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1Frege famously endorsed a principle of Thought-Sentence Correspondence that can be spelt out as follows:

(Corr1) For all sentences s, for all thoughts t, if r expresses t, then:
if a sense is expressed by a part of s then it is part of t, &
(Corr2) For all sentences s, for all thoughts t, if s expresses t, then:
if a sense is part of t then it is expressed by at least one part of s.

  • 1 1893: 50-51. References to Frege are always just by year and page. Frege’s articles are cited by pa (...)
  • 2 1919c. 156 = 1913: 20.
  • 3 1906a: 209 (192); cf. 1914b 262 (243).

2He clearly embraces Corr1 when he writes in § 32 of Grundgesetze, vol. I: ‘If a name is part of the name of a truth-value, then the sense of the former is part of the thought expressed by the latter’1. (In Grundgesetze sentences are taken to be names of truth-values, and each sense-carrying component of a name of a truth-value is also classified as a name.) Frege reaffirms Corr1 many years later: ‘The sense of a part of a sentence is part of the sense of that sentence, i.e. of the thought expressed by that sentence’2. And he explicitly endorses Corr2 when he says: ‘As the thought is the sense of the whole sentence, so a part of the thought is the sense of part of the sentence’3. Henceforth I shall refer to the conjunction of Corr1 and Corr2 as Correspondence.

3Unfortunately Frege seems also to be committed to a principle I shall call Difference that apparently clashes with Correspondence:

(Diff) There are sentences s and s' and there is a thought t such that s and s' express t, but the logical form of r differs from that of s'.

4In sections 2 and 4 of this paper we will see that Frege does indeed subscribe to Difference, and I shall postpone my exposition of the trouble that arises from asserting both Correspondence and Difference until I have presented some of the evidence for his commitment to Difference.

  • 4 Dummett 1981: 261-291, 323-342; Bell 1982: 178-182; Bell 1987; Dummett 1989; Bell 1996.
  • 5 Bell 1996: 594-596.

5Michael Dummett and David Bell are agreed that there really is a conflict4. Dummett goes on to reject Difference, and he suggests that Frege himself tacitly changed his mind as regards Difference. Bell and Bell’s Frege endorse Difference, and Bell thinks that Correspondence, though false as it stands, can be turned into a truth if we take the variable ‘t’ to range over senses of sentences rather than thoughts5. Since by Frege’s lights thoughts are senses of sentences, Bell’s conciliatory move makes for a major revision of Frege’s theory. The Bell-Dummett debate was focused on Frege’s Grundlagen (1884). I shall marshal evidence from Logische Untersuchungen (1918-1923) that decides the question whether Frege ever came round to giving up Difference. In section 1 of this paper I shall explain, motivate and emphasize various features of my formulation of Correspondence and Difference. In section 2 I will show how the tension between Correspondence and Difference becomes manifest in Frege’s last writings. In section 3 I will plead for a revision of Correspondence that tries to preserve as much of Frege’s theory as possible. The key concept in this revision will be that of articulating a thought in different ways. Unsurprisingly, the issue of identity criteria for thoughts will loom large in the central parts of this paper. In the final section I shall briefly consider, in the light of my revision of Correspondence, two kinds of concept attainment that play an important role in Frege’s theory and in the Bell-Dummett debate, one that proceeds via optional decomposition and one that proceeds via transformation into an identity-sentence.

61 Let me begin by trying to secure initial plausibility for Correspondence. It is open to prima facie strong objections that are quite independent of the tension, if any, between Correspondence and Difference and that arise even if one accepts the presupposition of Correspondence that thoughts are composed of senses. Conceding for the time being that this presupposition is correct, I shall try to defend Correspondence against those objections. Then I shall explain and motivate my formulation of Difference.

  • 6 Cf. 1903: § 99; 1906b: 213 (197); 1914b: 223 (206); 1918: 59-61; 1923: 39.

7How is the word ‘sentence’ in Correspondence and Difference to be understood? A type-sentence like Ann is ill’ does not express a thought. At best, it expresses a thought relative to a certain context, but Frege never employs such relativizations. In his usage, which I have adopted for the purposes of this paper, ‘sentence’ (and, more generally, ‘sign’) applies to perceptible objects, to tokens, and when he is talking about natural languages he primarily means audible tokens6. (Some visible tokens convey different messages in different contexts. Take an inscription of ‘Today I am out of office’ on an often used placard: what expresses a definite thought seems to be a mixed triple consisting of the inscription, one of its users and a time. I shall say a bit more about this below.)

8Are all pieces of a sentence parts of the sentenced? Surely, in the context of Correspondence only meaningful pieces will count as parts. But no less than four pieces of the last word in ‘All farmers own a stable’ are meaningful: do they count as parts of this sentence? If so, a proponent of Corr1 would have to say that ‘tab’, for example, contributes something to the thought that is expressed by that sentence; which is certainly an unwanted result. Frege takes for granted, reasonably enough, that an adequate syntactical account of our language will tell us that those pieces do not count as parts - meaning-carrying parts, that is - of our sentence (nor as parts of that word, for unlike, e.g., ‘stable-boy’ it is syntactically atomic). We know implicitly restricted uses of ‘part’ from other contexts, too: Ann is part of a happy family, but her right foot is not.

9If the sense of ‘(is) male’ is part of the thought that Donald is a drake we must take ‘expressed’ in Correspondence as short for ‘expressed or co-expressed’, where the neologism ‘x co-expresses y’ is stipulated to mean that y is a sense that is a (proper) part of the sense of x. — The phrase ‘at least one’ in Corr2 is meant to budget for the fact that one and the same sense may be expressed by several parts of a sentence, which may or may not be tokens of the same type-expression, as witness ‘Ann is happy, and Ben is happy’, ‘Ann is happy, and so is Ben’, ‘It is not the case that Ann is not happy’, or ‘Whoever is attacked by a serpent is attacked by a snake’.

10If your utterance is preceded by the appropriate question, you can express the thought that everybody wants to be happy by saying ‘Yes’ or ‘Happy’ or ‘Everybody does’, but then (if, as assumed in Correspondence, thoughts are composed of senses) some part or other of the thought expressed has no audible counterpart in the token you produced. Sometimes brachylogy does not even require help from explicit linguistic antecedents. Opening the door for Ben who kept her waiting for almost half an hour, Ann immediately gives voice to her anger: ‘35 minutes late’ Does Corr2 come to grief over these kinds of speech economy? Not really. That principle maintains a correspondence between thoughts and sentences. The prosentence ‘Yes’ is no more a sentence than pronouns are nouns. If you insist on calling the tokens produced in the other two breath-saving utterances sentences, a proponent of Corr2 can either appeal to the authority of those linguists who argue that sentences can contain covert constituents, or he can ask us to read the first noun in Corr2 as short for the phrase ‘surface-grammatically complete sentences’. In what follows I shall assume that he does the latter.

  • 7 Since I need the verb ‘articulate’ for my own purposes later in this paper, I refrain from using Jo (...)
  • 8 1887+'. 100 (91); 1914b: 230 (213); 1918: 64, 76. For more on hybrid thought-expressions see Künne (...)

11Corr2 comes under real pressure because of a fact Frege never confronted in his writings: often something that is essential to the identity of the thought expressed by a (sc. surface-grammatically complete) sentence is not represented on the surface of that sentence7. Take an audible token of the type-sentence (R) At present it is raining. The time of the utterance and its location are equally essential to the identity of the thought expressed, but the latter seems not to receive any linguistic representation in that token. This refutes Corr2 unless appearances are deceptive and a hidden indexical is in play - an unpronounced ‘here’, as it were. This hypothesis is not just an ad hoc attempt at defending Corr2: it would help explaining why somebody who says, ‘R, so at present it is raining at some place or other’, seems to argue as validly as somebody who says, ‘R, so it is raining at some time or other’, although in the former case the position quantified into is not audibly occupied. Now in the case of utterances in which (explicit) indexicals are used, Frege’s non-standard view is that the thought-expression does not only consist of words but also of those factors of the non-linguistic context of the utterance that one has to register if one is to recognize which thought is expressed8. Combining this view with the hypothesis just ventured we would have to say: a hybrid thought-expression whose audible component is a token of (R) contains among its sense-carrying parts two mixta composita, a ‘now’-token together with the time of the utterance, and a covert token of ‘here’ together with the place of the utterance. By itself an indexical does not have a Fregean sense. If you have good reasons for disliking the idea of hybrid signs and/or the idea of hidden indexicals, read Correspondence as implicitly restricted to non-indexical sentences.

  • 9 1919b: 275(255), my emphasis.

12Not all meaningful parts of a sentence are sense-carrying. This explains, I think, why Frege qualifies his claim that there is a correspondence (Entsprechung) between the structure of sentences and the composition of the thoughts they express9:

We can regard a sentence as a model of a thought in such a way that with the whole- part relation in the field of thoughts and their parts corresponds, by and large, the same relation in the field of sentences and their parts.

  • 10 Cf. 1918: 63-4; 1897: 152 (140).

