Revisiting Quine on Truth by Convention

Jared Warren

Abstract

In “Truth by Convention” W.V. Quine gave an influential argumentagainst logical conventionalism. Even today his argument is often taken todecisively refute logical conventionalism. Here I break Quine’s argumentsinto two—(i) the super-task argument and (ii) the regress argument—and argue that while these arguments together refute implausible explicit

versions of conventionalism, they cannot be successfully mounted againsta more plausible implicit version of conventionalism. Unlike some of hismodern followers, Quine himself recognized this, but argued that implicitconventionalism was explanatorily idle. Against this I show that pace

Quine’s claim that implicit conventionalism has no content beyond theclaim that logic is obvious, implicit rules of inference can be used to dis-tinguish the obvious truths from the conventional truths. In addition I ar-gue that the idea that syntactic rules of inference are part of our linguisticcompetence follows from the same methodology that leads contemporarylinguists and cognitive scientists to posit rules of phonology, morphology,and grammar. The upshot of my discussion is both a diagnosis of thefallacy in Quine’s critique of logical conventionalism and a re-opening ofpossibilities for an attractive conventionalist theory of logic.

Keywords: Conventionalism, Quine, Logic, Linguistic Rules

I Quine vs Logical Conventionalism

According to logical conventionalism, logical truths are true by linguistic con-vention or in virtue of meaning. Conventionalism was the philosophy of logicfavored by Carnap, Ayer, and the other logical positivists.1 But today logicalconventionalism is almost universally rejected; a major reason for this state ofaffairs is the influence of Quine’s 1936 article “Truth by Convention”, wherein

1See Carnap (1934) and Ayer (1946); more recent defenses of logical conventionalism arefound in Giannoni (1971) and Syverson (2003).

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a powerful case against conventionalism is propounded.2 Quine’s case has beenextremely influential and even today it is often taken to decisively refute anyform of logical conventionalism.

To give a small taste of its influence, after sketching Quine’s main argument,Scott Soames says:

This, in a nutshell, was one of the central arguments of Quine’spaper, “Truth by Convention,”...Although not fully appreciated rightaway, it eventually became a classic, and is now widely known forits powerful critique of the program of grounding a priori knowledgein knowledge of meaning.3

And in a recent book Theodore Sider advises those with a “hangover from logicalconventionalism” to:

...pop a couple of aspirins, re-read your Quine (1936)...and reportback.4

Very few critical pieces in philosophy are so highly regarded; many contemporaryphilosophers—perhaps even a majority—think that Quine’s arguments killedlogical conventional then, now, and for all time.

There has been resistance. For example, in a recent discussion, Gary Ebbsargued that Quine’s argument doesn’t actually refute any conventionalist thesisheld by Carnap.5 But Ebbs holds this view because he doesn’t think that Car-nap actually held any explanatory conventionalist thesis, contrary to popularphilosophical folk-history. This kind of revisionary reading of Carnap has alsobeen championed by Warren Goldfarb and Thomas Ricketts in recent years, butwhatever its exegetical worth, it isn’t my concern here.6 My discussion will notbe about whether or not Quine’s arguments refute Carnap’s position, but aboutwhether or not Quine’s arguments refute logical conventionalism, independentlyof whether Carnap himself was a logical conventionalist in the relevant sense.

2Quine (1936); Quine’s central argument is related to the famous regress problem fromCarroll (1895).

3Soames (2003), page 265.4Sider (2011), page 216.5Ebbs (2011).6See Goldfarb (1995) and Ricketts (1994). For what it’s worth, I disagree with the reading

of Carnap offered by these philosophers; a remark made by Hilary Putnam in response toRicketts is worth quoting: “Ricketts’s Carnap, the Carnap who holds no doctrines but onlyasks for “clarification,”...is just not the Carnap I knew and loved.” (quoted from Clark & Hale(1994), page 281).

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Contrary to widely held philosophical opinion, Quine’s arguments don’t un-dermine any plausible version of logical conventionalism. Some of the points Iwill make here have been made by other commentators before me—includingQuine himself—but there have been few general analyses of Quine’s “Truth byConvention”. I will provide such an analysis and argue that while Quine’s argu-ment against explicit conventionalism is successful, there is no way to extend hisargument so that it works against a plausible, implicit, version of conventional-ism. In addition I will show that Quine’s worries that implicit conventionalismis explanatorily idle cannot be upheld, and that the scientific methodology usedby linguists should lead us to posit explanatorily fruitful syntactic rules of infer-ence just as surely as they lead us to posit rules of morphology and grammar.Although Quine’s article serves as a jumping off point, my concerns here aremore philosophical than exegetical.

II Explicit Conventionalism and Quine’s Arguments

Logical conventionalism is the idea that logical truths are true by or accordingto our linguistic conventions:

Logical Conventionalism : for any logically true sentence �, ourlinguistic conventions make it the case that � is true

Though I won’t spend too much time discussing it here, based on the writ-ings of historical conventionalists (and, more importantly, based on what is themost interesting and plausible conventionalist thesis), the “make it the case”relation appealed to in this principle should be understood as an explanatoryrelationship rather than a causal relationship. Of course everyone, whetherconventionalist or not, will admit that our conventions partially explain thetruth of any given true sentence in our language; in order to be an interestingthesis, Logical Conventionalism should be understood as claiming that ourlinguistic conventions fully explain the truth of any given logical truth.7

But what are linguistic conventions? In his article Quine understands con-ventions as explicit stipulations:

Explicitness : a linguistic convention concerning a sentence takesthe form of an explicit stipulation concerning the sentence

7The conventionalist is also going to want to provide a similar explanation of the validityof logical rules like modus ponens—see the discussion of linguistic rules below for more onthis.

