Truth (Princeton Foundations of Contemporary Philosophy)

by Burgess, John P. ; Burgess, Alexis G.

  If one takes a fictionalist view of truth, one will doubtless want to take a similar view of other alethic notions such as satisfaction, and also (since the extension of a predicate is just the set of things that satisfy it) of the notion of extension. So from a fictionalist point of view, it is just a mistake to want to ask what the extension of the truth predicate really is. Extensions are fictional, not real.

  What becomes of the liar paradox reasoning on this proposal? Speaking about the fiction, what one says is precisely (14a). Speaking within the fiction, how could things fairly be said to stand “according to the fiction of truth” with respect to the liar paradox reasoning? The analogy with fiction in the literal sense of imaginative literature suggests comparison with a story about a mathematician who finds a counterexample to Fermat's theorem. How could things fairly be said to stand “according to the story” with respect to Wiles's proof of that theorem? Presumably in both cases one should say that according to the fiction there can be no genuine proof of a certain kind, so any purported such proof must contain a fallacy somewhere. But there is no one step one can point to and say, “Here is where, according to the fiction, the fallacy lies.”

  The fictionalist's feigned belief would thus be much like the real belief of those would-be consistency theorists who are dissatisfied with all existing consistency theories: There must be a fallacy somewhere in the liar paradox reasoning, though we can't (yet) say where. But probably the fictionalist philosopher will never be called upon by any member of the general public to express a belief about the liar paradox reasoning, since even today the proverbial “man in the street” will most likely never have heard of it. Be all that as it may, the within/about distinction works enough like Tarski's object/meta- distinction to prevent strengthened liars from being a problem (though this conclusion does depend on assuming that the “fiction of truth” isn't like one of those tricky fictions that refers to itself as fictitious).

  A third answer to the question what attitude the philosopher should take is that we should proceed as much as possible in the same unself-conscious way as those who have never encountered the liar, not keeping our fingers crossed as we speak, or saying “but all that is just according to a certain fiction” sotto voce after every remark to a neighbor. The fact that we have encountered the liar paradox reasoning and recognized the inconsistency of our intuitive notion of truth just means that if we ever do stumble upon similar reasoning in daily life we will be able to recognize it for what it is, and have the good sense not to “follow the argument wherever it leads,” since we will remember it leads us someplace we don't want to go.

  By way of justification for adopting such a nonchalant attitude towards contradiction, it may be noted that there is illustrious precedent for something like it. Mathematicians from the time of Leibniz noted that manipulations of infinite series can lead to paradox, thus:

  They nonetheless went right on using series, without any clear or distinct notion of the scope and limits of “safe” and “dangerous” manipulations, and if they stumbled into uses leading to paradox, they just ignored them. When mathematicians became differentiated into pure and applied, and pure mathematicians found reason to insist on strict rigor, they banned all series except those for which they could give a rigorous definition of sum (convergent series); but even then applied mathematicians and physicists went right on using series to which that definition did not apply (divergent series) for half a century before rigorous definitions of sum were found for these as well. If there was nothing unreasonable in the attitude of Leibniz and his successors—and in view of the great successes of mathematics and physics during the period it would be hard to argue that there was—why should there be thought to be anything unreasonable in retention, at any rate outside of fully rigorous pure mathematics, of a notion of truth found to be inconsistent in cases that in practice are seldom encountered and easily recognized when they are?

  All theories of the nature of truth, deflationist or inflationist, are controversial, and that is even more emphatically so for all approaches to the paradoxes. There is an understandable tendency for a philosopher already committed to a controversial position on one topic to want to avoid further controversies on others. Yet we would like to urge that a theory of the nature of truth can only really be satisfying if it can be matched with a satisfactory account of the paradoxes of truth.