13Frege has at least one good reason for rejecting the view that for each syntactically atomic meaningful element of a sentence there is a sense which is a part of the thought expressed by that sentence. This reason is provided by one kind of what he calls ‘tone’ or colouration : a sentence may contain a word that can be deleted without affecting the thought that is expressed by that sentence10. Consider the beginning of Faust’s monologue, ‘I’ve studied, alas, philosophy, jurisprudence, medicine,...’. Elimination of ‘alas’ would not affect the identity of the thought expressed. This interjection does not have a (Fregean) sense, any more than the sound of the speaker’s voice by means of which he might convey what ‘alas’ is used to convey has such a sense. So it does not contribute anything to the thought that is expressed. An expression may lack sense without lacking conventional linguistic meaning: ‘alas’ means the same as ‘ach’ in Goethe’s original, and it contributes to what Frege calls the content (Inhalt) of sentences containing it. The same holds, mutatis mutandis, for the word yet’ in ‘Ann is ill, and yet she is in a very good mood’: if it were eliminated the thought expressed would still be the same.

  • 11 1919a: 148; cf. 1914a: 127; 1914b: 243 (225), 262 (243); 1923: 36.

14Correspondence is formulated in such a way that deletable colouring words do not cause any trouble, for ‘sense’ in Frege is not a stylistic variant of ‘conventional linguistic meaning’. (When he claims that audible tokens of the type-sentence ‘Today is a holiday produced on different days have different senses, he does not deny that they have the same lexico-grammatical meaning). Not all meaningful parts of a sentence but only those that have a sense are relevant for the sentence/thought correspondence Frege has in mind when he says: ‘To the composition of the thought there corresponds the way the sentence is built up out of words’11.

15Let us finally turn to Difference, according to which two sentences may express the same thought even if they differ as regards their logical form. Which notion of logical form is invoked here? For the purposes of this paper I think the following explanation of the dyadic predicate ‘has the same q- logical form as will do, where ‘q-logical form’ abbreviates ‘logical form with respect to QL’ and ‘QL’ names the language of Frege’s first- and second-order quantificational logic with identity:

(LFq ) Two sentences s and s' have the same q-logical form iff:
for some x, some σ, some σ', x is a schema in QL &
σ is an instance of x & σ is a correct translation of s &
σ' is an instance of x & σ' is a correct translation of s'.

  • 12 Since ‘Socrates is wise, so for some x, x is wise’ is formally valid, its premiss is never to be (...)

16Thus understood, logical form is doubly relative: to Frege’s quantificational logic and to standards for being a correct translation into the language of QL. (I take it that an inscription can be a sentence of this language, no matter whether it is written in Frege’s two-dimensional concept-script, in the bracket-free Polish symbolism or in the more familiar Peano-Russell notation.) One standard will play an important role in the reflections to follow: if and only if an argument in a natural language is, pre-theoretically considered, formally valid, the translator ought to aim at a rendering into the language of QL that can be shown to be formally valid. So, a translation of a sentence s is not correct unless it is heedful of those structural features of s that are relevant to its role in (intuitively) formally valid inferences — insofar as they can be captured by QL12, and it is incorrect if it assigns a structure to s that validates inferences in QL which do not even appear to be formally valid in the original language. Thus the sentences

(S) Donald is a male duck
(T) Donald is a drake

  • 13 Similarities of the characterization of logical form in this paragraph with the view outlined in (...)

do not have the same q-logical form. ‘Is a duck (Donald) & Is male (Donald)’, an instance of the QL-schema ‘Fa & Ga’, is a correct translation of (S) but not of (T). Why? The argument ‘S, so Donald is male’ appears formally valid, and it is validated by QL if (S) is recast as an instance of that schema. By contrast, the equally valid argument ‘ T, so Donald is male’ does not even appear to be formally valid, so its translation should not validate it in QL. Hence (S) and (T) do not have the same q-logical form13. (For aesthetic reasons I shall henceforth drop the prefixed letter in ‘q-logical’, taking the restriction to be understood).

  • 14 1923+: 279 (259).

17Sameness of logical form is compatible with difference of grammatical surface-structure. Thus (S) has the same logical form as ‘Ann is an actress, and she is American’, since both correctly translate into instances of the same schema in QL. The correct translations of Ann and Ben are neighbours’ and ‘Brutus killed Caesar’ instantiate ‘R(a, b)’, hence they also have the same logical form. And so do ‘All men are mad’, ‘Every woman is sad’ and ‘If something is red it is extended’, for they can all correctly be rephrased as instances of the schema ‘∀x (Fx Gx)’14.

  • 15 Dummett 1989: 293 e 1991: 176.

182 Frege’s endorsement of Correspondence is in discord with quite a few other statements he makes, with statements that cannot be true unless Difference is true. Since all of them can be found in the last papers Frege published, they falsify Dummett’s presumption that Frege finally gave up Difference15.

Already in ‘Über Sinn und Bedeutung Frege maintained that every substitution instance of the identity schema

(Idem) The thought that p is the same as the thought that it is true that p

  • 16 1892a: 34; 1918a: 61-62; cfr. 1897: 153 (141). Bermudez’s alleged demonstration that this claim is (...)
  • 17 1915: 272 (252).

expresses a truth, and he strongly emphasized this again in ‘Der Gedanke16. (The indented schema is more demanding than its biconditional counterpart ‘It is true that p, if and only if p’: if you accept an instance of (Idem) you are committed to endorsing the corresponding instance of the biconditional schema, but there is no such obligation in the other direction.) The logical form of ‘It is true that nobody is perfect’ seems to differ from that of the embedded sentence. (I shall return to the logical-form issue in a minute.) So Frege’s identity claim, if correct, seems to be evidence for Difference. Now, unlike colouring words like ‘alas’ and ‘yet’, the truth prologue does have a sense, but Frege ascribes to this sense a truly remarkable property: ‘The word “true” has a sense that contributes nothing to the sense of the whole sentence in which it occurs as a predicate’17. This formulation is a bit careless: firstly, because the word ‘true’ isn’t a predicate but a general term, and secondly, because Frege’s claim can at best hold of the unary connective ‘It is true that’. If the sense of this phrase annihilates itself, as he says, then Corr1 is false. Corr2, however, remains unshaken; for if the thought expressed by ‘It is true that nobody is perfect’ is composed of senses, each of its components is expressed by a part of that sentence.

19Of course, one may very well wonder whether it was wise of Frege to claim that the sense of the truth prologue is self-effacing. Consider unrevealing truth ascriptions, singular ones such as (S) ‘What the witness said was true’ and general ones such as (G) ‘Whatever the Party says is true, in which the truth-candidates are not expressed (‘revealed’) by an embedded sentence. If (S) expresses a truth then there must be a substitution instance of ‘What the witness said was that p, and p’ which does so as well. But we can understand (S) without knowing what the witness said. If (G) expresses a truth then all substitution instances of ‘If the Party says that p then p’ must do so as well. Now for each of us there are many incomprehensible instances of that schema, since our vocabularies are fairly limited. But each of us can easily understand (G). So the truth-predicate as used in unrevealing truth ascriptions is here to stay, and these ascriptions express thoughts that contain the sense of the truth-predicate (provided that thoughts are composed of senses). Now one would hardly welcome the conclusion that ‘true’ as used in ‘The Pythagorean Theorem is true’ has a different sense than as used in ‘It is true that the square on the hypotenuse is equal to the sum of the squares on the other two sides’. We can avoid this conclusion if we treat the pronoun in ‘It is true that p’ as cataphoric - along the lines of ‘He was wise, the man who drank the hemlock’ and ‘It is true what Socrates said’, and regard instances of ‘ [The thought] that p is true’ as predications like their unrevealing singular counterparts.

  • 18 1892a: 37, 39.
  • 19 For the topics of the last two paragraphs see Künne 2003: chpt. 2.

20If Frege’s contention that ‘Nobody is perfect’ and ‘It is true that nobody is perfect’ express the same thought is correct, how does it confirm Difference? What is the logical form of revealing truth ascriptions? Can it be captured in QL? As intimated in the last paragraph, I take it that all revealing truth ascriptions can be correctly translated into QL as instances of the schema ‘Fa’ (which is certainly not instantiated by ‘Nobody is perfect’). If one accepts this logical-form proposal one can easily budget for the intuition that the following argument is formally valid: ‘The Pythagorean Theorem is true, the Pythagorean Theorem = the thought that the square (etc.); therefore, the thought that the square (etc.) is true’. One can say that it exemplifies the QL-valid argument-pattern ‘Fa, a = b ∴ Fb’. Frege himself states quite generally that ‘an abstract noun-clause (abstrakter Nennsatz)’, a ‘that’-clause, can be ‘regarded as a noun (Nennwort), indeed one could say: as a proper name (Eigenname) of that thought as whose name it entered into the context of the compound sentence’18. But he applies this only to oratio obliqua and to propositional attitude ascriptions, that is, to compound sentences in which the sentence prefixed with ‘that’ cannot always be exchanged salva veritate by another sentence that expresses a thought with the same truth- value. Obviously, ‘It is true that nobody is perfect’ is not a compound sentence of this kind, but neither is ‘If somebody were to believe that nobody is perfect, he would be right’. Furthermore, truth ascriptions interact with propositional attitude reports, as witness the compound sentence (Z) ‘It is true that Socrates is wise, but Xanthippe does not believe it’ or the argument (A) ‘Plato believes that Socrates is wise, and it is true that Socrates is wise; therefore Plato believes at least one thing that is true’. The anaphoric pronoun in (Z) harks back to the preceding ‘that’-clause, and what does this pronoun do if not pick up the reference of this clause? Intuitively, (A) is a formally valid argument, and just that is its QL-regimentation as an instance of ‘Fa & Ga ∴ ∃x (Fx & Gx)’19. So, there are good reasons for applying Frege’s general statement about abstract noun-clauses to truth ascriptions and hence for assigning to the latter the logical form of a predication.

