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Michael Dummett has argued that a formal semantics for our language is inadequate unless it can be shown to illuminate to our actual practice of speaking and understanding. This paper argues that Frege’s account of the semantics of predicate expressions according to which the reference of a predicate is a concept (a function from objects to truth values) has exactly the required characteristics. The first part of the paper develops a model for understanding the distinction between objects and concepts as (...) |
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It is widely assumed that Russell's problems with the unity of the proposition were recurring and insoluble within the framework of the logical theory of his Principles of Mathematics. By contrast, Frege's functional analysis of thoughts (grounded in a type-theoretic distinction between concepts and objects) is commonly assumed to provide a solution to the problem or, at least, a means of avoiding the difficulty altogether. The Fregean solution is unavailable to Russell because of his commitment to the thesis that there (...) |
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In this paper I reject the normative interpretation of logic and give reasons for a realistic account based on the ontological treatment of logical values. |
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Mental contents - Intentional contexts - The behavioristic approach 104; 5. Intentionality. Possible particulars - Possible states of affairs - The intentional nexus 144; 6. Realism. Direct and indirect knowledge - Perceptual and phenomenal objects - Delusive perceptual situations 180; Index 238-248. "This book avoids a number of traditional problems from the philosophy of mind. Emotions and volitions are hardly mentioned; and very little is said about imagination and memory. I am concerned in the main with only one topic: the (...) |
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Hans Herzberger as a philosopher and logician has shown deep interest both in the philosophy of Gottlob Frege, and in the topic of the inexpressible and the ineffable. In the fall of 1982, he taught at the University of Toronto, together with André Gombay, a course on Frege's metaphysics, philosophy of language, and foundations of arithmetic. Again, in the fall of 1986, he taught a seminar on the philosophy of language that dealt with 'the limits of discursive symbolism in several (...) |
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The paper deals with the problem of the nature of logic and its normativity in the context of the normativity of scientific knowledge in general. We proceed from a division between fundamental aspects of scientific knowledge which are related to the nature and subject matter of particular sciences, and its applied aspects which are related to the possible applications of sciences. This division fully applies to logic. The authors note that if we view logic as a completely objective discipline, devoid (...) |
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The paper deals with the semantics of mathematical notation. In arithmetic, for example, the syntactic shape of a formula represents a particular way of specifying, arriving at, or constructing an arithmetical object (that is, a number, a function, or a truth value). A general definition of this sense of "construction" is proposed and compared with related notions, in particular with Frege's concept of "function" and Carnap's concept of "intensional isomorphism." It is argued that constructions constitute the proper subject matter of (...) |
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