  It is widely held that since deflationism holds truth to have no nature, and only by appeal to some substantive nature of truth could one hope to solve the paradoxes, deflationism will have a harder time than its rivals dealing with them. This opinion, however, assumes that the paradoxes are to be dealt with by solving them, rather than by declaring them insoluble. We would like to suggest, on the contrary, that at present deflationism is ahead of its rivals precisely because it is well matched with an approach to the paradoxes, namely, the inconsistency theory, while other theories of the nature of truth remain without an obvious, natural partner.

  The background assumptions about meaning behind an integrated deflationist/defeatist theory might run as follows. Meaning can be given by rules (as on a holist account of the kind considered in §6.5), for there can be no objection to positing rules in semantics, given that linguists have been freely positing them in syntax and phonology ever since the downfall of behaviorism. Rules, however, can be inconsistent, and there is even a result in mathematical logic (Church's theorem) to the effect that there is no mechanical test for inconsistency of rules, making it unlikely we have any filter preventing us from ever internalizing inconsistencies. If we sometimes do so, we'll need some override mechanism to halt the operation of rules in emergencies, as a computer may stop and return a message of “TOO MUCH RECURSION” if it finds itself going round and round the same loop; and though internalizing rules may or may not be a matter of acquiring dispositions, it is certainly not a matter of acquiring irresistible compulsions, so there is no conceptual obstacle to positing such an emergency override mechanism. Such a general mechanism for suspending rules would make building separate safeguards into the rules for each separate term superfluous. Its operation would be in evidence whenever we felt the tug of the rules but resisted it, whenever we found a step intuitive, and yet refrained from taking it.

  Given such background assumptions, the specific claim about the truth predicate might be that its meaning is given by T-introduction and T-elimination rules, with no subtle and sophisticated restrictions to evade paradox, and these rules are simply inconsistent. The fact that each step in the liar paradox reasoning is felt to be intuitive, though we refrain from inferring arbitrary conclusions, would be construed as a case of the postulated general fail-safe mechanism at work.

  Whether or not such ideas are ultimately tenable, whether or not such an attempt to integrate the deflationist and inconsistency theories can ultimately succeed, we would suggest that the next step in the development of the theory of truth must be the closer integration of views about its nature with views about its paradoxes, if not in the way just sketched, then in some other.

  Further Reading

  THE TOPIC OF TRUTH leads off in multiple directions into others. Let us list some sources where the reader interested in one or another of these directions can pursue it further, taking the various topics in order by the chapter in this work to which they are most pertinent.

  Introduction. We have said that a satisfactory account of the nature of truth must incorporate an account of the paradoxes. One might add that it really ought also to incorporate accounts of approximate truth and of the value of truth, a pair of topics we set aside at the beginning of our survey as beyond its scope. The interested reader can make a start on the study of the first of the pair with Oddie (2008), which like other entries in the reference work of which it is a part offers an ample bibliography. The sort of thing analytic philosophers have found to say (mainly in opposition to postmodernism) about the second of the pair can be seen from Blackburn (2005), Lynch (2005), and most concisely
Frankfurt (2008). As to the issues we have not set aside, among single-author surveys with emphases different from ours we have found the article Glanzberg (2004) and the book Kirkham (1992) most useful. (We have borrowed the terminology congruence vs correlation from the latter, for instance.) Künne (2003) and Schmidt (1995) may also be mentioned.

  The reader with historical interests will find Candlish and Damnjanovic (2007) very useful. Such readers will ultimately also want to look at the actual formulations of Joachim, James, Russell, and other historical figures themselves. The Oxford Readings anthology Blackburn and Simmons (1999) conveniently makes available a number of historic texts going back to Frege, including selections from the three authors just named, the contributions of Austin and Strawson to their famous Aristotelian Society symposium, the passages in Ramsey that became the wellspring of deflationism, and more—as well as concise statements of their views by authors still actively contributing today. The rival anthology of Lynch (2001) contains similar material, along with material from the coherentist and pragmatist traditions (ranging from Blanshard to Putnam and Rorty). The reader whose interest is really piqued by coherentism may consult the survey Young (2008), or for a somewhat idiosyncratic book-length treatment, Walker (1989). The Lynch volume even includes token representation of Continental views, though unfortunately Nietzsche (1873/1954) is missing, along with anything from Jürgen Habermas.