  • 20 1897: 140 (129); 1918: 60.
  • 21 1918: 61-62.

21Although Frege declared the truth prologue to be redundant, he was not a redundancy theorist. For one thing, he certainly did not regard (Idem) as an explanation of the concept of truth, for he thought that this concept resists explanation20. Furthermore, in his concept-script each and every sentence contains the horizontal, and the horizontal as construed in Grundgesetze is a predicate that is used to ascribe the property of being identical with the True. So in Frege’s concept-script, reference to this truth-value is omnipresent and, consequently, the sense of the singular term ‘the True’ is a component of all thoughts expressed in that language. (Although in ‘Der Gedanke Frege comes close to denying that truth is a property21, he has to concede that every true thought has the property of being a mode of presentation of the True.)

22If Frege were to give up his contention that the sense of the truth prologue in a natural-language sentence annihilates itself, as I think he should, then his claim that ‘Nobody is perfect’ and ‘It is true that nobody is perfect’ express the same thought would no longer be incompatible with Corr1. But that is small consolation, for now it contradicts Corr2, since under this option a part of that thought is not expressed by any part of the shorter sentence. So Frege only gets out of the frying pan into the fire.

  • 22 For (lc) see 1923: 44; for (ld) see 1923: 39 n., 49; for (le) see 1923: 49.

23There is further trouble for Correspondence in Frege’s Logische Untersuchungen. He maintains that sentences structurally like the following five all express one and the same thought22:

24(la) Socrates is wise

25(lb) It is true that Socrates is wise

26(lc) It is not the case that Socrates is not wise

27(ld) Socrates is wise, and Socrates is wise

28(le) Socrates is wise, or Socrates is wise.

  • 23 There is a similar change of mind as regards pairs instantiating ‘p → q’ and ‘­q → ­p’ cf. 1919a: 1 (...)
  • 24 1919a: 156-157.
  • 25 Cf. 1919a: 146, 153; 1923: 44, 50.
  • 26 1897: 161 (149).

29As to the pair {(la), (lc)}, Frege changed his mind between the second and the third Logical Investigation23. In ‘Die Verneinung (1919) he refers to the thought that p and the thought that not-not p as two thoughts, and he says that in the latter thought the former is ‘wrapped in double negation’24. By ‘double negation’ he means the sense of ‘It is not the case that... not... ’. If somebody who is already wearing a coat now puts on another coat (Frege’s simile) the performance doesn’t look like a strip-tease. But the non-identity claim is hardly in accord with Frege’s presupposition, in ‘Die Verneinung and elsewhere, that for each thought t there is exactly one negation, this being the contradictory of t25. The relation which is referred to (bedeutet) by the predicate ‘... is the negation of... ’, he maintains, is ‘a symmetrical relation (eine umkehrbare Beziehung)’26. But the thought that p can only be the negation of the thought that not p if the former is identical with the thought that not-not p. It looks as though every thought would have infinitely many negations if the thought that not p were not identical with the thought that not not-not p, and so on for any odd number of repetitions. If they were different, how could one of them lay claim to being the contradictory of the thought that p? Four years later, in ‘Gedankengefüge’ (1923), Frege makes the identification that is apparently required for the uniqueness of the negation of a thought. Actually, his identifications as regards (la), (ld) and (le) also seem to be required for upholding that uniqueness. If the thought that (not p and not p) etc. and the thought that (not p or not p) etc. were not the same as the thought that not p, there would still appear to be infinitely many negations of the thought that p in the offing, for if they were different, how could one justify singling out one of them as the contradictory of the thought that not-p?

  • 27 ‘Two sentences A and B can stand in such a relation that anyone who accepts the content of A as t (...)

30Frege’s identity claims concerning (1a-e) can be justified by appeal to his partial criterion of identity for thoughts. From a manuscript of 1906 one can extract a definition of a relation between sentences which Frege, somewhat misleadingly, calls equipollence and which I prefer to call Cognitive Equivalence27:

(CE) Two sentences are cognitively equivalent if and only if nobody who fully understands both can assent to one of them without immediately being ready to assent to the other as well.

  • 28 Dummett 1991: 171; cf. his 1989: 294, 298, 301; 1994: 99. He no longer maintains this: see his 19 (...)
  • 29 1906b: 213 (197). Timothy Williamson has argued in his 2006 that no logical truth and no sentence w (...)
  • 30 1914b: 242 (224).

31Dummett once maintained that (for a long time) Frege regarded cognitive equivalence as a sufficient as well as necessary condition for identity of sense’28. That would account for Freges verdicts on sentences (la-e). But if cognitive equivalence were to guarantee identity of thought, Frege would have to swallow some intuitively bizarre consequences which are certainly not acceptable to him. The sentences ‘Everything is identical with itself’ and ‘Nothing is larger than itself’ are cognitively equivalent, since the content of either sentence is such that (to use Frege’s own words) ‘it would have to be immediately accepted as true by anyone who had grasped it properly’29. Hence if cognitive equivalence were a sufficient condition of sameness of thought, then our two sentences would express the same thought. All sentences the contents of which simply defy disbelief would express one and the same thought. In other words, there would be only one thought which is ‘self-evident (unmittelbar einleuchtend)’30. Surely Frege’s conception of an axiom does not allow him to accept this result. Furthermore, any conjunction one conjunct of which expresses a self-evident truth would express the same thought as the other conjunct by itself.

  • 31 ‘... I assume that there is nothing in the content of either of the two equipollent sentences ... t (...)

32None of these consequences are forthcoming if Frege takes cognitive equivalence only to be a necessary condition for identity of thought. We can gather what he regards as a Sufficient Identity Condition from the very same manuscript from which I culled CE31:

(SIC) Two (unambiguous) sentences express the same thought if
(i)they are cognitively equivalent, &
(ii) neither of them is, or contains a part which is, such that one cannot fully understand it without immediately being ready to assent to it — or without immediately being ready to dissent from it.

  • 32 Bermùdez 2001: 90 thinks that SIC(ii), up to is meant to exclude logical truths. But it does not ex (...)

33By adding condition (ii), up to ‘-’32, Frege forestalls the intuitively bizarre results I pointed out. Now one wouldn’t like to say of each disjunction one disjunct of which expresses a thought that self-evidently lacks truth (‘Something differs from itself’, ‘Something is larger than itself’) that it expresses the same thought as the other disjunct by itself. So I took the liberty of adding the dissent clause. (According to Frege, a thought can lack truth without being false. So he should allow for cases in which a thought self-evidently lacks truth although it isn’t false. The thought that the natural number between 5 and 6 is greater than 4, and the thought that the round square on this blackboard is white, fit this bill. Consequently, we must allow for cases of dissent which do not amount to imputations of falsity.)

  • 33 Rumfitt 1994: 609.

34Unfortunately, SIC still allows for cases which should be as unwelcome as those that motivated clause (ii) and for a very similar reason. Thus (a) ‘In some town there is a large object that is cubic’ does not seem to express the same thought as (b1) ‘In some town there is a large object that is cubic and not different from itself’ (nor the same as [b2] ‘... or different from itself’). After all, it would be wildly implausible not to treat {(a), (b1)}, say, in the same way as {‘The Kaaba is cubic’, ‘The Kaaba is cubic, and nothing is different from itself’}. But neither (a) nor (b1) contains a part that is excluded by SIC(ii). This objection, which is due to Ian Rumfitt33, may be a reason not for despair but for taking a deeper breath. After all, the (b)-sentences contain an unsaturated conjunct [disjunct] whose saturation by a non-empty singular term always results in a sentence which one cannot fully understand without immediately being ready to assent to it [to dissent from it]. So such pairs could be taken care of by a third clause covering unsaturated conjuncts and disjuncts.

35But let us put this complication aside. There is, of course, a price to be paid for shielding off the various odd consequences of taking cognitive equivalence by itself to be sufficient for sameness of thought: SIC is silent on sentences the content of which is, or contains a part which is, self-evidently (un)true. Never mind, SIC suffices for justifying Frege’s claim that sentences (la-e) express one and the same thought.

  • 34 Currie 1985: 296-297.

36Now this very claim is not compatible with Corr1. Consider {(la), (le)}. Obviously the thought expressed by (la) is not something of which the sense of (la) is a proper part, for the proper-part relation is irreflexive. But according to Corr1 the thought expressed by (le) is something of which the sense of (la) is a proper part. Hence (la) and (le) do not express the same thought, which contradicts Frege’s identity claim34. Furthermore, the thought expressed by (la) does not contain the sense of ‘or’, whereas, according to Corr1, the thought expressed by (le) does contain it. So (la) and (le) do not express the same thought, which is incompatible with Frege’s identity claim.

