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The Pragmatic Theory of Truth

1. History of the Pragmatic Theory of Truth

1.3 Dewey’s Pragmatic Theory of Truth

truth-pragmatic

First published Thu Mar 21, 2019

Dewey has an expansive understanding of “science”. For Dewey, science emerges from and is continuous with everyday processes of trial and error—cooking and small-engine repair count as “scientific” on his account—which means he should not be taken too strictly when he equates truth with scientific verification. (Peirce and James also had expansive understandings of science.) Rather, Dewey’s point is that true propositions, when acted on, lead to the sort of predictable and dependable outcomes that are hallmarks of scientific verification, broadly construed. From a pragmatic standpoint, scientific verification boils down to the process of matching up expectations with outcomes, a process that gives us all the “correspondence” we could ask for.

The Pragmatic Theory of Truth

1. History of the Pragmatic Theory of Truth

1.3 Dewey’s Pragmatic Theory of Truth

truth-pragmatic

First published Thu Mar 21, 2019

Dewey eventually came to believe that conventional philosophical terms such as “truth” and “knowledge” were burdened with so much baggage, and had become so fossilized, that it was difficult to grasp the practical role these terms had originally served. As a result, in his later writings Dewey largely avoids speaking of “truth” or “knowledge” while focusing instead on the functions played by these concepts. By his 1938 Logic: The Theory of Inquiry Dewey was speaking of “warranted assertibility” as the goal of inquiry, using this term in place of both “truth” and “knowledge” (1938 [2008: 15–16]). In 1941, in a response to Russell entitled “Propositions, Warranted Assertibility, and Truth”, he wrote that “warranted assertibility” is a “definition of the nature of knowledge in the honorific sense according to which only true beliefs are knowledge” (1941: 169). Here Dewey suggests that “warranted assertibility” is a better way of capturing the function of both knowledge and truth insofar as both are goals of inquiry. His point is that it makes little difference, pragmatically, whether we describe the goal of inquiry as “acquiring more knowledge”, “acquiring more truth”, or better yet, “making more warrantably assertible judgments”.

The Pragmatic Theory of Truth

1. History of the Pragmatic Theory of Truth

1.3 Dewey’s Pragmatic Theory of Truth

truth-pragmatic

First published Thu Mar 21, 2019

Because it focuses on truth’s function as a goal of inquiry, Dewey’s pragmatic account of truth has some unconventional features. To begin with, Dewey reserves the term “true” only for claims that are the product of controlled inquiry. This means that claims are not true before they are verified but that, rather, it is the process of verification that makes them true:

The Pragmatic Theory of Truth

1. History of the Pragmatic Theory of Truth

1.3 Dewey’s Pragmatic Theory of Truth

truth-pragmatic

First published Thu Mar 21, 2019

truth and falsity are properties only of that subject-matter which is the end, the close, of the inquiry by means of which it is reached. (1941: 176)

The Pragmatic Theory of Truth

1. History of the Pragmatic Theory of Truth

1.3 Dewey’s Pragmatic Theory of Truth

truth-pragmatic

First published Thu Mar 21, 2019

Second, Dewey insists that only “judgments”—not “propositions”—are properly viewed as truth-bearers. For Dewey, “propositions” are the proposals and working hypotheses that are used, via a process of inquiry, to generate conclusions and verified judgments. As such, propositions may be more or less relevant to the inquiry at hand but they are not, strictly speaking true or false (1941: 176). Rather, truth and falsity are reserved for “judgments” or “the settled outcome of inquiry” (1941: 175; 1938 [2008: 124]; Burke 1994): for claims, in other words, that are warrantedly assertible. Third, Dewey continues to argue that this pragmatic approach to truth is “the only one entitled to be called a correspondence theory of truth” (1941: 179) using terms nearly identical to those he used in 1911:

The Pragmatic Theory of Truth

1. History of the Pragmatic Theory of Truth

1.3 Dewey’s Pragmatic Theory of Truth

truth-pragmatic

First published Thu Mar 21, 2019

My own view takes correspondence in the operational sense…of answering, as a key answers to conditions imposed by a lock, or as two correspondents “answer” each other; or, in general, as a reply is an adequate answer to a question or criticism—; as, in short, a solution answers the requirements of a problem. (1941: 178)

The Pragmatic Theory of Truth

1. History of the Pragmatic Theory of Truth

1.3 Dewey’s Pragmatic Theory of Truth

truth-pragmatic

First published Thu Mar 21, 2019

Thanks to Russell (e.g., 1941: Ch. XXIII) and others, by 1941 Dewey was aware of the problems facing pragmatic accounts of truth. In response, we see him turning to the language of “warranted assertibility”, drawing a distinction between “propositions” and “judgments”, and grounding the concept of truth (or warranted assertibility) in scientific inquiry (Thayer 1947; Burke 1994). These adjustments were designed to extend, clarify, and improve on Peirce’s and James’ accounts. Whether they did so is an open question. Certainly many, such as Quine, concluded that Dewey was only sidestepping important questions about truth: that Dewey’s strategy was “simply to avoid the truth predicate and limp along with warranted belief” (Quine 2008: 165).

The Pragmatic Theory of Truth

1. History of the Pragmatic Theory of Truth

1.3 Dewey’s Pragmatic Theory of Truth

truth-pragmatic

First published Thu Mar 21, 2019

Peirce, James, and Dewey were not the only ones to propose or defend a pragmatic theory of truth in the nineteenth and early twentieth centuries. Others, such as F.C.S. Schiller (1864–1937), also put forward pragmatic theories (though Schiller’s view, which he called “humanism”, also attracted more than its share of critics, arguably for very good reasons). Pragmatic theories of truth also received the attention of prominent critics, including Russell (1909, 1910 [1994]), Moore (1908), Lovejoy (1908a,b) among others. Several of these criticisms will be considered later; suffice it to say that pragmatic theories of truth soon came under pressure that led to revisions and several successor approaches over the next hundred-plus years.

The Pragmatic Theory of Truth

1. History of the Pragmatic Theory of Truth

1.3 Dewey’s Pragmatic Theory of Truth

truth-pragmatic

First published Thu Mar 21, 2019

Historically Peirce, James, and Dewey had the greatest influence in setting the parameters for what makes a theory of truth pragmatic—this despite the sometimes significant differences between their respective accounts, and that over time they modified and clarified their positions in response to both criticism and over-enthusiastic praise. While this can make it difficult to pin down a single definition of what, historically, counted as a pragmatic theory of truth, there are some common themes that cut across each of their accounts. First, each account begins from a pragmatic analysis of the meaning of the truth predicate. On the assumption that describing a belief, claim, or judgment as “true” must make some kind of practical difference, each of these accounts attempts to describe what this difference is. Second, each account then connects truth specifically to processes of inquiry: to describe a claim as true is to say that it either has or will stand up to scrutiny. Third, each account rejects correspondence theories of truth as overly abstract, “transcendental”, or metaphysical. Or, more accurately, each attempts to redefine correspondence in pragmatic terms, as the agreement between a claim and a predicted outcome. While the exact accounts offered by Peirce, James, and Dewey found few defenders—by the mid-twentieth century pragmatic theories of truth were largely dormant—these themes did set a trajectory for future versions of the pragmatic theory of truth.

The Pragmatic Theory of Truth

2. Neo-Pragmatic Theories of Truth

truth-pragmatic

First published Thu Mar 21, 2019

Pragmatic theories of truth enjoyed a resurgence in the last decades of the twentieth century. This resurgence was especially visible in debates between Hilary Putnam (1926–2016) and Richard Rorty (1931–2007) though broadly pragmatic ideas were defended by other philosophers as well (Bacon 2012: Ch. 4). (One example is Crispin Wright’s superassertibility theory (1992, 2001) which he claims is “as well equipped to express the aspiration for a developed pragmatist conception of truth as any other candidate” (2001: 781) though he does not accept the pragmatist label.) While these “neo-pragmatic” theories of truth sometimes resembled the classical pragmatic accounts of Peirce, James, or Dewey, they also differed significantly, often by framing the concept of truth in explicitly epistemic terms such as assertibility or by drawing on intervening developments in the field.

