Meaning and Truth
Course Discussion Questions
(1) Logic and Language
(1) What is Frege’s main argument in ‘Separating a thought from its trappings’ (FR, pp. 239-44)? Is Frege right that ‘This dog [Hund] howled the whole night’ and ‘This cur [Köter] howled the whole night’ express the same thought? If you don’t find this particular example convincing, can you think of any better cases where two slightly different sentences can be regarded as expressing the same thought – or as having (more or less) the same meaning? In other words, can a viable distinction be made out between semantics and pragmatics?
(2) Explain the ambiguity of ‘Every student loves some philosophy course’. If you can, clarify this by formalizing into the predicate calculus, and indicating the scope of the quantifier. [Cf. FMS, pp. 45-6.]
(3) What reasons can be offered for construing ‘All A’s are B’ as ‘If anything is an A, then it is a B’? Do you think it would be right to see such a proposition as true if there are no A’s? How does this analysis illustrate Frege’s remark that he proceeds not from concepts, but from judgements? [Cf. FMS, pp. 43-5, 51-2.]
(4) Consider the following two propositions:
According to the analysis suggested in Q.3, both propositions come out as true. Why? Is such a view plausible? If it is not, how might the problem be avoided, whilst preserving the basic analysis? (Clue: consider the domain of discourse.) Is it legitimate to appeal to presuppositions? [Cf. FMS, § 2.4.]
(5) Discuss Frege’s argument in § 47 of The Foundations of Arithmetic (FR, pp. 99-100). What do you think he is saying? Is he right? [Cf. FMS, pp. 54-6.]
(6) Is Frege right in thinking that the following two propositions possess the same ‘conceptual content’?
How persuasive are the arguments that Frege himself offers in § 3 of the Begriffsschrift (FR, pp. 53-4)? Does Frege offer a good criterion for sameness of ‘conceptual content’? What criterion could you give? Can you suggest any other examples of propositions having the same ‘conceptual content’? [Cf. FMS, § 2.5.]
(7) Consider the following two pairs of examples:
Does (Eab) have the same ‘meaning’ as (Eba)? Does (Iab) have the same ‘meaning’ as (Iba)? Would it be better to say that they have the same ‘sense’ or ‘conceptual content’? Formalize the two propositions within the predicate calculus. Does this make it easier to see that they are logically equivalent? And does this provide a reason for treating them as having the same ‘sense’? [Cf. FMS, pp. 58-62.]
(8) Frege compares his logical system with a microscope (FR, p. 49)? Is this a good metaphor? What do you think is the value of logic? Can there be such a thing as an ideal language? What is the relationship between logic and semantics? [Cf. FMS, § 2.1.]
(2) Concepts, Objects and Numbers
Reading: Foundations, §§ 46-54 (FR, pp. 98-105); ‘On Concept and Object’ (FR, pp. 181-93).
(1) Is Frege right that logic would be crippled if ‘all transformation of the expression were forbidden on the plea that this would alter the content as well’ (FR, pp. 184-5, fn. G)? Consider the examples given under §(1) above, and in the lectures.
(2) Explain how Frege’s concept/object distinction provides a better solution to the traditional problem of the unity of the proposition than the subject/predicate distinction. (Clue: consider the role of the copula, and Frege’s doctrine of the ‘unsaturatedness’ of concepts.) [Cf. FMS, §7.1, p. 190.]
(3) Why did Frege want to say ‘The concept horse is not a concept’ (FR, p. 185)? Is there really a paradox here? Do you think concepts are objects? Can you think of any other examples where ‘a certain inappropriateness of linguistic expression’ is unavoidable (ibid., p. 193)? How might the paradox be resolved for Frege, and what implications would the resolution have? [Cf. FMS, §7.1, pp. 189-92; §7.3, pp. 200-1.]
(4) Explain the difference between subsumption and subordination. Explain the distinction between first-level and second-level concepts, giving examples of each. What does Frege mean by the ‘marks’ (‘Merkmale’) of a concept? (See FR, pp. 189-90; Foundations, §53 (FR, pp. 102-3).)
