Problems for Logical Pluralism

I argue that Beall and Restall's logical pluralism fails. Beall–Restall pluralism is the claim that there are different, equally correct logical consequence relations in a single language. Their position fails for two, related, reasons: first, it relies on an unmotivated conception of the ‘settled core’ of consequence: they believe that truth-preservation, necessity, formality and normativity are ‘settled’ features of logical consequence and that any relation satisfying these criteria is a logical consequence relation. I consider historical evidence and argue that their position relies on an unmotivated conception of the settled features of logical consequence. There are many features that are just as settled but which are inconsistent with pluralism. Second, I argue that Beall–Restall pluralism fails to hold in a single language with a single selection of logical constants, which they require for the position to be distinct from Carnap's. I consider various ways in which Beall and Restall can resist this meaning variance, particularly for negation, but argue that the strongest way relies on an unmotivated conception of the settled features of the logical constants.     

On the Cardinality of the Cardinal Virtues

This paper is a detailed study of what are traditionally called the cardinal virtues: prudence, justice, temperance and fortitude. I defend what I call the Cardinality Thesis, that the traditional four and no others are cardinal. I define cardinality in terms of three sub-theses, the first being that the cardinal virtues are jointly necessary for the possession of every other virtue, the second that each of the other virtues is a species of one of the four cardinals, and the third that many of the other virtues are also auxiliaries of one or more cardinals. I provide abstract arguments for each sub-thesis, followed by illustration from concrete cases. I then use these results to shed light on the two fundamental problems of the acquisition of the virtues and their unity, proving some further theses in the latter case.     

Projective Geometry in Logical Space: Rethinking Tractarian Thoughts

Customary interpretations state that Tractarian thoughts are pictures, and, a fortiori, facts. I argue that important difficulties are unavoidable if we assume this standard view, and I propose a reading of the concept taking advantage of an analogy that Wittgenstein introduces, namely, the analogy between thoughts and projective geometry. I claim that thoughts should be understood neither as pictures nor as facts, but as acts of geometric projection in logical space. The interpretation I propose thus removes the root of the identified difficulties. Moreover, it allows important clarification concerning some central aspects of the Tractarian theory of representation, and it yields a unifying elucidation regarding Wittgenstein’s remarks on the solipsistic thesis.     

Explanatory Exclusion and Causal Exclusion

Given Kim’s principle of explanatory exclusion (EE), it follows that in addition to the problem of mental causation, dualism faces a problem of mental explanation. However, the plausibility of EE rests upon the acceptance of a further principle concerning the individuation of explanation (EI). The two methods of defending EI—either by combining an internal account of the individuation of explanation with a semantical account of properties or by accepting an external account of the individuation of explanation—are both metaphysically implausible. This is not, however, to reject the problem of mental explanation, for EE can be replaced with a far weaker principle, which does not require the acceptance of EI, but which generates a similar problem for dualism.

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Problems in Epistemic Space

When a proposition might be the case, for all an agent knows, we can say that the proposition is epistemically possible for the agent. In the standard possible worlds framework, we analyze modal claims using quantification over possible worlds. It is natural to expect that something similar can be done for modal claims involving epistemic possibility. The main aim of this paper is to investigate the prospects of constructing a space of worlds—epistemic space—that allows us to model what is epistemically possible for ordinary, non-ideally rational agents like you and me. I will argue that the prospects look dim for successfully constructing such a space. In turn, this will make a case for the claim that we cannot use the standard possible worlds framework to model what is epistemically possible for ordinary agents.     

中国古代人生哲学的基本问题及其逻辑关系

人生理论在中国古代哲学中占有绝大的比重 ,内容丰富渊闳。本文将中国古代哲学史上的人生哲学思想作为完整的理论体系 ,探讨其中包含的基本问题及其逻辑关系。中国传统人生哲学 (“性命义理之学”)基本理论框架主要由三部分组成 :一是阐释天人关系、人性的“性命”学说 ,二是说明人生最高准则的“人道”论以及对人生范畴的讨论 ,三是说明修养途径、方法和人生境界的“为学之方”。而其中“人道”论则是该理论系统建构的核心     

Logical Truth and Tarskian Logical Truth

This paper examines the question of the extensional correctness of Tarskian definitions of logical truth and logical consequence. I identify a few different informal properties which are necessary for a sentence to be an informal logical truth and look at whether they are necessary properties of Tarskian logical truths. I examine arguments by John Etchemendy and Vann McGee to the effect that some of those properties are not necessary properties of some Tarskian logical truths, and find them unconvincing. I stress the point that since the hypothesis that Tarski's definitions are extensionally correct is deeply entrenched, the burden of proof is still on the shoulders of Tarski's critics, who have not lifted the burden. This revised version was published online in June 2006 with corrections to the Cover Date.     

