Do Sentences Have Identity? :: Equiformity Language Composition Papers

Do Sentences Have Identity? We study here equiformity, the standard identity criterion for sentences. This notion was put forward by Lesniewski, mentioned by Tarski and defined explicitly by Presburger. At the practical level this criterion seems workable but if the notion of sentence is taken as a fundamental basis for logic and mathematics, it seems that this principle cannot be maintained without vicious circle. It seems also that equiformity has some semantical features ; maybe this is not so clear for individual signs but sentences are often considered as meaningful combinations of signs. If meaning has to play a role, we are thus maybe in no better position than when dealing with identity criterion for propositions. In formal logic, one speaks rather about well-formed formulas, but closed formulas are called sentences because they are meaningful in the sense that they can be true or false. Formulas look better like mathematical objects than material inscriptions and equiformity does not seem to apply to t hem. Various congruencies can be considered as identities between formulas and in particular "to have the same logical form". One can say that the objects of study of logic are rather logical forms than sentences conceived as material inscriptions. 1. What is equiformity? Some logicians have rejected propositions in favour of sentences, arguing in particular that there is no satisfactory identity criterion for propositions (cf. Quine, 1970). But is there one for sentences? The idea that logic is about sentences rather than propositions and that sentences are nothing more that material inscriptions was already developed by Lesniewski, who also saw immediately the main difficulty of this conception and introduced the notion of equiformity to solve it. His attitude his well described in a footnote of one of Tarski’s famous early papers: As already explained, sentences are here regarded as material objects (inscriptions). (...) It is not always possible to form the implication of two sentences (they may occur in widely separated places). In order to simplify matters we have (...) committed an error; this consists in identifying equiform sentences (as S. Lesniewski calls them). This error can be removed by interpreting S as the set of all types of sentences (and not of sentences) and by modifying in an analogous manner the intuitive sense of other primitve concepts. In this connexion by the type of a sentence x we understand the set of all sentences which are equiform with x.