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Call the combination of Logical Conventionalism and Explicitness explicitconventionalism. Quine’s central argument in “Truth by Convention” is directedat versions of explicit conventionalism.

The first stage of the argument runs as follows: according to explicit con-ventionalism, for each logical truth �, we—as a linguistic community—havestipulated that � is to express a truth. But there are an infinite number of logi-cal truths expressible in our language, and there is no sense in which any humanbeing or finite collection of human beings could have made an infinite number ofexplicit stipulations. Furthermore, even if our lifespans were infinite it wouldn’thelp, since each stipulation would still take some small finite amount of timeand so there would be no point in time during our infinite lifespans at whichwe would have completed each stipulation and so no point in time when theall of the logical truths would have been made true. So the explicit stipulationpicture—applied individually to each of the infinitely many logical truths—ishopeless.

Let’s lay this out more carefully as Quine’s super-task argument :

1. If explicit conventionalism is true, then for each logical truth in our lan-guage �, we have explicitly stipulated that � is to express a truth (fromthe definition of explicit conventionalism)

2. There are an infinite number of logical truths in our language (uncontestedfact)

3. So: if explicit conventionalism is true, then we have made an infinitenumber of explicit stipulations (1, 2)

4. We have not made an infinite number of explicit stipulations (given thefinite number of humans and the nature of explicit stipulations)

5. So: explicit conventionalism is not true (3, 4)

I think Quine’s argument is valid, but is it sound? We need to say more aboutpremise (4) in order to assess the argument.

A task that is composed of an infinite number of sub-tasks is called a super-task.8 Quine takes it as obvious that the super-task of stipulating that eachlogical truth is true cannot be completed by any single human or by humanityas a whole, but this might be questioned. Some putative super-tasks, such as

8This terminology, in roughly this sense, was introduced in Thomson (1954); see alsoBenacerraf (1962) for important criticisms of some points in Thomson’s discussion.

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the Zeno-ian task of walking across a room, are completable in a finite amountof time. In Zeno-style cases, the time taken to complete each subsequent sub-task involved in the super-task diminishes in a disciplined manner so that theinfinite series associated with the super-task has a finite sum. The infinite seriesassociated with a given super-task is the sum of the times taken by each of theinfinitely many sub-tasks composing the super-task, where a unit representssome fixed interval of time.9 For the super-task we are considering, each sub-task is the exact same type of task, viz., stipulating that a given sentence istrue, and so each of the infinite sub-tasks will take at least some small finiteamount of time, call it “✏”. This means that in the infinite series associated withthe explicit conventionalist’s super-task, each term in the series will be greaterthan or equal to ✏, and no such series can have a finite sum, so this task cannotbe completed in any finite length of time. This is what justifies premise (4) inQuine’s super-task argument.

Perhaps in some science fiction scenario we can imagine getting better andbetter at stipulations such that, while the first stipulation takes ✏ units of time,each successive stipulation only takes half of the time of the previous stipulation,which would give us the following series:

✏+✏

2

+

✏

4

+ ...+✏

2

n�1+ ...

And this is the series familiar from Zeno-ian super-tasks, its sum is 2✏—a smallfinite number. Had things worked in this manner, we could have completed allof the infinitely many stipulations in a finite time, but clearly things did notwork in this manner. Even if this type of scenario is possible in some recherchésense, it simply doesn’t matter, for we are concerned with how the logical truthsin our actual language, all infinitely many of them, came to be true. This is whypremise (4) only claims that we have not made an infinite number of explicitstipulations, not that we could not have done so. And since no conventionalistwould ever maintain that the science fiction scenario imagined in this paragraphactually happened, they are forced to accept premise (4), whatever their viewson the possibility of the kind of speed-up we’re imagining.

The only way for an explicit conventionalist to resist the argument is amendtheir view so that stipulations only concern finitely many general claims, fromwhich the infinite number of particular logical truths can then be derived (this

9This is the standard diagnosis of Zeno’s paradoxes, supported by modern mathematicalanalysis, Russell (1929), pages 182-198 contains a canonical discussion; See Salmon (1967) fora wealth of important articles on Zeno’s paradoxes.

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would involve rejecting premise (1) of Quine’s super-task argument). For in-stance: we might say that we have stipulated that any sentence of the formp�_¬�q is to be true, and from this we derive that the infinitely many particu-lar instances of this schema (like “p_¬p”) are true. This type of picture is to beapplied to other logical truths as well. This solves the infinitude problem, butonly by appealing background logical principles that allow us to derive partic-ular instances from our general claims. In other words, this procedure explainslogical truth in terms of explicit conventions together with background logicalnotions.

Let’s illustrate this by working through an example. Imagine we have madethe following general stipulation:

(LEM) Any sentence of the form p� _ ¬�q is true

And we want to derive that the particular sentence “p _ ¬p” is true. To inferthis, we need the premise (i) “p_¬p” is of form p�_¬�q, and this is fine, since itexpresses a uncontested matter of syntactic fact. But this is not enough, for wealso need: (ii) if (LEM) and (i) are both true, then “p _ ¬p” is true. But nowthis premise, (ii), also needs to be added, and we are moved to: (iii) if (LEM)

and (i) and (ii) are true, then “p _ ¬p” is true. At this point, we are off on aregress—every premise we add will just be more grist for the mill to go into ourever-expanding stock of premises. The regress could be avoided by noting thatthese background principles were already true prior to our stipulations, butthat sins against explicit conventionalism. So even the “general stipulation”-version of explicit conventionalism is forced to claim that an infinite number ofstipulations have been made in order for any one of the proposed derivationsto go through. It appears that the general form of explicit conventionalism hasdone no better than the particular form we started with.

