Abstract
Having presented Frege’s reflections from ‘On Sense and Reference’, we now turn to the principal objections which the commentators have made against Frege’s semantics. This chapter will mainly deal with those critical positions which involve the bases of the Fregean analysis: other critiques which accept the bases but cast doubt on the application will be dealt with in the following chapters. In order to maintain clarity we will answer immediately upon presentation those critiques which are clearly based on a misunderstanding. Objections which can only be met on the basis of a more thorough study of Fregean texts are clearly formulated, and then answered in the second half of the chapter.
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References
Russell, B., ‘The Logical and Arithmetical Doctrines of Rege’, Appendix A in The Principles of Mathematics,London 1903 (2nd ed.: 1937), 475–496, resp. 501–522. References here to the second edition.
Russell, B. ‘On Denoting’, Mind,n. s. 14 (1905), 479–493.
The full quotation is: “According to the view I am espousing here, in ‘5>4’ or ‘2+3 =5’ one has to do only with expressions of truth-values, without anything having been asserted. This separation of the judgement from that which is judged seems unavoidable since a mere assumption or the positing of an instance, without deciding about its being the case, would be inexpressible” (FuB,21). - Even prior to the note in ‘On Denoting’, Russell indicated in his article ‘Meinong’s Theory of Complexes and Assumptions’ (Mind,n. s. 13 1904), similarities between the Fregean theory of sense and reference and Meinong’s theory of assumptions. Meinong, who had hitherto not been aware of Frege’s works (cf. Meinong, A., Über die Stellung der Gegenstandstheorie im System der Wissenschaften [On the Place of the Theory of Objects in the System of Sciences], Leipzig 1907, p. 4, n. 2), now thought he saw a similarity. In the second edition of his On Assumptions (Leipzig 1910, p. 6), he wrote: “If it ever happens - and much indicates that it should - that a history of the theory of assumptions is written, this will be in great part thanks to a sentence from Frege ‘s lecture on ‘Function and Concept’” (whereupon the above quotation is repeated). And, it seems that Wittgenstein took the expre scion ‘Fregean assumption’ from Russell. Cf. Notebooks 1914–1916 (edited by G.E.M. Anscombe, Oxford 1961, pp. 29 and 38); Philosophical Investigations, § 22 (pp. 10–11 in the Oxford edition of 1958); Tractatus,4.063. O.E.M. Anscombe (Mrs. Geach) was the first to draw attention to this misunderstanding (cf. An Introduction to Wittgenstein’s Tractatus,London 1959, 105–6, note).
Pr., 504, in this formulation. FuB,21, is inadvertently given as source.
Carnap, R. Meaning and Necessity. A Study in Semantics and Modal Logic,2nd ed., Chicago 1956 (1st ed.: 1947), 140.
Already in the ‘appendix’ of 1905, we find: “If we wish to speak of its meaning, we must use inverted commas or some such device” (pp. 27–28) (Pr.,502; the pages refer to SuB).
Already in the first lines of the article, what is conceived as the name of an expression appears once with, once without quotation marks. It is hard to see if Russell was confusing sign, sense, and reference or only sign and reference. Church is for the latter: “Russell’s reasons for rejecting Frege’s notion of sense are, in the reviewer’s opinion, without force. The point that some expressions, e.g., ‘the king of France in 1905’, have a sense but no designatum simply does not constitute a difficulty, except in the sense of a complicating factor in the construction of a formalized language. And Russell’s other objections, it would seem, are traceable merely to confusion between use and mention of expressions, of a sort which Frege is careful to avoid by the employment of quotation-marks. Russell applies quotation-marks to distinguish the sense of an expression from its denotation, but leaves himself without any notation for the expression itself; upon introduction of (say) a second kind of quotation-marks to signalize names of expressions, Russell’s objections to Frege completely vanish” (Church, A., Review of Carnap’s Introduction to Semantics, The Philosophical Review 52 (1943), 298–304; quotation from p. 302).
Jones, E.E.C., ‘Mr. Russell’s Objections to Frege’s Analysis of Propositions’, Mind, n. s. 19 (1910), 379–386.
Papst, op. cit.,28, with reference to the article mentioned in the previous note. Frege is also mentioned in Jones, E. E. C., ‘A New Law of Thought’ (Proc. Arist. Soc.,n. s. 11 (1911), 166–186). To judge by the article of 1910, the agreement involves aspects of the theory of sense and reference and, as the analysis in the text will show, the comparison should not be pushed too far. Papst’s affirmation about the influence of Frege on Jones will hardly bear scrutiny, since Jones’ ideas are to be found in the earlier work, Elements of Logic as a Science of Propositions,Edinburgh 1890, i.e., previous to the articles where Frege develops his second doctrine on judgement. As evidence, we offer the following quotation: “A significant Categorical Proposition, a Proposition in which the Predicate adds something to the Subject, may be defined as, A Proposition which affirms (or negates) Identity of Denotation in Diversity of Determination” (op. cit.,46).
