Revisionist Bilateralism

• Applicant: Dr. Sergei Drobyshevich
• Subject Area: Theoretical Philosophy ; Mathematics
• Term: since 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 533464993

Bilateralism is a paradigm in logic that gets its name from Ian Rumfitt's seminal "'Yes' and 'no'" and can be shortly summarized under a slogan that one should take falsity seriously in theories of meaning but also in philosophy and logic. At the core of bilateralism is an understandable frustration by some authors about the long-standing tradition in formal logic of treating falsity as a non-primitive notion understood through truth. Thus, one customarily models “the statement A is false” with the use of negation connective as “the property of being true holds for not-A”. This tradition ultimately originates with Frege’s "Negation" and got dubbed the Frege Point by Peter Geach. The Frege Point boils down to the claim that one has to have a primitive negation connective no matter what and if one does have it then there is no need in primitive falsity since then falsity can be expressed via truth of negated statements just as demonstrated above. By now there is a significant body of works challenging the Frege Point and arguing for introducing primitive denial into logical vocabulary. Such treatments of logic I call here bilateral, in contrast to unilateral treatments, i.e. those which do not employ primitive denial. Most of works on bilateralism—unfortunately, I think—are contained within discussions related to proof-theoretic semantics and the theory of meaning of the logical connectives more broadly, so that a convention which affects the bulk of practice of doing formal logic is only discussed in relation to some select topics in the philosophy of logic. The aim of this project is to take some steps towards rectifying this problem. Thus, the fundamental question that motivates this project is: how would formal logic develop if the Frege Point was not accepted as a given? The objectives of the project are divided into two main directions. The first one is dedicated to expanding the domain of topics and formal frameworks primitive denial can be introduced to. The second one is dedicated to enriching existing theories of denial and negation.

• DFG Programme: Research Grants