The Pragmatic Theory of Truth

2. Neo-Pragmatic Theories of Truth

truth-pragmatic

First published Thu Mar 21, 2019

At the outset, neo-pragmatism was motivated by a renewed dissatisfaction with correspondence theories of truth and the metaphysical frameworks supporting them. Some neo-pragmatic theories of truth grew out of a rejection of metaphysical realism (e.g., Putnam 1981; for background see Khlentzos 2016). If metaphysical realism cannot be supported then this undermines a necessary condition for the correspondence theory of truth: namely, that there be a mind-independent reality to which propositions correspond. Other neo-pragmatic approaches emerged from a rejection of representationalism: if knowledge is not the mind representing objective reality—if we cannot make clear sense of how the mind could be a “mirror of nature” to use Rorty’s (1979) term—then we are also well-advised to give up thinking of truth in realist, correspondence terms. Despite these similar starting points, neo-pragmatic theories took several different and evolving forms over the final decades of the twentieth century.

The Pragmatic Theory of Truth

2. Neo-Pragmatic Theories of Truth

truth-pragmatic

First published Thu Mar 21, 2019

At one extreme some neo-pragmatic theories of truth seemed to endorse relativism about truth (whether and in what sense they did remains a point of contention). This view was closely associated with influential work by Richard Rorty (1982, 1991a,b). The rejection of representationalism and the correspondence theory of truth led to the conclusion that inquiry is best viewed as aiming at agreement or “solidarity”, not knowledge or truth as these terms are traditionally understood. This had the radical consequence of suggesting that truth is no more than “what our peers will, ceteris paribus, let us get away with saying” (Rorty 1979: 176; Rorty [2010a: 45] admits this phrase is provocative) or just “an expression of commendation” (Rorty 1991a: 23). Not surprisingly, many found this position deeply problematic since it appears to relativize truth to whatever one’s audience will accept (Baghramian 2004: 147). A related concern is that this position also seems to conflate truth with justification, suggesting that if a claim meets contextual standards of acceptability then it also counts as true (Gutting 2003). Rorty for one often admitted as much, noting that he tended to “swing back and forth between trying to reduce truth to justification and propounding some form of minimalism about truth” (1998: 21).

The Pragmatic Theory of Truth

2. Neo-Pragmatic Theories of Truth

truth-pragmatic

First published Thu Mar 21, 2019

A possible response to the accusation of relativism is to claim that this neo-pragmatic approach does not aim to be a full-fledged theory of truth. Perhaps truth is actually a rather light-weight concept and does not need the heavy metaphysical lifting implied by putting forward a “theory”. If the goal is not to describe what truth is but rather to describe how “truth” is used, then these uses are fairly straightforward: among other things, to make generalizations (“everything you said is true”), to commend (“so true!”), and to caution (“what you said is justified, but it might not be true”) (Rorty 1998: 22; 2000: 4). None of these uses requires that we embark on a possibly fruitless hunt for the conditions that make a proposition true, or for a proper definition or theory of truth. If truth is “indefinable” (Rorty 2010b: 391) then this account cannot be definition or theory of truth, relativist or otherwise.

The Pragmatic Theory of Truth

2. Neo-Pragmatic Theories of Truth

truth-pragmatic

First published Thu Mar 21, 2019

This approach differs in some noteworthy ways from earlier pragmatic accounts of truth. For one thing it is able to draw on, and draw parallels with, a range of well-developed non-correspondence theories of truth that begin (and sometimes end) by stressing the fundamental equivalence of “S is p” and “‘S is p’ is true”. These theories, including disquotationalism, deflationism, and minimalism, simply were not available to earlier pragmatists (though Peirce does at times discuss the underlying notions). Furthermore, while Peirce and Dewey, for example, were proponents of scientific inquiry and scientific processes of verification, on this neo-pragmatic approach science is no more objective or rational than other disciplines: as Rorty put it, “the only sense in which science is exemplary is that it is a model of human solidarity” (1991b: 39). Finally, on this approach Peirce, James, and Dewey simply did not go far enough: they failed to recognize the radical implications of their accounts of truth, or else failed to convey these implications adequately. In turn much of the critical response to this kind of neo-pragmatism is that it goes too far by treating truth merely as a sign of commendation (plus a few other functions). In other words, this type of neo-pragmatism goes to unpragmatic extremes (e.g., Haack 1998; also the exchange in Rorty & Price 2010).

The Pragmatic Theory of Truth

2. Neo-Pragmatic Theories of Truth

truth-pragmatic

First published Thu Mar 21, 2019

A less extreme version of neo-pragmatism attempts to preserve truth’s objectivity and independence while still rejecting metaphysical realism. This version was most closely associated with Hilary Putnam, though Putnam’s views changed over time (see Hildebrand 2003 for an overview of Putnam’s evolution). While this approach frames truth in epistemic terms—primarily in terms of justification and verification—it amplifies these terms to ensure that truth is more than mere consensus. For example, this approach might identify “being true with being warrantedly assertible under ideal conditions” (Putnam 2012b: 220). More specifically, it might demand “that truth is independent of justification here and now, but not independent of all justification” (Putnam 1981: 56).

The Pragmatic Theory of Truth

2. Neo-Pragmatic Theories of Truth

truth-pragmatic

First published Thu Mar 21, 2019

Rather than play up assertibility before one’s peers or contemporaries, this neo-pragmatic approach frames truth in terms of ideal warranted assertibility: namely, warranted assertibility in the long run and before all audiences, or at least before all well-informed audiences. Not only does this sound much less relativist but it also bears a strong resemblance to Peirce’s and Dewey’s accounts (though Putnam, for one, resisted the comparison: “my admiration for the classical pragmatists does not extend to any of the different theories of truth that Peirce, James, and Dewey advanced” [2012c: 70]).

The Pragmatic Theory of Truth

2. Neo-Pragmatic Theories of Truth

truth-pragmatic

First published Thu Mar 21, 2019

To repeat, this neo-pragmatic approach is designed to avoid the problems facing correspondence theories of truth while still preserving truth’s objectivity. In the 1980s this view was associated with Putnam’s broader program of “internal realism”: the idea that “what objects does the world consist of? is a question that it only makes sense to ask within a theory or description” (Putnam 1981: 49, emphasis in original). Internal realism was designed as an alternative to metaphysical realism that dispensed with achieving an external “God’s Eye Point of View” while still preserving truth’s objectivity, albeit internal to a given theory. (For additional criticisms of metaphysical realism see Khlentzos 2016.) In the mid-1990s Putnam’s views shifted toward what he called “natural realism” (1999; for a critical discussion of Putnam’s changing views see Wright 2000). This shift came about in part because of problems with defining truth in epistemic terms such as ideal warranted assertibility. One problem is that it is difficult to see how one can verify either what these ideal conditions are or whether they have been met: one might attempt to do so by taking an external “god’s eye view”, which would be inconsistent with internal realism, or one might come to this determination from within one’s current theory, which would be circular and relativistic. (As Putnam put it, “to talk of epistemically ‘ideal’ connections must either be understood outside the framework of internal realism or it too must be understood in a solipsistic manner ” (2012d: 79–80).) Since neither option seems promising this does not bode well for internal realism or for any account of truth closely associated with it.

The Pragmatic Theory of Truth

2. Neo-Pragmatic Theories of Truth

truth-pragmatic

First published Thu Mar 21, 2019

If internal realism cannot be sustained then a possible fallback position is “natural realism”—the view “that the objects of (normal ‘veridical’) perception are ‘external’ things, and, more generally, aspects of ‘external’ reality” (Putnam 1999: 10)—which leads to a reconciliation of sorts with the correspondence theory of truth. A natural realism suggests “that true empirical statements correspond to states of affairs that actually obtain” (Putnam 2012a: 97), though this does not commit one to a correspondence theory of truth across the board. Natural realism leaves open the possibility that not all true statements “correspond” to a state of affairs, and even those that do (such as empirical statements) do not always correspond in the same way (Putnam 2012c: 68–69; 2012a: 98). While not a ringing endorsement of the correspondence theory of truth, at least as traditionally understood, this neo-pragmatic approach is not a flat-out rejection either.