As Quine himself noted, this regress is structurally identical to a generalregress for logical inference presented in a famous dialogue by Lewis Carroll.10

In Carroll’s dialogue, poor slow-witted Achilles is baffled by the clever Tortoiseas he tries to perform a basic inference out of Euclid; every time Achilles thinkshe has caught the Tortoise by adding another premise, the Tortoise points outthat a further premise now appears that must be accepted for the inference togo through. The standard diagnosis of Carroll’s regress is that it is based ona confusion between premises and rules of inference. I don’t claim that there

10Carroll (1895).

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is complete agreement here or that this issue has been sorted out and agreedupon in a perfectly clear manner, but I do think there is general agreement thatsomething in the ballpark of this response eliminates the headaches caused byCarroll’s regress.11

Is Quine’s regress problem as easily disposed of? I don’t think so. Thereason is that Quine’s target is a conventionalist who must assume that thedistribution of the truth values over sentences in our language doesn’t conformto any priorly given logical constraints. As such, it could be the case, for all theconventionalist has said, that (LEM) and (i) are both true, but “p_¬p” is not.If the conventionalist tries to close the gap by stipulating that an inference rulelike modus ponens is valid, the same problem as before seems to crop up, viz.,this stipulation can’t be assumed to conflict with a counterexample to modusponens also existing, except by appeal to some further logical principles. Everyway that the conventionalist tries to plug the gap seems to lead to more gapsopening up. So the attempt at a reconfigured, general version of explicit con-ventionalism reduces the conventionalist slogan that logic is true by conventionto the less impressive slogan that logic is true by conventions plus logic. For theexplicit conventionalist, any attempt to eliminate this lingering logical residuewill appeal to still further explicit conventions, which will generate the sameproblem going back a step, leading to a regress.

Let’s also lay this argument out more carefully, as Quine’s regress argument :

1. If explicit conventionalism is true, then we have stipulated the validity ofsome finite number of general logical principles (this is the proposal underconsideration)

2. There are an infinite number of logical truths in our language (uncontestedfact)

3. So: If explicit conventionalism is true, then we have to derive an infinitenumber of logical truths from our finite number of stipulated principles(1, 2)

4. This derivation requires that either a infinite number of explicit stipula-tions have been made or we appeal to some logical principles that aretrue but were not explicitly stipulated to be true (this was just argued forusing the Carroll-style regress)

11Two early responses to Carroll somewhere in this rough ballpark are Rhees (1951) andThomson (1960).

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5. So: explicit conventionalism is false (3, 4)12

Explicit conventionalists have a choice, appeal either to explicit stipulationsof particular sentences or to explicit stipulations of general principles. If theychoose the first, Quine’s super-task argument refutes them; if they choose thesecond, Quine’s regress argument refutes them. Either way, explicit conven-tionalism stands refuted. Let’s call this combination argument Quine’s masterargument against conventionalism or, more simply, Quine’s master argument.

In this section, I’ve upheld the verdict that Quine’s master argument refutesexplicit conventionalism. Perhaps this shouldn’t have been all that surpris-ing, since explicit conventionalism seems to rely upon a somewhat implausiblemetasemantic view according to which we can alter the truth values of sen-tences by mere stipulation or pronouncement. Whatever the merits of thismetasemantic view, Quine’s master argument shows that even if it is accepted,explicit logical conventionalism is untenable. This is a significant result, butthe really interesting question is whether or not Quine’s arguments also refutemeta-semantically plausible versions of logical conventionalism.

III Implicit Conventionalism and Quine’s Arguments

That the target of Quine’s (successful) argument isn’t the most interesting andplausible version of logical conventionalism has been recognized before; here isPaul Boghossian providing a clear statement after rehearsing Quine’s regressargument:

This argument of Quine’s has been very influential; and I thinkthat there is no doubt that it works against its target as specified.However, it is arguable that its target as specified isn’t the view thatneeds defeating.

For, surely, it isn’t compulsory to think of someone’s following arule R with respect to an expression e as consisting in his explicitlystating that rule in so many words in the way that Quine’s argumentpresupposes. On the contrary, it seems far more plausible to construex’s following rule R with respect to e as consisting in some sort offact about x’s behavior with e.13

12The argument as I’ve posed it here is technically an enthymeme, but the gaps could easilyfilled.

13Boghossian (1996), page 381.

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As Boghossian suggests, a more plausible way of understanding linguistic con-ventions takes them to be implicit, i.e., as somehow being based in the linguisticbehavior and behavioral dispositions of language users. The natural way of char-acterizing this is by appeal to implicitly followed linguistic rules:

Implicitness : a linguistic convention concerning a sentence takesthe form of an implicit rule concerning the sentence

With this understanding of “linguistic conventions”, logical conventionalism isthe idea that the rules governing the use of logical connectives fully explains thetruth of logically true sentences in our language. This is the form of convention-alism that Carnap and other historical conventionalists endorsed, as evidencedby their frequent talk of “rules of language”.14

This approach is naturally connected to logical inferentialism—the idea thatthe meanings of logical expressions are determined by the inference rules ac-cording to which the expressions are used.15 So, e.g., we might think that themeaning of the conditional “!” is determined by the following rules (conditionalproof and modus ponens):

(CP )

(�)n

...

�! n (MP )

� �!

The central idea behind inferentialism is that meaning constituting rules likethese are automatically valid (where a rule is valid just in case it is necessarilytruth-preserving). From this, the meanings of logical constants like “!” isforced.16 Against this inferentialist backdrop, one conventionalist option is tosee the truth of logical truths like those of the form p�! �q as fully explainedby the provability of all sentences of this form using the above rules.17 So thetruth of all instances of the schema p� ! �q is, for the conventionalist, fullyexplained by the provability of any instance of this schema using the inference

14Though see Ebbs (2011).15The founding documents of logical inferentialism are Carnap (1934) and Wittgenstein

(1974); see also See Boghossian (1996), Dummett (1991), Hacking (1979), and Peacocke(1987).

