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Note dell’autore

I thank Diego for a quarter century of philosophical conversations and friendship. A fuller version of the arguments in this paper can be found in a forthcoming book, Williamson 2007a, which in particular assesses the present standing of Quine’s critique of the analytic-synthetic distinction and develops more fully a positive account on which shared meanings do not require agreement on anything in particular. The acknowledgements there are relevant to this paper, but I should particularly mention the discussion of related material at the 2006 conference at Reggio Emilia on the question ‘Is there anything wrong with Wittgenstein?’, co-organized by Diego, at which I was present as a specimen anti-Wittgensteinian, the equivalent of the psychopath whom psychoanalysis cannot reach (I have received Wittgensteinian therapy on average at least once a month since 1973 without showing any sign of improvement). Thanks to Alberto Voltolini for helpful comments on an earlier version of this paper.

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1Among the topics to whose discussion Diego Marconi has contributed outstandingly over the years, two of the most notable are the nature of lexical competence and the status of the law of non-contradiction. The topics are linked by the popular idea that adherence to basic logical laws is a necessary condition of understanding logical words, in particular that adherence to the law of non-contradiction is a necessary condition of understanding words for negation. For example, it may be proposed that someone who asserts both ‘It is raining’ and ‘It is not raining’ in the very same context thereby demonstrates semantic incompetence with the word ‘not’. This is to attribute a sort of epistemological analyticity to a form of the law of non-contradiction. Diego Marconi’s work contains many important correctives to this crude picture, with respect to both the nature of lexical competence and the status of the law of non-contradiction. The present paper aims to clarify the prospects for some form of epistemological analyticity, with particular reference to the relation — or lack of it — between lexical competence and adherence to basic logical laws. Although it grants the intelligibility of a notion of linguistic meaning, it still reaches sceptical conclusions about the supposed phenomenon of epistemological analyticity.

21 If someone is unwilling to assent to the sentence ‘Every vixen is a female fox’, the obvious hypothesis is that they do not understand it, perhaps because they do not understand the word ‘vixen’. The central idea behind epistemological conceptions of analyticity is that, in such cases, failure to assent is not merely good evidence of failure to understand; it is constitutive of such failure. The unqualified link from understanding to assent is this:

UA Necessarily, whoever understands the sentence ‘Every vixen is a female fox’ assents to it.

3One proposal is to generalize UA to define an epistemological notion of analyticity: a sentence s is analytic just in case, necessarily, whoever understands s assents to s.

4Four glosses on UA must be taken as read throughout. First, it concerns ‘Every vixen is a female fox’ with its current meaning, for of course if the phonetically individuated sentence had meant something different, someone might easily have understood it and refused to assent. Second, assent is dispositional, for of course we are not actively assenting to any sentence whenever we understand it. Third, assent is a mental attitude, not a merely verbal one, for someone might easily understand ‘Every vixen is a female fox’ while refusing to give it overt assent, for example because overt assent to a triviality looks uncool. We could speak of belief rather than assent, but the latter term sounds more natural in relation to inference rules, to which the notion of analyticity is generalized. Fourth, assent is not a metalinguistic attitude: normally, in assenting to ‘Grass is green’, one is in effect saying or thinking that grass is green, not that the sentence ‘Grass is green’ or the thought grass is green is true. Assenting to the sentence ‘Grass is green’, for someone who understands it, is something like believing that grass is green under the guise of that sentence. In a context in which the sentence s expresses the proposition p, assenting to s, for someone who understands it, is something like believing p under the guise of s. For you, assenting to ‘I am hungry’ is something like believing that you are hungry under the guise of the sentence ‘I am hungry’, since in your context that sentence expresses the proposition that you are hungry, not the proposition that I am hungry.

  • 1 The case of deductive logic is a useful reminder that many short, trivial steps of no apparent sign (...)

5The notion of an understanding-assent link generalizes from individual sentences to rules of inference. For example, if someone is unwilling to assent to the inference from ‘This is red and round’ to ‘This is red’, the obvious hypothesis is that they do not understand one of the sentences, most probably because they do not understand the word ‘and’. For epistemological conceptions of analyticity, failure to assent in such cases is again not merely good evidence of failure to understand but constitutive of such failure. Gerhard Gentzen introduced the idea that some rules of his natural deduction systems of logic have definitional status. Following him, a tradition which includes Dag Prawitz, Michael Dummett, Per Martin-Löf, Christopher Peacocke, Robert Brandom, Paul Boghossian and many others has developed in various ways the conception of acceptance of such inference rules as playing a constitutive role in understanding the logical constants, and therefore in understanding the sentences in which they occur. For many of these thinkers, this is one step towards a quite general ‘inferentialist’ account of meaning and understanding for expressions in terms of their conceptual roles1.

6Understanding-assent links, or something like them, are commonly thought to play a leading role in the understanding of theoretical terms in science: if you don’t assent to some core sentences of electron theory, in which the word ‘electron’ occurs, you don’t understand the word, and therefore don’t understand those sentences.

7Given an understanding-assent link, what are its epistemological consequences? Our concern is knowledge or justification, not just belief or assent. Ideally, we want understanding-knowledge links like these:

UK Necessarily, whoever understands the sentence ‘Every vixen is a female fox’ knows ‘Every vixen is a female fox’.

8Here, knowing ‘Every vixen is a female fox’ amounts to knowing that every vixen is a female fox under the guise of the sentence ‘Every vixen is a female fox’. Since knowing something entails assenting to it (we may assume), UK entails UA. But since assenting to something does not entail knowing it, how are understanding-knowledge links to be extracted from understanding-assent links? UA does not entail UK in any obvious way.

9An even more elementary problem arises. Knowledge is factive. Thus understanding-knowledge links entail corresponding understanding-truth links:

UT Necessarily, someone understands the sentence ‘Every vixen is a female fox’ only if it is true.

10Thus if understanding-assent links somehow imply the corresponding understanding-knowledge links, a fortiori they also imply the understanding-truth links. Perhaps UT holds because the sentence ‘Every vixen is a female fox’ is necessarily true. But in other cases the question of truth becomes more urgent.

  • 2 In effect, Horwich 1998: 131-153 allows understanding-assent links for which the understanding-tr (...)