(5) It is sometimes said, rather loosely, that Frege construes number and existence as properties of concepts, not of objects (i.e. as second-level concepts). Explain what is meant by this, and why it is not, strictly speaking, correct. How should his view be expressed? Reading: Foundations, §§ 46-54, esp. §46 and §53 (FR, pp. 98-9, 102-3). [Cf. FMS, §4.1, pp. 92-6.]
(6) How widespread is the phenomenon of vagueness? Why are vague concepts a problem for classical (Fregean) logic? Discuss by setting out the so-called Sorites paradox (the paradox of the heap). How might this paradox be resolved? [Cf. FMS, §7.3.]
(7) Are numbers objects? If so, what sort of objects are they? [Cf. FMS, ch. 4.]
(3) Analysis and Definition
Reading: The Foundations of Arithmetic, selections in The Frege Reader (pp. 84-129), esp. §§ 3, 45-69, 88.
(1) Make sure that you understand the analytic/synthetic, a priori/a posteriori distinctions, as reformulated by Frege. What is involved in the Kantian claim that some truths are synthetic a priori? Check that Frege leaves open this possibility when offering his own criteria. But why does Frege himself think that arithmetic (unlike geometry) is a system of analytic a priori truths? Is he right? What do you think is the role of the empirical in our acquisition of mathematical knowledge? [Cf. FMS, §§ 3.4, 5.1 - 5.2.]
(2) What is the role of the context principle in Frege’s Foundations? What exactly do you think the principle means? Is it right? [Cf. FMS, §§ 4.1 - 4.2.]
(3) Consider the following pairs of propositions:
Do (Da) and (Db) have the same ‘content’? Do (Na) and (Nb) have the same ‘content’? Do (Ra) and (Rb) have the same ‘content’? If they do, then in each case, is it better to define the second in terms of the first, or the first in terms of the second? Which form, if any, is the more fundamental, and why? Can you think of other examples of such pairs? Do we have here a way of introducing/justifying reference to abstract objects? [Cf. FMS, §4.2.]
(4) Frege ends up offering the following explicit definition of the number 0:
Is Frege right to identify the number 0 with (in effect) the null set? Does this show that numbers are logical objects? [Cf. FMS, §§ 4.3, 4.5.]
(5) What is the paradox of analysis? Do you think that an analysis or definition can be both correct and informative? If so, how do you think it can be so? Does the resolution of the paradox require, at the very least, some kind of disambiguation of ‘meaning’? Can you think of any examples of (broadly) correct and informative analyses or definitions? Should we, in fact, distinguish analyses from ‘mere’ definitions? Consider the examples in the section of the Course Notes on the paradox of analysis: can one member of each pair be regarded as providing an analysis or definition of the other?
(6) Read §9 of Frege’s Begriffsschrift (FR, pp. 65-8) and §88 of his Foundations (FR, p. 122). What was Frege’s early response to the problem of analysis? How would you explain the idea of ‘splitting up content in a different way’? (Clue: consider the possibilities of function-argument analysis.) [Cf. FMS, §5.2.]
(7) Read Frege’s reply to Husserl’s critique of the Foundations (FR, pp. 224-6). Does Frege’s distinction between Sinn and Bedeutung resolve the paradox of analysis? If not, why not? I suggested in the Course Notes that the notion of ‘Bedeutung’ is too coarse-grained, and the notion of ‘Sinn’ too fine-grained. What is meant here? Can extensional equivalence be the sole criterion of correctness? What is it for two expressions to have different senses? [Cf. FMS, §5.4.]
(8) Read Frege’s account of definitions in ‘Logic in Mathematics’ (FR, pp. 313-8). Explain Frege’s distinction between ‘constructive’ and ‘analytic’ definitions. Does the appeal to reconstruction resolve the paradox as it relates to ‘analytic’ definitions? To what extent should analyses be answerable to our ordinary understanding? [Cf. FMS, §§ 5.5, 8.5.]
(4) Sense and Reference
(1) Compare §8 of the Begriffsschrift (FR, pp. 64-5) with the opening paragraph of ‘On Sinn and Bedeutung’ (FR, pp. 151-2). What is Frege’s early conception of ‘identity of content’, and what are his later objections to it? Is identity a relation between names or objects? What is Frege’s essential argument in that opening paragraph? How can identity statements be informative? What seems to be the main motivation behind the distinction between ‘Sinn’ and ‘Bedeutung’? How does it relate to Frege’s argument in the central sections of the Foundations, in particular, §§ 62-9? [Cf. FMS, §6.1.]