16This is not actually as straightforward as is sometimes assumed, see Carnap (1943).17This will only work in full generality for logics that are semantically complete; for simplic-

ity I am confining my discussion to such logics. I think that an inferentialist/conventionalistapproach can be applied to incomplete logics, but discussing this involves tackling obstaclesthat are irrelevant to an assessment of Quine’s arguments.

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rules of our language (see section IV, point (ii) for more on this).18

With rule-following so understood, let’s call the combination of Logical

Conventionalism and Implicitness implicit conventionalism. Before turningto the question of whether or not Quine’s master argument can refute implicitconventionalism as it did explicit conventionalism, three points of clarificationneed to be made.

Firstly, concerning rule-following and the idea of rules of inference: thenotion of an inference rule is widely used in philosophy and logic, but thereare different views about what rule-following behavior consists in. A standardassumption among naturalists is that following linguistic rules like (CP ) and(MP ) is a matter of having certain complex patterns of linguistic dispositions.Roughly and without attempting any analysis, when I say that an agent S fol-lows rule R I mean not just that S is disposed to act in accordance with R inthe vast majority of some class of independently specified standard situations,but also that S is disposed to accept corrections toward R quite readily; that wecan expect S’s behavior to continue in this manner in a wide variety of hithertounobserved situations; that there is some positive assessment by S of behaviorin conformity with R and some negative assessment of behavior not in confor-mity with R, etc.19 Rule-following behavior is only in place when a patternedcomplex of higher and lower-level behavioral regularities are in place, but tosay this is not to accept a simplistic dispositionalist analysis of rule-following.20

In actual cases there will likely be more than a little indeterminacy concerningexactly which linguistic rules we are following, but this is to be expected andshouldn’t seriously trouble us.21One of the most important points is that if aspeaker is correctly described as following rule R, then this rule has normativeforce for the speaker, e.g., the speaker will be making a mistake if they rejectthe conclusion of R while accepting all of its premises.

Secondly, above I tacitly distinguished between meaning constituting rulesof inference like (CP ) and (MP ) and other rules that might be valid but non-meaning constituting. Inferentialists and thus implicit conventionalists can dif-

18If applied to natural languages, we would need to supplement this type of an approachwith an account of which sentences were truth-apt; Wright (1992) spells out a use-basedstrategy for doing this that would be congenial to implicit conventionalists.

19Cf. Field (2001), page 388.20Kripke (1982) famously argued against dispositionalist accounts of rule-following; for

defenses of dispositionalism against Kripke’s arguments see, e.g., the discussions in Forster(2004), Horwich (1998), and Shogenji (1993).

21For simplicity I’ll be ignoring the role of patterned coordination by simply assuming thateveryone in the community follows the very same inference rules. In practice this might happenonly because ordinary speakers defer to logical experts.

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fer on this issue. Holist inferentialists think that every single rule in our languageis meaning constituting, so there is no distinction between meaning constitut-ing and non-meaning constituting rules. Non-holist inferentialists think there issuch a distinction, and require some non-ad hoc way of drawing it that applies tonatural languages. Historical conventionalists like Carnap almost always workedwith formal languages, so the meaning constituting inference rules were simplythose rules explicitly built into the specification of the formal language.22 Butobviously natural languages and their rules don’t come with any such labels,so how are we to distinguish the meaning constituting rules from non-meaningconstituting rules?

There are many possible strategies, but one that is particularly appealingmakes note of the fact that some inference rules seem to be accepted by speak-ers in a direct or unmediated fashion. If you were to ask a speaker why theyaccepted modus ponens arguments, no non-circular justification would be of-fered. And any justification using more complex rules for the conditional, ifsuch could be given, would be taken to have very little worth. By contrast,other rules seem to be the type that we accept only because we can see or showthat they must be valid given the direct rules. It would be natural for non-holistinferentialists/conventionalists to look to this kind of distinction in drawing theline between meaning constituting rules and non-meaning constituting rules ofinference. So that rules that we accept directly, like modus ponens, are meaningconstituting, but those we accept only indirectly, are not.

Thirdly, it’s worth pausing to clear up a terminological matter that couldbe tripping up some readers. Philosophical treatments of “convention”, start-ing with David Lewis’s influential study, typically make much of notions likesignaling and coordination.23 I won’t be dealing with these things here; allissues concerning how conventions are socially implemented will be subsumedunder rule-following by simply assuming, for the purposes of simplicity, that ina linguistic community every member of the community follows the very samelinguistic rules as every other member of the community. The actual story of ourlanguage and its rules will doubtless involves details that I don’t consider here,though I don’t think that filling out my story with those details will undermineanything I argue for here.24

22Carnap (1955) is a rare exception; there Carnap favors a dispositionalist style approachto rules and analyticity in natural language.

23Lewis (1969).24See also Quine’s introduction to Lewis (1969).

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With these important points of clarification made, let us now ask: doesQuine’s argument refute implicit conventionalism just as it refuted explicit con-ventionalism? To answer this question, we need to consider whether versionsof the super-task argument and the regress argument can be mounted againstimplicit conventionalism.

Clearly no version of Quine’s super-task argument can be mounted againstimplicit conventionalism. While following a rule like (MP ) does commit one toaccepting all of the infinitely many instances of (MP ), there need be no point intime at which one has performed all of these infinitely many inferences. Accord-ing to what was said about rule-following above, there will be some dispositionalanalysis that makes one correctly describable as following (MP ), and this com-mits one to accepting all of (MP )’s infinitely many instances (even where therelevant disposition is masked or blocked, like on a world where mind-numbinggas interferes with our brains). But nothing about this account requires that asuper-task be performed.