11Consider theoretical terms from discredited theories. If an understanding-assent link holds for ‘phlogiston’, and understanding ‘phlogiston’ necessitates assent to a core of phlogiston theory, how could it follow that someone understands sentences of phlogiston theory only if a core of it is true? Didn’t proponents of phlogiston theory understand their own theory, despite its actual untruth? Likewise, people who advise us to drop various ordinary terms, on the grounds that obsolete folk theories are built into the use of them, may be assuming that while an understanding-assent link obtains for critical sentences of the folk theory, the corresponding understanding truth-link fails (if so, they presumably do not count themselves as fully understanding the folk theory). For if one could understand the sentences which make up the false theory without assenting to them, in what sense is the theory built into the use of those terms? For example, we could use the terms to assert the negations of central principles of the theory2.

  • 3 See Eklund 2002 for a defence of the idea of inconsistent languages.
  • 4 Dummett 1973: 397, 454 claims that the rules for pejorative terms such as ‘Boche’ suffer from a r (...)

12Some understanding-assent links might even be to logically inconsistent sentences. For example, the ordinary notion of truth is sometimes held to be incoherent, on the grounds that a necessary condition for understanding ‘true’, and so for understanding sentences in which it occurs, is assent to a disquotational principle for ‘true’ which the Liar paradox shows to be inconsistent. Tarski’s description of natural languages as ‘inconsistent’ in virtue of the paradox (1983: 164-65) may involve such a view, for if we can understand ‘true’ in English without assenting to the troublesome instances of the disquotational principle, what prevents us from using English consistently3? Similarly, Prior’s connective ‘tonk’ has mismatched introduction and elimination rules with which any conclusion can be derived from any premise; the introduction rule licenses the inference from ‘P’ to ‘P tonk Q’, while the elimination rule licenses the inference from ‘P tonk Q’ to ‘Q’ (Prior I960). If assent to instances of those rules is necessary for understanding them, because necessary for understanding ‘tonk’, it hardly follows that the rules are truth-preserving (in the context of someone who understands ‘tonk’); they are so only if either every sentence or no sentence of the language is true (including atomic sentences, in which ‘tonk’ does not occur)4.

13Such examples can be interpreted in diverse ways. Nevertheless, they show at least that to advance from understanding-assent links to understanding-truth links, let alone to understanding-knowledge links, is no trivial task.

14One response to the examples is to stop trying to link understanding to knowledge and truth in this way, and try only to establish links to justification, conceived as non-factive. The hope would be to reach understanding-justification links like this:

UJ Necessarily, whoever understands the sentence ‘Every vixen is a female fox’ is justified in assenting to it.

15But this retreat from knowledge and truth to justification does less than full justice to the examples. Imagine a dogmatic proponent of phlogiston theory, who continues to accept it long after the accumulating negative evidence has made this unjustifiable. Suppose that phlogiston does indeed provide a counterexample to the putative entailment from the understanding-assent link to the understanding- truth links. Thus although understanding a core of phlogiston theory necessitates assent to that core, because understanding the core necessitates understanding the term ‘phlogiston’ and understanding ‘phlogiston’ necessitates assent to the core of phlogiston theory, someone can understand the core despite its untruth. But if anyone can understand the core of phlogiston theory, its proponents can. Moreover, they do not stop understanding it when they unjustifiably refuse to take seriously the mounting negative evidence. Thus our last-ditch defender of phlogiston theory understands its core but is unjustified in assenting to it: the understanding-justification links fail too. For more blatantly defective concepts, the assent mandated by understanding-assent links may be unjustifiable from the start, as with ‘tonk’. In such cases too, an understanding-assent link which lacks the understanding-truth link also lacks the understanding-justification link. The examples do not motivate a retreat from knowledge and truth to non-factive justification. Rather, if they work, they show that some understanding-assent links have no positive epistemological upshot.

16A different response to the examples is that they do not work: either the understanding-assent link fails or the understanding-truth link holds.

  • 5 See Peacocke 1992: 21 and Boghossian 2002.
  • 6 Boghossian 2003: 242-243, representing a change of view from Boghossian 2002.

17Since the relevant sentences in the examples are clearly untrue, the understanding-truth link can hold in them only vacuously. That is, in such pathological cases, understanding is impossible: no meaning is there to be grasped5. This response seems plausible for ‘tonk’. It also makes the finks from understanding to truth and any positive epistemic status hold vacuously. Where there is no understanding, we can hardly expect much of a positive epistemological upshot from a constraint on understanding. A trickier question is whether such cases of an illusion of understanding have negative epistemological repercussions for cases of genuine understanding, since a sceptical doubt can arise for the subject in the latter cases too as to whether the understanding is not an illusion. If it could avoid such repercussions, this response might maintain a general entailment from understanding-assent finks to understanding-knowledge finks and the rest. However, the response is less plausible for ‘phlogiston’, ‘true’ and some of the other examples than for ‘tonk’6. There is some difference between understanding the word ‘phlogiston’ or ‘true’ and not understanding it. Even if sentences with ‘phlogiston’ or ‘true’ fail to express propositions, because ‘phlogiston’ or ‘true’ fails to refer, they may still have linguistic meanings. Demonstratives such as ‘this’ have linguistic meanings, teachable to non-native speakers even in contexts in which no attempt has been made to assign them a reference. If a meaningful expression like ‘this’ can lack reference in some contexts, perhaps a meaningful expressions like ‘phlogiston’ can lack reference in all contexts.

