On the semantics of mathematical statements

• Autor(a) principal: Rosado Haddock, Guillermo E.
• Data de Publicação: 1996
• Tipo de documento: Artigo
• Idioma: por
• Título da fonte: Manuscrito (Online)
• Texto Completo: https://periodicos.sbu.unicamp.br/ojs/index.php/manuscrito/article/view/8659607
• topic: Husserl; Semântica; Filosofia da matemática

Husserl developed – independently of Frege - a semantics of sense and reference. There are, however, some important differences, specially with respect to the referents of statements. According to Husserl, an assertive sentence refers to a state of affairs, which has as its basis what he called a situation of affairs. Situations of affairs could also be considered as an alternative referent for statements in their own right, although for Husserl they were simply a sort of referential basis. Both Husserlian states of affairs and situations of affairs are extensional.Tarskian semantics can be rendered as a sort of state of affairs semantics. However, to adequately assess the existence of dual theorems in mathematics and, more generally, seemingly unrelated interderivable statements like the Axiom of Choice and its many equivalents, states of affairs (and truth-values) are not enough. We need a sort of refinement of the notion of a situation of affairs, namely, what we have called elsewhere an abstract situation of affairs. We are going to introduce abstract situations of affairs as equivalence classes of states of affairs denoted by closed sentences of a given language which are true in the same models. We first sketch the procedure for a first-order many-sorted language and then for a second-order many-sorted language.