  • 35 Davidson 1969: 38.

37Is the thought that Socrates is wise supposed to contain the sense of the negation operator twice? If so, the identity claim as regards {(la), (lc)} is incompatible with Corr2. Furthermore, if twice, then n-times for each even number n, which would make that thought about Socrates, as well as every other thought, infinitely fat. Or is the thought that it is not the case that Socrates is not wise supposed not to contain the sense of the negation operator at all? In that case, the idea would have to be that the operator ‘It is not the case that... not...’ has a sense that contributes nothing to the thought expressed by the whole sentence of which it is a part. (As you will remember, this was Frege’s contention concerning the operator ‘It is true that’. No wonder Davidson once nicknamed the redundancy theory of truth ‘the double-negation theory of truth’35). But if this is the idea then the identity claim as regards {(la), (lc)} clashes with Corr1. If one wants to apply the idea of self-effacing senses also to (ld) and (le), one should say something like this: for any sentence s, the sense of the expression which consists of an ‘and’ (‘or’) followed by s annihilates itself when this expression is appended to s. Of course, this is again incompatible with Corr1 .

  • 36 It may be worth mentioning that I myself very much prefer to give up SIC (see Kiinne 1997 and 200 (...)
  • 37 1923: 36; cf. 1919: 155.

38Frege must either give up his identity claims and the principle SIC which backs them, or he has to reject, or to modify, Correspondence. Since he upholds the former in his last writings, I shall propose a charitable emendation of the latter36. Frege himself did not regard part/whole talk about thoughts as entirely unproblematic37:

To be sure we really talk figuratively when we transfer the relation of whole and part to thoughts; yet the figure of speech is so ready to hand and so generally appropriate that we are hardly ever bothered by the limping that occurs from time to time.

39But this plays down the malady, I am afraid. Since the occasional hobble foreshadows an imminent paralysis, we ought to be seriously worried.

  • 38 For earlier explorations of something like this contrast see my 1997 and 2003: 42-52.

403 Let us make preparations for this revision by contrasting cognitive equivalence with another relation between sentences38:

(CB) Two sentences s and s' are conceptually balanced if and only if
(i) there is no concept whose mastery has to be exercised in (occurrently) understanding s but not in (occurrently) understanding s', &
(ii) there is no concept whose mastery has to be exercised more often in (occurrently) understanding s than in (occurrently) understanding s'.

  • 39 In this paper (just as in the Bell-Dummett debate) ‘concept’ is not used in the technical way Frege (...)
  • 40 Cf. Dummett 1994: 58-60, 101-103, 109, 133.

41You possess a concept, as this term is used in CB, if you fully understand an expression the sense of which is that concept39. You occurrently understand the sentence ‘Two is prime’ only at those times at which you actually entertain the thought that two is prime, whereas you can at any time correctly be said to understand that sentence provided your English is good enough40. Clause (ii) is meant to ensure that no cognitive balance obtains between an instance of ‘not p and the corresponding instance of ‘not-not p’. Two sentences may be cognitively equivalent without being conceptually balanced. ‘On that blackboard there is a diagram that is square’ and ‘On that blackboard there is a parallelogram that is square’ are cognitively equivalent. But mastery of the concept of a parallelogram is only required for understanding the second sentence. So they are not conceptually balanced.

42Now is conceptual balance a necessary condition for two sentences expressing the same thought? If so, then (la), (ld) and (le) do not express the same thought. Mastery of the concepts of conjunction or of disjunction is not required for understanding (la): surely one can fully understand (la) before having learnt to cope with compound sentences. Frege need not deny, and he should not deny, that one must have mastered the concepts of conjunction and disjunction if one is to understand sentences (ld) and (le), that is, if one is to recognize which thought is expressed by them. But this conceptual competence is not required, Frege can say, if one is to grasp the thought that is expressed by them. For this purpose the cognitive equipment that is required for understanding (la) is amply sufficient. - As for the pairs {(la), (lb)} and {(la), (le)}, I am also inclined to think that their members are not conceptually balanced. Admittedly, it is a substantial philosophical question whether one can understand any (declarative) sentence without having mastered the concept of truth and the concept of negation. But even if that mastery were required, this would not show that one has to actually exercise one’s mastery of these concepts whenever one reads a sentence like (la) with understanding.

43If we replace the sentence-letters in

44(2a) p
(2b) p

by the same sentence, we obtain two sentences that are cognitively equivalent, but they are not conceptually balanced, since they do not comply with CB(ii). The same holds for pairs instantiating

45(3a) p & q
(3b) (p &q) &c(p &c q).

46So once again, the assumption that conceptual balance is a necessary condition for expressing the same thought turns out to be clearly incompatible with Frege’s identity claims.

  • 41 Dummett 1989: 295. Note that the assumption that conceptual balance is a necessary condition for sa (...)

47Dummett’s counterpart to that assumption is his Principle K: ‘If one sentence involves a concept that another sentence does not involve, the two sentences cannot express the same thought’41. (I take it that by ‘sentence S involves concept C’he means: S contains a component which expresses C.) This principle, to which Dummett subscribes, does not deliver the above results for (2-3), and that should not be to his liking, for the logical form of the prodigal (b)-sentences differs from that of their more parsimonious (a)-counterparts. But his Principle K does deliver the same result for the pairings of (la) with any of (lb-e). So I would be extremely hesitant to ascribe this principle to Frege, as Dummett does, for I find it hard to believe that Frege simply overlooked that this principle disallows his identity claims about such pairs.

  • 42 Bell 1996: 596; cf. Wagner 1983, Kemmerling 1990.
  • 43 This is the reading of Frege proposed in Kemmerling 1990: 20-24.

48Now I think that conceptual balance as well as sameness of logical form can be assigned their proper role without rejecting Frege’s identity claims concerning (la-e) and (2-3), if we follow Bell and ‘deny that thoughts have a determinate, intrinsic structure’42. This still allows for the possibility that thoughts are like lines in being divisible43.I propose to go a step further and to shun part-whole talk about thoughts entirely. Let me introduce a notion which will help (or so I hope) to turn this into a positive doctrine:

  • 44 Since it is not a matter of course that all (declarative) sentences can be correctly translated int (...)

(ART) Two sentences articulate the same thought in the same way iff
(i) they express the same thought &
(ii) they are conceptually balanced &
(iii) they have the same logical form44.

49Note that not any old difference between two formulations of the same thought amounts to a difference in articulation - in my use of this term. ‘The man who drank the hemlock was wise’ and ‘He was wise, the man who drank the hemlock’ (‘a and b are parallel’ and ‘a is parallel to b’) are two formulations of the same thought which do not articulate it in different ways, since they have the same logical form.

  • 45 Dummett’s Frege who has come to reject Difference is obliged to deny this. That makes him a very un (...)
  • 46 Compare G.E. Moores constraint on sentences expressing a conceptual analysis: ‘The expression use (...)

50Being conceptually balanced, though (by Frege’s lights) not a necessary condition for two sentences expressing the same thought, is a necessary condition for two sentences articulating the same thought in the same way. Sameness of logical form, too, is a conditio sine qua non for that. ‘Donald is a drake’ and ‘Donald is a male duck’ comply with SIC, so they express the same thought45. They are also conceptually balanced, for the sense of ‘drake’ is male duck. But since they do not have the same logical form, the thought they both express receives different articulations46. Considering Freges identity claims concerning (la-e) in the light of ART we can say: according to SIC, these sentences express one and the same thought, but they articulate it in different ways, since no pair consisting of (la) and one of (lb-e) complies with ART(ii), and none containing (la) and one of (lc-e) satisfies ART(iii).

51Is there any trace of the notion of articulation in Frege’s writings? According to SIC the same thought is expressed by

(S) The accused convinced at least one member of the jury of her innocence
(P) There is at least one member of the jury whom the accused convinced of her innocence

  • 47 1906 a: 203 (187); cfr. 1906b: 218 (201-202); and already 1887+: 117 (107): 1892b: 199- 200.

52But (S) makes this thought appear as a singular thought, whereas (P) makes it appear as a particular thought. Here is Frege’s comment on this47 :

Incidentally, being singular is not really a feature of a thought in itself, but only with respect to a possible carving. It is possible for the same thought, with respect to a different carving, to appear as particular.

53Isn’t Zerlegung articulation by another name? No, it is not. Firstly, Frege’s description presupposes that thoughts are divisible wholes. Secondly, the pair {(S), (P)} contrasts sharply with those we were concerned with: its members comply with ART (ii) and ART (iii), so they do not articulate one thought in two ways. Their difference does not come to more than the difference in parsing between ‘(Brutus) kills Caesar’ and ‘(Brutus) kills (Caesar)’, where a thought first appears as a thought to the effect that an object has a certain relational property and then as a thought to the effect that a certain relation obtains between two objects.

  • 48 1884: § 107.
  • 49 This example will come in for discussion in sect. 4 below. The passage just alluded to can be fou (...)
  • 50 1891: 11.

