A Blind-Spot Argument Against Dispositionalist Accounts of Belief

Dispositionalist accounts of belief define beliefs in terms of specific sets of dispositions. In this article, I provide a blind-spot argument against these accounts. The core idea of the argument is that beliefs having the form [p and it is not manifestly believed that p] cannot be manifestly believed. This means that one cannot manifest such beliefs in one’s assertions, conscious thoughts, actions, behaviours, or any other type of activity. However, if beliefs are sets of dispositions, they must be manifestable in some way. Therefore, according to my argument, beliefs are not sets of dispositions. The argument is defended against some possible objections.     

An Extension of Kuczek's Argument to Nonnearest Neighbor Contact Processes

The right edge of a nearest neighbor supercritical contact process satisfies a central limit theorem.^{(8, 9)} In this paper, a block construction is created to extend the argument by Kuczek⁽⁹⁾ to the nonnearest neighbor case. The proof of the following fact in the nonnearest neighbor case is the key to the extension: There is a positive chance that the rightmost particle at time 0 infects the rightmost particle at every time.     

The Easy Argument

Suppose Ted is in an ordinary house in good viewing conditions and believes red, his table is red, entirely because he sees his table and its color; he also believes not-white, it is false that his table is white and illuminated by a red light, because not-white is entailed by red. The following three claims about this table case clash, but each seems plausible: 1. Ted’s epistemic position is strong enough for him to know red. 2. Ted cannot know not-white on the basis of red. 3. The epistemic closure principle, suitably restricted, is true. Stewart Cohen has called this three-way clash of intuitions the problem of easy knowledge. If we wish to resolve the clash without accepting skepticism, we seem to have two options. According to the hard argument, the best response is to reject 3. The easy argument rejects 2. But there may be a third alternative, the reverse argument, which rejects 1 without ceding a substantial amount of ground to the skeptic. In this essay I criticize recent versions of the reverse argument and the hard argument, thereby lending support to the easy argument.     

An Old Solution to the Problem of Mixed Atomics

This paper examines a difficulty for various forms of truth pluralism, known in the literature as the problem of ‘mixed atomics’. It is argued that two prominent attempts to respond to the difficulty—those of Jeremy Wyatt and Gila Sher—fail. In their place, an alternative is offered based on parts of Crispin Wright’s Truth and Objectivity programme. It is argued that the Wrightian approach works because it substitutes traditional conceptions of truth-relevant properties, for example correspondence and coherence, for criteria of objectivity pertaining to discursive practices. This allows us to give expression to the nuanced way in which the pluralist wants to treat mixed atomics.     

The Argument from Silence

The argument from silence is a pattern of reasoning in which the failure of a known source to mention a particular fact or event is used as the ground of an inference, usually to the conclusion that the supposed fact is untrue or the supposed event did not actually happen. Such arguments are widely used in historical work, but they are also widely contested. This paper surveys some inadequate attempts to model this sort of argument, offers a new analysis using a Bayesian probabilistic framework that isolates the most problematic step in such arguments, illustrates a key problem besetting many uses of the argument, diagnoses the attraction of the argument in terms of a known human cognitive bias affecting the critical step, and suggests a standard that must be met in order for any argument from silence to have more than a very weak influence on historical reasoning.     

Understanding the Small Object Argument

The small object argument is a transfinite construction which, starting from a set of maps in a category, generates a weak factorisation system on that category. As useful as it is, the small object argument has some problematic aspects: it possesses no universal property; it does not converge; and it does not seem to be related to other transfinite constructions occurring in categorical algebra. In this paper, we give an “algebraic” refinement of the small object argument, cast in terms of Grandis and Tholen’s natural weak factorisation systems, which rectifies each of these three deficiencies.

Understanding the Small Object Argument

The small object argument is a transfinite construction which, starting from a set of maps in a category, generates a weak factorisation system on that category. As useful as it is, the small object argument has some problematic aspects: it possesses no universal property; it does not converge; and it does not seem to be related to other transfinite constructions occurring in categorical algebra. In this paper, we give an “algebraic” refinement of the small object argument, cast in terms of Grandis and Tholen’s natural weak factorisation systems, which rectifies each of these three deficiencies.     

The Ontological Argument in the Tractatus

The intention of this article is to show that the Tractatus deals with the problem of the relation between reality, possibility, and necessity as traditionally considered in the ontological argument, that is, in relation to the idea of limit, and that in Section 5.5521, we find an especially clarifying formulation of this question; the formulation itself, however, is not at all clear, so that a lengthy commentary of it is justified.     

On Differential Equations with Retarded Argument

We study the limit properties of solutions to one class of systems of differential equations as the number of equations and some parameters tend to infinity. We establish a close connection between solutions to these systems and differential equations with retarded argument. Our convergence theorems provide a new method for approximation of solutions to nonlinear differential equations with retarded argument.Original Russian Text Copyright © 2005 Demidenko G. V. and Likhoshvai V. A.The authors were supported by the Russian Foundation for Basic Research (Grants 03-01-00328, 03-04-48506, 03-04-48829, 03-07-96833, 04-01-00458, 05-04-49068, and 05-07-90274), the Integration Grant of the Siberian Branch of the Russian Academy of Sciences (No. 119 and 148), the Program Development of the Scientific Potential of Higher School of the Ministry for Education of the Russian Federation (Grant 8273), and NSF:FIBR (Grant EF-0330786).__________Translated from Sibirskii Matematicheskii Zhurnal, Vol. 46, No. 3, pp. 538–552, May–June, 2005.     

A Humean Argument for Personal Identity

Considering various arguments in Hume’s Treatise, I reconstruct a Humean argument against personal identity or unity. According to this argument, each distinct perception is separable from the bundle of perceptions to which it belongs and is thus transferable either to the external, material reality or to another psychical reality, another bundle of perceptions. Nevertheless, such transference (Hume’s word!) is entirely illegitimate, otherwise Hume’s argument against causal inference would have failed; furthermore, it violates private, psychical accessibility. I suggest a Humean thought experiment clearly demonstrating that, to the extent that anything within a psychical reality is concerned, no distinction leads to separation or transference and that private, psychical accessibility has to be allowed in the Humean argument for personal identity or unity. Private accessibility and psychical untransferability secure personal identity and unity. Referring to the phenomenon of multiple personality along the lines of the Humean argument for personal identity or unity, I illustrate both private accessibility and a possible notion of one and the same person distinct from his/her alters or psychical parts. Finally, I show why Parfit’s Humean argument against personal identity must fail.     

Deformation Argument under PSP Condition and Applications

In this paper we introduce a new deformation argument, in which C~0-group action and a new type of Palais-Smale condition PSP play important roles. This type of deformation results are studied in [17, 21] and has many different applications [10,11, 17, 21] et al. Typically it can be applied to nonlinear scalar field equations. We give a survey in an abstract functional setting. We also present another application to nonlinear elliptic problems in strip-like domains. Under conditions related to [5,6], we show the existence of infinitely many solutions. This extends the results in [8].     

A Skew-Duoidal Eckmann-Hilton Argument and Quantum Categories

A general result relating skew monoidal structures and monads is proved. This is applied to quantum categories and bialgebroids. Ordinary categories are monads in the bicategory whose morphisms are spans between sets. Quantum categories were originally defined as monoidal comonads on endomorphism objects in a particular monoidal bicategory ?. Then they were shown also to be skew monoidal structures (with an appropriate unit) on objects in ?. Now we see in what kind of ? quantum categories are merely monads.