The Pragmatic Theory of Truth

2. Neo-Pragmatic Theories of Truth

truth-pragmatic

First published Thu Mar 21, 2019

Viewing truth in terms of ideal warranted assertibility has obvious pragmatic overtones of Peirce and Dewey. Viewing truth in terms of a commitment to natural realism is not so clearly pragmatic though some parallels still exist. Because natural realism allows for different types of truth-conditions—some but not all statements are true in virtue of correspondence—it is compatible with the truth-aptness of normative discourse: just because ethical statements, for example, do not correspond in an obvious way to ethical state of affairs is no reason to deny that they can be true (Putnam 2002). In addition, like earlier pragmatic theories of truth, this neo-pragmatic approach redefines correspondence: in this case, by taking a pluralist approach to the correspondence relation itself (Goodman 2013).

The Pragmatic Theory of Truth

2. Neo-Pragmatic Theories of Truth

truth-pragmatic

First published Thu Mar 21, 2019

These two approaches—one tending toward relativism, the other tending toward realism—represented the two main currents in late twentieth century neo-pragmatism. Both approaches, at least initially, framed truth in terms of justification, verification, or assertibility, reflecting a debt to the earlier accounts of Peirce, James, and Dewey. Subsequently they evolved in opposite directions. The first approach, often associated with Rorty, flirts with relativism and implies that truth is not the important philosophical concept it has long been taken to be. Here, to take a neo-pragmatic stance toward truth is to recognize the relatively mundane functions this concept plays: to generalize, to commend, to caution and not much else. To ask for more, to ask for something “beyond the here and now”, only commits us to “the banal thought that we might be wrong” (Rorty 2010a: 45). The second neo-pragmatic approach, generally associated with Putnam, attempts to preserve truth’s objectivity and the important role it plays across scientific, mathematical, ethical, and political discourse. This could mean simply “that truth is independent of justification here and now” or “that to call a statement of any kind…true is to say that it has the sort of correctness appropriate to the kind of statement it is” (2012a: 97–98). On this account truth points to standards of correctness more rigorous than simply what our peers will let us get away with saying.

The Pragmatic Theory of Truth

3. Truth as a Norm of Inquiry and Assertion

truth-pragmatic

First published Thu Mar 21, 2019

More recently—since roughly the turn of the twenty-first century—pragmatic theories of truth have focused on truth’s role as a norm of assertion or inquiry. These theories are sometimes referred to as “new pragmatic” theories to distinguish them from both classical and neo-pragmatic accounts (Misak 2007b; Hookway 2016). Like neo-pragmatic accounts, these theories often build on, or react to, positions besides the correspondence theory: for example, deflationary, minimal, and pluralistic theories of truth. Unlike some of the neo-pragmatic accounts discussed above, these theories give relativism a wide berth, avoid defining truth in terms of concepts such as warranted assertibility, and treat correspondence theories of truth with deep suspicion.

The Pragmatic Theory of Truth

3. Truth as a Norm of Inquiry and Assertion

truth-pragmatic

First published Thu Mar 21, 2019

On these accounts truth plays a unique and necessary role in assertoric discourse (Price 1998, 2003, 2011; Misak 2000, 2007a, 2015): without the concept of truth there would be no difference between making assertions and, to use Frank Ramsey’s nice phrase, “comparing notes” (1925 [1990: 247]). Instead, truth provides the “convenient friction” that “makes our individual opinions engage with one another” (Price 2003: 169) and “is internally related to inquiry, reasons, and evidence” (Misak 2000: 73).

The Pragmatic Theory of Truth

3. Truth as a Norm of Inquiry and Assertion

truth-pragmatic

First published Thu Mar 21, 2019

Like all pragmatic theories of truth, these “new” pragmatic accounts focus on the use and function of truth. However, while classical pragmatists were responding primarily to the correspondence theory of truth, new pragmatic theories also respond to contemporary disquotational, deflationary, and minimal theories of truth (Misak 1998, 2007a). As a result, new pragmatic accounts aim to show that there is more to truth than its disquotational and generalizing function (for a dissenting view see Freedman 2006). Specifically, this “more” is that the concept of truth also functions as a norm that places clear expectations on speakers and their assertions. In asserting something to be true, speakers take on an obligation to specify the consequences of their assertion, to consider how their assertions can be verified, and to offer reasons in support of their claims:

The Pragmatic Theory of Truth

3. Truth as a Norm of Inquiry and Assertion

truth-pragmatic

First published Thu Mar 21, 2019

once we see that truth and assertion are intimately connected—once we see that to assert that p is true is to assert p—we can and must look to our practices of assertion and to the commitments incurred in them so as to say something more substantial about truth. (Misak 2007a: 70)

The Pragmatic Theory of Truth

3. Truth as a Norm of Inquiry and Assertion

truth-pragmatic

First published Thu Mar 21, 2019

Truth is not just a goal of inquiry, as Dewey claimed, but actually a norm of inquiry that sets expectations for how inquirers conduct themselves.

The Pragmatic Theory of Truth

3. Truth as a Norm of Inquiry and Assertion

truth-pragmatic

First published Thu Mar 21, 2019

More specifically, without the norm of truth assertoric discourse would be degraded almost beyond recognition. Without the norm of truth, speakers could be held accountable only for either insincerely asserting things they don’t themselves believe (thus violating the norm of “subjective assertibility”) or for asserting things they don’t have enough evidence for (thus violating the norm of “personal warranted assertibility”) (Price 2003: 173–174). The norm of truth is a condition for genuine disagreement between people who speak sincerely and with, from their own perspective, good enough reasons. It provides the “friction” we need to treat disagreements as genuinely needing resolution: otherwise, “differences of opinion would simply slide past one another” (Price 2003: 180–181). In sum, the concept of truth plays an essential role in making assertoric discourse possible, ensuring that assertions come with obligations and that conflicting assertions get attention. Without truth, it is no longer clear to what degree assertions would still be assertions, as opposed to impromptu speculations or musings. (Correspondence theories should find little reason to object: they too can recognize that truth functions as a norm. Of course, correspondence theorists will want to add that truth also requires correspondence to reality, a step “new” pragmatists will resisting taking.)

The Pragmatic Theory of Truth

3. Truth as a Norm of Inquiry and Assertion

truth-pragmatic

First published Thu Mar 21, 2019

It is important that this account of truth is not a definition or theory of truth, at least in the narrow sense of specifying necessary and sufficient conditions for a proposition being true. (That is, there is no proposal along the lines of “S is true iff…”; though see Brown (2015: 69) for a Deweyan definition of truth and Heney (2015) for a Peircean response.) As opposed to some versions of neo-pragmatism, which viewed truth as “indefinable” in part because of its supposed simplicity and transparency, this approach avoids definitions because the concept of truth is implicated in a complex range of assertoric practices. Instead, this approach offers something closer to a “pragmatic elucidation” of truth that gives “an account of the role the concept plays in practical endeavors” (Misak 2007a: 68; see also Wiggins 2002: 317).

The Pragmatic Theory of Truth

3. Truth as a Norm of Inquiry and Assertion

truth-pragmatic

First published Thu Mar 21, 2019

The proposal to treat truth as a norm of inquiry and assertion can be traced back to both classical and neo-pragmatist accounts. In one respect, this account can be viewed as adding on to neo-pragmatic theories that reduce truth to justification or “personal warranted assertibility”. In this respect, these newer pragmatic accounts are a response to the problems facing neo-pragmatism. In another respect, new pragmatic accounts can be seen as a return to the insights of classical pragmatists updated for a contemporary audience. For example, while Peirce wrote of beliefs being “fated” to be agreed upon at the “ideal limit” of inquiry—conditions that to critics sounded metaphysical and unverifiable—a better approach is to treat true beliefs as those “that would withstand doubt, were we to inquire as far as we fruitfully could on the matter” (Misak 2000: 49). On this account, to say that a belief is true is shorthand for saying that it “gets thing right” and “stands up and would continue to stand up to reasons and evidence” (Misak 2015: 263, 265). This pragmatic elucidation of the concept of truth attempts to capture both what speakers say and what they do when they describe a claim as true. In a narrow sense the meaning of truth—what speakers are saying when they use this word—is that true beliefs are indefeasible. However, in a broader sense the meaning of truth is also what speakers are doing when they use this word, with the proposal here that truth functions as a norm that is constitutive of assertoric discourse.