54But there are traces of the notion of articulation in Frege’s writings. In the recapitulation at the end of Grundlagen Frege maintains that sometimes it is justified ‘to construe a content as that of a recognition judgement’48. In § 64 he had presented his famous paradigm for such a ‘construal’: the content of the judgement voiced by (Par), ‘The straight line a is parallel to the straight line b’, he had argued, ‘can be construed as’ the content of the judgement voiced by (Id), 'The direction of a is the same as the direction of b49. This can be effortlessly rephrased in my language: (Par) and (Id) express the same thought, but only (Id) articulates this thought as the possible content of a recognition judgement. Clearly, (Par) and (Id) satisfy neither ART (ii) not ART (iii). About two sentences which also offend against these clauses of ART Frege says in ‘Funktion und Begriff’ that one of them ‘expresses the same sense’ as the other ‘but in a different way (drückt zwar denseIben Sinn aus,... aber in anderer Weise)’50. This seems to be just an improvable stylistic variant of ‘expresses the same thought but articulates it in a different way’.

  • 51 Restricting what Axiom V says about functions in general to the special case of Fregean concepts, (...)

55It has to be conceded that there is something embarrassing about the last passage: the two sentences that are said to express the same thought instantiate the two sides of what was to become the fatal Axiom V of Grundgesetze51. A couple of years later Frege was confronted with a conclusive reason for withdrawing attributions of sense-identity to pairs of sentences instantiating the two sides of that axiom. This fact does not by itself show that such attributions do not hold for any structurally similar pairs, such as {(Par), (Id)} above. But it does show that the imputation of cognitive equivalence which underlies ascriptions of sense-identity is sometimes rather risky. As can be seen from CE, the statement that two sentences are cognitively equivalent makes a modalized general claim. Sometimes a forceful argument demonstrates that for a given pair {S, S'} this claim cannot rationally be upheld, even though it is true that everybody who understands both S and S' is inclined to assent to one as soon as she assents to the other. This inclination survives the discovery that it would be unwise to yield to it. Compare Muller-Lyer illusions in perception: even after you have found out that both lines have the same length, you cannot help having the impression that one of them is longer than the other.

56The notion of articulating a thought in one way rather than another can help us to find a way out of Freges quandary. If Frege were to replace Correspondence by Correspondence*

Corr* For all sentences s, for all thoughts t, if s expresses t, then: one grasps t in its articulation by s iff one recognizes which sense the (canonical) parts of s have and understands their mode of combination,

  • 52 Compare: In order to hear KV 466 as currently being played by Alfred Brendel, it does not suffice (...)
  • 53 1914a: 127; 1914b: 243, 262 (225, 243); 1923: 36.

he would no longer be obliged to assume that thoughts are wholes, let alone that they have a determinate, intrinsic structure, and the conflict with Difference would disappear. Since he never gave up Difference, this is the revision I propose - for the sake of restoring coherence in his theory of thought and language. (The point of the qualification ‘canonical’ in Correspondence* will become clear in section 4.) In order to grasp the thought T as currently being articulated by utterance S it does not suffice to grasp T52: you must (occurrently) understand S, that is to say, you must recognize which thought S expresses. Frege took Correspondence to explain why we are often able to recognize which thought is expressed by a sentence although we have never come across any expression of that thought before53. Correspondence*, if true, can very well serve this explanatory purpose.

57The ‘only if’-prong of the biconditional in Correspondence* seems to be beyond reasonable doubt. If a monoglot Englishman hears a sentence in a foreign language he will not grasp a thought as currently being articulated by that utterance even when he has been authoritatively told that it expresses the thought that English is not the only language worth knowing. Sentences that contain idioms, e.g. the death-notice ‘Ben’s father kicked the bucket’, only show that sometimes understanding the words that make up a locution is irrelevant to understanding a sentence in which it occurs: in its slangy use ‘kicked the bucket’ has no greater complexity than ‘died’. (The logical form of the death-notice is not that of ‘Ben’s father shot the rabbit’).

  • 54 Cp. Sainsbury 2001.
  • 55 1881: 13 (12-13).
  • 56 1914b: 230 (213).

58But many sentences of natural languages contain constructions that seem to show that the ‘if’-prong of the biconditional in Correspondence* is untenable54. Compounded nouns are one type of such constructions. Consider (X), This is a glass-house’. Surely our recognition which thought is expressed by (X) is partly due to the fact that we recognize which senses ‘glass’ and ‘house’ have and that we understand the construction of the compounded noun. But this seems to give us too little, namely knowledge that according to (X) this is a house which has something to do with glass. Such knowledge does not suffice for recognizing which thought is expressed. In order to accomplish this feat we must know what exactly the house in question (allegedly) has to do with glass. Frege did not overlook the problem55. Sentences with compounded nouns only show that something is amiss with Correspondence* if we take ‘understanding the mode of combination’ to amount to nothing more than knowing which roles the first and the second noun generally play in such a construction. But we should insist on a more demanding conception of understanding. (After all, knowing the lexico-grammatical meaning of a sentence often does not suffice for recognizing which thought is expressed by it. Thus knowing which sense is expressed by the predicate in a certain atomic first-person utterance and knowing which role first-person pronouns standardly play in an utterance is not enough for recognizing which thought is expressed.) Now it is noteworthy that one can say, ‘In more than one sense, this is a glass-house: it is a building with a glass roof and glass walls, and it is a building where glass is made’. You do not understand the mode in which ‘glass’ and ‘house’ are combined in (X) unless you recognize which relation between a house and glass the speaker of (X) has in mind: only then do you know in which sense the object pointed at is said to be a glass-house, and before that you do not recognize which thought is expressed by (X). ‘But a language that is intended for scientific employment’, Frege maintains, ‘must not leave anything to guesswork’56. ‘Guesswork’ is hardly a very felicitous title for the way we ascertain the intended reading. Frege’s requirement is best read, I think, as a call for maximal explicitness. In ‘a language that is intended for scientific employment’ either all compounded nouns are replaced by locutions in which the pertinent relation is made explicit, or there is a relation R such that for all compounded nouns in that language it is stipulated that the compounding signifies R. In any case, whether our language is unreformed or regimented in one way or another, the credibility of the ‘if’-prong of the biconditional in Correspondence* is not undermined by compounded nouns.

59Nor is it undermined by so-called possessive constructions, I think. Take (Y), ‘This is Ann’s book. Is it the book she wrote, the book she is currently reading, the book she has lent,...? One can hear Frege complaining that here, too, a great deal is left to guesswork. In ‘a language that is intended for scientific employment’ either all possessive constructions are replaced by locutions in which the pertinent relation is made explicit, or there is a relation R such that for all possessive constructions in that language it is stipulated that their manner of composition signifies R. Again it is noteworthy that we can say, ‘In more than one sense, this is Ann’s book.’ You do not understand the mode in which ‘Ann’ and ‘book’ are combined in (Y) unless you recognize which relation between Ann and the book in question the speaker of (Y) has in mind: only then do you know in which sense the object pointed at is said to be Ann’s book. As long as you have not yet acquired such an understanding of the possessive construction in (Y), you cannot recognize which thought is expressed.

  • 57 1919a: 150; cf. 1897:162 (150).

60Correspondence* also helps us to (dis)solve a problem Frege faced in ‘Die Verneinung’: ‘It is by no means easy to state what is a negative thought’57. Apparently, the thought expressed by

61(4a) No other mountain in the Alps is as high as, or higher than, Mont Blanc is a negative thought. But then, according to SIC, the same thought is expressed by
(4b) Mont Blanc is the highest mountain in the Alps,

and when we stare at (4b) we may feel inclined to say that the thought expressed is affirmative.

  • 58 Removing the (final) singular term in (4a) we obtain a complex predicate that can be used to say (...)

62With a sigh of relief Frege observes that logic, though badly in need of the dyadic predicate ‘x is the negation of y’, does not require the services of the monadic predicate ‘x is a negative thought’. One may sympathize with this reaction and yet find it a bit evasive. If thoughts have a determinate, intrinsic structure the question remains: does the thought expressed by both (4a) and (4b) contain the sense of the negation operator, or does it not? If thoughts are not intrinsically structured this question no longer arises. Correspondence* allows us to say that as articulated by (4a) the thought expressed is a negative thought, for the negation operator is one of the (canonical) parts of (4a), but as articulated by (4b) it is an affirmative thought. (Compare, ‘As a university teacher she is paid miserably, but as a novelist she earns a lot of money’.) Actually, in both pairs the first member can be decomposed in such a way that under this decomposition it articulates the thought it expresses in the way that is highlighted by the second member58. In the final section we will look more closely at what is going on in such an optional decomposition.

  • 59 1879: § 9; cf. Dummett 1981: 341; 1991: 173-175; 1997: 247-248.

634 Let us now consider two kinds of concept acquisition in the light of the revised Fregean view we arrived at in the last section. The first one will also give point to the restriction ‘canonical’ in Correspondence*. Frege uses the following example to explain (what I propose to call) concept attainment by optional decomposition59:

64(5a) Cato killed Cato
(5b) Cato killed himself.

  • 60 Dummett 1989: 297; 1991: 173-175.
  • 61 Rumfitt 1994: 610.

