Empty Logics

PAILOS, FEDERICO MATÍAS

JOURNAL OF PHILOSOPHICAL LOGIC

Springer

Año: 2021

0022-3611

TS is a logic that has no valid inferences. But, could there be a logic without valid metainferences? We will introduce TSω, a logic without metainferential validities. Notwithstanding, TSω is not as empty?i.e., uninformative?as it gets, because it has many antivalidities. We will later introduce the two-standard logic [TSω, STω], a logic without validities and antivalidities. Nevertheless, [TSω, STω] is still informative, because it has manycontingencies. The three-standard logic [TSω, STω,rHH, HHs] that we willfurther introduce, has no validities, no antivalidities and also no contingencieswhatsoever. We will also present two more validity-empty logics. The first onehas no supersatisfiabilities, unsatisfabilities and antivalidities˚. The secondone has no invalidities nor non-valid-nor-invalid (meta)inferences. All theseconsiderations justify thinking of logics as, at least, three-standard entities,corresponding, respectively, to what someone who takes that logic as correct,accepts, rejects and suspends judgement about, just because those things are,respectively, validities, antivalidities and contingencies of that logic. Finally, wewill present some consequences of this setting for the monism/pluralism/nihilismdebate, and show how nihilism and monism, on one hand, and nihilism and pluralism, on the other hand, may reconcile?at least according to how GillianRussell understands nihilism, and provide some general reasons for adoptinga multi-standard approach to logics