18Alternatively, someone might maintain that the understanding-assent links in these examples fail, but that understanding-assent link for other sentences hold. Thus the examples involve genuine understanding. On this view, understanding-assent links may still be held to entail the corresponding understanding- knowledge links. It claims that the examples selected the wrong candidates for understanding-assent links. Either such links hold only for non-defective words or for those defective cases they hold only for cautiously circumscribed sentences. For instance, rather than the core of phlogiston theory itself, we might have the conditional ‘If phlogiston exists then ...’, with that core filling in the dots. Arguably, however, since ‘phlogiston’ fails to refer, that conditional too fails to express a proposition, so even this more cautious sentence is not true, although it is also not false. A more general objection is that this response treats our practices as though they are bound to have anticipated from the beginning all problems which could subsequently arise for them. Presumably, if understanding-assent links hold, they do so because they are part of the linguistic practices at issue. Suppose, for instance, that understanding ‘true’ necessitates assent to a disquotational principle carefully and ingeniously modified to avoid all the semantic paradoxes. But since they scarcely ever arise in ordinary life, why was our ordinary practice with the word ‘true’ tailored in advance to avoid them? Indeed, the puzzlement they cause suggests quite the opposite. That such precautions are part of every possible linguistic practice is even less likely. If understanding-assent links hold for some other reason than that they are part of the linguistic practices at issue, what is that other reason? Even if one moderates the approach by substituting understanding-justification links for understanding-knowledge links, a version of the objection still applies. If our linguistic practices can make assent to inference rules a precondition of understanding, nothing seems to stop foolish practices from requiring such assent to rules which blatantly generate consequences not involving the original word at issue, as with ‘tonk’. Such consequences may include arbitrary pernicious dogmas (such as racist ones) for which no justification is provided. More cautious fallbacks need not even implicitly have been provided; the practice simply breaks down once the dogma is abandoned. So this alternative way of maintaining a general entailment from understanding-assent links to understanding-justification links, let alone understanding-knowledge links, is unpromising. The objections tell equally against the putative understanding-knowledge or understanding-justification links, even if no attempt is made to derive them from understanding-assent links.

  • 7 The treatment of the issue in Boghossian 2003 is of this general kind. For detailed criticism see (...)

19A more moderate response concedes that defective practices give rise to understanding-assent links without corresponding links to truth or any positive epistemological status, but maintains that understanding-assent links for non-defective practices do yield such links. For instance, one might try to tell a story on which understanding-assent links for non-defective practices constrain the reference of the relevant words so that the sentences in the links come out true (for defective practices, this constraint cannot be met). Under such conditions, understanding-assent links generate understanding-truth links. Thus assent to those sentences (while understanding them) is, completely reliably, assent to truths. One might hope to squeeze understanding-knowledge links out of such reliability considerations, perhaps when enhanced by an argument that the reliability is not completely hidden from the subject. Clearly, much work would be needed to vindicate such a programme7.

20A lazy alternative simply postulates understanding-knowledge or understanding-justification links for non-defective practices without attempting to derive them from understanding-assent links. But this has little explanatory value. I understand ‘Every vixen is a female fox’, and it has some positive epistemic status for me. How does it get that status? How do I know ‘Every vixen is a female fox’? Why am I justified in assenting to it? The lazy theorist may try to dismiss the question, saying that it is simply part of our linguistic practice that ‘Every vixen is a female fox’ has that positive epistemic value for whoever understands it. But the examples of defective practices show that it is not simply up to linguistic practices to distribute positive epistemic status however they please. That the practice is to treat a given sentence as having some positive epistemic status for competent speakers of the language does not imply that it really has that epistemic status for them. Their belief may be untrue and unjustified, however much the practice deems otherwise. Thus the only plausible way to make the relevant practice guarantee the putative link from understanding to the positive epistemic status is by making absence of the epistemic status constitute absence of understanding, just as absence of assent was supposed to do. On this account, whoever does not know ‘Every vixen is a female fox’ or is not justified in assenting to it thereby fails to understand it. But this direction of explanation does not trivialize the positive epistemic status, to which it assigns the role of constituter, not constituted. Thus the lazy theorist cannot simply dismiss the question: how does ‘Every vixen is a female fox’ gets its positive epistemic for whoever understands it? Positing direct links from understanding to knowledge or justification does not remove the need for substantive epistemology here. Even when the relevant sentence has the positive epistemic status at issue, the reason is not simply that the linguistic practice deems it to be so — which of course is not to say that the practice is irrelevant to its epistemic status. Understanding- assent links are a better place to start, if not to finish.

212 The standard natural deduction rules constitute perhaps the simplest nontrivial case for an inferentialist account of meaning, and favourite candidates for epistemologically analytic inference rules. By the introduction rule for ‘and’, a conclusion of the form ‘A and B’ follows from the corresponding premises ‘A’ and ‘B’ together. By the elimination rule for ‘and’, the conclusion ‘A’ follows from the premise ‘A and B’, as does ‘B’ from the same premise. Are these rules indeed epistemologically analytic, in the sense that assent to such deductions is a necessary condition of understanding the word ‘and’?

22One must formulate what acceptance of the introduction rule requires with particular care, since the probability of a conjunction may be less than the probability of either disjunct. Iterations of the introduction rule yield the Lottery and Preface paradoxes. Given a lottery known to have at most a million tickets and only one winner, each premise of the form ‘Ticket i will lose’ is overwhelmingly probable, even though their conjunction is known to be false. The author of a book may endorse each individual statement in it, yet admit in the preface that, despite all her efforts, it is bound to contain errors, and on those grounds reject the conjunct of the individual premises. Of course, these paradoxes do not show that the introduction rule fails to preserve truth, although they might be used as grounds for rejecting the rule by a theorist who (mistakenly) used a probabilistic criterion for acceptance. The elimination rule does not suffer from these problems, since the probability of a conjunction is never higher than the probability of any given conjunct.

  • 8 In discussion, Boghossian suggested conjunction elimination as a fallback example of a non- discret (...)

23Let us therefore concentrate on the elimination rule for conjunction, as having the best chance of being non-discretionary for competent speakers8. Imagine a native speaker of English who shows no sign of linguistic deviance, at least until adulthood. He then starts to be worried by the problem of vagueness. Like many philosophers, although not the present author, he comes to the conclusion that vague statements in borderline cases are neither true nor false. Instead, he regards them as undefined in truth-value. He also reflects on the question of how the status of a complex statement such as a conjunction, disjunction, negation or material conditional as true, false or undefined depends on the status of its constituent sentences. He comes to the conclusion that if every constituent sentence is either true or false, then the complex sentence is true or false, as determined by the classical two-valued truth-table for the relevant connective, but that if at least one constituent sentence is undefined in truth-value, then the complex sentence is undefined in truth-value too. His picture is that since the truth or falsity of the complex sentence is defined as a function of the truth or falsity of the constituent sentences, if one of the latter fails to deliver an input, the definition cannot deliver an output, because the function does not have all the required arguments; consequently, the result is undefinedness. Formally, the upshot corresponds to Stephen Kleene’s so-called weak three-valued tables (1952: 334). Furthermore, our imagined subject regards undefined statements as within the speaker’s discretion, and therefore both truth and undefinedness as acceptable (designated) semantic statuses for an assertion: what matters is to avoid falsity. The joint implication of these views is that any conj unction, disjunction, negation or material conditional with a borderline constituent is undefined in truth-value and therefore assertible - of course, on his view, most such sentences should not be uttered, on the pragmatic grounds that they violate the conversational maxim of relevance (Grice 1989: 27). Now suppose that ‘A’ is simply false while ‘B’ is borderline. Consequently, on his view, ‘B’ is undefined, so ‘A and B’ is also undefined. Thus the corresponding instance of conjunction elimination – ‘A and B; therefore A’ - has a designated premise and an undesignated conclusion. On these grounds, he accepts the premise and rejects the conclusion of that instance. He regards the inference as invalid. Let us assume that he is in fact mistaken; the standard elimination rule for conjunction is valid after all. If not, we can change the example, describing new characters who are deviant with respect to some inferences that really are elementary logical validities.