65This pair clearly complies with SIC. Applying Correspondence*, we can say: (5a-b) articulate one and the same thought in different ways, for they are not conceptually balanced. One must have mastered the concept of killing oneself if one is to recognize which thought is expressed by (5b). (Pace Dummett60, one need not yet have mastered the concept of committing suicide, for somebody might kill himself without intentionally doing so, and then he does not commit suicide.) In order to grasp the thought that is expressed by both sentences the conceptual equipment needed for understanding (5a) is sufficient. You cannot understand (5a) unless you understand the name ‘Cato’ and the dyadic predicate that also occurs in, say, ‘Brutus killed Caesar’61, but you need not spot in (5a) a predicate that applies to all and only those who kill themselves. (Compare camouflage cases in perception: you may see the trunk with four butterflies sitting on the side facing you without seeing the four butterflies.) In other words, under its canonical decomposition (5a) is a substitution instance of ‘x killed y’, and under one of its optional decompositions it turns out to be also an instance of ‘x killed x’, and this predicate can be used to introduce a ‘new’ predicate, sc. ‘x killed him/ herself’. (Here one begins to realize that talk of decomposition has to be taken with a grain of salt. The tokens of the predicate, which can be found in ‘Cato killed Cato’ and ‘Seneca killed Seneca’ but not in ‘Brutus killed Caesar’, are not exactly components of the former: they are discernible within a sentence, but not detachable from it.) The way (5a) articulates the thought it expresses differs from the way the same thought is articulated by (5b) — or by (5a) under the optional ‘decomposition’ that can serve as an explanation of (5b). In this manner we can characterize the relation between (5a) and (5b) without postulating a ‘laxer’ and a ‘stricter’ criterion for thought-identity, as Dummett does.

  • 62 1884: §§ 64, 66 n.**; cf. § 107.

66Concept attainment by optional decomposition is to be sharply distinguished from concept attainment by transformation into an identity-sentence (Verwandlung in eine Gleichung). Recall Frege’s famous paradigm62:

67(6a) The axis of this telescope is parallel to the Earth’s axis
(6b) The direction of the axis of this telescope is the same as that of the Earth’s axis.

  • 63 In his middle period Frege introduced two successor concepts for the notion of a judgeable content (...)
  • 64 1884: 74-75 (bracketed numerals inserted for ease of reference).

68Analogous transformations deliver identity-sentences of the form ‘the F of a is the same as the F of b’ for all sentences of the form ‘aRb’ in which the binary predicate refers to (bedeutet) a relation that is reflexive, symmetrical and transitive. In each such pair, Frege claims, the members express the same thought (or content, as he puts it in Grundlagen) 63. But they do not have the same logical form, nor are they conceptually balanced. Once again, this is all to the good, for the very point of the transformation would be lost if they were balanced. Mastery of the concept of a direction, a higher-order concept that applies to properties, is not a prerequsite for fully understanding (6a), but one must have this concept if one is to recognize which thought is expressed by (6b). If both sentences really express the same thought, the conceptual repertoire that is required for understanding (6a) is amply sufficient for grasping that thought. Now let us scrutinize Frege’s often quoted comments on the step from (6a) to (6b)64:

[1] The judgement ‘The straight line a is parallel to the straight line b’, in symbols a // b, can be construed as an equation. If we do this, we attain the concept of a direction and say, ‘The direction of the straight line a is equal to the direction of the straight line b’. We thus replace the symbol //by the more general symbol =, by distributing the particular content of the former to a and b. [2] We split up the content in a way different from the original way and thereby acquire a new concept. [3] Admittedly, the matter is often seen in reverse, and some school-teachers define: parallel straight lines are straight lines whose directions are equal... It is only a pity that this stands the true state of affairs on its head!

  • 65 As Hale 1997: 93 observes, what Frege actually says in [1-2] is that the content of the dyadic pred (...)
  • 66 I find it most unlikely that Frege overlooked this glaring difference. On this point I side with (...)
  • 67 Field 1984; cf. also Potter & Smiley 2001: 336-338.
  • 68 Apparently, Dummett would be ready to scold him: ‘Anyone who understands both [(9a)] and [(9b)] . (...)

69According to [1], (6a) and (6b) express the same thought, but only (6b) articulates this thought as the possible content of a ‘recognition judgement’. If thoughts were intrinsically structured, [2] would be entirely appropriate as a description of the decomposing step from (6a), say, to (6b): the ‘original way’ of carving up the content of (6a) would correspond to the canonical decomposition of this sentence, and the ‘new’ way of carving it up would correspond to an optional decomposition which discloses the presence of the ascription of a very complex property to a certain number65. But, of course, no decomposition of (6a) will disclose the presence of the name-forming operator on names ‘the direction of ( )’ or of the predicate ‘( ) is a direction’66. (Here a comparison with camouflage cases in perception would be entirely inapt.) In this respect Frege’s contention in Grundlagen that (6a-b) express one and the same thought is in the same boat as the identity claims concerning (la) and (lb-e) in Logische Untersuchungen: no amount of decomposing ‘Socrates is wise’ will reveal the presence of, say, the connective ‘and’. But there is another feature of the transformation of (6a) into an identity sentence which separates this case both from that of optional decompositions and from the identity claims concerning (la) and (lb-e). In the latter cases one cannot reasonably doubt that the same thought is expressed if SIC deserves its name, and in any case none of these identity claims will cause any ontological worries. But an adamant ‘nominalist’ like Hartry Field is ready to accept (6a) while refusing to accept (6b) and its ilk67. So Frege’s contention that they express the same thought is not beyond question. If one were to appeal to SIC, and thereby to CE, in defence of this identity claim one would have to scold Field for not understanding at least one of two rather plain English sentences, which seems to be somewhat harsh on him68.

70Of course, if you do not suffer from ‘nominalist’ scruples (clin. eidophobía) you might take (6b) as your starting-point and decompose (6b) in such a way that you obtain a dyadic predicate which applies to axes and other lines:

71H The direction of ( ) = the direction of [ ].

72You could then use H to define the dyadic predicate in (6a), that is,

73J( ) is parallel to [ ].

74But this is precisely what Frege castigates in part [3] of the above quotation as the wrong order of explanation.

  • 69 Judging from Frege’s own example the primary point of explaining (6b) via (6a) cannot be that of al (...)
  • 70 Field emphatically denies that acceptance of (6a) involves such a commitment, but if Wright 1990 is (...)

75Now somebody who respects the order of explanation might surmise 2that H is related to J as ‘( ) kicked the bucket’ is related to ‘( ) died’, where the second predicate can be used to explain the first. From the slangy death notice ‘Ben’s father kicked the bucket’ one would not conclude that there is something he kicked, since in this usage the noun phrase isn’t a genuine singular term. So if uttering (6b) is just an idiomatic way of saying what (6a) says, we cannot conclude from what is said that there is something that is identical with the direction of the Earth’s axis. But Frege wants us to conclude this. He takes the phrases that flank the identity sign in (6b) to be genuine singular terms. So what this sentence expresses cannot be true unless there is something that is identical with the direction of the Earth’s axis69. But if (6b) expresses the same thought as (6a), nothing can follow from what is expressed by one of these sentences which does not follow from what is expressed by the other, and one cannot incur an ontological commitment by assenting to one of them which one does not incur by assenting to the other. So there can only be this difference: the articulation which the thought (allegedly) expressed by both sentences receives through (6b) makes some of the ontological commitments one incurs when one accepts that thought as true more salient70. Consider a harmless exemplification of this situation. If SIC is correct the sentences ‘Somebody is a superior’ and ‘Somebody is an inferior’ express the same thought. Here one sentence does indeed make explicit what you are already committed to when you accept the other. But by contrast with (6a-b), here it is beyond reasonable doubt that cognitive equivalence obtains, and the move from one sentence to the other does not introduce a ‘new’ concept, for the concepts of a superior and of an inferior are coeval, as it were: one cannot have one without having the other. So Frege’s paradigm in Grundlagen is far more problematic than all the other pairs I have been brooding upon in this paper.

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Bibliografia

Bell D., (1982), “Review of Dummett 1981”, Grazer Philos. Stud., 18, pp. 170-182.

Bell D., (1987), “Thoughts”, Notre Dame Journal of Formal Logic, 28, pp. 36-50.

Bell D., (1996), “The Formation of Concepts and the Structure of Thoughts”, Philosophy and Phenomenological Research, 56, pp. 583-596.

Bermudez J.L., (2001), “Frege on Thoughts and Their Structure”, Logical Analysis and History of Philosophy, 4, pp. 87-105.

Currie G., (1985), “The Analysis of Thoughts”, Australasian Journal of Philosophy, 63, pp. 283-298.

Davidson D., (1969), “True to the Facts”, as reprinted in his: Inquiries into Truth and Interpretation, Clarendon, Oxford 1984, pp. 37-54.

Davidson D., (1970), “Reply to Cargile” [‘Davidson’s Notion of Logical Form’], as reprinted in his Essays on Actions and Events, Clarendon, Oxford 1980, pp. 137-146.

Dummett M., (1981), The Interpretation of Frege’s Philosophy, Duckworth, London.

Dummett M., (1989), “More about Thoughts”, as reprinted in his Frege and Other Philosophers, Oxford 1991, pp. 289-314.