The Pragmatic Theory of Truth

3. Truth as a Norm of Inquiry and Assertion

truth-pragmatic

First published Thu Mar 21, 2019

As we have seen, pragmatic accounts of truth focus on the function the concept plays: specifically, the practical difference made by having and using the concept of truth. Early pragmatic accounts tended to analyze this function in terms of the practical implications of labeling a belief as true: depending on the version, to say that a belief is true is to signal one’s confidence, or that the belief is widely accepted, or that it has been scientifically verified, or that it would be assertible under ideal circumstances, among other possible implications. These earlier accounts focus on the function of truth in conversational contexts or in the context of ongoing inquiries. The newer pragmatic theories discussed in this section take a broader approach to truth’s function, addressing its role not just in conversations and inquiries but in making certain kinds of conversations and inquiries possible in the first place. By viewing truth as a norm of assertion and inquiry, these more recent pragmatic theories make the function of truth independent of what individual speakers might imply in specific contexts. Truth is not just what is assertible or verifiable (under either ideal or non-ideal circumstances), but sets objective expectations for making assertions and engaging in inquiry. Unlike neo-pragmatists such as Rorty and Putnam, new pragmatists such as Misak and Price argue that truth plays a role entirely distinct from justification or warranted assertibility. This means that, without the concept of truth and the norm it represents, assertoric discourse (and inquiry in general) would dwindle into mere “comparing notes”.

The Pragmatic Theory of Truth

4. Common Features

truth-pragmatic

First published Thu Mar 21, 2019

Pragmatic theories of truth have evolved to where a variety of different approaches are described as “pragmatic”. These theories often disagree significantly with each other, making it difficult either to define pragmatic theories of truth in a simple and straightforward manner or to specify the necessary conditions that a pragmatic theory of truth must meet. As a result, one way to clarify what makes a theory of truth pragmatic is to say something about what pragmatic theories of truth are not. Given that pragmatic theories of truth have often been put forward in contrast to prevailing correspondence and other “substantive” theories of truth (Wyatt & Lynch, 2016), this suggests a common commitment shared by the pragmatic theories described above.

The Pragmatic Theory of Truth

4. Common Features

truth-pragmatic

First published Thu Mar 21, 2019

One way to differentiate pragmatic accounts from other theories of truth is to distinguish the several questions that have historically guided discussions of truth. While some have used decision trees to categorize different theories of truth (Lynch 2001a; Künne 2003), or have proposed family trees showing relations of influence and affinity (Haack 1978), another approach is to distinguish separate “projects” that examine different dimensions of the concept of truth (Kirkham 1992). (These projects also break into distinct subprojects; for a similar approach see Frapolli 1996.) On this last approach the first, “metaphysical”, project aims to identify the necessary and sufficient conditions for “what it is for a statement…to be true” (Kirkham 1992: 20; Wyatt & Lynch call this the “essence project” [2016: 324]). This project often takes the form of identifying what makes a statement true: e.g., correspondence to reality, or coherence with other beliefs, or the existence of a particular state of affairs. A second, “justification”, project attempts to specify “some characteristic, possessed by most true statements…by reference to which the probable truth or falsity of the statement can be judged” (Kirkham 1992: 20). This often takes the form of giving a criterion of truth that can be used to determine whether a given statement is true. Finally, the “speech-act” project addresses the question of “what are we doing when we make utterances” that “ascribe truth to some statement?” (Kirkham 1992: 28). Unfortunately, truth-theorists have not always been clear on which project they are pursuing, which can lead to confusion about what counts as a successful or complete theory of truth. It can also lead to truth-theorists talking past each other when they are pursuing distinct projects with different standards and criteria of success.

The Pragmatic Theory of Truth

4. Common Features

truth-pragmatic

First published Thu Mar 21, 2019

In these terms, pragmatic theories of truth are best viewed as pursuing the speech-act and justification projects. As noted above, pragmatic accounts of truth have often focused on how the concept of truth is used and what speakers are doing when describing statements as true: depending on the version, speakers may be commending a statement, signaling its scientific reliability, or committing themselves to giving reasons in its support. Likewise, pragmatic theories often focus on the criteria by which truth can be judged: again, depending on the version, this may involve linking truth to verifiability, assertibility, usefulness, or long-term durability. With regard to the speech-act and justification projects pragmatic theories of truth seem to be on solid ground, offering plausible proposals for addressing these projects. They are on much less solid ground when viewed as addressing the metaphysical project. As we will see, it is difficult to defend the idea, for example, that either utility, verifiability, or widespread acceptance are necessary and sufficient conditions for truth or are what make a statement true.

The Pragmatic Theory of Truth

4. Common Features

truth-pragmatic

First published Thu Mar 21, 2019

This would suggest that the opposition between pragmatic and correspondence theories of truth is partly a result of their pursuing different projects. From a pragmatic perspective, the problem with the correspondence theory is its pursuit of the metaphysical project that, as its name suggests, invites metaphysical speculation about the conditions which make sentences true—speculation that can distract from more central questions of how the truth predicate is used and how true beliefs are best recognized and acquired. (Pragmatic theories of truth are not alone in raising these concerns (David 2016).) From the standpoint of correspondence theories and other accounts that pursue the metaphysical project, pragmatic theories will likely seem incomplete, sidestepping the most important questions (Howat 2014). But from the standpoint of pragmatic theories, projects that pursue or prioritize the metaphysical project are deeply misguided and misleading.

The Pragmatic Theory of Truth

4. Common Features

truth-pragmatic

First published Thu Mar 21, 2019

This supports the following truism: a common feature of pragmatic theories of truth is that they focus on the practical function that the concept of truth plays. Thus, whether truth is a norm of inquiry (Misak), a way of signaling widespread acceptance (Rorty), stands for future dependability (Peirce), or designates the product of a process of inquiry (Dewey), among other things, pragmatic theories shed light on the concept of truth by examining the practices through which solutions to problems are framed, tested, asserted, and defended—and, ultimately, come to be called true. Pragmatic theories of truth can thus be viewed as making contributions to the speech-act and justification projects by focusing especially on the practices people engage in when they solve problems, make assertions, and conduct scientific inquiry. Of course, even though pragmatic theories of truth largely agree on which questions to address and in what order, this does not mean that they agree on the answers to these questions, or on how to best formulate the meaning and function of truth.

The Pragmatic Theory of Truth

4. Common Features

truth-pragmatic

First published Thu Mar 21, 2019

Another common commitment of pragmatic theories of truth—besides prioritizing the speech-act and justification projects—is that they do not restrict truth to certain topics or types of inquiry. That is, regardless of whether the topic is descriptive or normative, scientific or ethical, pragmatists tend to view it as an opportunity for genuine inquiry that incorporates truth-apt assertions. The truth-aptness of ethical and normative statements is a notable feature across a range of pragmatic approaches, including Peirce’s (at least in some of his moods, e.g., 1901b [1958: 8.158]), Dewey’s theory of valuation (1939), Putnam’s questioning of the fact-value dichotomy (2002), and Misak’s claim that “moral beliefs must be in principle responsive to evidence and argument” (2000: 94; for a dissenting view see Frega 2013). This broadly cognitivist attitude—that normative statements are truth-apt—is related to how pragmatic theories of truth de-emphasize the metaphysical project. As a result, from a pragmatic standpoint one of the problems with the correspondence theory of truth is that it can undermine the truth-aptness of normative claims. If, as the correspondence theory proposes, a necessary condition for the truth of a normative claim is the existence of a normative fact to which it corresponds, and if the existence of normative facts is difficult to account for (normative facts seem ontologically distinct from garden-variety physical facts), then this does not bode well for the truth-aptness of normative claims or the point of posing, and inquiring into, normative questions (Lynch 2009). If the correspondence theory of truth leads to skepticism about normative inquiry, then this is all the more reason, according to pragmatists, to sidestep the metaphysical project in favor of the speech-act and justification projects.