24If the standard elimination rule for conjunction is epistemologically analytic, in the sense of satisfying an understanding-assent link, then our imagined speaker does not understand the word ‘and’, at least, not with its customary English sense. Is that plausible?

25In principle, our imagined speaker is highly deviant, and not only with respect to conjunction. For example, he regards both ‘B’ and ‘Not B’ as assertible in a borderline case. In practice, however, conversational considerations mask most of the deviance. Like many other people with strange views, he adapts himself to society by not insisting on them unless they are strictly relevant. Occasionally he cannot avoid the problem and sounds pedantic, as many academics too, but that hardly constitutes a failure to understand the words at issue. When challenged on his logical deviations, he defends himself fluently. In fact, he has published widely read articles on the issues in leading refereed journals of philosophy, in English. He appears like most philosophers, thoroughly competent in his native language, a bit odd in some of his views.

26It might be objected that he appears to be using the word ‘and’ in its standard English sense because he is really using it in a sense very similar to, but not exactly the same as, the standard one. Indeed, it may be argued, his non-standard sense was explained above, by reference to the Kleene three-valued semantics with two designated values, on which conjunction elimination is invalid, whereas by hypothesis it is valid on the standard semantics for English. But matters are not so simple. Our imagined speaker is emphatic that he intends his words to be understood as words of our common language, with their standard English senses. He uses ‘and’ as a word of that public language. He believes that his semantic theory is correct for English as spoken by others, not just by himself, and that if it turned out to be (heaven forbid!) incorrect for English as spoken by others, it would equally turn out to be incorrect for English as spoken by himself. Giving an incorrect theory of the meaning of a word is not the same as using the word with an idiosyncratic sense — linguists who work on the semantics of natural languages often do the former without doing the latter. Our imagined speaker’s semantic beliefs about his own use of ‘and’ may be false, even if he sometimes relies on those beliefs in conscious processes of truth-evaluation. Indeed, we may assume that he does not regard the three-valued weak Kleene table for conjunction as capturing the way in which the meaning of ‘and’ is presented to him or any other English speaker simply in understanding it, any more than it is so presented by the classical two-valued truth-table. He regards ‘and’ as a semantically unstructured connective for which a homophonic statement of meaning would be more faithful. For him, the more elaborate articulations are simply convenient records of important logical facts about ‘and’. Only in tricky cases does he resort to his non-standard semantic theory in evaluating non-metalinguistic claims.

  • 9 This conclusion contrasts with the discussion of paraconsistent logic in Marconi 1987: 73-96. Willi (...)

27Our imaginary speaker learned English in the normal way. He acquired his non-standard views as an adult. At least before that, nothing in his use of English suggested semantic deviation. Surely he understood ‘and’ with its ordinary meaning then. But the process by which he acquired his eccentricity did not involve forgetting his previous semantic understanding. For example, on his present understanding of ‘and’, he has no difficulty in remembering why he used to assent to it. He was young and foolish then, with a tendency to accept claims on the basis of insufficient reflection. By ordinary standards, he understands ‘and’ quite well. Although his rejection of conjunction elimination might on first acquaintance give an observer a defeasible reason to deny that he understood ‘and’, any such reason is defeated by closer observation of him. He genuinely doubts conjunction elimination as we use it. Nor is he a marginal case of understanding: his linguistic competence is far more secure than that of young children or native speakers of other languages who are in the process of learning English. If some participants in a debate have an imperfect linguistic understanding of one of the key words with which it is conducted, they need to have its meaning explained to them before the debate can properly continue. But to stop our logical debate with the imaginary speaker in order to explain to him what the word ‘and’ means in English would be irrelevant and gratuitously patronising. The understanding which he lacks is logical, is not semantic. His attitude to conjunction elimination manifests only some deviant patterns of belief and belief-formation. Since there clearly could have been, and perhaps are, people such as our imaginary speaker, we have a counterexample to the understanding-assent link for conjunction elimination9.

  • 10 The seminal paper is Tversky and Kahnmen 1983. We can also imagine speakers who reject instances of (...)

28It is arguable that linguistically competent violations of conjunction elimination are actual, not just possible, in the Conjunction Fallacy, a much-studied psychological phenomenon in which subjects assign a higher probability to a conjunction than to one of its conjuncts10.

29By tweaking the example, we can construct a counterexample to the original understanding-assent link UA, for ‘Every vixen is a female fox’. Imagine a speaker who uses the same weak Kleene three-valued tables, but treats only truth as a designated value. Furthermore, this speaker treats a universal generalization of the form ‘Every F is a G’ as true if and only if the conditional ‘x is an F → x is a G’ is true for every value of the variable ‘x’ in the contextually relevant domain. Thus he treats ‘Every vixen is a female fox’ as true if and only if the conditional ‘x is a vixen → x is a female fox’ is true for every such value of V. But there are borderline cases for ‘vixen’, for example when one retraces the maternal line of a fox back to an evolutionary ancestor that was borderline for membership of the current species. For that value of ‘x’, ‘x is a vixen’ is undefined on the envisaged account of vagueness (‘Every vixen is a female fox’ is intended to cover past animals as well as present ones), so, by the weak Kleene table for →, ‘x is a vixen —> x is a female fox’ is also undefined. Consequently, ‘Every vixen is a female fox’ receives an undesignated value on the account with only one designated value. Thus our second imagined speaker does not assent to ‘Every vixen is a female fox’. Nevertheless, he understands it with its ordinary English sense, for reasons similar to those already sketched.

