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 (...) both logic and mathematics, and that a coherent semantic account of mathematical formulas cannot be given without assuming that they serve as names of constructions. (shrink)

§0. Alonzo Church's contributions to philosophy and to that most philosophical part of logic, intensional logic, are impressive indeed. He wrote relatively few papers actually devoted to specifically philosophical issues, as distinguished from related technical work in logic. Many of his contributions appear in reviews for The Journal of Symbolic Logic, and it can hardly be maintained that one finds there a “philosophical system”. But there occur a clearly articulated and powerful methodology, terse arguments, often of “crushing cogency”, and philosophical (...) observations of the first importance.Many of the less formal philosophical contributions center around questions concerning meaning, but there are important clarifications and insights into matters of the epistemology and ontology of the sciences, especially the formal sciences.1.1. The logistic method. Church's writings on philosophical matters exhibit an unwavering commitment to what he called the “logistic method”. The term did not catch on and now one would just speak of “formalization”. The use of these ideas is now so common and familiar among logicians and logically-oriented philosophers that they are simply taken for granted. But they deserve to be celebrated and re-emphasized, for there are philosophers who seriously underestimate and even consciously reject these techniques. (shrink)

The debate about concepts has always been shaped by a contrast between subjectivism, which treats them as phenomena in the mind or head of individuals, and objectivism, which insists that they exist independently of individual minds. The most prominent contemporary version of subjectivism is Fodor's RTM. The Fregean charge against subjectivism is that it cannot do justice to the fact that different individuals can share the same concepts. Proponents of RTM have accepted shareability as a 'non-negotiable constraint'. At the same (...) time they insist that by distinguishing between sign-types and -- tokens the Fregean objection cannot just be circumvented but revealed to be fallacious. My paper rehabilitates the Fregean argument against subjectivism. The RTM response rests either on an equivocation of 'concept'--between types which satisfy the non-negotiable constraint and tokens which are mental particulars in line with RTM doctrine--or on the untenable idea that one and the same entity can be both a shareable type and hence abstract and a concrete particular in the head. Furthermore, subjectivism cannot be rescued by adopting unorthodox metaphysical theories about the type/token and universal/particular contrasts. The final section argues that concepts are not representations or signs, but something represented by signs. Even if RTM is right to explain conceptual thinking by reference to the occurrence of mental representations, concepts themselves cannot be identical with such representations. (shrink)

Quine claims that a) considering meaning as a separate object leads to mentalism and b) to overcome mentalism we have to accept an empirical analysis. The paper shows that a) is wrong and not accepting mentalism we can apply a logical, i.e., not empirical approach.

The vision informing 20th Century philosophy has been aptly described as one of a desert landscape. Philosophers behave as if in expectation of an ontological tax collector to whom they will owe the less the fewer entities they declare. The metaphysical purge is perpetrated under a banner emblazoned with Occam’s Razor. But Occam never counselled ontological genocide at all cost. He only cautioned against multiplying entities beyond necessity His Razor is thus in full harmony with the complementary principle, known as (...) Menger’s Comb, which cautions against trying to do with less what requires more. The two methodological precepts are just two sides of the same coin. (shrink)

There is an obvious difference between what a term designates and what it means. At least it is obvious that there is a difference. In some way, meaning determines designation, but is not synonymous with it. After all, “the morning star” and “the evening star” both designate the planet Venus, but don't have the same meaning. Intensional logic attempts to study both designation and meaning and investigate the relationships between them.

The classical theory of semantic information (ESI), as formulated by Bar-Hillel and Carnap in 1952, does not give a satisfactory account of the problem of what information, if any, analytically and/or logically true sentences have to offer. According to ESI, analytically true sentences lack informational content, and any two analytically equivalent sentences convey the same piece of information. This problem is connected with Cohen and Nagel's paradox of inference: Since the conclusion of a valid argument is contained in the premises, (...) it fails to provide any novel information. Again, ESI does not give a satisfactory account of the paradox. In this paper I propose a solution based on the distinction between empirical information and analytic information. Declarative sentences are informative due to their meanings. I construe meanings as structured hyperintensions, modelled in Transparent Intensional Logic as so-called constructions. These are abstract, algorithmically structured procedures whose constituents are sub-procedures. My main thesis is that constructions are the vehicles of information. Hence, although analytically true sentences provide no empirical information about the state of the world, they convey analytic information, in the shape of constructions prescribing how to arrive at the truths in question. Moreover, even though analytically equivalent sentences have equal empirical content, their analytic content may be different. Finally, though the empirical content of the conclusion of a valid argument is contained in the premises, its analytic content may be different from the analytic content of the premises and thus convey a new piece of information. (shrink)

The boundary between analytic and synthetic sentences is well definable. Quine’s attempt to make it vague is based on a misunderstanding: instead of freeing semantics from shortcomings found, e.g. in Carnap’s work, Quine actually rejects semantics of natural language and replaces it by behavioristically articulated pragmatics. Semantics of natural language as a logical analysis is however possible and it can justify hard and fast lines between analyticity and syntheticity.

The debate about concepts has always been shaped by a contrast between subjectivism, which treats them as phenomena in the mind or head of individuals, and objectivism, which insists that they exist independently of individual minds. The most prominent contemporary version of subjectivism is Fodor's RTM. The Fregean charge against subjectivism is that it cannot do justice to the fact that different individuals can share the same concepts. Proponents of RTM have accepted shareability as a ‘non-negotiable constraint’. At the same (...) time they insist that by distinguishing between sign-types and – tokens the Fregean objection cannot just be circumvented but revealed to be fallacious. My paper rehabilitates the Fregean argument against subjectivism. The RTM response rests either on an equivocation of ‘concept’—between types which satisfy the non-negotiable constraint and tokens which are mental particulars in line with RTM doctrine—or on the untenable idea that one and the same entity can be both a shareable type and hence abstract and a concrete particular in the head. Furthermore, subjectivism cannot be rescued by adopting unorthodox metaphysical theories about the type/token and universal/particular contrasts. The final section argues that concepts are not representations or signs, but something represented by signs. Even if RTM is right to explain conceptual thinking by reference to the occurrence of mental representations, concepts themselves cannot be identical with such representations. (shrink)