In fact, according to Jones, Frege is of the mind that every affirmative proposition ‘S is P’ asserts the identity of S and P while the senses are simultaneously different. However, reservations are in order since Jones’ concept of reference does not seem to be that of Frege; cf. the equating of “denotation or application or applicability” (loc. cit.,382).
Papst, op. cit., 25, without sourcing. We could not find the text where Russell makes this objection. The problem is touched on in the introduction of the term ‘proper name’ by F. von Kutschera in Die Antinomien der Logik. Semantische Untersuchungen [Logical Antinomies. Semantic Investigations], Freiburg/Munchen 1964.
Example: “I call proper name or name of an object a sign which should designate an object” (Gg.,I, 43). Only an interpretation of ‘should’ in the sense that every proper name should be specified as the name of an object already known to exist (conventional ‘should’) corresponds to the view of the Basic Laws. This is our interpretation, but it does not suffice to eliminate the other view that the ‘should’ indicates that a proper name intends an object (intentional ‘should’).
Frege’s designation of ‘the greatest proper fraction’ as ‘senseless’ (Gl.,88 n.) does not contradict our interpretation. In a letter to Husserl, Frege says: “In the Foundations I had not yet made the distinction between sense and reference. In § 97 I would now put ‘referential’ instead of ‘senseful’. Elsewhere, too - e.g. in § 100, 101, 102 - I would in many instances put ‘reference’ for ‘sense“‘ (letter of May 24, 1891).
Hamburg 1951. Typed dissertation.
We are convinced that, on the basis of his presuppositions, Bierich was not obliged to carry out his proof of the correctness of Russell’s first objection in just this way. Since in Bierich’s interpretation of Frege an assertory sentence does not designate but asserts (or not only designates but also asserts), this is enough to make the relation between sentence and truth-value other than that between description and descriptional reference. In this case the relation between sentence and thought is not a genuine expressional relation and that between sentence and truth-value is not a genuine designational relation. Since this argument neither uses nor presupposes the concept of sense, the communication of the reference by the sense is of importance only for the special form of Bierich’s argument. But we do not recognize the presuppositions of either of these arguments and, a fortiori,of Bierich’s procedures of proof.
One looks in vain for a serious treatment of this theory in the commentaries. Granted Frege’s statements are easily misunderstood, this does not justify the superficial treatment that one finds. Even the recognition of Frege’s usage of ‘assertion’ — essential as it is for any critique — is sometimes missing Linke objects to the view that assertion is the declaration of a judgement: “It is clear that usage [!] contains assertions where the asserted is in no way held to be true, i.e., assertions which take place without and even against the conviction of the asserter. Every lie proves this“ (Linke, P. F., Was ist Logik?’ [What is Logic?], Wissenschaftliche Zeitschrift der Friedrich-SchillerUniversität Jena,3 (1953–54), Gesellschafts-u. sprachwissenschaftliche Reihe,Nr. 2/3, 179–190, here p. 184). All this says is that everyday usage knows as assertion a comportment which is not oriented toward the truth or falsity of the asserted. This does not refute Frege’s deviationist usage, where a false sentence cannot be asserted: “Since it is false, it cannot be expressed with assertory force” (Vern., 148). Cf. Geom., IV, 400: “For one who does not want to be fooled by words but wants to get to the bottom of things, word-usage by itself can decide nothing. One must always ask: is the word-usage in accordance with the thing?”
We are limiting ourselves to the German which Frege used, without prejudice to the validity of the above for other languages.
It is clear that only complete sentential questions are involved here.
A sign-series “I- (I- A)” would not be correctly constructed. And even this solution does not bring ultimate certainty. One could imagine the objections of a Wittgenstein: “But cannot someone in a stage-play write ‘I- A’ on a blackboard?” and would the “I- A” here not be without assertory force? A possible answer to this question is that “I- A” here stands in a context similar to that of expressions in indirect (e.g., quoted) discourse. But the described situation would have to be investigated further; and the objection itself is not without sophistication.
In this interpretation we have made extensive use of Fregean terminology. It would be better, in an independent presentation, to drop the expression ‘assertory sentence’, which can lead to misunderstanding, and to use a form of propositional sentence in opposition to interrogative, imperative, etc. sentences, with the complementary condition that only propositional sentences can be asserted. Whether a sentence is an assertion or not is decided from the context.
Geach, P.T., ‘Russell’s Theory of Descriptions’, Analysis 10 (1950), 84–88 (here p. 85).
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Thiel, C. (1968). Description, Designation, Assertion: Russell, Jones and Bierich on Frege’s Semantics. In: Sense and Reference in Frege’s Logic. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2981-9_7
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