  For the ins and outs of propositionalism vs sententialism, see Soames's volume Philosophy of Language in the present series.

  Tarski. The monumental monograph of Tarski (1935/1956) is tough going for any reader, but the volume cited for the English translations also contains translations of some of Tarski's semi-popular expositions of the same ideas, complementing our discussion in chapter 2. For the impact of Tarski on logic, see any contemporary textbook, for instance, Boolos, Burgess, and Jeffrey (2007). See Patterson (2008) for a wide range of views on Tarski, with emphasis on his impact on philosophy.

  Deflationism. The Lynch anthology contains material from Quine (1990) and Field (1994) on disquotationalism, but the fullest collection of material on that topic is to be found in Armour-Garb and Beall (2005), an anthology entirely devoted to the pros and cons of deflationism in the various guises we discussed in chapter 3 and others besides. There one can find the Pittsburgh philosophers Brandom (neoprosentialism) and Gupta (antideflationism) debating each other, for instance. But for the somewhat idiosyncratic “thick deflationism” of McGinn one will have to turn to another useful collection, Schantz (2001), which consists entirely of essays written specially for that volume; while for the objection that there is a need for a “transcendent” application of the truth predicate one should see Shapiro (2003). If all this is not enough, Grover (1992) and Horwich (1990) have provided book-length expositions of their views, with responses to critics. The former incorporates the minor classic Grover et al. (1972), the latter amounts to a little catechism of minimalism. J. P. Burgess (2002) defends an idiosyncratic view on the optimal formulation of deflationism that we have not insisted upon here. For an overview with different emphases from ours, see Stoljar and Damnjanovic (2009).

  Indeterminacy. The philosophical literature on the topics we introduce in chapter 4 is enormous, though unfortunately the connections with the literature on the nature of truth are often made only in scattered passages. For a logical approach to vagueness we barely mentioned in passing, see Hajek (2009), which provides basic information and references on fuzzy logic and the view that truth comes in numerical degrees. Fuzzy logic is criticized by Haack (1996), which also treats other nonclassical logics, while Smith (2008) defends an elaborate numerical-degrees theory.

  There is a recent whole anthology Kölbel and García-Carpintero (2008) devoted to MacFarlane-style relativism, including a contribution by MacFarlane himself, while Field (2001) has published a collection of his lengthy papers on truth and “nonfactualism.” See also Boghossian (2006) for a fuller enunciation of the arguments we sketchily indicated in our discussion of global vs local.

  Realism. The spread of views called “realism” in the literature is even wider than what we have indicated in chapter 5. Like deflationist theories, realist theories have their own anthology, Greenough and Lynch (2006), though the editors' conception of “realism” differs from that adopted in this book. Hill (2002) sees less incompatibility between deflationism and realism than most others, and Alston (1996) offers a quasideflationist version of realism.

  As to unblushingly metaphysical theories, see David (2009) for a survey of correspondence views. For the identity theory, which we barely mention, see the article Candlish (2008), or for advocacy of a particular version, the book Dodd (1981). See Armstrong (2004) for the fullest statement of the views of the preeminent truthmaker theorist, addressing in particular issues about negative and general truths. Merricks (2007) surveys the metaphysical controversies over truthmakers, supervenience, and more, from a critical point of view. For an even more critical point of view, see Soames (2008). And then there is the unforgettable “fuggedaboutit” paper Lewis (2001).

  And as to physicalist theories, Field (1972), castigating Tarski for his insufficient “physicalism,” is classic, as for that matter is the reply of Soames (1984) (which also includes a brief version of the argument that the question whether all truth is verifiable isn't really about truth). A more-or-less physicalist position is taken in Devitt (1997), to be compared with the same author's earlier work on causal theories of reference (1981). Related works of Putnam (1978) and Leeds (1978) concern, among other things, the utility issue. Price (1989) is a large-scale study by a writer whose position on truth is best known for his emphasis on normativity.

