Online research in philosophy

Examples growing out of the Newcomb problem have convinced many people that decision theory should proceed in terms of some kind of causal probability. I endorse this view and define and investigate a variety of causal probability. My definition is related to Skyrms' definition, but proceeds in terms of objective probabilities rather than subjective probabilities and avoids taking causal dependence as a primitive concept.

In Zettel, Wittgenstein considered a modified version of Cantor’s diagonal argument. According to Wittgenstein, Cantor’s number, different with other numbers, is defined based on a countable set. If Cantor’s number belongs to the countable set, the definition of Cantor’s number become incomplete. Therefore, Cantor’s number is not a number at all in this context. We can see some examples in the form of recursive functions. The definition "f(a)=f(a)" can not decide anything about the value of f(a). The definiton is incomplete. The definition of "f(a)=1+f(a)" can not decide anything about the value of f(a) too. The definiton is incomplete.

According to Wittgenstein, the contradiction, in Cantor's proof, originates from the hidden presumption that the definition of Cantor’s number is complete. The contradiction shows that the definition of Cantor’s number is incomplete.

According to Wittgenstein’s analysis, Cantor’s diagonal argument is invalid. But different with Intuitionistic analysis, Wittgenstein did not reject other parts of classical mathematics. Wittgenstein did not reject definitions using self-reference, but showed that this kind of definitions is incomplete.

Based on Thomson’s diagonal lemma, there is a close relation between a majority of paradoxes and Cantor’s diagonal argument. Therefore, Wittgenstein’s analysis on Cantor’s diagonal argument can be applied to provide a unified solution to paradoxes.

Several scholars have argued that Wittgenstein held the view that the notion of number is presupposed by the notion of one-one correlation, and that therefore Hume's principle is not a sound basis for a definition of number. I offer a new interpretation of the relevant fragments on philosophy of mathematics from Wittgenstein's Nachlass, showing that if different uses of ‘presupposition’ are understood in terms of de re and de dicto knowledge, Wittgenstein's argument against the Frege-Russell definition of number turns out to be valid on its own terms, even though it depends on two epistemological principles logicist philosophers of mathematics may find too ‘constructivist’.

In this paper, I shall discuss the issue whether the standard meter in Paris is in fact one meter long. Whether one could meaningfully assert this proposition depends on how the unit of length a meter is defined. I would like to suggest three conceivable definitions. (1) One meter long is everything that has the same length as an arbitrary chosen rod S now has. (2) According to the second definition one meter long is everything that coincides in the endpoints with the rod S when placed alongside. (3) The third definition states that one meter long is-in a literal sense-the rod S solely. Other objects are one meter long-although in a derived sense-if they coincide in the endpoints with S when placed alongside. The first definition is in essence the standpoint of Kripke, the second one can be attributed to Wittgenstein, the last definition is the proposal I would like to advocate here. In particular, I hold that the third definition can be attributed to Wittgenstein as well. A language-game of measuring presupposes a preparatory game of fixing a unit of measure. The meaning of the expression "standard meter" must thus be derived from this preparatory game. Therefore with all other objects, one can say only in a derived sense that they are one meter long or not.

In a paper from 2001, Michael C. Rea considers the question of what pornography is. First, he examines a number of existing definitions of ‘pornography’ and after having rejected them all, he goes on to present his own preferred definition. In this short paper, I suggest a counterexample to Rea’s definition. In particular, I suggest that there is something that, on the one hand, is pornography according to Rea’s definition, but, on the other hand, is not something that we would intuitively describe as being an instance of pornography.

While I do not accept any current analysis of theoretical terms I also reject certain criticisms of them. Specifically, I reject the criticism that the paradoxes of material implication and the counterfactual problem eliminate the explicit definition view; and I also reject the criticism that explicitly defined theoretical terms do not refer to anything which "really exists" or do not have "excess meaning." I do argue, however, that the explicit definition view confuses and conflates the concepts of criterion and meaning analysis. I also defend reduction sentences against the counterfactual difficulty, but show, too, how this view is already logically committed to the network or postulational view of meaning. Finally, I show how the concept of reduction sentences confuses in several ways the concepts of criterion and meaning analysis--although not in quite the same way as explicit definitions do.

The claim that the functions of art liable to change over time appears to suggest that any attempt to define art in terms of a limited set of functions will fail. Robert Stecker has offered a functionalist definition which seeks to accommodate this criticism by making the functions which are relevant to an artwork's status those which are 'standard or correctly recognized' for some art form. I argue that Stecker does not offer a clear enough distinction between the 'standard or correctly recognized' and the accidental functions of an art form; that his account of the 'standard or correctly recognized' functions of an art form does not exhaust important artistic functions; and that his proposed definition is neither necessary nor sufficient for an object to count as an artwork. For these reasons I suggest that Stecker's functionalist account of art should be rejected.

It is common to define egalitarianism in terms of an inequality ordering, which is supposed to have some weight in overall evaluations of outcomes. Egalitarianism, thus defined, implies that levelling down makes the outcome better in respect of reducing inequality; however, the levelling down objection claims there can be nothing good about levelling down. The priority view, on the other hand, does not have this implication. This paper challenges the common view. The standard definition of egalitarianism implicitly assumes a context. Once this context is made clear, it is easily seen that egalitarianism could be defined alternatively in terms of valuing a benefit to a person inversely to how well off he is relative to others. The levelling down objection does not follow from this definition. Moreover, the common definition does not separate egalitarian orderings from prioritarian ones. It is useful to do this by requiring that on egalitarianism, additively separable orderings should be excluded. But this requirement is stated as a condition on the alternative definition of egalitarianism, from which the levelling down objection does not follow.

A general definition theory should serve as a foundation for the mathematical study of definitional structures. The central notion of such a theory is a precise explication of the intuitively given notion of a definitional structure. The purpose of this paper is to discuss the proof theory of partial inductive definitions as a foundation for this kind of a more general definition theory. Among the examples discussed is a suggestion for a more abstract definition of lambda-terms (derivations in natural deduction) that could provide a basis for a more systematic definitional approach to general proof theory.

According to the standard philosophical definition of lying, you lie if you say something that you believe to be false with the intent to deceive. Recently, several philosophers have argued that an intention to deceive is not a necessary condition on lying. But even if they are correct, it might still be suggested that the standard philosophical definition captures the type of lie that philosophers are primarily interested in (viz., lies that are intended to deceive). In this paper, I argue that the standard philosophical definition is not adequate as a definition of deceptive lying either. I then suggest two plausible alternative definitions of this concept.