Exclusion Problems and the Cardinality of Logical Space

Wittgenstein’s atomist picture, as embodied in his Tractatus, is initially very appealing. However, it faces the famous colour-exclusion problem. In this paper, I shall explain when the atomist picture can be defended (in principle) in the face of that problem; and, in the light of this, why the atomist picture should be rejected. I outline the atomist picture in Section 1. In Section 2, I present a very simple necessary and sufficient condition for the tenability (in principle) of the atomist picture. The condition is: logical space is a power of two. In Sections 3 and 4, I outline the colour-exclusion problem, and then show how the cardinality-condition supplies a response to exclusion problems. In Section 5, I explain how this amounts to a distillation of a proposal due to Moss (2012), which goes back to Carruthers (1990: 144–7). And in Section 6, I show how all this vindicates Wittgenstein’s ultimate rejection of the atomist picture. The brief reason is that we have no guarantee that there are any solutions to a given exclusion problem but, if there are any, then there are far too many.     

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.     

直接民主与间接民主--《代议制政府》的重新解读

直接民主与间接民主的问题,是当代政治哲学的一个热点。本文通过对密《代议制政府》的重新解读,澄清了直接民主和间接民主的关系。密尔系统地阐述了代议制民主的问题,他的间接民主理论中包含着直接民主的因素。一方面密尔把人民亲自参政的直接民主视为代议制民主的基础和前提,阐明了人民参政的直接民主的正当性、合理性;另一方面他又深刻地分析了人民参政的直接民主可能带来的弊病和危险。实际上,直接民主是一把双刃剑,它既可以成为克服暴政的武器,又可能导致多数的暴政;既可以成为自由的保障,也可能成为自由的敌人。因此,需要根据实际情况,扬利避害,在政治制度的设计中,正确地适度地运用直接民主的形式,保证人民的政治参与。     

The Phenomenology of Democracy

Molly Farneth’s Hegel’s Social Ethics hearkens back to the tradition of Josiah Royce, which has continued in the work of Richard Bernstein and Jeffrey Stout. At the same time, it reflects the impact of three decades of interpretive work which has offered an alternative to the 19th and early 20th century reading of Hegel as a metaphysical systematizer. In this new reading he was from the beginning a social critic and political theorist who looked to lay the groundwork for post-Enlightenment vision of the social world as evolving toward one of social cooperation based on mutual recognition. Farneth has developed this reading of Hegel into one of powerful resources for democratic pluralism.     

The Logical Form of Interventionism

This paper argues that, notwithstanding the remarkable popularity of Woodward??s (2003) interventionist analysis of causation, the exact definitional details of that theory are surprisingly little understood. There exists a discrepancy in the literature between the insufficient appreciation of the logical details of interventionism, on the one hand, and the amount of theoretical work interventionism is expected to do, on the other. The first part of the paper distinguishes four significantly different readings of the logical form of Woodward??s analysis and identifies the two readings that best capture Woodward??s intentions in (2003) and (2008a), respectively. In the second part, I show that these different readings are not clearly kept apart in the literature, and, moreover, that neither of them can do all the work that interventionists would like the theory to do.     

The Logical Deduction of Doctrine

The idea that Roman Catholic doctrines for which there is no early testimony can be explained as logical deductions from undoubtedly early teachings is usually dismissed as obviously false. By invoking the logical properties of doctrines expressed as explicit generalizations, however, and by distinguishing deductions in which all the assumptions represent Apostolic doctrine from those in which all the doctrinal assumptions are Apostolic, a way is found to deduce the disputed doctrines while leaving the immutability of doctrine intact. Although a theory of theological development is thus not needed to justify doctrinal additions, developments in theology nevertheless often motivate the authoritative pronouncements cited by doctrinal deductions. Finally, it is argued that a correct understanding of such deductions improves the prospects for reunion between those whose doctrinal axioms coincide even if differing historical information has rendered them incapable of following the same chain of deductions.     

The Logical Evaluation of Arguments

In this paper I will defend the controversial thesis that all argumentation in natural language can be reconstructed, for the purposes of assessment, as a deductively valid argument. Evaluation of the argumentation amounts to evaluation of the logical coherence of the premises. I will be taking the pragma-linguistic theory of Bermejo-Luque as an initial starting point.     

协商民主的路径——公共权力制约的民主选择

协商民主理论主张以沟通、交往的理性实践观来实现公民主体与权力主体的平等交流,强调通过讨论、交流、对话等方式培养交往主体的公共理性精神,实现政治民主.协商民主以理性对话的柔性机制,创新了对公共权力制约的民主形式,符合当代中国政治民主化转型时期社会稳定的需要,可以作为政治民主化改革的重要路径.     

The Tractatus on Logical Consequence

Abstract: I discuss the account of logical consequence advanced in Wittgenstein's Tractatus. I argue that the role that elementary propositions are meant to play in this account can be used to explain two remarkable features that Wittgenstein ascribes to them: that they are logically independent from one another and that their components refer to simple objects. I end with a proposal as to how to understand Wittgenstein's claim that all propositions can be analysed as truth functions of elementary propositions.     

The Logical Structure of Classical Genetics

We present a reconstruction of so-called classical, formal or Mendelian genetics using a notation which we believe is more legible than that of earlier accounts, and lends itself easily to computer implementation, for instance in PROLOG. By drawing from, and emending, earlier work of Balzer and Dawe (1986,1997), the present account presents the three most important lines of development of classical genetics: the so-called Mendel's laws, linkage genetics and gene mapping, in the form of a theory-net. This shows that the set theoretic representation format used in the structuralist approach to the philosophy of science also applies to the domain of genetic theories. There construction is intended to lend more clarity to theme thodological, philosophical and didactical discussions of the foundations of genetics, and on the other hand to defend a formally, logically minded view of theories which seems to have become contested through the work of Feyerabend, Kuhn and Kitcher. This revised version was published online in August 2006 with corrections to the Cover Date.