Reducing Truth Through Meaning


Horwich has attempted to combine an anti-reductionist deflationism about sentential truth with a reductionist theory of meaning. Price has argued that this combination is inconsistent, but his argument is fallacious. In this paper I attempt to repair Price’s argument.

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  1. 1.

    1995; 1997: 99–106; 1998a: 27–30, 68–71, ch. 4; 2005: ch. 3; 2010: ch. 6.

  2. 2.

    Field (1992: 326–328) hints that he is sympathetic to this conclusion, and McGrath (1997: 79–85) offers a different, but to my mind weaker, argument for it.

  3. 3.

    For evidence that Horwich would likely be happy with abundantism, see 1998a: 21, 1998b: 37.

  4. 4.

    Horwich subscribes to this position in 1995: 356; 1997: 106; 1998a: 5; 2005: 63; 2010: 107–108.

  5. 5.

    Horwich sometimes (e.g. 2010: 103–104 fn. 5) writes this schema as: \(\forall x (x\hbox{ means }\langle p \rangle \rightarrow (x\hbox{ is true }\leftrightarrow p)).\)

  6. 6.

    1995: §1; 1998a: 28–29, 70–71, ch. 4; 2005: 74–75; 2010: 103–104. Occasionally Horwich weakens his position to the claim that we have no reason to expect a naturalistic reduction of truth (e.g. 2005: 75). This paper will show that even this weaker stance is incompatible with meaning reductionism: if we have a reduction of meaning then we have every reason to expect a reduction of truth.

  7. 7.

    I have changed every occurrence of ‘non-semantic’ in this quotation for ‘naturalistic’ to bring it in line with Horwich’s terminology. I have also made trivial changes in the notation to avoid clashes with that of my paper.

  8. 8.

    In fairness to Price, at one time Horwich (1998a: 5) did propose identifying each predicate-meaning f with the property it stands for F. If we assume this then (1) becomes less problematic. However, Horwich later retracted this thesis in his (2005: 33–34), and so Horwich’s (2005) timeslice is able to resist Price’s argument. And setting aside Horwich’s change of mind, Price’s argument as it stands at most establishes that anti-reductionist deflationism, meaning reductionism and the thesis that in general f is identical to F are together inconsistent, not the advertised conclusion that the first two theses are inconsistent with each other.

  9. 9.

    Price has made precisely this suggestion to me in correspondence.

  10. 10.

    It is, of course, controversial to bind predicate variables with quantifiers at all. However, given the assumption that there are properties, which Horwich (e.g. 1998a: 21) grants, such quantification is permissible.

  11. 11.

    Indeed, he has denied it precisely to avoid an argument closely related to the one just presented; see 1998a: 65–68; 2005: 73–74.

  12. 12.

    1998a: 25–27, 65–68; 2005: 73.

  13. 13.

    Thanks to an anonymous reviewer for pointing out that it does not follow from (S) alone that true of reduces to, or is even co-extensive with, the disjunction of the relations of the form (4). (S) does not rule out the possibility that there is some x and y such that x is true of y but there is no f such that x means f. This is, however, a shortcoming of (S): that possibility should be ruled out. Horwich (2001: 158 n.21) is aware of this general problem, and his strategy, which is surely correct, is to add the principle ‘For any x and yx is true of y only if there is some f such that x means f’ to his deflationist account of true of.

  14. 14.

    That is assuming that there is a definite totality of them at all; if there are not then this reduction is in even worse shape.

  15. 15.

    1995: 356; 1998a: 25; 2005: 77; 2010: 106–107.

  16. 16.

    A ban on infinitely disjunctive reductions will also block the identification/reduction of true of to the disjunction of instances of (4).

  17. 17.

    This marks a change from his 1998a (20–21) position I mentioned in fn. 8.

  18. 18.

    In fact, Horwich suggests reducing x means f to x instantiates y. However, I take it that Horwich is charitably interpreted as meaning (6): it obviously does not follow from the fact that Horwich instantiates some property or other, for instance the property of being a human, that Horwich means something.

  19. 19.

    In moving from (6) to (\(6^{\prime}\)), Horwich is making a pun. ‘U’ in (6) is a first-order variable, but in (\(6^{\prime}\)) it is a second-order one. For the sake of argument I will ignore this slide.

  20. 20.

    It is worth noting that my uses of ‘first-order’ and ‘higher-order’ are not intended to line up with their uses in ‘first-order logic’ and ‘higher-order logic’.

  21. 21.

    Here is a more Horwich-specific presentation of this problem. Horwich (1998a: esp. ch. 2–3; 2005: ch. 2) claims that the reductive bases of meaning-properties are lawlike “use-properties”. What Horwich must do is find a way of describing the use of each meaningful predicates which is general enough that all of the uses have a (non-infinitely disjunctive) naturalistic feature in common. It is difficult to see what common use all predicates are put to apart from being applied to the members of their extension. But if we think of use-properties in this way then they will be of the form ‘R(xF)’. Therefore, by reducing the meaning-properties to these use-properties, Horwich will be giving a strongly relational reduction of meaning.

  22. 22.

    I suppose we might wonder whether Horwich should be interpreted as saying that truth is not reducible in the sense in which meaning is, or whether he is using two different senses of ‘reducible’. But there is textual evidence that Horwich meant the two senses to be the same (e.g. 2005: 34–35); he even goes so far as to say that “we have no reason to expect any sort of reductive analysis of the truth-theoretic properties and relations” (2005: 75, original emphasis). But even if Horwich did mean to use different senses of ‘reducible’, it is still a substantial lesson to learn that there are serious problems with saying that the meaning-properties are reducible but that truth isn’t reducible in the same sense.

  23. 23.

    This is Price’s (1997: 114–115) recommendation.

  24. 24.

    ANONYMOUS has recommended this option to me.


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Thanks to Timothy Button, Christina Cameron, Paul Horwich, Steven Methven, Michael Potter, Huw Price, Adam Stewart-Wallace and everyone at the Serious Metaphysics Group.

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Correspondence to Robert Trueman.

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Trueman, R. Reducing Truth Through Meaning. Erkenn 78, 823–832 (2013).

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  • Relational Reduction
  • Naturalistic Property
  • Naturalistic Feature
  • Propositional Truth
  • Reductive Base