  • 11 Compare Harman 1999: 151 on problems in analysing ‘bachelor’ as ‘unmarried adult male’ and Nozick 2 (...)
  • 12 One problem with interpreting speakers as all speaking their own idiolects is that it tends to unde (...)

30Our imaginary speakers are not so different from actual native speakers of English who deny that a man who has lived with a partner for several years without getting married is a bachelor, or assert that someone who underwent a sex-change operation after giving birth is a mother without being a female parent11. Suppose that they are in fact mistaken; ‘bachelor’ is synonymous in some sense that entails sameness of intension with ‘unmarried man’, and ‘mother’ with ‘female parent’. They falsely believe that ‘bachelor’ is not synonymous in that sense with ‘unmarried man’ or that ‘mother’ is not synonymous with ‘female parent’. Nevertheless, they fall well within the range of permissible variation for linguistically competent speakers. They are only giving more weight than others to an inclination that most speakers feel in some degree to classify the cases that way. Without regarding them as having spoken parrot-fashion, we report their beliefs using the words ‘bachelor’ and ‘unmarried’. We classify them as believing that some unmarried men are not bachelors and that some mothers are not female parents because we interpret them as having used the words with their normal English meanings, despite their errors. That is how they intend to be interpreted, not as using the words with idiosyncratic senses12. If we believe that all unmarried men are bachelors and all mothers are female parents, we therefore classify their beliefs in question as untrue, for the belief that some unmarried men are not bachelors is true if and only if some unmarried men are not bachelors, and the belief that some mothers are not female parents is true if and only if some mothers are not female parents. Given that we correctly interpret them as using the words with their normal English meanings, they understand the words in the relevant sense of ‘understand’. Although they are ignorant of some facts about the normal English meanings of the words, such ignorance is quite compatible with linguistic competence, which is why native speakers of English take university courses in the semantics of English. Arguably, their error is not primarily semantic: they have the semantic belief that the word ‘bachelor’ does not apply to all unmarried men because they have the non-semantic belief that some unmarried men are not bachelors and the semantic knowledge that ‘bachelor’ applies only to bachelors; they have the semantic belief that the word ‘mother’ does not apply only to female parents because they have the non-semantic belief that some mothers are not female parents and the semantic knowledge that the word ‘mother’ applies to all mothers.

31Such cases also help answer the objection that, in such cases, the awkward subject who consciously denies that P also has unconscious, semantically derived knowledge (or belief) that P. When a competent native speaker denies that every unmarried man is a bachelor, the postulation of unconscious knowledge (or belief) that every unmarried man is a bachelor serves no good explanatory purpose. The speaker tends to apply ‘bachelor’ to something once they have applied ‘unmarried’ and ‘man’ to it, but the tendency is defeasible. Such defeasible connections can be explained without postulation of unconscious belief in a universal generalization. In such cases, there need be no hint of the cognitive dissonance or tension that one might expect from a direct contradiction between conscious and unconscious beliefs. Given that there is no contradicted unconscious knowledge in these simple cases, it is not clear what better reason there is supposed to be in postulating it for more complex cases either.

32To try to save understanding-assent links by restricting them to rational agents would be pointless. By ordinary standards, our imagined speakers are rational agents. Although they fall short of some high standards of rationality, so do most humans. Understanding-assent links that do not apply to most humans would be of limited epistemological interest. The picture was that those who appear to reject sentences that are candidates for epistemological analyticity can be excluded from the discussion because they lack the linguistic competence to engage in it; but we cannot exclude humans who reject such sentences on those grounds if the connection between rejecting them and lacking competence holds only for super-humans, not for humans.

33One might try to salvage something from understanding-assent links by weakening the putatively necessary condition for understanding from assent to a disposition to assent, with the thought that our imagined speakers understand ‘and’ and other logical words only because they have an unmanifested disposition to make the logically orthodox inferences, masked by a superficial overlay of unorthodox theorizing. Space does not permit detailed exploration of that proposal here. However, empirical evidence from the psychology of reasoning tells against the postulation of underlying classical logical dispositions of the required kind: humans have nothing like a deductive logic module isolated from the effects of unorthodox theorizing. The case for treating lack of a disposition to assent to a sentence such as ‘Every vixen is a vixen’ as lack of linguistic competence depends on the status of the sentence as an elementary truth of deductive logic. But human deductive competence is far more sensitive than linguistic competence to high intelligence and advanced education. Deductive competence is a reflective skill, often painfully acquired and under one’s personal control. It is not insulated from one’s conscious theorizing. Thus deductive proficiency is not a precondition of linguistic competence (Williamson 2006, 2007a).

34No given argument or statement is immune from rejection by a linguistically competent speaker. Quine’s epistemological holism in ‘Two Dogmas of Empiricism’ undermines his later claim about the deviant logician’s predicament: ‘when he tries to deny the doctrine he only changes the subject’ (1970: 81).

354 Some special cases deserve separate discussion.

36For example, some metalinguistic sentences look analytic for distinctive reasons. Consider theoretical terms. We can understand the word ‘phlogiston’ without believing phlogiston theory. Might we do so because we still believe that ‘phlogiston’ is generally associated with that theory, just as one can understand a natural kind such as ‘gorilla’ without believing the associated stereotype (‘Gorillas are ferocious’) because one still believes that ‘gorilla’ is generally associated with that stereotype? However, such sociolinguistic beliefs are no more immune than logical beliefs from the challenge of theoretical unorthodoxy without change of meaning. If T is any version of phlogiston theory, someone can understand ‘phlogiston’ and associate it with T without believing that it is generally associated with T, in the belief that ‘phlogiston’ is and was generally associated not with T but with somewhat different versions of phlogiston theory. This is clear if T is a strong version of the theory. Even if T is a weak version, they may believe that the word is generally associated with a stronger version, and deny that it is ipso facto associated with T. On such grounds, they may even disbelieve that they themselves associate the word with T. Let such sociolinguistic beliefs be false; nevertheless, holding them is quite consistent with understanding ‘phlogiston’. It is futile to multiply disjuncts and restrictive clauses in the hope of formulating a sociolinguistic claim so anodyne that anyone who understands ‘phlogiston’ must accept it. The result will just be a complex theoretical claim that ordinary speakers can legitimately doubt, on the grounds that such matters are hard to determine.