(2) How good are Frege’s arguments for his view that the Bedeutung of a sentence is its truth-value? Are there any better candidates for the Bedeutung of a sentence? [Cf. FMS, §6.2.]
(3) What is the problem of intensional contexts? Explain Frege’s distinction between ‘customary’ and ‘indirect’ Bedeutung and Sinn. Does this help solve the problem? [Cf. FMS, §6.5.]
(4) Do all proper names have both a sense and a reference? Do fictional names, in particular, have both a sense and a reference? Would it matter if they didn’t? Should a distinction be drawn between ‘modes of presentation’ and ‘modes of determination’? What is the message of Frege’s notorious footnote on p. 153 of FR? How is the sense of a proper name to be given? Is it, for example, to be equated with the sense of some definite description? What objections might be raised to this? Should a distinction be drawn between ‘simple’ proper names and definite descriptions? Say which of the following two principles holds of each:
What would the essential difference be in the formalization of (SMI) and (MIS)?
(5) Now that you appreciate something of Frege’s philosophy, how do you think that ‘Bedeutung’ should be translated? (Cf. FR, pp. 36-46.)
(5) Russell’s Theory of Descriptions
(1) How does Russell analyse ‘The present King of France is bald’? Is he right that this sentence is false if there is no King of France? How does Russell’s account of propositions containing denotationless phrases compare with Frege’s (cf. FR, p. 385)? Do such propositions express genuine thoughts? If so, how might these thoughts be alternatively expressed? If not, do they still have meaning, under some construal of ‘meaning’?
(2) Have you stopped enjoying philosophy of language?
(3) What are Strawson’s objections to Russell’s theory of descriptions? Is Strawson right to say that ‘The present King of France is bald’ is neither true nor false? Is it in fact meaningful, according to Strawson? Explain Strawson’s distinction between sentence and statement. Does the use of a sentence involving reference-failure, on Strawson’s account, result in a statement that is neither-true-nor-false or no statement at all? Explain Strawson’s notion of ‘presupposition’. How important do you think ‘presuppositions’ are in using and understanding linguistic expressions?
(4) How do you think the dispute between Russell and Strawson can be resolved? Does Donnellan help things here? Explain his distinction between attributive and referential uses of definite descriptions. Does Donnellan himself ignore the distinction between what is strictly said on a given occasion and what is conveyed? Is Strawson right in his later comment that ‘ordinary usage does not deliver a clear verdict for one party or the other’ (‘Identifying Reference and Truth-Values’, p. 82)? If so, then what is the moral of the whole dispute?
(6) Thought and Indexicality
(1) Make sure that you understand the differences between the three criteria for sameness of thought formulated in the relevant section of the Course Notes by providing your own examples of pairs of propositions that come out differently depending on the criterion applied. Which criterion corresponds most closely to Frege’s early criterion for sameness of ‘conceptual content’? Is even the third criterion for sameness of sense adequate?
(2) Does ‘I am hot’ said by me and ‘You are hot’ said by you to me, on the same occasion, express the same thought? If so, what is that thought, and how else might it be expressed? If not, does this mean that there are some kinds of thought that we can never share?
(3) How, in general, would you explain the sense of an indexical? Do we need to introduce, as well as the notions of sense and reference, the notion of linguistic role? How pervasive is the phenomenon of context-dependence? Do we ever utter ‘complete’ sentences, in which all indexicality has been ‘cashed out’? (Cf. FR, pp. 30-6; FMS, §§ 7.4 - 7.5.)
(4) Construct an example of your own to illustrate ‘the problem of the essential indexical’. In your example, to what extent could one speak of ‘dynamic thoughts’?
(5) If I beat my breast or stamp my foot, exclaiming, like Descartes, ‘I know I am here now’, what is the content of my thought? How might it be ‘cashed out’? Imagine waking up in the middle of a dense forest after a night of complete drunkenness and drug-taking, remembering nothing of who you are (but still being able to speak). What now is the content of your Cartesian thought? Could you share it with me (however unpleasant that might be for me)?
© Mike Beaney
February 1999
Meaning and Truth 
Mike Beaney