The Pragmatic Theory of Truth

4. Common Features

truth-pragmatic

First published Thu Mar 21, 2019

As we have seen, pragmatic theories of truth take a variety of different forms. Despite these differences, and despite often being averse to being called a “theory”, pragmatic theories of truth do share some common features. To begin with, and unlike many theories of truth, these theories focus on the pragmatics of truth-talk: that is, they focus on how truth is used as an essential step toward an adequate understanding of the concept of truth (indeed, this come close to being an oxymoron). More specifically, pragmatic theories look to how truth is used in epistemic contexts where people make assertions, conduct inquiries, solve problems, and act on their beliefs. By prioritizing the speech-act and justification projects, pragmatic theories of truth attempt to ground the concept of truth in epistemic practices as opposed to the abstract relations between truth-bearers (such as propositions or statements) and truth-makers (such as states of affairs) appealed to by correspondence theories (MacBride 2018). Pragmatic theories also recognize that truth can play a fundamental role in shaping inquiry and assertoric discourse—for example, by functioning as a norm of these practices—even when it is not explicitly mentioned. In this respect pragmatic theories are less austere than deflationary theories which limit the use of truth to its generalizing and disquotational roles. And, finally, pragmatic theories of truth draw no limits, at least at the outset, to the types of statements, topics, and inquiries where truth may play a practical role. If it turns out that a given topic is not truth-apt, this is something that should be discovered as a characteristic of that subject matter, not something determined by having chosen one theory of truth or another (Capps 2017).

The Pragmatic Theory of Truth

5. Critical Assessments

truth-pragmatic

First published Thu Mar 21, 2019

Pragmatic theories of truth have faced several objections since first being proposed. Some of these objections can be rather narrow, challenging a specific pragmatic account but not pragmatic theories in general (this is the case with objections raised by other pragmatic accounts). This section will look at more general objections: either objections that are especially common and persistent, or objections that pose a challenge to the basic assumptions underlying pragmatic theories more broadly.

The Pragmatic Theory of Truth

5. Critical Assessments

5.1 Three Classic Objections and Responses

truth-pragmatic

First published Thu Mar 21, 2019

Some objections are as old as the pragmatic theory of truth itself. The following objections were raised in response to James’ account in particular. While James offered his own responses to many of these criticisms (see especially his 1909 [1975]), versions of these objections often apply to other and more recent pragmatic theories of truth (for further discussion see Haack 1976; Tiercelin 2014).

The Pragmatic Theory of Truth

5. Critical Assessments

5.1 Three Classic Objections and Responses

truth-pragmatic

First published Thu Mar 21, 2019

One classic and influential line of criticism is that, if the pragmatic theory of truth equates truth with utility, this definition is (obviously!) refuted by the existence of useful but false beliefs, on the one hand, and by the existence of true but useless beliefs on the other (Russell 1910 [1994] and Lovejoy 1908a,b). In short, there seems to be a clear and obvious difference between describing a belief as true and describing it as useful:

The Pragmatic Theory of Truth

5. Critical Assessments

5.1 Three Classic Objections and Responses

truth-pragmatic

First published Thu Mar 21, 2019

when we say that a belief is true, the thought we wish to convey is not the same thought as when we say that the belief furthers our purposes; thus “true” does not mean “furthering our purposes”. (Russell 1910 [1994: 98])

The Pragmatic Theory of Truth

5. Critical Assessments

5.1 Three Classic Objections and Responses

truth-pragmatic

First published Thu Mar 21, 2019

While this criticism is often aimed especially at James’ account of truth, it plausibly carries over to any pragmatic theory. So whether truth is defined in terms of utility, long-term durability or assertibility (etc.), it is still an open question whether a useful or durable or assertible belief is, in fact, really true. In other words, whatever concept a pragmatic theory uses to define truth, there is likely to be a difference between that concept and the concept of truth (e.g., Bacon 2014 questions the connection between truth and indefeasibility).

The Pragmatic Theory of Truth

5. Critical Assessments

5.1 Three Classic Objections and Responses

truth-pragmatic

First published Thu Mar 21, 2019

A second and related criticism builds on the first. Perhaps utility, long-term durability, and assertibility (etc.) should be viewed not as definitions but rather as criteria of truth, as yardsticks for distinguishing true beliefs from false ones. This seems initially plausible and might even serve as a reasonable response to the first objection above. Falling back on an earlier distinction, this would mean that appeals to utility, long-term durability, and assertibility (etc.) are best seen as answers to the justification and not the metaphysical project. However, without some account of what truth is, or what the necessary and sufficient conditions for truth are, any attempt to offer criteria of truth is arguably incomplete: we cannot have criteria of truth without first knowing what truth is. If so, then the justification project relies on and presupposes a successful resolution to the metaphysical project, the latter cannot be sidestepped or bracketed, and any theory which attempts to do so will give at best a partial account of truth (Creighton 1908; Stebbing 1914).

The Pragmatic Theory of Truth

5. Critical Assessments

5.1 Three Classic Objections and Responses

truth-pragmatic

First published Thu Mar 21, 2019

And a third objection builds on the second. Putting aside the question of whether pragmatic theories of truth adequately address the metaphysical project (or address it at all), there is also a problem with the criteria of truth they propose for addressing the justification project. Pragmatic theories of truth seem committed, in part, to bringing the concept of truth down to earth, to explaining truth in concrete, easily confirmable, terms rather than the abstract, metaphysical correspondence of propositions to truth-makers, for example. The problem is that assessing the usefulness (etc.) of a belief is no more clear-cut than assessing its truth: beliefs may be more or less useful, useful in different ways and for different purposes, or useful in the short- or long-run. Determining whether a belief is really useful is no easier, apparently, than determining whether it is really true: “it is so often harder to determine whether a belief is useful than whether it is true” (Russell 1910 [1994: 121]; also 1946: 817). Far from making the concept of truth more concrete, and the assessment of beliefs more straightforward, pragmatic theories of truth thus seem to leave the concept as opaque as ever.

The Pragmatic Theory of Truth

5. Critical Assessments

5.1 Three Classic Objections and Responses

truth-pragmatic

First published Thu Mar 21, 2019

These three objections have been around long enough that pragmatists have, at various times, proposed a variety of responses. One response to the first objection, that there is a clear difference between utility (etc.) and truth, is to deny that pragmatic approaches are aiming to define the concept of truth in the first place. It has been argued that pragmatic theories are not about finding a word or concept that can substitute for truth but that they are, rather, focused on tracing the implications of using this concept in practical contexts. This is what Misak (2000, 2007a) calls a “pragmatic elucidation”. Noting that it is “pointless” to offer a definition of truth, she concludes that “we ought to attempt to get leverage on the concept, or a fix on it, by exploring its connections with practice” (2007a: 69; see also Wiggins 2002). It is even possible that James—the main target of Russell and others—would agree with this response. As with Peirce, it often seems that James’ complaint is not with the correspondence theory of truth, per se, as with the assumption that the correspondence theory, by itself, says much interesting or important about the concept of truth. (For charitable interpretations of what James was attempting to say see Ayer 1968, Chisholm 1992, Bybee 1984, Cormier 2001, 2011, and Perkins 1952; for a reading that emphasizes Peirce’s commitment to correspondence idioms see Atkins 2010.)

The Pragmatic Theory of Truth

5. Critical Assessments

5.1 Three Classic Objections and Responses

truth-pragmatic

First published Thu Mar 21, 2019

This still leaves the second objection: that the metaphysical project of defining truth cannot be avoided by focusing instead on finding the criteria for truth (the “justification project”). To be sure, pragmatic theories of truth have often been framed as providing criteria for distinguishing true from false beliefs. The distinction between offering a definition as opposed to offering criteria would suggest that criteria are separate from, and largely inferior to, a definition of truth. However, one might question the underlying distinction: as Haack (1976) argues,

The Pragmatic Theory of Truth

5. Critical Assessments

5.1 Three Classic Objections and Responses

truth-pragmatic

First published Thu Mar 21, 2019

the pragmatists’ view of meaning is such that a dichotomy between definitions and criteria would have been entirely unacceptable to them. (1976: 236)

The Pragmatic Theory of Truth

5. Critical Assessments

5.1 Three Classic Objections and Responses

truth-pragmatic

First published Thu Mar 21, 2019

If meaning is related to use (as pragmatists generally claim) then explaining how a concept is used, and specifying criteria for recognizing that concept, may provide all one can reasonably expect from a theory of truth. Deflationists have often made a similar point though, as noted above, pragmatists tend to find deflationary accounts excessively austere.