Dummett M., (1991), Frege - Philosophy of Mathematics, London.

Dummett M., (1994), Origins of Analytical Philosophy, Cambridge MA.

Dummett M., (1997), “Comments on Wolfgang Künne’s Paper”, Grazer Philos. Stud., 53, pp. 241-248.

Field H., (1984), “Platonism for Cheap?”, as reprinted in his: Realism, Mathematics and Modality, New York 1989, pp. 79-124.

Frege G., (KS), Kleine Schrifien ed. I. Angelelli, Darmstadt 1967 (trans, as: Collected Papers on Mathematics, Logic, and Philosophy, 1984).

Frege G., (NS), Nachgelassene Schriften, eds. H. Hermes et al., Hamburg 1969 (trans, as: Posthumous Writings, Oxford 1979).

Frege G., (WB), Wissenschaftlicher Briefwechsel, eds. G. Gabriel et al., Hamburg 1976b (trans, as: Philosophical and Mathematical Correspondence, 1979). 71

Frege G., (1879), Begriffsschrift (trans, as: Conceptual Notation, 1972).

Frege G., (1881), Booles rechnende Logik und die Begriffschrift, in: NS, pp. 9-52 (trans, as: Booles Logical Calculus and the Concept-Script).

Frege G., (1884), Die Grundlagen der Arithmetik, (trans, as: The Foundations of Arithmetic, 1950).

Frege G., (1887+), [Eine kritische Auseinandersetzung mit Kerry], in: NS, pp. 96-127 (trans, as: On Concept and Object [≠ 1892b]).

Frege G., (1891), Function und Begriff in: KS (trans, as: Function and Concept).

Frege G., (1892a), Über Sinn und Bedeutung, in: KS (trans, as: On Sense and Meaning)

Frege G., (1892b), Ueber Begriff und Gegenstand, in: KS (trans, as: On Concept and Object).

Frege G., (1893), Grundgesetze der Arithmetik, I. Band (partially trans, in: The Basic Laws of Arithmetic, 1964).

Frege G., (1897), Logik, in: NS, pp. 137-163 (trans, as: Logic).

Frege G., (1903), Grundgesetze der Arithmetik, II. Band (partially trans in: The Basic Laws of Arithmetic, 1964).

Frege G., (1906a), Einleitung in die Logik, in: NS, pp. 201-212 (trans, as: Introduction to Logic).

Frege G., (1906b), Kurze Ubersicht meiner logischen Lehren, in: NS, pp. 213-218 (trans, as: Correspondence Brief Surview of my Logical Doctrines).

Frege G., (1913), Lecture on Begriffsschrift/Lecture Notes by Rudolf Carnap, ed. G. Gabriel, in: History & Philosophy of Logic, 17, 1996, pp. 20-41.

Frege G., (1914a), Letter to Philip Jourdain, in: WB, pp. 126-129.

Frege G., (1914b), Logik in der Mathematik, in: NS, pp. 219-270 (trans, as: Logic in Mathematics).

Frege G., (1915), Meine grundlegenden logischen Einsichten, in: NS, pp. 271-272 (trans, as: My Basic Logical Insights).

Frege G., (1918), Der Gedanke, in: KS (trans, as: Thoughts).

Frege G., (1919a), Die Verneinung, in: KS (trans, as: Negation).

Frege G., (1919b), [Aufzeichnungen für Ludwig Darmstaedter ], in: NS, pp. 273-277.

Frege G., (1923), Gedankengefüge, in: KS (trans, as: Compound Thoughts).

Frege G., (1923+), Logische Allgemeinheit, in: NS, pp. 278-281 (trans, as: Logical Generality).

Hale B., (1997), Grundlagen § 64, as reprinted in Hale B. & Wright C. (2001), pp. 91-116.

Hale B., (2001), “A Response to Potter & Smiley”, in Proc. Aristotelian Society, 101, pp. 339-358. Hale B., Wright C. (2001), Reasons Proper Study, Oxford.

Kemmerling A., (1990), “Gedanken und ihreTeile”, in Grazer Phil. Stud., 37, pp. 1-30.

Künne W., (1992), “Hybrid Proper Names”, in Mind, 101, pp. 721-731.

Künne W., (1997), “Propositions in Bolzano and Frege”, Grazer Phil. Stud., 53, pp. 203-240.

Künne W., (2001), “Constituents of Concepts - Bolzano vs. Frege”, in A. Newen et al. (eds.), Building on Frege, Stanford, pp. 267-286.

Künne W., (2003), Conceptions of Truth, Oxford.

Marconi D., (1997), Lexical Competence, Cambridge/Mass.

Moore G.E., (1942), “Analysis (Reply to C.H. Langford)”, in P.A. Schilpp (ed.), The Philosophy of G.E. Moore, Evanston, pp. 660-667.

Potter M., Smiley T., (2001), “Abstraction by Recarving”, Proc. Aristotelian Society, 101, pp. 327-338.

Rumfitt I., (1994), “Freges Theory of Predication: An Elaboration and Defense, with Some New Applications”, Philosophical Review, 103, pp. 599-637.

Sainsbury M., (2001), “Two Ways to Smoke a Cigarette”, as reprinted in his Departing from Frege, London 2002, pp. 192-204.

Textor M., (2004), “Frege’s Theory of Hybrid Proper Names Developed and Defended” (Ms.).

Wagner S., (1983), “Frege’s Definition of Number”, in Notre Dame Journal of Formal Logic, 24, pp. 1-21.

Williamson T., (2006), “Conceptual Truth”, in Proc. Aristotelian Society, SV 80, forthcoming.

Wright C., (1990), “Field and Fregean Platonism”, as reprinted in Hale B. & Wright C. (2001), pp. 153-168.

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Note

1 1893: 50-51. References to Frege are always just by year and page. Frege’s articles are cited by page number of the original publication, since the original pagination is given both in the German collection KS and in its English translation; references to NS are followed, in brackets, by the page number of the English translation (see Bibliography). I have occasionally seen reason to modify the translations.

2 1919c. 156 = 1913: 20.

3 1906a: 209 (192); cf. 1914b 262 (243).

4 Dummett 1981: 261-291, 323-342; Bell 1982: 178-182; Bell 1987; Dummett 1989; Bell 1996.

5 Bell 1996: 594-596.

6 Cf. 1903: § 99; 1906b: 213 (197); 1914b: 223 (206); 1918: 59-61; 1923: 39.

7 Since I need the verb ‘articulate’ for my own purposes later in this paper, I refrain from using John Perry’s well-established title ‘unarticulated constituents’ at this point.

8 1887+'. 100 (91); 1914b: 230 (213); 1918: 64, 76. For more on hybrid thought-expressions see Künne 1992; 2003: 277-278; and Textor 2004.

9 1919b: 275(255), my emphasis.

10 Cf. 1918: 63-4; 1897: 152 (140).

11 1919a: 148; cf. 1914a: 127; 1914b: 243 (225), 262 (243); 1923: 36.

12 Since ‘Socrates is wise, so for some x, x is wise’ is formally valid, its premiss is never to be formalized by a sentence letter. To be sure, its internal structure is irrelevant to the validity of many inferences in which it occurs, but it will not affect our assessment of those inferences if we shun sentence letters altogether.

13 Similarities of the characterization of logical form in this paragraph with the view outlined in Davidson 1970 are not coincidental, of course.

14 1923+: 279 (259).

15 Dummett 1989: 293 e 1991: 176.

16 1892a: 34; 1918a: 61-62; cfr. 1897: 153 (141). Bermudez’s alleged demonstration that this claim is incompatible with the project of truth-conditional semantics depends on confusing It is true that Socrates is wise with the semantical sentence ‘Socrates is wise' expresses a truth (Bermudez 2001: 101).

17 1915: 272 (252).

18 1892a: 37, 39.

19 For the topics of the last two paragraphs see Künne 2003: chpt. 2.

20 1897: 140 (129); 1918: 60.

21 1918: 61-62.

22 For (lc) see 1923: 44; for (ld) see 1923: 39 n., 49; for (le) see 1923: 49.

23 There is a similar change of mind as regards pairs instantiating ‘p → q’ and ‘­q → ­p’ cf. 1919a: 146 vs. 1923: 48.

24 1919a: 156-157.

25 Cf. 1919a: 146, 153; 1923: 44, 50.

26 1897: 161 (149).

27 ‘Two sentences A and B can stand in such a relation that anyone who accepts the content of A as true must straightaway accept the content of B as true, and conversely, that anyone who accepts the content of B as true must immediately accept that of A as true (equipollence). It is here being assumed that there is no difficulty in grasping the content of A and B ...’ (1906b: 213 [197]). ‘Equipollence’ is standardly used in the sense of ‘logical equivalence’, and clearly sentences that are logically equivalent do not always comply with the condition Frege outlines.

