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Modeling Truth


Many in philosophy understand truth in terms of precise semantic values, true propositions. Following Braun and Sider, I say that in this sense almost nothing we say is, literally, true. I take the stand that this account of truth nonetheless constitutes a vitally useful idealization in understanding many features of the structure of language. The Fregean problem discussed by Braun and Sider concerns issues about application of language to the world. In understanding these issues I propose an alternative modeling tool summarized in the idea that inaccuracy of statements can be accommodated by their imprecision. This yields a pragmatist account of truth, but one not subject to the usual counterexamples. The account can also be viewed as an elaborated error theory. The paper addresses some prima facie objections and concludes with implications for how we address certain problems in philosophy.

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  1. 1.

    I use ‘idealize’ and ‘idealization’ very broadly to cover any inaccuracy where the implication is that the inaccuracy won’t spoil the intended application.

  2. 2.

    See my (Teller 2001, 401) for the illustration of complementary hydrodynamic and statistical mechanical accounts of water.

  3. 3.

    Henceforth “properties” will be understood as “properties and relations”.

  4. 4.

    In discussions of vagueness, many use (im)precise as I do. For example, Williamson (1994) uses “precise” as the antonym of “vague” throughout his book.

  5. 5.

    This is supported in my (Teller 2004a, 432–3, 436–7)

  6. 6.

    For much more on the idealized status of quantity terms in physics see my (P. Teller, “Measurement Accuracy Realism”, unpublished).

  7. 7.

    In chapter II of his (2006) Giere provides a compelling summary of the grounds for the conclusion that color perception involves all kinds of shortcuts short of exact reflectancies of external objects.

  8. 8.

    Note that this exception is systematic and fits into the larger scheme developed below: It can be seen as the limiting case in which truth-apt imprecise statements coincide with their idealized semantic alter-ego counterparts. See below.

  9. 9.

    As Braun and Sider recognize, this thinking goes back to Frege. See their note 1, p. 133 for some references

  10. 10.

    And for which I will argue in section 8.

  11. 11.

    Braun and Sider understand the plainly unproblematic activity of ascribing truth to utterances by saying that “ordinarily speakers typically and harmlessly ignore vagueness.” (135), but provide no account of how this works. My positive account of truth will, in section 11 , support a developed analog of what they suggest.

  12. 12.

    I believe that Braun and Sider’s problem cannot be resolved by any of the existing accounts of vagueness. To some extent Braun and Sider support this claim in their paper. I will defend this claim in (P. Teller “Language and the Complexity of the World”, unpublished) and here continue with the positive approach of showing how their issue can be addressed directly by refashioning how we think about truth.

  13. 13.

    I here shift from Braun and Sider’s use of ‘sentence’ and ‘utterance’ to ‘statement’ to bring their terminology into line with mine. Since what counts here are the semantic values, nothing turns on whether we take these to be values of sentences, utterances, or statements.

  14. 14.

    As I argue in my (Teller 2004a).

  15. 15.

    Compare Russell (1923, p. 68): “All vagueness in language and thought is essentially analogous to this vagueness which may exist in a photograph.”

  16. 16.

    This initial formulation gives the idea but does not exactly agree with the more detailed analysis given in the next two sections.

  17. 17.

    If I say that no completely precise statement is true, won’t I have to say, with Braun and Sider, that none are false either? Yes. Use of ‘false’ here is a special case of the expository simplifications assumed in this section, addressed with the considerations of section 9, and more generally, section 11. Section 9 will direct us to take the statement as presupposing that there is some precise number that is John’s height in centimeters but that this number is not 180 cm. On this reading the statement fails of presupposition and so comes out as truth valueless. But what I say about functioning as an exact truth is not affected.

  18. 18.

    I will expand on this requirement below.

  19. 19.

    Compare: The top of my table is flat. Not geometrically flat, but close enough that differences won’t matter for present concerns.

  20. 20.

    Below I will explain why conditions of applications are not traditional truth conditions.

  21. 21.

    The considerations of note 17 apply likewise here.

  22. 22.

    “Deidealize” must always be understood as reducing, not eliminating idealization.

  23. 23.

    I spell out this very compressed argument sketch in much more detail in my (P. Teller, “Language and the Complexity of the World”, unpublished).

  24. 24.

    This way of thinking of functioning as an exact truth is suggested to me by Millgram’s thorough-going appeal to the function of inference in his characterization of “partial truth” throughout his (Millgram 2009).

  25. 25.