The Pragmatic Theory of Truth

5. Critical Assessments

5.1 Three Classic Objections and Responses

truth-pragmatic

First published Thu Mar 21, 2019

Even so, there is still the issue that pragmatic criteria of truth (whatever they are) do not provide useful insight into the concept of truth. If this concern is valid, then pragmatic criteria, ironically, fail the pragmatic test of making a difference to our understanding of truth. This objection has some merit: for example, if a pragmatic criterion of truth is that true beliefs will stand up to indefinite inquiry then, while it is possible to have true beliefs, “we are never in a position to judge whether a belief is true or not” (Misak 2000: 57). In that case it is not clear what good it serves to have a pragmatic criterion of truth. Pragmatic theories of truth might try to sidestep this objection by stressing their commitment to both the justification and the speech-act project. While pragmatic approaches to the justification project spell out what truth means in conversational contexts—to call a statement true is to cite its usefulness, durability, etc.—pragmatic approaches to the speech-act project point to what speakers do in using the concept of truth. This has the benefit of showing how the concept of truth—operating as a norm of assertion, say—makes a real difference to our understanding of the conditions on assertoric discourse. Pragmatic theories of truth are, as a result, wise to pursue both the justification and the speech-act projects. By itself, pragmatic approaches to the justification project are likely to disappoint.

The Pragmatic Theory of Truth

5. Critical Assessments

5.1 Three Classic Objections and Responses

truth-pragmatic

First published Thu Mar 21, 2019

These classic objections to the pragmatic theory of truth raise several important points. For one thing, they make it clear that pragmatic theories of truth, or at least some historically prominent versions of it, do a poor job if viewed as providing a strict definition of truth. As Russell and others noted, defining truth in terms of utility or similar terms is open to obvious counter-examples. This does not bode well for pragmatic attempts to address the metaphysical project. As a result, pragmatic theories of truth have evolved often by focusing on the justification and speech-act projects instead. This is not to say that each of the above objections have been met. It is still an open question whether the metaphysical project can be avoided as many pragmatic theories attempt to do (e.g., Fox 2008 argues that epistemic accounts such as Putnam’s fail to explain the value of truth as well as more traditional approaches do). It is also an open question whether, as they evolve in response to these objections, pragmatic theories of truth invite new lines of criticism.

The Revision Theory of Truth

1. Semiformal introduction

truth-revision

First published Fri Dec 15, 1995; substantive revision Tue Jun 2, 2015

Let's take a closer look at the sentence (1), given above:

The Revision Theory of Truth

1. Semiformal introduction

truth-revision

First published Fri Dec 15, 1995; substantive revision Tue Jun 2, 2015

(1) is not true. (1)

The Revision Theory of Truth

1. Semiformal introduction

truth-revision

First published Fri Dec 15, 1995; substantive revision Tue Jun 2, 2015

It will be useful to make the paradoxical reasoning explicit. First, suppose that

The Revision Theory of Truth

1. Semiformal introduction

truth-revision

First published Fri Dec 15, 1995; substantive revision Tue Jun 2, 2015

(1) is not true. (2)

The Revision Theory of Truth

1. Semiformal introduction

truth-revision

First published Fri Dec 15, 1995; substantive revision Tue Jun 2, 2015

It seems an intuitive principle concerning truth that, for any sentence p, we have the so-called T-biconditional

The Revision Theory of Truth

1. Semiformal introduction

truth-revision

First published Fri Dec 15, 1995; substantive revision Tue Jun 2, 2015

‘p’ is true iff p. (3)

The Revision Theory of Truth

1. Semiformal introduction

truth-revision

First published Fri Dec 15, 1995; substantive revision Tue Jun 2, 2015

(Here we are using ‘iff’ as an abbreviation for ‘if and only if’.) In particular, we should have

The Revision Theory of Truth

1. Semiformal introduction

truth-revision

First published Fri Dec 15, 1995; substantive revision Tue Jun 2, 2015

‘(1) is not true’ is true iff (1) is not true. (4)

The Revision Theory of Truth

1. Semiformal introduction

truth-revision

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Thus, from (2) and (4), we get

The Revision Theory of Truth

1. Semiformal introduction

truth-revision

First published Fri Dec 15, 1995; substantive revision Tue Jun 2, 2015

‘(1) is not true’ is true. (5)

The Revision Theory of Truth

1. Semiformal introduction

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Then we can apply the identity,

The Revision Theory of Truth

1. Semiformal introduction

truth-revision

First published Fri Dec 15, 1995; substantive revision Tue Jun 2, 2015

(1) = ‘(1) is not true.’ (6)

The Revision Theory of Truth

1. Semiformal introduction

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First published Fri Dec 15, 1995; substantive revision Tue Jun 2, 2015

to conclude that (1) is true. This all shows that if (1) is not true, then (1) is true. Similarly, we can also argue that if (1) is true then (1) is not true. So (1) seems to be both true and not true: hence the paradox. As stated above, the three-valued approach to the paradox takes the liar sentence, (1), to be neither true nor false. Exactly how, or even whether, this move blocks the above reasoning is a matter for debate.

The Revision Theory of Truth

1. Semiformal introduction

truth-revision

First published Fri Dec 15, 1995; substantive revision Tue Jun 2, 2015

The RTT is not designed to block reasoning of the above kind, but to model it-or most of it.[2] As stated above, the central idea is the idea of a revision process: a process by which we revise hypotheses about the truth-value of one or more sentences.

The Revision Theory of Truth

1. Semiformal introduction

truth-revision

First published Fri Dec 15, 1995; substantive revision Tue Jun 2, 2015

Consider the reasoning regarding the liar sentence, (1) above. Suppose that we hypothesize that (1) is not true. Then, with an application of the relevant T-biconditional, we might revise our hypothesis as follows:

The Revision Theory of Truth

1. Semiformal introduction

truth-revision

First published Fri Dec 15, 1995; substantive revision Tue Jun 2, 2015

Hypothesis: (1) is not true. T-biconditional: ‘(1) is not true’ is true iff (1) is not true. Therefore: ‘(1) is not true’ is true. Known identity: (1) = ‘(1) is not true’. Conclusion: (1) is true. New revised hypothesis: (1) is true.

The Revision Theory of Truth

1. Semiformal introduction

truth-revision

First published Fri Dec 15, 1995; substantive revision Tue Jun 2, 2015

We could continue the revision process, by revising our hypothesis once again, as follows:

The Revision Theory of Truth

1. Semiformal introduction

truth-revision

First published Fri Dec 15, 1995; substantive revision Tue Jun 2, 2015

New hypothesis: (1) is true. T-biconditional: ‘(1) is not true’ is true iff (1) is not true. Therefore: ‘(1) is not true’ is not true. Known identity: (1) = ‘(1) is not true’. Conclusion: (1) is not true. New new revised hypothesis: (1) is not true.

The Revision Theory of Truth

1. Semiformal introduction

truth-revision

First published Fri Dec 15, 1995; substantive revision Tue Jun 2, 2015

As the revision process continues, we flip back and forth between taking the liar sentence to be true and not true.

The Revision Theory of Truth

1. Semiformal introduction

truth-revision

First published Fri Dec 15, 1995; substantive revision Tue Jun 2, 2015

Example 1.1 It is worth seeing how this kind of revision reasoning works in a case with several interconnected sentences. Let's apply the revision idea to the following three sentences: (8) is true or (9) is true. (7) (7) is true. (8) (7) is not true. (9) Informally, we might reason as follows. Either (7) is true or (7) is not true. Thus, either (8) is true or (9) is true. Thus, (7) is true. Thus (8) is true and (9) is not true, and (7) is still true. Iterating the process once again, we get (8) is true, (9) is not true, and (7) is true. More formally, consider any initial hypothesis, h0, about the truth values of (7), (8) and (9). Either h0 says that (7) is true or h0 says that (7) is not true. In either case, we can use the T-biconditional to generate our revised hypothesis h1: if h0 says that (7) is true, then h1 says that ‘(7) is true’ is true, i.e. that (8) is true; and if h0 says that (7) is not true, then h1 says that ‘(7) is not true’ is true, i.e. that (9) is true. So h1 says that either (8) is true or (9) is true. So h2 says that ‘(8) is true or (9) is true’ is true. In other words, h2 says that (7) is true. So no matter what hypothesis h0 we start with, two iterations of the revision process lead to a hypothesis that (7) is true. Similarly, three or more iterations of the revision process, lead to the hypothesis that (7) is true, (8) is true and (9) is not true — regardless of our initial hypothesis. In Section 3, we will reconsider this example in a more formal context.

