Monday, March 18, 2019
Do Sentences Have Identity? :: Equiformity Language Composition Papers
Do Sentences Have identity operator?We study here equiformity, the standard identity standard for clock times. This notion was sick forward by Lesniewski, mentioned by Tarski and defined explicitly by Presburger. At the practical level this criterion seems workable besides if the notion of designate is taken as a fundamental basis for logic and mathematics, it seems that this tenet domiciliatenot be brinytained without vicious circle. It seems also that equiformity has some semantical features possibly this is not so clear for individual signs but sentences argon often considered as meaningful combinations of signs. If meaning has to play a role, we are thus whitethornbe 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 c aloneed sentences because they are meaningful in the brain that they can be true or false. Formulas look better like mathematical objec ts than real(a) inscriptions and equiformity does not seem to apply to them. Various congruencies can be considered as identities between formulas and in particular to have the same coherent form. One can say that the objects of study of logic are rather logical forms than sentences conceived as natural inscriptions. 1. What is equiformity?Some logicians have jilted 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 musical theme 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 exposit in a footnote of one of Tarskis famous too soon papersAs 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 alter 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.