What about the regress argument? I will consider two ways that this ar-gument might be pressed against the implicit conventionalist—one implausibleway and one prima facie plausible way.

(i) It might be argued that rule-following itself gives rise to a regress problem.The thought here is that in following a rule like (MP ) to infer from premises� and p� ! q, what one is actually doing is reasoning from the premises �and p�! q and p((�! )^�) ! q to p q via a modus ponens step. If thisis assumed, then obviously we are off on a Carroll-style infinite regress, sincethis new instance of modus ponens will require another instance and so forthand so on. This attempt to reformulate Quine’s regress argument to targetthe implicit conventionalist is extremely radical in that it assumes that rule-following itself, aside from any controversial conventionalist thesis, leads to aproblematic regress. A natural response is to take this regress to be a reductioof this modus ponens-style picture of rule-following. As I discussed above, abetter account of rule-following take rules to be followed implicitly, and indeed,this is constitutive of implicit conventionalism. Implicit rule-following is nearlyubiquitously accepted, so those who reject it have problems that go beyondconventionalism.

(ii) A more subtle and prima facie plausible attempt to raise a regressproblem for the implicit conventionalist is as follows: the rules of modus ponens(MP ) and conditional proof (CP ) aren’t the only valid rules for reasoningwith the conditional, as I noted above, there are other valid rules that aren’t

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typically taken to be meaning constituting. For instance, the rule of hypotheticalsyllogism is a (classically) valid rule involving the conditional and no otherlogical constants:

(HS)�! ! �

�! �

Holists will take (HS) to be meaning constituting just as surely as (CP ) and(MP ), but many find such a position implausible, so conventionalists wouldbe more likely to build their implicit conventionalism upon a non-holist formof logical inferentialism, according to which rules like (HS) are valid but non-meaning constituting. There are an infinite number of forms of valid rules likethis, so it might be suspected that a problem analogous to the regress problemabove plagues implicit conventionalism. The thought is that only a finite numberof rules are meaning constituting, but from this we must somehow extract theinfinitely many non-meaning constituting but valid rules and that this extractionwill involve logical reasoning that isn’t explained conventionally.

A version of this problem is raised by Patricia Blanchette in criticizing anymeaning-based explanation of logical validity:

To say that the meanings of a collection of terms ’suffices for’ or’guarantees’ the truth of a sentence seems to mean little more thatthat the sentence’s truth follows logically from facts about thosemeanings. . . And if this is right, then one cannot, without viciouscircularity, give a characterization of logical properties and relationsin terms of meanings. . . . the circularity of the proposed analysis,would seem likely to pose difficulties for virtually any attemptedanalysis of. . . logical properties and relations. . . to say that certainfeatures F of a sentence or claim make that claim a logical truthis to say something dangerously close to saying that the sentence’shaving F entails that the sentence is a logical truth.25

Applied to the case at hand, the worry is that we need to logically derive a rulelike (HS) from our basic rules, and this derivation will need to appeal to logicalprinciples that are not explained conventionally, thus leading to a variant ofQuine’s regress argument, this time aimed at the implicit conventionalist.

As tempting as it might initially seem, this argument fails. In contrastto the explicit case, non-meaning constituting rules—like (HS)—are not being

25Blanchette (2001), pages 132-133.

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explicitly derived. We could, of course, explicitly derive the validity of the rule(HS) using (CP ), (MP ), and the transitivity of deducibility, but that isn’t thecentral point. The central point is that if (CP ), (MP ), and our structural rulesare valid, then so too will (HS) be valid. This can be seen with the followingproof (for ease of reading, I will present the proof in a linear format ratherthan the tree format in which the rules were presented; on each line I haveexplicitly noted the assumptions, by line number, that the line rests on and,when applicable, which assumptions are discharged in the application of therule used to deliver that line):26

1. �! {1} Assumption

2. ! � {2} Assumption

3. � {3} Assumption

4. {1, 3} MP (1, 3)

5. � {1, 2, 3} MP (2, 4)

6. �! � {1, 2} CP (5) discharge(3)

While this proof shows that (HS) is valid, the validity of (HS), according tothe implicit conventionalist, doesn’t at all depend upon language users havingdiscovered and reflected upon this proof or another like it. It only requires thatthey follow the rules used in this derivation, since following those rules sufficesfor also following (HS) as a derived rule.

Following the rules (CP ) and (MP ) suffices for following the rule (HS) andother such rules and the conventionalist explains validity in terms of the rulesof inference that we follow, and so (HS) will be valid in our language when(CP ) and (MP ) are. Following these meaning constituting rules suffices forfollowing a non-meaning constituting rule like (HS) in the sense that if youhave the dispositions that constitute following the rules (CP ) and (MP ) youthereby have the dispositions that constitute following the rule (HS). There areother ways to have the disposition that amounts to following this rule, but thisis one way. Following the rule (HS) is, roughly, being disposed to accept theconclusion p�! �q whenever one accepts the premises p�! q and p ! �q.But this claim isn’t about logical reasoning to an explicit conclusion—we aren’t

26The presentation used here is something like that found in Lemmon (1965) or Mates(1965).

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reasoning to the conclusion that (HS) is valid. Rather, as the above proofdemonstrates, in a sense, if (MP ) and (CP ) are valid, then so too is (HP )

(assuming the transitivity of entailment). It also shows that when you followthe rules (MP ) and (CP ) you thereby follow the rule (HS) and similarly forother valid but non-meaning constituting rules for the conditional.27

Any plausible attempt to reformulate Quine’s regress argument to targetimplicit conventionalism must be based on having to derive all non-meaningconstituting but valid logical rules from the few basic meaning constitutingrules. But a variant of the above line of response will defeat any such attempt,so there is no analogous regress problem for the implicit conventionalist. Quine’smaster argument fails to refute implicit conventionalism. Since Quine’s argu-ment fails against the implicit conventionalism and implicit conventionalism isso much more plausible than explicit conventionalism, it might be wonderedwhy philosophers like Soames and Sider are so quick to cite Quine’s article assigning conventionalism’s death warrant.28 I have no answer for this, especiallyin light of two important further points: (i) as mentioned briefly above, implicitconventionalism was plausibly the form of conventionalism favored by Carnapand other logical positivists; and (ii) Quine himself recognized and admittedthat his argument failed against implicit conventionalism.