37A more minimalist line of argument for metalinguistic analyticities appeals to the connection between understanding and knowledge of reference. Suppose that someone understands this sentence:

(1) ‘Tree’ applies to all and only trees.

38Then they understand its constituent words, in particular ‘tree’ as used at the end of (1). So they know what ‘tree’ means. For common nouns, knowledge of meaning requires knowledge of application conditions. Consequently, they know that ‘tree’ applies to all and only trees. Moreover, since knowledge entails belief, they also believe that ‘tree’ applies to all and only trees. Since they understand (1), they know that it means that ‘tree’ applies to all and only trees. Thus, it seems, they should knowledgeably assent to (1). The argument generalizes to a large class of disquotational claims (disquotationality is crucial, since understanding of the expression used on the right-hand side would not imply knowledge of a truth about a distinct expression mentioned on the left-hand side).

39Nevertheless, those who understand (1) may refuse assent to it. Our second imagined speaker is an example, since on his view a universally quantified biconditional with borderline cases for both sides is not definitely true. Indeed, some supervaluationists about vagueness even deny such disquotational principles for vague terms. However erroneous such theories of vagueness, holding them is consistent with ordinary linguistic understanding of (1). If understanding really does involve tacit propositional knowledge of meaning, that knowledge may contradict conscious beliefs.

40Let us grant for the sake of argument that understanding (1) entails knowing both that ‘tree’ applies to all and only trees and that (1) means that ‘tree’ applies to all and only trees. How then can one understand (1) without assenting to it? We lack direct conscious access to whatever tacit knowledge linguistic understanding is supposed to consist in, otherwise semantics as a branch of empirical linguistics would be much easier than it actually is. We consciously entertain the proposition that ‘tree’ applies to all and only trees as presented by sentence (1). In tacitly knowing that ‘tree’ applies to all and only trees (if we do), we tacitly entertain that proposition under a quite different mode of presentation. Thus understanding-assent links such as UA* fail for sentences of natural language:

UA* Necessarily, whoever understands the sentence ‘“Tree” applies to all and only trees’ assents to it.

  • 13 See also Soames 1995 for relevant considerations.

41For any tacit assent to the proposition that ‘tree’ applies to all and only trees is not to it under the modes of presentation that UA* requires13.

42If linguistic understanding involves tacit propositional knowledge of meaning, it presumably involves tacit assent to the relevant propositions under modes of presentation of some sort. To determine in exactly what sense of ‘tacit’, if any, understanding does involve tacit propositional knowledge of meaning lies beyond the scope of this paper. Whatever the answer, no reflective intellectual discipline operates at the level of tacit assent and dissent, even if such a tacit level is necessary for its operation. For instance, linguists’ tacit knowledge of their native language does not satisfy the goal of linguistics.

43One remaining concern is that logical skills must play some role in linguistic competence because logical features play a role in determining well-formedness. An example is the category of negative polarity items. Consider these sentences:

(2) If she ate any of the cake, she was hungry.
(3) If she was hungry, she ate any of the cake.

44‘Any’ is a negative polarity item. To a first approximation, the reason why ‘she ate any of the cake’ is acceptable as the antecedent of the conditional but not as the consequent is that the antecedent is in a downward entailing (negative) context while the consequent is instead in an upward entailing (positive) context. A context C is upward entailing just in case whenever A entails B, C(A) entails C(B); C is downward entailing just in case whenever A entails B, C(B) entails C(A). Thus recognition of the logical features of contexts seems to be needed in order to distinguish between well-formed and ill-formed sentences. But things are not so simple. Consider these sentences:

(4) Exactly four people in the room were of any help.
(5) Few people in the room were of any help.

  • 14 Ladusaw 1996: 325-337 surveys issues concerning negative polarity.

45Logically, ‘few’ creates a downward entailing context; ‘exactly four’ does not. However, (4) is acceptable provided that in the context it is taken to imply (5), but not generally otherwise. Thus the phenomenon involves a significant pragmatic element: which contexts are suitable for ‘any’ cannot be determined on purely logico-linguistic grounds. If we disagree with the speaker of (4) about how many people were in the room or what proportion of them could have been expected to help, we may find her use of ‘any’ inappropriate without regarding her as linguistically incompetent. Similarly, if a speaker has deviant views as to which contexts are downward entailing, but uses ‘any’ in just those contexts which she regards as downward entailing, we can find her deviant use of ‘any’ inappropriate without regarding her as linguistically incompetent, precisely because the deviation is explained by logical rather than linguistic unorthodoxy. Thus the role of logical knowledge in such cases does not make it part of purely linguistic competence. All our knowledge is potentially relevant to judging the appropriateness of a given use of ‘any’14.

465 Understanding words in a natural language has much to do with the ability to use them in ways that facilitate smooth and fruitful interaction with other members of the community That ability can be realized in indefinitely various forms. Speakers can compensate for their deviance on one point by their orthodoxy on others, their ability to predict the reactions of non-deviant speakers, their willingness in the long run to have their utterances evaluated by public standards. As we have seen, such compensation is often possible when the deviance results from localized interference in the normal practice of using a word by high-level theoretical concerns. Thus there is no litmus test for understanding. Whatever local test is proposed, someone could fail it and still do well enough elsewhere with the word to count as understanding it.

47Could an inferentialist reply that such objections trade on a loose everyday sense of ‘understanding’ that must be replaced by something more precise for theoretical purposes? It is far from clear that a stricter sense would do a better job. The relevant features of the ordinary conception of understanding are not mere unreflective sloppiness. Rather, they are an appropriate response to an important constraint on a theory of linguistic meanings: that there is little point in talking about them unless they can be shared across significant differences in belief, between different individuals at the same time or the same individual at different times. They can survive factual learning and factual disagreement. Although inferentialist accounts respect the letter of that constraint, they violate its underlying spirit, by setting inflexible limits to the scope for genuine disagreement. The more holistic ordinary notion of understanding permits localized disagreement at virtually any point.

  • 15 An example is Peacocke’s discussion of deference-dependent propositional attitude ascriptions (1992 (...)

