Frege's Logic

MEDIEVAI AND RENAISSANCF LOGIC

WILLIAM OFOCKHAM, Ockham's theory of propositions. Part I1 of Summa logicae. Translated by Alfred J. Freddoso and Henry Schuurman, with an introduction by Alfred J. Freddoso. University of Notre Dame Press, 1980. viii + 212 pp. £ 12.00.

WILHELM RISSE, Bibliagraphia Logica. Verzeichnis der Handschriften zur Logik. Band IV. Hildesheim, New York: Georg 0lm.s Verlag, 1979. vii + 390pp. DM 98.

G. W .F. H EGEL, Wissenschaft der Logik. Erster Band. Die objektive Logic (l812/1813) (Gesammelte Werke, Hand 11) Herausegeben von F. Hogemannund W. Jaeschhc. Hamburg: Felix hleiner Verlag, 1978. xii + 441 S. DM 118.

G.W.F. HEGEI., Wissenschaft der Logik. Zweiter Band. Die subjektive Logik (1816). (Gesammelte Werke, Band 12.) Herausgegeben von F. Hogemann und W. Jaeschke. Hamburg: Felix Meiner Verlag, 1981. viii + 358 S. DM 122.

G. GUNTHER, Idee und Grundriss einer nicht-aristotelischen Logik. Die Idee und ihre philosophischen Voraussetzungen. Appendix by R. Kaehr. Hamburg: Felix Meiner Verlag,1978,xxx + 417 + 117 pp. DM 84.

LOGIC AND PHILOSOPHY

BFN-AMI SCHARFSTEI N, The philosophers: their lives and the nature of their thought. Oxford: Basil Blackwell, 1980. x + 486 pp. £18.00.

DESMONDLEE (ed.), Wittgenstein's lectures: Cambridge 1930 - 1932. From the notes of John King and Desmond Lee. Oxford: Blackwell, 1980. xix + 124 pp. £7.95.

0. HANFLING, Logical positivism. Oxford: Basil Blackwell, 1981. viii + 181 pp. £14.00 (cloth)/£5.50 (paper).

0. HANFLING(ed.),Essenliai readings in iogicai podivihrn. Oxford: Basil Biackwell, 1981. viii + 248 pp. £5.95(paper).     

Frege's Elucidatory Holism

I argue against the two most influential readings of Frege's methodology in the philosophy of logic. Dummett's “semanticist” reading sees Frege as taking notions associated with semantical content—and in particular, the semantical notion of truth—as primitive and as intelligible independently of their connection to the activity of judgment, inference, and assertion. Against this, the “pragmaticist” reading proposed by Brandom and Ricketts sees Frege as beginning instead from the independent and intuitive grasp that we allegedly have on the latter activity and only then moving on to explain semantical notions in terms of the nature of such acts. Against both readings, I argue, first, that Frege gives clear indication that he takes semantical and pragmatical notions to be equally primitive, such that he would reject the idea that either sort of notion could function as the base for a non-circular explanation of the other. I argue, secondly, that Frege's own method for conveying the significance of these primitive notions—an activity that Frege calls “elucidation”—is, in fact, explicitly circular in nature. Because of this, I conclude that Frege should be read instead as conceiving of our grasp of the semantical and pragmatical dimensions of logic as far more of a holistic enterprise than either reading suggests.     

Was Wittgenstein Frege's Heir

Dummett has claimed that Wittgenstein's views, as expressed in The Blue and Brown Books and Philosophical Investigations , build on the attack on psychologism initiated by Frege. Frege's rejection of psychologism led him to the view that the meanings of sentences are thoughts which objectively exist in a third realm. It was Wittgenstein, according to Dummett, who, inheriting Frege's insights, provided a genuinely anti-psychologistic account of understanding by insisting that we explain understanding a sentence in terms of the use that is made of it. I challenge this interpretation of the relationship between Wittgenstein and Frege. I argue that the analysis does not sufficiently distinguish anti-psychologism and anti-mentalism. In the light of this distinction we can see that Wittgenstein misrepresents Frege's views, and confuses concepts with ideas. By being more faithful to Frege's actual views concerning the objectivity of concepts we can give a robustly realist account of mathematical truth which does not involve any objectionable psychologism or mentalism.
email : Karen.Green@arts.monash.edu.au     

II. Frege's realism

In this note the claim is defended that Frege was a realist in the sense that he attributed causal efficacy to certain abstract objects. The arguments of Dummett and Sluga (cf. Inquiry, Vols. 18, 19, and 20 [1975–77]) to the contrary are criticized.     