IV Quine’s Challenge for Implicit Conventionalism

Quine’s arguments refute the implausible, explicit version of logical convention-alism but are powerless against the much more plausible, implicit version oflogical conventionalism. Interestingly, as just noted, unlike some of his modernfollowers, Quine himself agreed with this assessment. In his original discussionQuine considers an implicit rule-following type of response to his arguments butcomplains that it is difficult to see such a position as a distinctive doctrine thatgoes beyond the mere claim that logic is obvious or a priori :

In dropping the attributes of deliberateness and explicitness fromthe notion of linguistic convention we risk depriving the latter of anyexplanatory force and reducing it to an idle label. We may wonderwhat one adds to the bare statement that the truths of logic and

27This type of response will only apply to valid but derivable rules of inference. Here I haveignored valid but non-derivable rules (see the discussion of the restriction to semanticallycomplete logics above in footnote 17).

28As the context from which the quotes above are drawn makes clear, neither Soames norSider are limiting themselves to rejecting explicit conventionalism.

15

mathematics are a priori, or to the still barer behavioristic statementthat they are firmly accepted, when he characterizes them as trueby convention in such a sense.29

It is important to remember that—despite the rhetoric engaged in by Soames,Sider, and others—once we settle on a plausible, implicit version of convention-alism, the entire force of Quine’s discussion rests on the force of the complaintvoiced in this quote.

The conventionalist’s challenge is to distinguish the mere claim that a sen-tence “p” is firmly accepted or obvious from the claim that “p” is true by con-vention. The natural strategy, one that was presaged above in the definition ofimplicit conventionalism, is to claim that a sentence is true by convention justin case it is provable from the rules of language alone and then to argue thatthis allows us to cleanly differentiate the firmly accepted sentences like “it hasrained at some point in the past” from the conventionally true sentences like “itis either raining or it is not raining”. This response to Quine’s challenge for im-plicit conventionalism consists of two distinct steps: (i) arguing in detail for theacceptance of linguistic rules of inference and (ii) showing how, once posited,these rules allow for the non-ad hoc differentiation of the conventionally truefrom the merely obvious or firmly accepted. Let’s take each step in turn.

(i) Linguistic rules of inference. Modern linguistics takes implicit linguis-tic rules to be a central explanatory posit and, as I’ll argue here, the reasonslinguists have for positing rules of morphology, phonology, and grammar alsoapply to rules of inference. As an illustration of the data that leads linguistsand cognitive scientists to posit linguistic rules, consider the famous wug-test.In 1958 the psychologist Jean Berko Gleasen showed four to seven year old chil-dren an illustration of an indeterminate bird-like creature accompanied with thefollowing text:

This is a wug.

Now there is another one.

There are two of them.

There are two ______29Quoted from the close of Quine (1936); see also Quine (1960) for extended related discus-

sion as well as the quotations in the next section of the paper.

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The children were asked to fill in the blank. About 75% of the pre-schoolers and99% of the first-graders replied with “wugs”.30 Since the word “wug” was just amade up term, in forming this plural the children weren’t appealing to a pluralform that they had heard from adults, instead they were following a rule forforming the plural form of a regular noun: for regular noun ↵, the plural formis ↵a

”s”.31 This is a rule of morphology—a rule for forming complex words.Some also argue for rules of phonology, which tell us how to pronounce

words.32 And, most importantly in contemporary linguistics, there are rules ofgrammar concerning how words are formed into phrases and phrases into novelsentences of great complexity. Grammatical rules have received the bulk of at-tention from linguists and cognitive scientists since the pioneering work of NoamChomsky.33 Empirical data suggests that syntactic judgments that a sequenceof words is or isn’t grammatical aren’t piggybacking on some understanding ofthe meaning of the words. This is illustrated by Chomsky’s famous and shop-worn nonsense sentence “colorless green ideas sleep furiously”—the sentence ismeaningless but easily recognized as grammatical without any prompting. Con-versely, we can recognize the sequence of familiar terms “Plato dinosaur orange”as not being a grammatical sentence. Linguists and cognitive scientists havetaken points like these as forcing us to accept autonomous grammatical rules:grammatical rules that aren’t covertly appealing to semantic rules or some otherkind of rules.34

As already noted, the person most responsible for this rule-based vision ofnatural language is Noam Chomsky.35 Here’s Chomsky arguing for a rule-basedapproach to grammar in his famous review of arch-behaviorist B.F. Skinner’sVerbal Behavior :

We constantly read and hear new sequences of words, recognize themas sentences, and understand them. It is easy to show that the newevents that we accept and understand as sentences are not related tothose with which we are familiar by any simple notion of formal (or

30See Berko (1958); my account of the wug test is based on that of Pinker (1999), pages14-15.

31The symbol “a” expresses the concatenation function: so ”a”a”b” = ”ab”.32See Chomsky and Halle (1968).33See Chomsky (1957) and (1965); Chomsky’s theories of syntax have changed since these

initial presentations, see Jackendoff (2002) for a partial overview.34See Pinker (1994) for a comprehensive popular account of the deliverances of mainstream

linguistic theory.35For an account of the development of linguistics in the twentieth century and the pivotal

but often controversial role of Chomsky, see Harris (1993).