48Cases of logical deviance hint at ways in which the failure of individualist accounts of meaning go deeper than the immediate lessons of the original anti-individualist arguments of Putnam (1975) and Burge (1979). Their cases are often analysed in terms of a distinction between experts with full understanding and lay-people with partial understanding who defer to the experts, in virtue of which one may correctly ascribe to them attitudes to the contents that experts determine15. Such asymmetries are postulated by Putnam’s Hypothesis of the Universality of the Division of Linguistic Labor:

Every linguistic community [...] possesses at least some terms whose associated ‘criteria’ are known only to a subset of the speakers who acquire the terms, and whose use by the other speakers depends upon a structured cooperation between them and the speakers in the relevant subsets (1975: 228).

49But experts themselves can make deviant applications of words as a result of theoretical errors and still count as fully understanding their words. Although they defer to nobody on the matters at issue, they are more than adequately integrated members of the speech community with respect to those very words. Their assignments of meaning to those words are not parasitic on the assignments that more privileged individuals make. Rather, each individual uses words as words of a public language; their meanings are determined not individually but socially, through the spectrum of linguistic activity across the community as a whole. The social determination of meaning requires nothing like an exact match in use between different individuals; it requires only enough connection in use between them to form a social practice. Full participation in that practice constitutes full understanding. That is why there is no litmus test for understanding.

50A complex web of interactions and dependences can hold a linguistic or conceptual practice together even in the absence of a common creed that all participants at all times are required to endorse. This more tolerant form of unity arguably serves our purposes better than would the use of platitudes as entrance examinations for linguistic practices.

  • 16 Davidson famously endorses a holistic principle of charity while rejecting the analytic-synthetic d (...)

51Evidently, much of the practical value of a language consists in its capacity to facilitate communication between agents in epistemically asymmetric positions, when the speaker or writer knows about things about which the hearer or reader is ignorant, perhaps mistaken. Although disagreement is naturally easier to negotiate and usually more fruitful against a background of extensive agreement, it does not follow that any particular agreement is needed for disagreement to be expressed in given words. A practical constraint on useful communication should not be confused with a necessary condition for literal understanding. Moreover, the practical constraint is holistic; agreement on any given point can be traded for agreement on others. The same applies to principles of charity as putatively constitutive conditions on correct interpretation: imputed disagreement on any given point can be compensated for by imputed agreement on others16.

  • 17 For examples of rational debate for and against a law of non-contradiction see Priest, Beall and Ar (...)

52It is far easier and more rewarding to discuss the existence of true contradictions with a dialetheist such as Graham Priest than creationism with a Christian fundamentalist or Holocaust denial with a neo-Nazi17. The difficulty of engaging in fruitful debate with fundamentalists or neo-Nazis is not plausibly attributed to some failure of linguistic understanding on their part (or ours); it arises from their wilful disrespect for the evidence. Such difficulty as there is in engaging in fruitful debate with dialetheists provides no significant reason to attribute to them (or us) a failure of linguistic understanding. Competence with the English language no more requires acceptance of some law of non-contradiction or any other logical law than it requires acceptance of the theory of evolution or the historical reality of the Holocaust.

  • 18 W. B. Gallie’s intriguing account of the positive function of essentially contested concepts’ is re (...)

53We cannot anticipate all our disagreements in advance. What strike us today as the best candidates for analytic or conceptual truth some innovative thinker may call into question tomorrow for intelligible reasons. Even when we hold fast to our original belief, we can usually find ways of engaging rationally with the doubter. If a language imposes conditions of understanding that exclude such a doubt in advance, as it were in ignorance of its grounds, it needlessly limits its speakers’ capacity to articulate and benefit from critical reflection on their ways of thinking. Such conditions are dysfunctional, and natural languages do not impose them18.

  • 19 Someone who understands a word without being disposed to utter it (perhaps because they find it o (...)

54There is, of course, a distinction between understanding a word and not understanding it. One can lack understanding of a word through lack of causal interaction with the social practice of using that word, or through interaction too superficial to permit sufficiently fluent engagement in the practice. But sufficiently fluent engagement in the practice can take many forms, which have no single core of agreement19.

  • 20 Some rationalist defenders of intuition seem to have something like this in mind.

556 At this point, someone sympathetic to the spirit of epistemological analyticity may suspect that the mistake was to go for the idea that understanding is somehow psychologically sufficient for assent. Instead, the suggestion is, we should go for the idea that understanding is somehow epistemologically sufficient for assent20. Externally, logically deviant speakers are in a position to know (or to assent with justification). They seem to be willfully and perversely turning their backs on knowledge that is available to them. It is there for the taking, but they are psychologically blocked from taking it.

56We must be careful about the source of the blockage. Suppose that it is lack of logical insight. Although our imagined speaker understands the word ‘and’, he lacks the logical insight competently to apply conjunction elimination. Other people just like him except for having more logical insight do competently apply conjunction elimination. Anyone who understands ‘and’ and has a modicum of logical insight can competently apply conjunction elimination. That story assigns no special role to linguistic understanding, beyond the usual role that it plays as a precondition for all intelligent discourse: the decisive role is assigned to logical competence, not semantic competence.

57For semantic competence to play the decisive role, something like this is needed:

KU Whoever competently applies conjunction elimination for ‘and’ in the normal way does so simply on the basis of their understanding of ‘and’.

58(Treat ‘on the basis of’ more like ‘by an exercise of’ than like ‘by inference from’.) KU may be plausible at first sight. It does not imply that whoever understands ‘and’ applies conjunction elimination for ‘and’ or even has a disposition to do so, competently or otherwise.

59What does the definite description ‘their understanding of “and”’ in KU denote? There are thick and thin candidates. The thin candidate is the mere fact that they understand ‘and’. The thick candidate is the body of underlying facts that constitute the thin candidate, the facts that realize this particular subject’s understanding of ‘and’ at this particular time. The thin candidate is exactly similar for any two people who understand ‘and’, since they have the same property of understanding it. The thick candidate may differ between any two people who understand the word, since different underlying facts can constitute their doing so. These characterizations are schematic, but will do for present purposes.

60Suppose that the definite description in KU denotes the thick candidate. KU remains plausible on this reading. Then, given the picture of linguistic understanding in previous sections, KU has much less epistemological significance than might have been hoped. The facts that constitute your understanding of a given word include various cognitive capacities that are not in general necessary for understanding that word, but help to make up your particular competence with it. For example, the facts that constitute the understanding of ‘and’ on the part of the imagined speaker who rejects conjunction elimination for ‘and’ include his logical capacities and dispositions. The basis cited in KU includes cognitive capacities that are not in general necessary for understanding the word. Thus the thick candidates are too thick to yield bases for analyticity; they involve knowledge that is not semantic in any relevant sense.