28 Dummett 1991: 171; cf. his 1989: 294, 298, 301; 1994: 99. He no longer maintains this: see his 1997:247-248.

29 1906b: 213 (197). Timothy Williamson has argued in his 2006 that no logical truth and no sentence which can by exchange of synonyms be transformed into a logical truth is such that one cannot understand it without straightaway being ready to assent to it. He takes it that a similar conclusion is reached in Marconi 1997: 56. (Obviously, Williamson regards sentences as truth-value bearers.) Even if his argument were sound it would not justify his conclusion that “there is no conceptual truth”. His argument depends on finding or inventing some relevant form of logical unorthodoxy. One gathers that this will be a difficult feat in the case of instances of ‘If p and q, then q’. But in any case, no logical unorthodoxy can undermine a competent speaker’s readiness to assent to ‘Nothing is larger than itself’, for this sentence doesn’t belong to either of the two categories Williamson considers. But it seems that logical unorthodoxy can under mine a speaker’s readiness to assent to (la) once she has assented to (lc). (To prevent distraction by other problems, let us assume that Socrates is one of our contemporaries.) For Frege and all adherents of classical logic, every instance of ‘If not-not p, then p’ expresses a truth, whereas intuitionist logicians contest that. At least in mathematics, they maintain, a statement X is stronger than its double negation, because, so they argue, a proof of the latter is a proof that one cannot disprove X, and that does not amount to a proof of X. Would an advocate of intuitionist logic, who took this to be a reason for withholding assent from (la) after having assented to (lc), thereby show that he does not fully understand at least one of these sentences? Is his understanding somewhat impaired by ‘Dutch’ indoctrination? One can deny this without simply giving up the claim that (1a) and (1c) are cognitively equivalent. If one takes classical and intuitionist logicians to understand ‘not’ differently, one can maintain that (lc) is cognitively equivalent with (la) under the former reading of ‘not’.

30 1914b: 242 (224).

31 ‘... I assume that there is nothing in the content of either of the two equipollent sentences ... that would have to be at once immediately accepted as true by anyone who had grasped it properly... [The thought expressed] is the same in equipollent sentences of the kind given above' (1906b: 213-214 [197-198], my italics).

32 Bermùdez 2001: 90 thinks that SIC(ii), up to is meant to exclude logical truths. But it does not exclude all logical truths, and it does not only exclude logical truths (as witness ‘Nothing is larger than itself’).

33 Rumfitt 1994: 609.

34 Currie 1985: 296-297.

35 Davidson 1969: 38.

36 It may be worth mentioning that I myself very much prefer to give up SIC (see Kiinne 1997 and 2003). At present my aim is to find out how coherence in Frege’s views can be restored with minimum deviation from what he actually says.

37 1923: 36; cf. 1919: 155.

38 For earlier explorations of something like this contrast see my 1997 and 2003: 42-52.

39 In this paper (just as in the Bell-Dummett debate) ‘concept’ is not used in the technical way Frege uses it most of the time, i.e. as applying to functions from objects to truth-values. Most of the time, but not always: when he says in 1919: 273 (253), ‘I do not start from concepts and put them together to form a thought ... out of them; rather I come by the parts of a thought by splitting up (Zerfällung) the thought,’ he means by ‘concept’ the sense of a predicate rather than its reference (Bedeutung).

40 Cf. Dummett 1994: 58-60, 101-103, 109, 133.

41 Dummett 1989: 295. Note that the assumption that conceptual balance is a necessary condition for sameness of thought is neutral as regards the question whether thoughts have an intrinsic structure that is mirrored by thought-expressions, and hence it is not open to Bell’s strategic complaint concerning Principle K (Bell 1996: 593).

42 Bell 1996: 596; cf. Wagner 1983, Kemmerling 1990.

43 This is the reading of Frege proposed in Kemmerling 1990: 20-24.

44 Since it is not a matter of course that all (declarative) sentences can be correctly translated into instances of schemata in QL (see LFq in sect. 1), let us take ART to be implicitly restricted to sentences that can be thus regimented.

45 Dummett’s Frege who has come to reject Difference is obliged to deny this. That makes him a very unlikely figure, it seems to me, and in any case, 1914b: 225 (208) gives us a very good reason for not identifying this figure with Frege: If the definiens (der erklarende Ausdruck) occurs in a sentence and we replace it by the definiendum (das erklarte Zetchen), this does not affect the thought at all’.

46 Compare G.E. Moores constraint on sentences expressing a conceptual analysis: ‘The expression used for the analysans must explicitly mention concepts which are not explicitly mentioned by the expression used for the analysandum. Thus the expression “x is a male sibling” explicitly mentions the concepts male and sibling, whereas the expression “x is a brother” does not’ (Moore 1942: 666, my italics).

47 1906 a: 203 (187); cfr. 1906b: 218 (201-202); and already 1887+: 117 (107): 1892b: 199- 200.

48 1884: § 107.

49 This example will come in for discussion in sect. 4 below. The passage just alluded to can be found in part [1] of the text excerpted there.

50 1891: 11.

51 Restricting what Axiom V says about functions in general to the special case of Fregean concepts, the axiom states: For all concepts F, G, whatever falls under F falls under G, and vice versa, iff the extension of F = the extension of G.

52 Compare: In order to hear KV 466 as currently being played by Alfred Brendel, it does not suffice to hear that piano concerto, - you have to listen to this pianist.

53 1914a: 127; 1914b: 243, 262 (225, 243); 1923: 36.

54 Cp. Sainsbury 2001.

55 1881: 13 (12-13).

56 1914b: 230 (213).

57 1919a: 150; cf. 1897:162 (150).

58 Removing the (final) singular term in (4a) we obtain a complex predicate that can be used to say of the referent (Bedeutung) of that term what is said of it in (4b).

59 1879: § 9; cf. Dummett 1981: 341; 1991: 173-175; 1997: 247-248.

60 Dummett 1989: 297; 1991: 173-175.

61 Rumfitt 1994: 610.

62 1884: §§ 64, 66 n.**; cf. § 107.

63 In his middle period Frege introduced two successor concepts for the notion of a judgeable content as used in Grundlagen and earlier works: truth-value and thought (1892b: 198). Frege never used ‘judgeable content’ in such a way that all truths (falsehoods) have the same content, and talk of splitting up a truth-value makes little or no sense anyway, although at one point Frege himself talked of distinguishing parts within truth-values (1892a: 35). So, like Bell and Dummett and many others, I assume that, read in the light of the latter bifurcation, our text takes thoughts to be divisible. (This nicely fits with the heading of 1884: §§ 62-69, ‘In order to attain the concept of a number one has to determine the sense (Sinn) of an equation’, and with the wording of the summary in §§ 106-107.) Hale 1997, 98 ff introduces a notion of ‘weak senses’ of sentences, of senses that are less finely individuated than thoughts. This notion is not sanctioned by anything in Frege’s writings, and Hale does not claim that it is.

64 1884: 74-75 (bracketed numerals inserted for ease of reference).

65 As Hale 1997: 93 observes, what Frege actually says in [1-2] is that the content of the dyadic predicate in (6a) is carved up, but if contents of sentences were intrinsically structured then by dissecting that content we would dissect the content of (6a), since the content of that predicate would be part of the content of this sentence.

66 I find it most unlikely that Frege overlooked this glaring difference. On this point I side with Hale 1997: 97-98, as against Dummett 1989: 295-198 e 1991: 175.

67 Field 1984; cf. also Potter & Smiley 2001: 336-338.

68 Apparently, Dummett would be ready to scold him: ‘Anyone who understands both [(9a)] and [(9b)] ... must straightaway recognise them as equivalent’ (Dummett 1991: 171). The pair of sentences Kemmerling focuses upon has the same structure as this one: (α) ‘Socrates is wise’ and (β) ‘Wisdom is one of Socrates’s properties’. In one respect they are in the same boat as Frege’s (6a-b): every ‘nominalist’ will claim to be a living counter-example to Kemmerling’s contention (1990: 10) that (α) and (β) are cognitively equivalent.

69 Judging from Frege’s own example the primary point of explaining (6b) via (6a) cannot be that of alleviating ‘nominalist’ worries about the possibility of referring to, and acquiring knowledge about, causally inert objects, for (6a) is already about two such objects (cf. 1884: 35).

70 Field emphatically denies that acceptance of (6a) involves such a commitment, but if Wright 1990 is right in his neo-Fregean counter-attack then Field ought to yield. Cf. also the reply to Potter & Smiley in Hale 2001, and Hale & Wright 2001: 142-150.

71 Many thanks go to the participants my seminars on Frege in Hamburg, Salzburg and Gottingen and to the participants of the 2006 Finnish-German Workshop at my institute, especially to Stephan Kraemer, Béatrice Lienemann, Ahti-Veikko Pietarinen, Maik Siihr, MarkTextor, Robert SchwartzkopfF, Alexander Steinberg and, above all, to Miguel Hoeltje and Benjamin Schnieder.

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Wolfgang Künne, «A dilemma in Frege’s philosophy of thought and language»Rivista di estetica, 34 | 2007, 95-120.

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Wolfgang Künne, «A dilemma in Frege’s philosophy of thought and language»Rivista di estetica [Online], 34 | 2007, online dal 30 novembre 2015, consultato il 24 juin 2024. URL: http://0-journals-openedition-org.catalogue.libraries.london.ac.uk/estetica/3874; DOI: https://0-doi-org.catalogue.libraries.london.ac.uk/10.4000/estetica.3874

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