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semantic or statistical) similarity or identity of grammatical frame.. . . It appears that we recognize a new item as a sentence not becauseit matches some familiar item in any simple way, but because it isgenerated by the grammar that each individual has somehow and insome form internalized.36

These grammatical rules are discrete combinatorial systems: they take somefinite number of initial inputs (words drawn from a lexicon) and combine them invarious ways to make phrases and sentences. For example, a simple grammaticalrule might tell us that concatenating a noun phrase like “the drunk philosopher”with a verb phrase like “ran away” results in a sentence (“the drunk philosopherran away”). Another feature of grammatical rules is that they are recursive: theoutput of some of our grammatical rules can be fed back in as input to the samerule. So if we have a rule like “it is not that case that”a� is a sentence when � isa sentence, this very same rule’s output sentence (“it is not that case that”a�)can be fed back into the rule to produce a new sentence (“it is not that casethat”a“it is not that case that”a�) and so on ad infinitum.37

There are various natural questions about linguistic rules that arise: Howhave we learned these rules? Did we learn these rules? How are the rules inter-nalizes by speakers? Are the rules perfectly determinate? Etc. Happily though,we can avoid these issues here. My only concern thus far is that linguistic rulesthat were not explicitly adopted by speakers in some act of declaration, are offundamental importance in modern science’s study of mind and language. Thismeans that in lodging his complaint about explanatory worthlessness of implicitrules, Quine is already swimming against the current of contemporary scientificthought (Quine himself was well aware of this—his remarks on post-Chomskylinguistics will be discussed below).

In order to vindicate implicit conventionalism, the conventionalist needs toposit inference rules, and while mainstream linguistics generally takes it as es-tablished that humans use phonological, morphological, and grammatical rules,they rarely if ever talk about inference rules. But the very reasons that linguistsposit rules of morphology and grammar apply as well to rules of inference. Al-

36From Chomsky (1959), quoted from page 59 of Block (1980); Chomsky’s review is ofSkinner (1957).

37Recursive grammatical rules are often taken to be universal amongst human languages,but recently Daniel L. Everett has argued that the language used by the Pirahã people in theAmazon lacks recursion; see Everett (2012) for a popular presentation. It’s worth stressing thatEverett thinks that the Pirahã are capable of a type of recursive thinking and that recursionin some sense is central to human thought, it is just that he denies sentence recursion occursin their language.

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though this hasn’t—as far as I am aware—been noted in the literature, uponreflection this should be relatively unsurprising. It is, afterall, very widely be-lieved that English speakers follow natural language versions of the rule modusponens (MP ) when reasoning with “if”.38

Recall that linguists have been persuaded that speakers follow rules of mor-phology and grammar because they (speakers) tend to agree about a huge num-ber of hitherto unencountered cases, but it seems highly plausible that directlyanalogous reasoning would lead us to posit syntactic rules of inference. Considerthe following argument:

1. Wugs eat computers

2. If wugs eat computers then lugs eat computers

3. So: lugs eat computers (1, 2)

Almost all English speakers, perhaps including fairly young children, wouldagree that this argument is valid, correct, or otherwise acceptable. Moreover,if we presented English speakers with (1) and (2) and asked them what, ifanything, they could conclude from these two claims, it’s likely that a largemajority of them would come up with something very much like or even identicalto (3). Not being a psychologist, or an experimental philosopher, I haven’tperformed the relevant experiments, but I think it’s extremely likely that theywould go in the way I’m predicting.

Despite their neglect by syntacticians and linguists, rules of inference seemto have just as much a claim to being theoretical posits of ours as do rules ofmorphology or grammar. The argument is the same in each case: speakers reactin a uniform way to cases that they not only have not encountered, but couldnot have encountered before. Uniformity of extension to novel cases is the sinequa non of rule-following behavior. We all apply rules like modus ponens incases that we have never encountered before, perhaps on a daily basis. Thatspeakers follow rules of this kind and aren’t merely generalizing from experiencein some simplistic manner is well-established by the facts of day-to-day life.

Quine might be able to shrug off arguments like this because he was a be-haviorist, but few contemporary linguists or philosophers would follow him here.For us, the question is not are there rules of inference in natural language, but

38This has been challenged, e.g., by McGee (1985); see Bennett (2003) for extensive discus-sion of all aspects of natural language conditionals.

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rather, are these rules truly syntactic rules, as the conventionalist seems to re-quire? Just as linguists argue that grammatical judgments aren’t responsiveto prior semantic judgments by showing that we make grammatical judgmentsabout nonsensical strings, in the example of a novel inference above the sen-tences involved are nonsensical but grammatical sentences of (some expansionof) English. And since sentences (1) and (3) in the above argument aren’tactually sentences of English, there is no way that the argument above couldhave been arrived at by performing semantic operations on its various premisesand their components. So once again, the case for positing autonomous (non-semantic) rules of inference as part of our linguistic competence exactly parallelsthe case for positing autonomous (non-semantic) rules of grammar as part ofour linguistic competence.

Despite the general consensus in favor of rules, some cognitive scientists havetaken issue with the general case for linguistic rules. For example, connectionistspresent models of (aspects of) our linguistic competence that eschew formalrules and instead work with mere pattern association and training implementedon computational systems meant to model the parallel and distributed aspectsof the brain. Some connectionists models have been able to simulate certainaspects of human linguistic competence that are usually thought to requirerules—for example David Rumelhart and James McClelland’s work on verbsand past tense. Despite these successes, by and large, mainstream linguisticsand cognitive science continue to think that that rules of various kinds cannotbe eliminated from our models of human linguistic competence.39

Another challenge to my case for inference rules comes from general psy-chology rather than linguistics. There are results in the psychology of reasoningthat some may take to undermine my argument for positing linguistic rulesof inference. It is well know that humans fare quite poorly on many abstractreasoning tasks, including some that task them with verifying or falsifying arule stated using the conditional (“if...then...”).40 It has also been demonstratedthat people do much, much better on structurally identical tasks that are mademore concrete, say by embedding them in some type of familiar social setting,i.e., when the rule being verified/falsified is not abstract, but is one that could

39See Rumelhart & McClelland (1986); see also the discussion of connectionism in Church-land (1995) for endorsement by a philosopher; Pinker & Prince (1988) is comprehensive rebut-tal to connectionist theories of human language; Pinker (1999) contains a popular treatmentof arguments against connectionism.

