Online research in philosophy

The paper develops an objection to the extensional model of time consciousness—the view that temporally extended events or processes, and their temporal properties, can be directly perceived as such. Importantly, following James, advocates of the extensional model typically insist that whole experiences of temporal relations between non-simultaneous events are distinct from mere successions of their temporal parts. This means, presumably, that there ought to be some feature(s) differentiating the former from the latter. I try to show why the extensional models offers no credible ground for positing such a difference.

New light is shed on Leibniz’s commitment to the metaphysical priority of the intensional interpretation of logic by considering the arithmetical and graphical representations of syllogistic inference that Leibniz studied. Crucial to understanding this connection is the idea that concepts can be intensionally represented in terms of properties of geometric extension, though significantly not the simple geometric property of part-whole inclusion. I go on to provide an explanation for how Leibniz could maintain the metaphysical priority of the intensional interpretation while holding that logically the intensional and the extensional stand in strictly inverse relation to each other.

The principal aim of this paper is to present a construction method for nontotal extensional combinatory algebras. This is done in $\S2$ . In $\S0$ we give definitions of some basic notions for partial combinatory algebras from which the corresponding notions for (total) combinatory algebras are obtained as specializations. In $\S1$ we discuss some properties of nontotal extensional combinatory algebras in general. $\S2$ describes a "partial" variant of reflexive complete partial orders yielding nontotal extensional combinatory algebras. Finally, $\S3$ deals with properties of the models constructed in $\S2$ , such as incompletability, having no total submodel and the pathological behaviour with respect to the interpretation of unsolvable λ-terms.

Extension of the system that includes the key substrates for sensation, perception, emotion, volition, and cognition, and all representational sources for cognition, supports the view that there is an extended mind and an extended body. These intellectual views can be made practical in a humanist system based on extensions and in religious systems based on extensions. Independently, there is also an institutional extension of secularism. Hence, I maintain, there are five principal forms of extension.

We explore the social context of mathematical knowledge: Even though, the community of mathematicians may look homogeneous from the outside, it is actually structured into various sub-communities that differ in preferred notations, the choice of basic assumptions, or e.g. in the choice of motivating examples. We contend that we cannot manage mathematical knowledge for human recipients if we do not take these factors into account. As a basis for a future extension of MKM systems, we analyze the social context of information in terms of Communities of Practice (CoP; a concept from learning theory) and present a concrete extensional model for CoPs in mathematics.

Professor Davidson's anomalous monism has been subject to the criticism that, despite advertisements to the contrary, if it were true mental properties would be epiphenomenal. To this Davidson has replied that his critics have misunderstood his views concerning the extensional nature of causal relations and the intensional character of causal explanations. I call this his 'extension reply'. This paper argues that there are two ways to read Davidson's 'extension reply'; one weaker and one stronger. But the dilemma is that: (i) the weak extension reply on its own isn't sufficient to support the principle of the nomological character of causality, (ii) anything strong enough to support that principle under the weak extension reply would be strong enough to warrant the strong extension reply; but (iii) the strong extension reply threatens the very stability of anomalous monism by threatening the causal potency and reality of the mental. For these reasons, I claim that either version of the 'extension reply' is bad news for anomalous monism. I conclude by suggesting that a form of absolute idealism circumvents the very assumptions that generate these kinds of difficulty for committed monists.

When it comes to Wittgenstein's philosophy of mathematics, even sympathetic admirers are cowed into submission by the many criticisms of influential authors in that field. They say something to the effect that Wittgenstein does not know enough about or have enough respect for mathematics, to take him as a serious philosopher of mathematics. They claim to catch Wittgenstein pooh-poohing the modern set-theoretic extensional conception of a real number. This article, however, will show that Wittgenstein's criticism is well grounded. A real number, as an 'extension', is a homeless fiction; 'homeless' in that it neither is supported by anything nor supports anything. The picture of a real number as an 'extension' is not supported by actual practice in calculus; calculus has nothing to do with 'extensions'. The extensional, set-theoretic conception of a real number does not give a foundation for real analysis, either. The so-called complete theory of real numbers, which is essentially an extensional approach, does not define (in any sense of the word) the set of real numbers so as to justify their completeness, despite the common belief to the contrary. The only correct foundation of real analysis consists in its being 'existential axiomatics'. And in real analysis, as existential axiomatics, a point on the real line need not be an 'extension'.

It has been argued that prototypes cannot compose, and that for this reason concepts cannot be prototypes (Osherson and Smith in Cognition 9:35–58, 1981; Fodor and Lepore in Cognition 58:253–270, 1996; Connolly et al. in Cognition 103:1–22, 2007). In this paper I examine the intensional and extensional approaches to prototype compositionality, arguing that neither succeeds in their present formulations. I then propose a hybrid extensional theory of prototype compositionality, according to which the extension of a complex concept is determined as a function of what triggers its constituent prototypes. I argue that the theory escapes the problems traditionally raised against extensional theories of compositionality.

7.3.1 Ostension 7.3.2 Extensional Definition by Naming 7.3.3 Extensional Definition by Unique Description 7.4 Two Case Studies in the Application of the Intension/Extension Distinction 7.4.1 "God exists, by definition" 7.4.2 The 'Width' of an Intensional Definition..