    A more careful statement will have to treat just what needs to be included in the range of cases for which a statement must work in order to count as true. For example an attribution of ‘short’ will count as true when it can be relied on, not for any case, but for the ones that are contextually relevant. But I should have said enough to show that the account has the resources for dealing with this issue.

  26. 26.

    See my (P. Teller, “Measurement Accuracy Realism”, unpublished).

  27. 27.

    See my (P. Teller, “Measurement Accuracy Realism”, unpublished) for much more detailed argument for this claim.

  28. 28.

    Braun and Sider cover this aspect of the analysis with an unanalyzed conception described as “approximate truth”.

  29. 29.

    For a more detailed presentation of the compressed argument of the last two paragraphs see my (2012) section 5. Dewey scholars tell me that all of this corresponds well to Dewey’s intent.

  30. 30.

    In note 22 to page 60 Millgram (2009) distances his account of “partial truth” from pragmatism, apparently because he is thinking of pragmatism only as an account of exact truth, in particular an account that obscures the ubiquitous utility of departing from exact truth. He writes: “[R]ecall that one well-known pragmatist slogan tells us that it’s true if it works. We have been examining cases where it works precisely because it’s not true.” One of the many differences between my account and Millgram’s is that by tying an understanding of imprecision to explicit truth, the present proposal clarifies the connection with pragmatism.

  31. 31.

    So the present analysis narrows the analogical gap between our use of ‘true’ in application to statements and the older use as in “She is a true friend”.

  32. 32.

    Space does not permit here addressing the worry, when historically the needs and interests of a whole community shift, can what was true become false? See my (Teller 2009, 261–3).

  33. 33.

    This was also the apparent difficulty addressed in note 17.

  34. 34.

    See Kuhn 1970, pp. 19–20 and ch 2, 3, and 4 passim.

  35. 35.

    I take the foregoing to be an important consideration, but only one, explaining the presumption that we have many unqualified truths. This prejudice runs deep in Western culture.

  36. 36.

    In an isolated remark, Lewis (1979, 352) suggested what I have discussed in this section: “If a sentence is true enough (according to our beliefs) we are willing to assert it, assent to it without qualification, file it away among our stocks of beliefs, and so forth.”

  37. 37.

    As Nancy Cartwright has argued in too many places to enumerate. This paper, together with material in (P. Teller “Language and the Complexity of the World”) also develop a novel and promising way of understanding ceteris paribus conditions.

  38. 38.

    In Hard Truths (2009) Millgram is wresting with many of the same issues addressed here but with a different model building approach. Millgram works with a notion of “partial truth” understood as an attitude towards statements (or “thoughts”) that are “inferentially restricted” (40) in the sense that one will use a statement only for a certain range of inferences: “When a thought is acknowledge to be partially true, and is nevertheless being used in inference, there is a recognized mismatch between representation and world – but not in any way that requires changing the representation…. assessing a claim as partially true allows for slack…but only so much of it” (108–9). With my modelers’ methodology I am obviously not going to urge that there is room for only one of these model building approaches, but rather that we must see, first, how well both can be developed, and then evaluate both for what they deliver by way of principled understanding of facts about language.

    Graff’s (2000) (now Graff Fara) shares with me a role for interests: For example, for Graff someone counts as tall if they are significantly taller than some contextually specified norm, where significance is interest based. The account is thus only for gradable adjectives. My functions as a truth is likewise interest based; but my account applies to all of language and incorporates a role for interests of any kind.

    Lynch’s (2009) proposes a functionalist account of truth. Explicitly modeled on psychofunctionalism, the realizers of the truth function can be very differently realized by different subject matters. Lynch’s has interesting overlap with my account. The idealized alter-egos treat, as an idealization, each predicate as signifying a property. But the connections between these idealizations and the world could work out very differently for different subject matters. The ways in which “morally wrong” is property-like could be radically different from the case of “red”. There is also room for various function-realizations in “functions as an truth”. Lynch’s account, however, is utterly unlike mine in doing nothing to address the question of what it is for imprecise statements to be true.

    Elgin (2004) has a study of how being “true enough” often does duty for what we think of as being reserved for strict truth.


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  16. Teller, P (2012) “Modeling, Truth, and Philosophy” Metaphilosophy, 43(3) 257–274.

  17. Williamson, T. (1994). Vagueness. London: Routledge.

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Teller, P. Modeling Truth. Philosophia 45, 143–161 (2017).

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  • Truth
  • Accuracy
  • Precision
  • Models
  • Pragmatism
  • Common ground