61Suppose instead that the definite description in KU denotes the thin candidate. But it is not the basis in any useful sense for competently applying conjunction elimination for ‘and’ in the normal way, although confusion with the thick candidate may suggest otherwise. The thin candidate implies no specific logical capacity at all. It is not as though in such cases a subject’s understanding quietly tells them to make the inference but they override the advice; it is providing no such advice to be overridden. Consequently, understanding in the thin sense provides no basis for assent to anyone. Of course, understanding ‘and’ is a precondition for competently applying conjunction elimination for ‘and’, and in that sense may be part of the basis for so applying it, but that point is quite general; it is neutral between the analytic and the synthetic. Thus the thin candidate is too thin to be a basis for knowledge.

62We could try eliminating the talk of bases, for instance in a formulation like this:

AJ Whoever understands ‘and’ and applies conjunction elimination for ‘and’ does so with justification.

63But such principles are false, since someone who understands ‘and’ but applies conjunction elimination for ‘and’ because his manifestly unreliable guru told him to does so without justification. The obvious way to avoid such counterexamples and make the connection with semantic competence is to qualify ‘applies conjunction elimination’ by ‘on the basis of that understanding’. But that returns us to the problems of KU.

64The problem is general. The idea that, in the cases at issue, understanding is epistemologically sufficient for assent to the inference is the idea that assent on the basis of understanding has the desired positive epistemic status. But once we disambiguate ‘understanding’ between thick and thin candidates, we can see that the thin candidates are too thin to be bases for assent while the thick candidates are not purely semantic or conceptual. The attempt to base the epistemology of obviously valid inference rules such as conjunction elimination on preconditions for linguistic competence with them rests on a confusion between linguistic competence and logical competence. Similarly, dissent from the law of non-contradiction in its various forms is simply a logical failure; dialetheists such as Graham Priest manifest semantic competence with the logical particles of their native languages in their ordinary senses. Epistemological analyticity is an illusion.

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1 The case of deductive logic is a useful reminder that many short, trivial steps of no apparent significance can be chained together into a long, non-trivial argument of obvious significance: the short steps were not really insignificant after all: no apologies for concentrating on them here.

2 In effect, Horwich 1998: 131-153 allows understanding-assent links for which the understanding-truth links fail.

3 See Eklund 2002 for a defence of the idea of inconsistent languages.

4 Dummett 1973: 397, 454 claims that the rules for pejorative terms such as ‘Boche’ suffer from a related kind of incoherence; Brandom 1994: 126; 2000: 69-70 and Boghossian 2003: 241-242, amongst others, have relied on his description of the practice of using such terms. I argue that it is mistaken in Williamson 2003 and 2007b, and suggest an alternative.

5 See Peacocke 1992: 21 and Boghossian 2002.

6 Boghossian 2003: 242-243, representing a change of view from Boghossian 2002.

7 The treatment of the issue in Boghossian 2003 is of this general kind. For detailed criticism see Williamson 2003.

8 In discussion, Boghossian suggested conjunction elimination as a fallback example of a non- discretionary rule if modus ponens fails. Peacocke writes of the possession-condition for the concept of conjunction, ‘On any theory, this possession-condition will entail that thinkers must find the transition from A and B to A compelling, and must do so without relying on any background information’ (2004: 172).

9 This conclusion contrasts with the discussion of paraconsistent logic in Marconi 1987: 73-96. Williamson 1989 responds critically to that discussion.

10 The seminal paper is Tversky and Kahnmen 1983. We can also imagine speakers who reject instances of conjunction elimination through muddling truth and conversational appropriateness. ‘Did she take the money and give it back? Yes. Did she take the money? No, she took-the-money- and-gave-it-back.’

11 Compare Harman 1999: 151 on problems in analysing ‘bachelor’ as ‘unmarried adult male’ and Nozick 2001: 135-136 on the non-synonymy of ‘mother’ and ‘female parent’.

12 One problem with interpreting speakers as all speaking their own idiolects is that it tends to undermine testimonial knowledge: if Y gets some knowledge from X and passes it on to Z in the same words, they do not mean in Y’s mouth what they meant in X’s.

13 See also Soames 1995 for relevant considerations.

14 Ladusaw 1996: 325-337 surveys issues concerning negative polarity.

15 An example is Peacocke’s discussion of deference-dependent propositional attitude ascriptions (1992: 29-33). Burge 1986 extends his earlier arguments in ways related to the arguments of this paper, in his account of the understanding of words such as ‘sofa’, and argues for such a deeper lesson. Goldberg 2000 replies on behalf of Burge to Bach 1988 and Elugardo 1993. Although the discussion of Putnam and Burge’s semantic anti-individualism in Marconi 1997 is hostile, Williamson 1998 argues that much in Marconi’s account of lexical competence can be reconciled with semantic anti-individualism once, following Burge, it is combined with psychological anti-individualism, as it needs to be.

16 Davidson famously endorses a holistic principle of charity while rejecting the analytic-synthetic distinction (2001: 144-149). See Williamson 2007a for more discussion of charity. Of course, he takes the notion of a shared language less seriously than here (Davidson 1986).

17 For examples of rational debate for and against a law of non-contradiction see Priest, Beall and Armour-Garb 2004.

18 W. B. Gallie’s intriguing account of the positive function of essentially contested concepts’ is relevant here; his examples are ‘the concepts of a religion, of art, of science, of democracy and of social justice’ (1964: 168).

19 Someone who understands a word without being disposed to utter it (perhaps because they find it obscene or unpronounceable) can still count as sufficiently engaged in the practice of using it. The account should also be read so as to allow for understanding of dead languages.

20 Some rationalist defenders of intuition seem to have something like this in mind.

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Timothy Williamson, «Logical deviance and semantic competence»Rivista di estetica, 34 | 2007, 121-142.

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Timothy Williamson, «Logical deviance and semantic competence»Rivista di estetica [Online], 34 | 2007, online dal 30 novembre 2015, consultato il 16 juin 2024. URL:; DOI:

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