The Revision Theory of Truth

1. Semiformal introduction

truth-revision

First published Fri Dec 15, 1995; substantive revision Tue Jun 2, 2015

One thing to note is that, in Example 1.1, the revision process yields stable truth values for all three sentences. The notion of a sentence stably true in all revision sequences will be a central notion for the RTT. The revision-theoretic treatment contrasts, in this case, with the three-valued approach: on most ways of implementing the three-valued idea, all three sentences, (7), (8) and (9), turn out to be neither true nor false.[3] In this case, the RTT arguably better captures the correct informal reasoning than does the three-valued approach: the RTT assigns to the sentences (7), (8) and (9) the truth-values that were assigned to them by the informal reasoning given at the beginning of the example.

The Revision Theory of Truth

2. Framing the problem

2.1 Truth languages

truth-revision

First published Fri Dec 15, 1995; substantive revision Tue Jun 2, 2015

The goal of the RTT is not to give a paradox-free account of truth. Rather, the goal of the RTT is to give an account of our often unstable and often paradoxical reasoning about truth. RTT seeks, more specifically, to give a a two-valued account that assigns stable classical truth values to sentences when intuitive reasoning would assign stable classical truth values. We will present a formal semantics for a formal language: we want that language to have both a truth predicate and the resources to refer to its own sentences.

The Revision Theory of Truth

2. Framing the problem

2.1 Truth languages

truth-revision

First published Fri Dec 15, 1995; substantive revision Tue Jun 2, 2015

Let us consider a first-order language L, with connective &, ∨, and ¬, quantifiers ∀ and ∃, the equals sign =, variables, and some stock of names, function symbols and relation symbols. We will say that L is a truth language, if it has a distinguished predicate T and quotation marks ‘ and ’, which will be used to form quote names: if A is a sentence of L, then ‘A’ is a name. Let SentL = {A : A is a sentence of L}.

The Revision Theory of Truth

2. Framing the problem

2.1 Truth languages

truth-revision

First published Fri Dec 15, 1995; substantive revision Tue Jun 2, 2015

It will be useful to identify the T-free fragment of a truth language L: the first-order language L− that has the same names, function symbols and relation symbols as L, except the unary predicate T. Since L− has the same names as L, including the same quote names, L− will have a quote name ‘A’ for every sentence A of L. Thus ∀xTx is not a sentence of L−, but ‘∀xTx’ is a name of L− and ∀x(x = ‘∀xTx’) is a sentence of L−.

The Revision Theory of Truth

2. Framing the problem

2.2 Ground models

truth-revision

First published Fri Dec 15, 1995; substantive revision Tue Jun 2, 2015

Other than the truth predicate, we will assume that our language is interpreted classically. More precisely, let a ground model for L be a classical model M = <D, I > for L−, the T-free fragment of L, satisfying the following:

The Revision Theory of Truth

2. Framing the problem

2.2 Ground models

truth-revision

First published Fri Dec 15, 1995; substantive revision Tue Jun 2, 2015

Clauses (1) and (2) simply specify what it is for M to be a classical model of the T-free fragment of L. Clauses (3) and (4) ensure that L, when interpreted, can talk about its own sentences. Given a ground model, we will consider the prospects of providing a satisfying interpretation of T. The most obvious desideratum is that the ground model, expanded to include an interpretation of T, satisfy Tarski's T-biconditionals, i.e., the biconditionals of the form

The Revision Theory of Truth

2. Framing the problem

2.2 Ground models

truth-revision

First published Fri Dec 15, 1995; substantive revision Tue Jun 2, 2015

T ‘A’ iff A

The Revision Theory of Truth

2. Framing the problem

2.2 Ground models

truth-revision

First published Fri Dec 15, 1995; substantive revision Tue Jun 2, 2015

for each A ∈ SentL.

The Revision Theory of Truth

2. Framing the problem

2.2 Ground models

truth-revision

First published Fri Dec 15, 1995; substantive revision Tue Jun 2, 2015

Some useful terminology: Given a ground model M for L and a name, function symbol or relation symbol X, we can think of I(X) as the interpretation or, to borrow a term from Gupta and Belnap, the signification of X. Gupta and Belnap characterize an expression's or concept's signification in a world w as “an abstract something that carries all the information about all the expression's [or concept's] extensional relations in w.” If we want to interpret Tx as ‘x is true’, then, given a ground model M, we would like to find an appropriate signification, or an appropriate range of significations, for T.

The Revision Theory of Truth

2. Framing the problem

2.3 Three ground models

truth-revision

First published Fri Dec 15, 1995; substantive revision Tue Jun 2, 2015

We might try to assign to T a classical signification, by expanding M to a classical model M′ = <D′, I′ > for all of L, including T. Also recall that we want M′ to satisfy the T-biconditionals: for our immediate purposes, let us interpret these classically. Let us say that an expansion M′ of a ground model M is Tarskian iff M′ is a classical model and all of the T-biconditionals, interpreted classically, are true in M′. We would like to expand ground models to Tarskian models. We consider three ground models in order to assess our prospects for doing this.

The Revision Theory of Truth

2. Framing the problem

2.3 Three ground models

truth-revision

First published Fri Dec 15, 1995; substantive revision Tue Jun 2, 2015

Ground model M1 Our first ground model is a formalization of Example 1.1, above. Suppose that L1 contains three non-quote names, α, β, and γ, and no predicates other than T. Let M1 = <D1, I1 > be as follows: D1 = SentL1 I1(α) = Tβ ∨ Tγ I1(β) = Tα I1(γ) = ¬Tα Ground model M2 Suppose that L2 contains one non-quote names, τ, and no predicates other than T. Let M2 = <D2, I2 > be as follows: D2 = SentL2 I2(τ) = Tτ Ground model M3 Suppose that L3 contains one non-quote names, λ, and no predicates other than T. Let M3 = <D3, I3 > be as follows: D3 = SentL3 I3(λ) = ¬Tλ

The Revision Theory of Truth

2. Framing the problem

2.3 Three ground models

truth-revision

First published Fri Dec 15, 1995; substantive revision Tue Jun 2, 2015

Theorem 2.1 (1) M1 can be expanded to exactly one Tarskian model: in this model, the sentences (Tβ ∨ Tγ) and Tα are true, while the sentence ¬Tα is false. (2) M2 can be expanded to exactly two Tarskian models, in one of which the sentence Tτ is true and in the other of which the sentence Tτ is false. (3) M3 cannot be expanded to a Tarskian model.

The Revision Theory of Truth

2. Framing the problem

2.3 Three ground models

truth-revision

First published Fri Dec 15, 1995; substantive revision Tue Jun 2, 2015

The proofs of (1) and (2) are beyond the scope of this article, but some remarks are in order.

The Revision Theory of Truth

2. Framing the problem

2.3 Three ground models

truth-revision

First published Fri Dec 15, 1995; substantive revision Tue Jun 2, 2015

Re (1): The fact that M1 can be expanded to a Tarskian model is not surprising, given the reasoning in Example 1.1, above: any initial hypothesis about the truth values of the three sentences in question leads, after three iterations of the revision process, to a stable hypothesis that (Tβ ∨ Tγ) and Tα are true, while ¬Tα is false. The fact that M1 can be expanded to exactly one Tarskian model needs the so-called Transfer Theorem, Gupta and Belnap 1993, Theorem 2D.4.

The Revision Theory of Truth

2. Framing the problem

2.3 Three ground models

truth-revision

First published Fri Dec 15, 1995; substantive revision Tue Jun 2, 2015

Remark: In the introductory remarks, above, we claim that there are consistent classical interpreted languages that refer to their own sentences and have their own truth predicates. Clauses (1) of Theorem 2.1 delivers an example. Let M1′ be the unique Tarskian expansion of M1. Then the language L1, interpreted by M1′ is an interpreted language that has its own truth predicate satisfying the T-biconditionals classically understood, obeys the rules of standard classical logic, and has the ability to refer to each of its own sentences. Thus Tarski was not quite right in his view that any language with its own truth predicate would be inconsistent, as long as it obeyed the rules of standard classical logic, and had the ability to refer to its own sentences.

