverse inference/, as that involving only inference from falsity to falsity.“ The colloquium addresses issues including logical bilateralism, falsity, negation, and contradictoriness versus triviality. Program: 09:00-09:10 Introduction 09:10-09:55 Sara Ayhan, Mapping the landscape of logical bilateralism & discussion 09:55-10:00 Break 10:00-10:45 Hitoshi Omori, Falsity forward & discussion 10:45-10:50 Break 10:50-11:35 Graham Priest, Falsity Backwards & discussion 11:35-12:00 General discussion | ||
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Mapping the landscape of logical bilateralism Ruhr University Bochum, Germany Logical bilateralism can be very generally described as an approach to meaning and consequence on the grounds of a symmetry between certain notions, like assertion and denial, proof and refutation or truth and falsity, in that both are taken as primitive and not, as in conventional ‘unilateralist’ approaches, merely reducing the latter to the former, more primary notion. In recent years, the field of logical bilateralism has seen significant development with various systems being developed that showcase a wide scope of orientations within this framework. This ranges from using signed formulas to express speech acts in the proof system to interpreting validity via speech acts to proof systems capturing a duality of inferential relationships by displaying provability and refutability relations. In this talk I want to give an overview of the directions in bilateralism and clarify some common misconceptions. I want to show the differences between these approaches but also similarities with respect to their motivation, their technical implementations and their consequences. Falsity forward Tohoku University, Japan In almost all logics, validities are defined in terms of truth preservation forward. That suits very well for the purpose of paving paths to truth. However, for the purpose of paving paths to falsity, which is the direction suggested in the title of colloquium, we need to take seriously the idea of falsity preservation forward. This paper explores some of the implications within the FDE family and some of their expansions. Somewhat surprisingly, there are some connections to Aristotle's thesis, one of the key principles of connexive logic. Falsity Backwards CUNY Graduate Center, United States of America LP is a three-valued logic in which validity is defined in terms of truth preservation forward. Falsity is not preserved backwards. This paper concerns the logic PK, which one obtains when one adds the preservation of falsity backwards to the definition of validity. It discusses the properties of this system, and its relation to other well-known logics, such as Strong Kleene logic, K_3. | ||