This paper is an attempt to put forward a new kind of partial model for representing belief states. I first introduce some philosophical motivations for working with partial models. Then, I present the standard (total) model proposed by Hintikka, and the partial models studied by Humberstone and Holliday. I then show how to reduce Hintikka’s semantics in order to obtain a partial model which, however, differs from Humberstone’s and Holliday’s. The nature of such differences is assessed, and I provide motivations (...) for using the newly proposed semantics rather than the existing ones. Finally, I review some promising philosophical applications of the ideas developed throughout the discussion. (shrink)

The fact that names refer to individuals is a basic assumption of referentialist theories of proper names, but the notion of individual is systematically taken for granted in those theories. The present paper follows that basic assumption, but proposes to analyze the notion of individual prior to the development of any semantic theory of proper names. It will be argued that a particular perdurantist conception of individual should be adopted, which distinguishes the notions of individual occurrence, and individual simpliciter. A (...) new theory of proper names (called the cluster-occurrence theory) is presented, according to which names refer to individual occurrences, and the intension associated with a name is an individual simpliciter. The merits of the new theory are then assessed in confrontation with its standard rival accounts. (shrink)

The initial goal of the present paper is to reveal a mistake committed by Hintikka in a recent paper on the foundations of mathematics. His claim that independence-friendly logic is the real logic of mathematics is supported in that article by an argument relying on uniformity concepts taken from real analysis. I show that the central point of his argument is a simple logical mistake. Second and more generally, I conclude, based on the previous remarks and on another standard fact (...) of IFL, that first-order logic can adequately express uniformity concepts in real analysis, whereas IFL cannot. This not only radically contradicts Hintikka’s particular claim in that article, but also undermines his whole enterprise of founding mathematics on his logic system. (shrink)

Every theory of pure quotation embraces in some form or another the intuitively obvious thesis that pure quotations refer to their quoted expressions. However, they all remain vague about the nature of these latter. This paper proposes to take seriously the fact that quoted items are semantic, not syntactic objects, and to develop therefrom a semantics for pure quotation that retains the basic intuitions and at the same time circumvents standard problems.

This paper briefly traces the evolution of the function concept until its modern set theoretic definition, and then investigates its relationship to the pre-formal notion of variable dependence. I shall argue that the common association of pre-formal dependence with the modern function concept is misconceived, and that two different notions of dependence are actually involved in the classic and the modern viewpoints, namely effective and functional dependence. The former contains the latter, and seems to conform more to our pre-formal conception (...) of dependence. The idea of effective dependence is further investigated in connection with the notions of function content and intensionality. Finally, the relevance of the distinction between the two kinds of dependence to mathematical practice is considered. (shrink)