Frege's Puzzle for Perception

According to an influential variety of the representational view of perceptual experience—the singular content view—the contents of perceptual experiences include singular propositions partly composed of the particular physical object(s) a given experience is about or of. The singular content view faces well‐known difficulties accommodating hallucinations; I maintain that there is also an analogue of Frege's puzzle that poses a significant problem for this view. In fact, I believe that this puzzle presents difficulties for the theory that are unique to perception in that strategies that have been developed to respond to Frege's puzzle in the case of belief cannot be employed successfully in the case of perception. Ultimately, I maintain that this perceptual analogue of Frege's puzzle provides a compelling reason to reject the singular content view of perceptual experience.     

The Structure of Frege's Thoughts

Fregean thoughts (i.e. the senses of assertoric sentences) are structured entities because they are composed of simpler senses that are somehow ordered and interconnected. The constituent senses form a unity because some of them are ‘saturated’ and some ‘unsaturated’. This paper shows that Frege's explanation of the structure of thoughts, which is based on the ‘saturated/unsaturated’ distinction, is by no means sufficient because it permits what I call ‘wild analyses’, which have certain unwelcome consequences. Wild analyses are made possible because any ‘unsaturated’ sense that is a mode of presentation of a concept together with any ‘saturated’ sense forms a thought. The reason is that any concept can be applied to any object (which is presented by a ‘saturated’ sense). This stems from the fact that Frege was willing to admit only total functions. It is also briefly suggested what should be done to block wild analyses.     

Frege's Content-Principle and Relevant Deducibility

Given the harmony principle for logical operators, compositionality ought to ensure that harmony should obtain at the level of whole contents. That is, the role of a content qua premise ought to be balanced exactly by its role as a conclusion. Frege's contextual definition of propositional content happens to exploit this balance, and one appeals to the Cut rule to show that the definition is adequate.We show here that Frege's definition remains adequate even when one relevantizes logic by abandoning an unrestricted Cut rule. The proof exploits the fact that in the relevantized logic, which abandons the unrestricted rule of Cut, any failure of the transitivity of deduction is offset by the epistemic gain involved in learning that a stronger-than-expected result holds.     

Taking Frege's name in vain

A widely held view about Fregean Sense has it that the determination of a sign's referent by the sign's sense is achieved viasatisfaction: the sense specifies a condition (or set of conditions) and the referent is that entity, if any, which uniquely satisfies that (set of) condition(s). This is usually held in conjunction with the claim that the sense is existentially and qualitatively independent of the referent: if the referent did not exist, or did not uniquely satisfy the sense, the sense would still exist and would still specify the same condition(s) that it actually does (and might determine a different referent than its actual one). Proponents of this view give several reasons for holding it. I describe these reasons and argue that they are not convincing. More generally, I try to show that the notion of satisfaction has no useful application within Frege's system. I then suggest an alternative account of the determination of a referent by a sense that I think is truer to Frege and more illuminating. Compared to the satisfaction view, my account construes determination as a more naturalistic and epistemically real relation between speakers and things in the world.     

关于弗雷格"Bedeutung"一词的翻译

作者详细考察了“Bedeutung”一词在德语中的标准意义,以及弗雷格在其著述中使用它的各种情况,并仔细回顾了在英语哲学界对这个词的翻译和理解所发生的争论及其理由。他不太赞成把“Bedeutung”译为“meaning”（意义）和“significance”（意谓）一类的词,他还反驳了支持这类译法的三个论证。“公正地讲,‘reference’（所指）和‘refer to’（指称）是得到最广泛认可的翻译。”他区分了“Bedeutung”的水平意义和垂直意义,前者是指语言表达式相互之间的关系,后者是指语言表达式与语言之外的对象之间的关系,并认为弗雷格更多地从“对象”的意义上使用“Bedeutung”一词。鉴于弗雷格使用“Bedeutung”的模糊性和怪异性,作者建议用“reference”及其近似词来翻译“Bedeutung”及其近似词,它兼有“指称”（作为关系）和“所指”（作为对象）的模糊性;并把该德语原词置于相应译文之后的括号内。     

Frege's theorem and his logicism

As is well known, Frege gave an explicit definition of number (belonging to some concept) in §68 of his Die Grundlagen der Arithmetik     

弗雷格定理:一个导言

戈特洛布·弗雷格是现代数理逻辑的奠基人,也是分析哲学的创始人之一。他的大部分工作都致力于建立一种数学哲学———逻辑主义:算术真理都是逻辑真理。长久以来,哲学家一直认为,罗素悖论彻底瓦解了弗雷格的工作。然而实际的情况是,在弗雷格那里隐藏着另一个证明:算术公理可以纯粹逻辑地从休谟原则推出。休谟原则是说,概念F的数和概念G的数相同当且仅当存在F和G之间的一一对应关系。这一结果被称为弗雷格定理,它引发了一种新的逻辑主义的兴起。