Timothy Williamson - The Philosophy of Philosophy

Analytic philosophy at its best uses logical rigor and semantic sophistication to achieve a sharpness of philosophical vision unobtainable by other means. To sacrifice those gains would be to choose blurred vision. Fortunately, one can do more with good vision than look at eyes.

Many have been attracted to the idea that all philosophical problems are linguistic or conceptual through the question: if the method of philosophy is a priori reflection, how can it lead to substantive knowledge of the world? Those who find that question compelling may propose that it informs us of relations of ideas rather than matters of fact, or that its truths are analytic rather than synthetic, or that it presents rules of grammar disguised as descriptions, or that its aim is the analysis of thought or language. In short, on this view, philosophical truths are conceptuals truths. We may suspect the presence of empiricist presuppositions in the background – or, as with Ayer, in the foreground. Not starting with such presuppositions, we should be open to the idea that thinking just as much as perceiving is a way of learning how things are. Even if one does not fully understand how thinking can provide new knowledge, the cases of logic and mathematics constitute overwhelming evidence that it does so. The case of the original question, which is philosophical yet queries a theorem of classical logic, shows that we cannot segregate logic from philosophy and claim that armchair thinking illuminates the former but not the latter. In particular, conceptions of logic and mathematics as (unlike philosophy) somehow trivial or non-substantial have not been vindicated by any clear explanation of the relevant sense of “trivial” or “non-substantial.” Whether a given formal system of logic or mathematics is consistent is itself a non-trivial question of logic or mathematics. We know from Gödel’s second incompleteness theorem that the consistency of most standard systems of elementary mathematics cannot be decided in equally elementary mathematics, unless the original system is already inconsistent. The next two chapters investigate in more depth the prospects for conceptual truth and its role in philosophy.

1 1 On vagueness in general see, for a start, Graff and Williamson (2002), Keefe (2000), Keefe and Smith (1997), and Williamson (1994a). On vague objects see Williamson (2003b) and references therein.

2 2 Classical logic is the standard logic of expressions such as “every,” “either … or …” and “not” on the assumption that there is a mutually exclusive, jointly exhaustive dichotomy of sentences into the true and the false.

3 3 See also Quine (1970: 11).

4 4 A recent example of a supervaluationist rejecting such disquotational equivalences for borderline cases is Keefe (2000: 213–20). For further discussion see Williamson (1994a: 162–4) and McGee and McLaughlin (2000).

5 5 Even if a word retains its linguistic meaning, its reference may shift with the context of utterance (“I,” “now,” “here”). If “dry” undergoes such contextual shifts, T2a and T2b may fail when interpreted as generalizations about utterances of “dry” in contexts other than the theorist’s own. It might be argued that concepts can also undergo contextual shifts in reference: you use the concept I to refer (in thought) to yourself but I use the same concept to refer to myself; at noon we use the concept now to think of noon but at midnight we use the same concept to refer to midnight; at the North Pole we use the concept here to refer to the North Pole but at the South Pole we use the same concept to refer to the South Pole. If so, TC2a and TC2b may also fail when interpreted as generalizations about uses of the concept dry in contexts other than the theorist’s own.

6 6 For intuitionist logic in general see Dummett (1977). For its application to the problem of vagueness see Graff and Williamson (2002: 473–506) and Chambers (1998).

7 7 One proves by mathematical induction on n that if An is the conjunction of n instances of excluded middle then ¬ is intuitionistically inconsistent.

8 8 This point does not generalize to the semantics of conditionals in fuzzy logic, given the popular rule that if the consequent is lower than the antecedent in degree of truth then the degree of truth of the conditional falls short of 1 by the amount by which the consequent falls short of the antecedent in degree of truth; otherwise the degree of truth of the conditional is 1. Hence if A has a higher degree of truth than B but both are indefi nite then A → B is indefi nite while B → A is perfectly true. Thus the information that the antecedent and consequent are indefi nite does not determine whether the conditional is indefi nite.

9 9 See Graff and Williamson (2002: 279–351) on higher-order vagueness.

10 10 See Williamson (1994a: 193–5).

11 11 Of course, monolingual speakers of another language may know whether Mars was always dry or not dry without ever hearing of the original question, which is an interrogative sentence of English; they use a synonymous sentence of their own language. They do not know whether the original English question has a positive answer. Someone may even know whether the original English question has a positive answer without understanding the question, because the knowledge can be passed along a chain of testimony; understanding of the original question is needed only at one end of the chain. These quibbles do not affect the argument.

12 12 The issue of Smith’s intentions concerns his thoughts, but we may suppose that the question immediately at issue is whether Smith was even involved in Jones’s death.

13 13 Non-testimonial evidence may be taken to include non-linguistic items such as a bloodied knife; this is what lawyers call “real evidence.” For an argument that all evidence in an epistemologically central sense of the term is propositional see Williamson (2000a: 194–200). For example, the evidence in this sense might include the proposition that the bloodied knife was found at the scene of the crime, but not the knife itself.

14 14 Popularization has its place, in philosophy as in physics, but should not be confused with the primary activity.

“Philosophical questions are more conceptual in nature than those of other disciplines”: that can easily pass for a statement of the obvious. 1Many philosophers consciously seek conceptual connections, conceptual necessities, conceptual truths, conceptual analyses. In effect, they present themselves as seeking far more general and less obvious analogues of “Vixens are female foxes.” The suggestion is that an armchair methodology is appropriate to their quest because it concerns truths in some sense less substantial, less world-involving than those of other disciplines: in Humean terms, relations of ideas rather than matters of fact. Our conceptual or linguistic competence, retained in the armchair, is to suffice for a priori knowledge of the relevant truths.

As already argued, philosophical truths are not generally truths about words or concepts. However, analytic truths are not supposed to be always about words or concepts, even if words or concepts are supposed to play a special role in explaining their truth. The sentence “Vixens are female foxes” is in no useful sense about the word “vixen” or any other words; it is about vixens, if anything. Its meaning is not to be confused with that of the metalinguistic sentence “ ‘Vixens are female foxes’ is true.” Similarly, the thought vixens are female foxes is not about the concept vixen or any other concepts; it too is about vixens, if anything. It is not to be confused with the metaconceptual thought the thought VIXENS ARE FEMALE FOXES is true .