Notes on intensional theories

Discusiones Filosóficas 12 (18):13 - 49 (2011)
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Abstract

La cuestión de si los lenguajes intensionalesson más expresivos que los lenguajes nointensionalessurge en el marco de unaperspect i va semánt i ca de l as t eorí as.Desde esta perspectiva, la cuestión esesta. ¿Hay clases modelo que se puedencaracterizar mediante teorías que usanconceptos intensionales que no se puedencaracterizar mediante teorías que no usanconceptos intensionales? Se sugiere unaformulación precisa de esta cuestión, perono se ofrece una respuesta.Para aproxi marse a est a cuest i ón, seresume la teoría de modelos de primerorden [II] y se revisa el enfoque semánticode las teorías que emplea incrementost eóri cos, no i nt ensi onal es, de pri merorden [III].Los i nc r e me nt os t e ór i c os de pr i me rorden se bosquejan pero no se definenr i g u r o s a me n t e [ I V] . E s t e l e n g u a j ei n t e n s i o n a l pr o po r c i o n a e l a p a r a t op a r a a t r i b u i r u s o d e l l e n g u a j e yact i t udes i nt ens i onal es a i ndi vi duoscuyo comportami ento es el obj eto deinvestigación. También proporciona elaparato para habl ar sobre traducci óndel lenguaj e atribuido al lenguaj e delinvestigador.La cuestión inicial se convierte entoncesen si hay clases modelo que se puedanc a r a c t e r i z a r me d i a n t e i n c r e me n t o sintencionales de lógica de primer ordenq ue n o pue de n s e r c a pt ur a do s po rincrementos teóricos no-intensionales [V].The ques t i on of whet her i nt ens i onallanguages are more expressive than nonintensional languages is raised within the framework of a semantic view of theories. Fromthis perspective, the question isthis. Are there model classes that can becharacterized by theories using intensionalconcepts that cannot be characterizedby theories that do not use intensionalconcepts? A precise formulation of thisquestion is suggested, but no answer isgiven.To approach this question, model theory offirst order theories is summarized [II] andthe semantic approach to theories usingnon-intensional, theoretical augmentationsof first order theories is reviewed [III].I n t e n s i o n a l a u g me n t a t i o n s o f f i r s torder theories are sketched [IV] but notr i gor ous l y de f i ne d. Thi s i nt e ns i onall anguage provi des t he apparat us f orattributing language use and intensionalattitudes to individuals whose behavioris the object investigation. It also providesapparatus for talking about translationf r om t he at t r i but e d l anguage t o t heinvestigator’s language.T h e i n i t i a l q u e s t i o n t h e n b e c o me swhet her t here are model cl asses t hatc a n be c ha r a c t e r i z e d by i nt e ns i ona laugmentations of first order logic thatcannot be captured by non-intensionaltheoretical augmentations [V]

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