Logical Consequence and the Paradoxes

We group the existing variants of the familiar set-theoretical and truth-theoretical paradoxes into two classes: connective paradoxes, which can in principle be ascribed to the presence of a contracting connective of some sort, and structural paradoxes, where at most the faulty use of a structural inference rule can possibly be blamed. We impute the former to an equivocation over the meaning of logical constants, and the latter to an equivocation over the notion of consequence. Both equivocation sources are tightly related, and can be cleared up by adopting a particular substructural logic in place of classical logic. We then argue that our perspective can be justified via an informational semantics of contraction-free substructural logics.     

Democracy and the Right to Exclusion

A defining feature of democracy is the inclusion of members of the political association. However, the corresponding right to exclusion has attracted undeservedly scant attention in recent debates. In this paper, the nature of the right to exclusion is explored. On the assumption that inclusion requires the allocation of legal power-rights to the people entitled to participate in the making of collective decisions, two conceptions of the right to exclusion are identified: the liberty-right to exclude and the claim-right to exclude. The choice between them depends on the nature of the interests that justifies the power-rights of people included. The position is defended that if rights to democratic participation are power-rights, we must also accept that the people included have claim-rights to the exclusion of non-members.     

邓小平理论的逻辑起点和内在逻辑联系论纲

学界流行的观点有二：一是认为邓小平理论的逻辑起点是“什么是社会主义，怎样建设社会主义？”二是认为其起点是“实事求是、群众路线，走自己的路。”我认为这两种观点都欠妥，因为理论的逻辑起点只能是一个最简单最抽象而又蕴含着生发反映事物运动的一切范畴、命题的萌...     

Functionalism and Causal Exclusion

Abstract: Recent work by Jaegwon Kim and others suggest that functionalism leaves mental properties causally inefficacious in some sense. I examine three lines of argument for this conclusion. The first appeals to Occam's Razor; the second appeals to a ban on overdetermination; and the third charges that the kind of response I favor to these arguments forces me to give up "the homogeneity of mental and physical causation". I show how each argument fails. While I concede that a positive theory of mental causation is desirable, there is no reason to think that functionalism renders such a theory unattainable.     

The Concept of Number: Multiplicity and Succession between Cardinality and Ordinality

Abstract

This article sets out to analyse some of the most basic elements of our number concept - of our awareness of the one and the many in their coherence with multiplicity, succession and equinumerosity. On the basis of the definition given by Cantor and the set theoretical definition of cardinal numbers and ordinal numbers provided by Ebbinghaus, a critical appraisal is given of Frege’s objection that abstraction and noticing (or disregarding) differences between entities do not produce the concept of number. By introducing the notion of subject functions, an account is advanced of the (nominalistic) reason why Frege accepted physical, kinematic and spatial properties (subject functions) of entities, but denied the ontic status of their quantitative properties (their quantitative subject function). With reference to intuitionistic mathematics (Brouwer, Weyl, Troelstra, Kreisel, Van Dalen) the primitive meaning of succession is acknowledged and connected to an analysis of what is entailed in the term ‘Gleichzahligkeit’ (‘equinumerosity’). This expression enables an analysis of the connections between ordinality and cardinality on the one hand and succession and wholeness (totality) on the other. The conceptions of mathematicians such as Frege, Cantor, Dedekind, Zermelo, Brouwer, Skolem, Fraenkel, Von Neumann, Hilbert, Bernays and Weyl, as well as the views of the philosopher Cassirer, are discussed in order to arrive at an assessment of the relation between ordinality and cardinality (also taking into account the relation between logic and arithmetic) - and on the basis of this evaluation, attention is briefly given to the definition of an ordered pair in axiomatic set theory (with reference to the set theory of Zermelo-Fraenkel) and to the defmition of an ordered pair advanced by Wiener and Kuratowski.