Equality of Opportunity and Personal Identity

One of the central theses of egalitarian liberals in the domain of distributive justice is that talented individuals should not be allowed to keep their entire market-income even if it flows solely from their greater abilities. This claim is usually supported by one of several arguments or some mixture of them, but in the present paper, I want to concentrate on the version that invokes equality of opportunity as its starting point. Namely, it is claimed that every human being should enjoy an equal starting point in the life-race but that this is not secured insofar as some have greater natural talents than others. Therefore, egalitarians hold that results that arise from such an unfair situation are unjust and should be corrected by a redistributive taxation. I want to criticize this argument by hoping to show that it presupposes an untenable view about identity of persons.

Baker on the Psychological Account of Personal Identity

Lynne Rudder Baker’s Constitution View of human persons has come under much recent scrutiny. Baker argues that each human person is constituted by, but not identical to, a human animal. Much of the critical discussion of Baker’s Constitution View has focused upon this aspect of her account. Less has been said about the positive diachronic account of personal identity offered by Baker. Baker argues that it is sameness of what she labels ‘first-person perspective’ that is essential to understanding personal identity over time. Baker claims that her account avoids the commitment to indeterminacy of personal identity entailed by the psychological account. Further, the psychological account, but not her account, is plagued by what Baker labels the ‘duplication problem’. In the end, I argue that neither of these considerations forces us to renounce the psychological account and adopt Baker’s favored account.

Mind in a Humean World

The paper defends Humean approaches to autonomous mental causation against recent attacks in the literature. One important criticism launched at Humean approaches says that the truth-makers of the counterfactuals in question include laws of nature, and there are laws that support physical-to-physical counterfactuals, but no laws in the same sense that support mental-to-physical counterfactuals. This paper argues that special science causal laws and physical causal laws cannot be distinguished in terms of degrees of strictness. It follows that mental-to-physical counterfactuals are supported—or not supported—by laws in just the same way as are physical-to-physical counterfactuals.     

A Circumradius-Inradius Identity and an Identity Relating Volumes for a Simplex

We establish an identity for an n-dimensional simplex relating the circumradius and the inradius, and an identity relating its volume and the pedal volume. As applications, we derive some known inequalities for simplices and generalizations of such inequalities.     

Humean Supervenience in the Light of Contemporary Science

It is shown that Lewis’ ontological doctrine of Humean supervenience incorporates at its foundation the so-called separability principle of classical physics. In view of the systematic violation of the latter within quantum mechanics, the claim that contemporary physical science may posit non-supervenient relations beyond the spatiotemporal ones is reinforced on a foundational basis concerning constraints on the state representation of physical systems. Depending on the mode of assignment of states to quantum systems — unit state vectors versus statistical density operators — we distinguish between strongly and weakly non-Humean, non-supervenient relations. It is demonstrated that in either case, the relations of quantum entanglement constitute prototypical examples of irreducible physical relations that do not supervene upon a spatiotemporal arrangement of Humean qualities, weakening, thereby, the thesis of Humean supervenience. In this respect, the status of Lewis’ recombination principle is examined, whereas his conception of lawhood is critically investigated. It is concluded that the assumption of ontological reductionism, as expressed in Lewis’ Humean doctrine, cannot be regarded as a reliable code of the nature of the physical world and its contents. It is proposed instead that due to the undeniable existence of non-supervenient relations, a metaphysic of relations of a moderate kind ought to be acknowledged as an indispensable part of our understanding of the natural world at a fundamental level.     

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.     

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.     

A New Version of the Mind Argument Refuted

Peter van Inwagen attempts to demonstrate the apparent incompatibility of free will and indeterminism through an imaginative thought experiment. He imagines God repeatedly “rolling the world back” to its state one minute prior to the performance of an undetermined, putatively free action and then letting it “go forward” again. Van Inwagen argues that the outcome most friendly to the supposition that the agent acted freely, in which she does otherwise about half the time, is one which apparently shows that her original act was a matter of chance, and thus not free. I argue that neither this outcome nor any other implies that her action was not free.     

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.     

四阶p-Laplacian方程多时滞问题周期解的存在性

通过使用Mawhin连续性定理,研究四阶p-Laplacian微分方程多时滞问题(φ_p(x″(t)))″+f(t,x″(t))+(?)β_i(t)g(x(t-γ_i(t)))=p(t)周期解的存在性,并得到了存在周期解的充分性条件     

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.     

Linear Programming Bounds for Codes via a Covering Argument

We recover the first linear programming bound of McEliece, Rodemich, Rumsey, and Welch for binary error-correcting codes and designs via a covering argument. It is possible to show, interpreting the following notions appropriately, that if a code has a large distance, then its dual has a small covering radius and, therefore, is large. This implies the original code to be small. We also point out that this bound is a natural isoperimetric constant of the Hamming cube, related to its Faber–Krahn minima. While our approach belongs to the general framework of Delsarte’s linear programming method, its main technical ingredient is Fourier duality for the Hamming cube. In particular, we do not deal directly with Delsarte’s linear program or orthogonal polynomial theory. This research was partially supported by ISF grant 039-7682.     

Multidimensional Tauberian Theorem for Holomorphic Functions of Bounded Argument

Doklady Mathematics - Generalized functions with a Laplace transform having a bounded argument in a tube domain over the positive orthant are considered. Necessary and sufficient conditions for the...     

双线性等式的一个组合学证明

双线性等式是近年来日本学者Dete,Jimbo,Kashiwara与Miwa(DJKM)等人提出来的,是用于引出KP方程的一个关键等式。但DJKM的原证不仅不够严格,而且晦涩难懂(见Newll评论)。本文给出了这一等式的一个简单而初等的组合学证明,并将这一等式推广到矩阵情形,还导出了KP方程族的明显表达式。     

A Matrix Identity on the Schur Complement

This article presents a matrix identity on the Schur complement along with various applications. In particular, it gives a simple and transparent proof for the Crabtree–Haynsworth quotient formula for the Schur complement. Although its proof is straightforward, the identity yields a number of important results that appear to be unrelated.     

A Matrix Identity on the Schur Complement

This article presents a matrix identity on the Schur complement along with various applications. In particular, it gives a simple and transparent proof for the Crabtree-Haynsworth quotient formula for the Schur complement. Although its proof is straightforward, the identity yields a number of important results that appear to be unrelated.     

Qualia and the Argument from Illusion: A Defence of Figment

This paper resurrects two discredited ideas in the philosophy of mind. The first: the idea that perceptual illusion might have something metaphysically significant to tell us about the nature of phenomenal consciousness. The second: that the colours and other qualities that ‘fill’ our sensory fields are occurrent properties (rather than representations of properties) that are, nevertheless, to be distinguished from the ‘objective’ properties of things in the external world. Theories of consciousness must recognize the existence of what Daniel Dennett mockingly labels ‘figment,’ but this result—though metaphysically and epistemologically significant—is not incompatible with either physicalism or naturalized semantics.