意义的体系——维特根斯坦的《逻辑哲学论》与形式语义学

人们把一般形式语义学的起源追溯到弗雷格、塔尔斯基、蒙塔古和戴维森等哲学家。但是人们忽略了维特根斯坦的《逻辑哲学论》。维特根斯坦在这本著作中提出了一种特定的关于语言、意义和世界的看法,它牵涉到普遍论、内涵指称论和组合原则等重要的哲学假定,而这样的哲学假定也是形式语义学先驱的著作中所假定的。因此,维特根斯坦的意义理论对于形式语义学的基本原则和哲学假定的确立是至关重要的。斯托克霍夫教授的研究不是历史性的,而是系统地比较了维特根斯坦的意义理论和形式语义学的先驱的著作。     

Multimedia-Supported Metaphors for Meaning Making in Mathematics

We examined a number-line metaphor presented using interactive multimedia as a means of helping students build connections between an arithmetic procedure and their existing conceptual knowledge. Elementary school children learned to add and subtract signed numbers through a computer-based multimedia program over 4 training sessions. Participants received 64 example problems presented only in symbolic form (single-representation [SR] group) or in symbolic, visual, and verbal forms (multiple-representation [MR] group). In Experiment 1, compared to the SR group, the MR group (a) showed a larger pretest-to-posttest gain for high-achieving students but not for low-achieving students, (b) showed a greater gain on difficult problems but not easy problems, (c) learned faster during training, and (d) showed a greater pretest-to-posttest reduction in the use of conceptual bugs reflecting conceptually confusion between negative signs and subtraction operators. In Experiment 2, high spatial ability students in the MR group outperformed low spatial ability students on pretest-to-posttest gain. Productive learning with MRs is strongest when working memory is not overloaded, so cognitive load and MR theories can be reconciled.     

Symbols in Wittgenstein's Tractatus

This paper is concerned with the status of a symbol in Wittgenstein's Tractatus . It is claimed in the first section that a Tractarian symbol, whilst essentially a syntactic entity to be distinguished from the mark or sound that is its sign, bears its semantic significance only inessentially. In the second and third sections I pursue this point of exegesis through the Tractarian discussions of nonsense and the context principle respectively. The final section of the paper places the forgoing work in a secondary context, addressing in particular a debate regarding the realism of the Tractatus .     

Truth in the Tractatus

My paper takes issue both with the standard view that the Tractatus contains a correspondence theory and with recent suggestions that it features a deflationary or semantic theory. Standard correspondence interpretations are mistaken, because they treat the isomorphism between a sentence and what it depicts as a sufficient condition of truth rather than of sense. The semantic/deflationary interpretation ignores passages that suggest some kind of correspondence theory. The official theory of truth in the Tractatus is an obtainment theory – a sentence is true iff the state of affairs it depicts obtains. This theory differs from deflationary theories in that it involves an ontology of states of affairs/facts; and it can be transformed into a type of correspondence theory: a sentence is true iff it corresponds to, i.e. depicts an obtaining state of affairs (fact). Admittedly, unlike correspondence theories as commonly portrayed, this account does not involve a genuinely truth-making relation. It features a relation of correspondence, yet it is that of depicting, between a meaningful sentence and its sense – a possible state of affairs. What makes for truth is not that relation, but the obtaining of the depicted state of affairs. This does not disqualify the Tractatus from holding a correspondence theory, however, since the correspondence theories of Moore and Russell are committed to a similar position. Alternatively, the obtainment theory can be seen as a synthesis of correspondence, semantic and deflationary approaches. It does justice to the idea that what is true depends solely on what is the case, and it combines a semantic explanation of the relation between a sentence and what it says with a deflationary account of the agreement between what the sentence says and what obtains or is the case if it is true     

转折与革命——逻辑经验主义的数学哲学:从《逻辑哲学论》到《逻辑句法》

与经验主义或实证主义之前的形式相比,逻辑和数学哲学是最具逻辑经验主义特征的。逻辑经验主义不仅因此得名,而且也为科学经验主义的成功点燃了希望。然而,经验主义者的心理主义与实证主义者的逻辑主义对数学本质的探讨始终不能达成共识。基于这种背景,维特根斯坦《逻辑哲学论》的发表对于维也纳小组的影响深远、意义重大。逻辑经验主义在20世纪20年代的数学哲学都是植根于《逻辑哲学论》的。本文在第一部分阐释了它何以成为该学派在"哲学上的转折点"。而维也纳学派从一开始就试图对《逻辑哲学论》进行革新,使之服务于其本身的纲领。本文在第二部分着重探讨了他们关于这些问题所展开的激烈讨论。这种状况一直持续到1931年卡尔纳普提出了"句法"纲领,该纲领从根本上超越了逻辑经验主义的原有框架。但由于当时欧洲逻辑经验主义者受到纳粹的迫害而四分五散,"句法"观点并未受到广泛关注。本文在第三、第四部分具体分析了逻辑经验主义如何由《逻辑哲学论》向"句法"思想转变的过程。     

Variable Names and Constant Names in Wittgenstein's Tractatus

In this paper, I argue that the Tractatus classifies names into constant names and variable names. A variable name, via the application of the existential quantifier against the background of picturing, picks out and denotes an unspecified object from the range of objects of the form shown by the relevant variable. A constant name labels an object picked out from a scope of the existential quantifier. I also refute two types of attempts to argue that the Tractarian relation between a name and its meaning is not realist, and to explain why it is more reasonable to hold that it is.