Frege's ‘On the Concept of Number’ (1891) – an unnoticed publication

A short piece by Frege, heretofore overlooked, containing a précis of his views on the concept of number, is presented, after some very brief questions about Frege's possible involvement in the wider intellectual milieu.     

Truth in Frege's ‘law of truth’

I wish to thank Peter Hylton, from whom I have learned much in discussion of these issues, and whose comments upon a previous draft of this paper helped to give it its present shape. I must also thank two anonymous referees, who were most helpful on both specific and general points, and Axel Boldt, who helped with the German.     

On the Logic of β-pregroups

In this paper we concentrate mainly on the notion of β-pregroups, which are pregroups (first introduced by Lambek [18] in 1999) enriched with modality operators. β-pregroups were first proposed by Fadda [11] in 2001. The motivation to introduce them was to limit (locally) the associativity in the calculus considered. In this paper we present this new calculus in the form of a rewriting system, prove the very important feature of this system - that in a given derivation the non-expanding rules must always proceed non-contracting ones in order the derivation to be minimal (normalization theorem). We also propose a sequent system for this calculus and prove the cut elimination theorem for it. As an illustration we show how to use β-pregroups for linguistical applications. Special Issue Categorial Grammars and Pregroups Edited by Wojciech Buszkowski and Anne Preller     

On the Consistency of a Plural Theory of Frege’s <Emphasis Type="Italic">Grundgesetze</Emphasis>

PG (Plural Grundgesetze) is a predicative monadic second-order system which is aimed to derive second-order Peano arithmetic. It exploits the notion of plural quantification and a few Fregean devices, among which the infamous Basic Law V. In this paper, a model-theoretical consistency proof for the system PG is provided.     

On Structural Features of the Implication Fragment of Frege’s <Emphasis Type="Italic">Grundgesetze</Emphasis>

We set out the implication fragment of Frege’s Grundgesetze, clarifying the implication rules and showing that this system extends Absolute Implication, or the implication fragment of Intuitionist logic. We set out a sequent calculus which naturally captures Frege’s implication proofs, and draw particular attention to the Cut-like features of his Hypothetical Syllogism rule.     

On Confucius’ Principle of Consanguineous Affection: A Reading of the Dialogue about the Three-Year Mourning in the Lunyu 1

In his dialogue with Zai Wo about the three-year mourning, Confucius establishes a principle of ‘justification by feeling at ease,’ and insists that one should transcend natural desires by moral emotions. More significantly, he further regards kinship love as the ultimate root and supreme principle of human life. Thus, this dialogue contains almost all the basic elements of the Confucian spirit of consanguineous affection.     

On the {↔, ∼} -reduct of the intuitionistic consequence operation

The intuitionistic consequence operation restricted to the language with (equivalence) and (negation) as the only connectives is axiomatized by means of a finite set of sequential rules of inference.To the memory of Professor Roman Suszko     

On the “recovery” of masked targets

Subjective magnitude characteristics for vibrotaction were determined by the method of numerical magnitude balance for three body sites varying in the density of neural innervation: the distal pad of the middle finger, the thenar eminence, and the volar forearm. The effects of a rigid surround upon threshold and the rate of growth of subjective intensity were measured. The results support the suggestion that absolute threshold and the rate of growth of subjective intensity are inverse functions of the total number of sensory neural units stimulated rather than being related simply to the density of neural innervation.     

On the Subjectivity of the Experience of Victory: Who Are the Election Winners?

Elections represent key moments in democratic countries, and an established finding from the existing literature is that winners of elections display higher levels of satisfaction with democracy. Yet we know almost nothing about the times when voters feel like winners of an election. Using panel data in four countries, this article finds that while the objective performance of the supported party—measured using vote share and changes in vote share from the previous election—has a very important effect on feeling like an election winner, prior expectations regarding the election’s outcome as well as preferences for the supported party significantly moderate the effect of party performance on voter feelings. It seems also that the identification of the winners and losers of elections are clearer in majoritarian‐style democracies than in proportional systems with coalition governments. Ultimately, the findings indicate that measuring who are the winners of an election using exclusively objective measures of party performance may provide a distorted view of public opinion following the elections.     

On the problem of the meaning of life in ��Chinese Philosophy��

The goal of “(modern) Chinese Philosophy” established during the period of the May 4th Movement is to reestablish the meaning of life for Chinese people. However, because it takes the approach of interpreting Chinese thinking through a Western lens, thus forming a discourse pattern of “Chinese A is Western B,” which is only capable of manifesting Western culture, “Chinese Philosophy” is made logically impossible as the ideological source from which modern Chinese thinkers could construct the meaning of life. The ideological source of the still lasting traditional lifestyle is Yili Xue 义理学 (The Learning of Righteousness and Principles); whereas that of modern life, which was established as an imitation of the West, is Western culture. Neither of them takes “Chinese Philosophy” as its ideological source. Therefore, “Chinese Philosophy” is excluded from the construction of the meaning of life, and falls into the dilemma of life meaning.