The Revision Theory of Truth

2. Framing the problem

2.3 Three ground models

truth-revision

First published Fri Dec 15, 1995; substantive revision Tue Jun 2, 2015

Re (2): The only potential problematic self-reference is in the sentence Tτ, the so-called truth teller, which says of itself that it is true. Informal reasoning suggests that the truth teller can consistently be assigned either classical truth value: if you assign it the value t then no paradox is produced, since the sentence now truly says of itself that it is true; and if you assign it the value f then no paradox is produced, since the sentence now falsely says of itself that it is true. Theorem 2.1 (2) formalizes this point, i.e., M2 can be expanded to one Tarskian model in which Tτ is true and one in which Tτ is false. The fact that M2 can be expanded to exactly two Tarskian models needs the Transfer Theorem, alluded to above. Note that the language L2, interpreted by either of these expansions, provides another example of an interpreted language that has its own truth predicate satisfying the T-biconditionals classically understood, obeys the rules of standard classical logic, and has the ability to refer to each of its own sentences.

The Revision Theory of Truth

2. Framing the problem

2.3 Three ground models

truth-revision

First published Fri Dec 15, 1995; substantive revision Tue Jun 2, 2015

Proof of (3). Suppose that M3′ = <D3, I3′ > is a classical expansion of M3 to all of L3. Since M3′ is an expansion of M3, I3 and I3′ agree on all the names of L3. So

The Revision Theory of Truth

2. Framing the problem

2.3 Three ground models

truth-revision

First published Fri Dec 15, 1995; substantive revision Tue Jun 2, 2015

I3 ′(λ) = I3(λ) = ¬Tλ = I3(‘¬Tλ’) = I3 ′(‘¬Tλ’).

The Revision Theory of Truth

2. Framing the problem

2.3 Three ground models

truth-revision

First published Fri Dec 15, 1995; substantive revision Tue Jun 2, 2015

So the sentences Tλ and T ‘¬Tλ’ have the same truth value in M3′. So the T-biconditional

The Revision Theory of Truth

2. Framing the problem

2.3 Three ground models

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First published Fri Dec 15, 1995; substantive revision Tue Jun 2, 2015

T ‘¬Tλ’ ≡ ¬Tλ

The Revision Theory of Truth

2. Framing the problem

2.3 Three ground models

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is false in M3′.

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2. Framing the problem

2.3 Three ground models

truth-revision

First published Fri Dec 15, 1995; substantive revision Tue Jun 2, 2015

Remark: The language L3 interpreted by the ground model M3 formalizes the liar's paradox, with the sentence ¬Tλ as the offending liar's sentence. Thus, despite Theorem 2.1, Clauses (1) and (2), Clause (3) strongly suggests that in a semantics for languages capable of expressing their own truth concepts, T cannot, in general, have a classical signification; and the ‘iff’ in the T-biconditionals will not be read as the classical biconditional. We take these suggestions up in Section 4, below.

The Revision Theory of Truth

3. Basic notions of the RTT

3.1 Revision rules

truth-revision

First published Fri Dec 15, 1995; substantive revision Tue Jun 2, 2015

In Section 1, we informally sketched the central thought of the RTT, namely, that we can use the T-biconditionals to generate a revision rule — a rule for revising a hypothesis about the extension of the truth predicate. Here we will formalize this notion, and work through an example from Section 1.

The Revision Theory of Truth

3. Basic notions of the RTT

3.1 Revision rules

truth-revision

First published Fri Dec 15, 1995; substantive revision Tue Jun 2, 2015

In general, let L be a truth language and M be a ground model for L. An hypothesis is a function h : D → {t, f}. A hypothesis will in effect be a hypothesized classical interpretation for T. Let's work with an example that combines Examples 2.1 and 2.3. We will state the example formally, but reason in a semiformal way, to transition from one hypothesized extension of T to another.

The Revision Theory of Truth

3. Basic notions of the RTT

3.1 Revision rules

truth-revision

First published Fri Dec 15, 1995; substantive revision Tue Jun 2, 2015

Example 3.1 Suppose that L contains four non-quote names, α, β, γ and λ and no predicates other than T. Also suppose that M = <D, I > is as follows: D = SentL I(α) = Tβ ∨ Tγ I(β) = Tα I(γ) = ¬Tα I(λ) = ¬Tλ It will be convenient to let A be the sentence Tβ ∨ Tγ B be the sentence Tα C be the sentence ¬Tα X be the sentence ¬Tλ Thus: D = SentL I(α) = A I(β) = B I(γ) = C I(λ) = X Suppose that the hypothesis h0 hypothesizes that A is false, B is true, C is false and X is true. Thus h0(A) = f h0(B) = t h0(C) = f h0(X) = f Now we will engage in some semiformal reasoning, on the basis of hypothesis h0. Among the four sentences, A, B, C and X, h0 puts only B in the extension of T. Thus, reasoning from h0, we conclude that ¬Tα since the referent of α is not in the extension of T Tβ since the referent of β is in the extension of T ¬Tγ since the referent of γ is not in the extension of T ¬Tλ since the referent of λ is not in the extension of T. The T-biconditional for the four sentence A, B, C and X are as follows: (TA) A is true iff Tβ ∨ Tγ (TB) B is true iff Tα (TC) C is true iff ¬Tα (TX) X is true iff ¬Tλ Thus, reasoning from h0, we conclude that A is true B is not true C is true X is true This produces our new hypothesis h1: h1(A) = t h1(B) = f h1(C) = t h1(X) = t Let's revise our hypothesis once again. So now we will engage in some semiformal reasoning, on the basis of hypothesis h1. Hypothesis h1 puts A, C and X, but not B, in the extension of the T. Thus, reasoning from h1, we conclude that Tα since the referent of a is in the extension of T ¬Tβ since the referent of β is in the extension of T Tγ since the referent of γ is not in the extension of T Tλ since the referent of λ is not in the extension of T Recall the T-biconditional for the four sentence A, B, C and X, given above. Reasoning from h1 and these T-biconditionals, we conclude that A is true B is true C is not true X is not true This produces our new new hypothesis h2: h2(A) = t h2(B) = t h2(C) = f h2(X) = f □

The Revision Theory of Truth

3. Basic notions of the RTT

3.1 Revision rules

truth-revision

First published Fri Dec 15, 1995; substantive revision Tue Jun 2, 2015

Let's formalize the semiformal reasoning carried out in Example 3.1. First we hypothesized that certain sentences were, or were not, in the extension of T. Consider ordinary classical model theory. Suppose that our language has a predicate G and a name a, and that we have a model M = <D, I > which places the referent of a inside the extension of G:

The Revision Theory of Truth

3. Basic notions of the RTT

3.1 Revision rules

truth-revision

First published Fri Dec 15, 1995; substantive revision Tue Jun 2, 2015

I(G)(I(α)) = t

The Revision Theory of Truth

3. Basic notions of the RTT

3.1 Revision rules

truth-revision

First published Fri Dec 15, 1995; substantive revision Tue Jun 2, 2015

Then we conclude, classically, that the sentence Ga is true in M. It will be useful to have some notation for the classical truth value of a sentence S in a classical model M. We will write ValM(S). In this case, ValM(Ga) = t. In Example 3.1, we did not start with a classical model of the whole language L, but only a classical model of the T-free fragment of L. But then we added a hypothesis, in order to get a classical model of all of L. Let's use the notation M + h for the classical model of all of L that you get when you extend M by assigning T an extension via the hypothesis h. Once you have assigned an extension to the predicate T, you can calculate the truth values of the various sentences of L. That is, for each sentence S of L, we can calculate

The Revision Theory of Truth

3. Basic notions of the RTT

3.1 Revision rules

truth-revision

First published Fri Dec 15, 1995; substantive revision Tue Jun 2, 2015

ValM + h(S)

The Revision Theory of Truth

3. Basic notions of the RTT

3.1 Revision rules

truth-revision

First published Fri Dec 15, 1995; substantive revision Tue Jun 2, 2015

In Example 3.1, we started with hypothesis h0 as follows:

The Revision Theory of Truth

3. Basic notions of the RTT

3.1 Revision rules

truth-revision

First published Fri Dec 15, 1995; substantive revision Tue Jun 2, 2015

h0(A) = f h0(B) = t h0(C) = f h0(X) = f