  Antirealism. Practically everything Dummett has written—and he has written a lot, from Dummett (1959), the locus classicus for the normativity objection to deflationism, onwards—is related to his antirealism. The less technical first half of Dummett (1973) is perhaps the place to start tackling that author's works. J. P. Burgess (1984) is one of many, many replies this work has provoked.

  The background literature on Davidsonianism, often Dummett's ultimate target even if Dummett seldom mentions Donald Davidson by name, is again enormous, though works explicitly connecting it to debates over the nature of truth are less common than one might expect. The Soames volume in this series contains extended discussion of the ups and downs of the Davidson program. The statement of Davidson (1996) himself, endorsing primitivism, is of course a must-read. Bar-On et al. (2001) is also important. See Lepore and Ludwig (2007) for, among many other things, a version of “Davidsonianism” that, if it does not exactly minimize the role of truth in truth-conditional semantics, anyhow maximizes the indirectness of that role.

  For pluralism see Wright (1992), a work containing much more than the ideas we have sketched and criticized, and Lynch (2009), a work heavily influenced thereby, and much concerned to address the objection about mixed inferences, for which the locus classicus is Tappolet (1997). Among even newer views than pluralism, about which no very large literature has yet gathered, but which can be expected to generate discussion, Richard (2008) will repay study, as may Millgram (2009).

  Kripke. There is no substitute for tackling Kripke (1975), directly—and one can say the same thing for Kripke (1972), though it has played only a walk-on part in our discussion. How far Kripke transformed discussion of the paradoxes becomes clear on comparing the pre- and post-Kripke anthologies Martin (1970) and Martin (1984). Some guidance beyond what we were able to provide in chapter 7 may be desirable. Soames (1999) is especially recommended, and not just for its treatment of Kripke. Martin and Woodruff (1975) is the most important precursor of Kripke's theory of truth on its technical side. Visser (1989) is, for those with the requisite background in logic, one of the earliest and still one of the best comparative guides to Kripke and his revisionist rivals. As to Kripke's successors, shorter and longer statements of such revisionist positions can be found in the various works of He
rzberger, Gupta, and Belnap listed in our bibliography below; for further advocacy see Yaqub (1993), and for a more neutral survey, Kremer (2009).

  We have written as if there were a clear separation between technical additions and amendments to Kripke and philosophical discussions of the paradoxes, but a look at the actual literature will show that many works straddle the border. That is clearly the case with Barwise and Etchemendy (1987), which consists partly of a formal reconstruction of a Kripke-type theory using Peter Aczel's theory of non-well-founded sets, but also of an attempted solution to the paradoxes drawing (remote) inspiration from Austin. Likewise with McGee (1991), which gives a treatment of the paradoxes of truth and of vagueness making heavy use of a notion of determinateness, besides including substantial exposition and evaluation of Kripke's theory. (A little gem by the same author, McGee (1992), shows that the policy “Retain as many instances of the T-scheme as possible without inconsistency” leads to no definite result.) And then there is Field (2008), presenting, along with a good deal of informative discussion of earlier proposals, an elaborate construction claimed to be “revenge-free.” That claim seems to have been a main impetus for putting together the anthology Beall (2007). Among critiques of Field there, Rayo and Welch (2007) may be the most useful.

  Only the reader well trained in logic will want to tackle the work on complexity of J. P. Burgess (1987/1988) and Welch (2009) (to cite only the most recent contribution of that prolific author). For axiomatic theories, the forthcoming studies by Halbach (2011) and Horsten (2011) will be indispensable, and perhaps more accessible than the seminal papers of Feferman (1991) and Friedman and Sheard (1987). Versions of the curious objection to deflationism based on the “nonconservativeness” of truth theories can be found in Shapiro (1998) and Ketland (1999); such criticisms are one of the topics discussed by Horsten, who is specifically concerned with axiomatic theories and deflationism.