RésuméL'interprétation substitutionnelle de la quantification impose une redéfinition des principaux concepts du calcul logique.Son intérêt majeur réside dans le fait qu'elle permet d'esquisser une théorie de l'intensionnalité qui lève les difficultés résultant du traitement logique des contextes de modalité, de croyance et de citation.Pour autant, on ne saurait éluder la traditionnelle question de la référence et de l'existence. Celle‐ci relève maintenant d'une construction sémantique de modèles.SummaryThe substitutional interpretation of quantification modifies the main concepts of logical calculus.Its principal interest lies in (...) that it permits to sketch a theory of intensionality which removes the difficulties rising from the logical treatment of the contexts of modality, belief and quotation.For all that, we cannot evade the traditional question of reference and existence. This now depends on a semantical construction of models.ZusammenfassungDie substitutionelle Interpretation der Quantifikation erfordert eine neue Definition der Grundbegriffe des Logikkalküls.Ihr Hauptinteresse besteht darin, dass sie den Entwurf einer Theorie der Intensionalität ermöglicht; dadurch werden die Schwierigkeiten behoben, die bei der Behandlung von Kontexten mit Modal‐ und Meinungswörtern und Zitaten entstehen.Die traditionelle Frage nach der Referenz und der Existenz wird dabei nicht umgangen, indem sie nunmehr vermittelst von semantischen Modellen behandelt wird. (shrink)

The paper argues that no second order theory is ontologically commited to anything beyond what its individual variables range over.

Quineans have taken the basic expression of ontological commitment to be an assertion of the form '' x '', assimilated to theEnglish ''there is something that is a ''. Here I take the existential quantifier to be introduced, not as an abbreviation for an expression of English, but via Tarskian semantics. I argue, contrary to the standard view, that Tarskian semantics in fact suggests a quite different picture: one in which quantification is of a substitutional type apparently first proposed by (...) Geach. The ontological burden is borne by constant symbols, and truth is defined separately from reference. (shrink)

Peter Geach proposed a substitutional construal of quantification over thirty years ago. It is not standardly substitutional since it is not tied to those substitution instances currently available to us; rather, it is pegged to possible substitution instances. We argue that (i) quantification over the real numbers can be construed substitutionally following Geach's idea; (ii) a price to be paid, if it is that, is intuitionism; (iii) quantification, thus conceived, does not in itself relieve us of ontological commitment to real (...) numbers. (shrink)