40A classic example is the Wason selection task or Wason card task; see Wason (1966) and(1968) and Wason & Shapiro (1971).

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be encountered in an actual practical situation, people do much better, despitethe practical task and the abstract task being structurally identical and thusthe same from a logical point of view. In response to results like these, someevolutionary psychologists have argued that human reasoning proceeds not viageneral, all-purpose, abstract rules, but rather via specific mental modules fordealing with various situations that were encountered in the ancestral environ-ment in which the brain was evolving.41

These claims are controversial and have been met with vociferous criticism.42

But it is important to note that, by and large, my claims here bypass this debate.When linguists posit morphological, phonological, and grammatical rules, theydo so against the backdrop of a distinction between our linguistic performanceand our linguistic competence.43 Our performance results from our competencetogether with the myriad factors that can interfere with it: failures of memory,computational errors, etc. The key is that a speaker S following a inference ruleR is compatible with S being quite bad at following R in certain situations. Thismeans that despite failures of performance, even systematic failures, S may stillbe said to be following R if S is disposed to accept corrections toward R, admiterrors when they are pointed out, etc. A remark made by Johan van Benthamis relevant here:

A psychologist, not very well disposed toward logic, once confessed tome that despite all problems in short-term inferences like the WasonCard Task, there was also the undeniable fact that he had never metan experimental subject who did not understand the logical solutionwhen it was explained to him, and then agreed that it was correct.44

The behaviors this psychologist is referencing provide strong evidence for think-ing that speakers are following rules of inference when performing various rea-soning tasks, despite initial poor performance in some contexts. But just likewith other aspects of our linguistic competence, many factors can improve orimpede performance of a task in some contexts. In general: thinking that thereis a mental module that assists with cognitive tasks involving certain social as-pects is fully compatible with taking speakers to be following linguistic rules ofinference like modus ponens when reasoning with the conditional. Against thebackground of a performance/competence distinction, such a mental module

41The original argument for this position is in Cosmides & Tooby (1992).42See, e.g., Davies, et al (1995).43This distinction was introduced by Chomsky in his (1965).44Quoted from van Bentham (2008).

21

is best seen as helping us to avoid various performance errors, rather than asundermining the very idea that we follow rules like (MP ).

More could obviously be said, but we have already seen that standard lin-guistic methodology leads us to posit syntactic rules of inference as part of ourlinguistic competence; and particularist and context-sensitive approaches in thepsychology of reasoning are not necessarily incompatible with this posit, despitewhat is sometimes thought. In order to fully answer Quine’s challenge for theimplicit conventionalist we must argue that, with these rules in hand, we canusefully distinguish the conventional truths from truths that are obvious andperhaps a priori but non-conventional.

(ii) Conventional truth isn0t just obviousness. The heart of Quine’s com-plaint against implicit conventionalism is that the implicit conventionalist’s po-sition doesn’t go beyond the mere claim that logical truths are obvious or firmlyaccepted. However, once linguistic rules of inference are accepted, we can sin-gle out those sentences that follow from the rules of inference alone, with nopremises. To illustrate: assuming for the moment that the rules of our languageare roughly those of classical logic, then every instance of the law of excludedmiddle will be provable from our rules with no premises. By contrast,a neces-sary but non-logical truth like “water is H2O” will not be provable on the basisof the rules of language alone (presumably). There may be some non-logicalconceptual truths, perhaps like “bachelors are unmarried”, that are also prov-able from the rules of language alone, but given a distinction between logicalconstants like “and”, “not”, and “if” and non-logical constants like “bachelor”,a conventionalist can single out the logical truths as those that are provablefrom zero premises using only the rules of inference for logical vocabulary. Ofcourse, spelling out this theory in detail requires that the conventionalist offera theory concerning what makes a term or a rule count as “logical” (Carnapand other conventionalists attempted this, and there are many proposals fromnon-conventionalists in the literature that conventionalists could appropriate).

Clearly distinguishing the supposed logical truths from the merely obvioustruths like “it has rained at least once in the past” will be the first step to animplicit conventionalist theory of logic; the second will involve explaining whyprovability suffices for truth. The standard conventionalist answer, going backat least to Carnap, involves accepting some kind of metasemantic inferentialismaccording to which the basic rules of inference of our language are meaningconstituting for the vocabulary in our language and are thus automatically valid.In other words, implicit conventionalism naturally combines with a version of

22

metasemantic inferentialism according to which the rules of inference in ourlanguage are automatically truth-preserving. Thus, since it follows from thelogical rules of our language that either the Patriots won Super Bowl XXXVIor the Patriots did not win Super Bowl XXXVI, and all of these rules arenecessarily truth-preserving, then the sentence “either the Patriots won SuperBowl XXXVI or the Patriots did not win Super Bowl XXXVI” is necessarilytrue. And its truth is explained not by any fact about the world, but by thesentence following from the logical rules of our language alone, i.e., this andother sentences provable from the logical rules alone are true by convention. Invery rough outline this is one way that an implicit conventionalist theory will,suitably fleshed out, be able to use linguistic rules of inference to explain howlogical truths are true by convention without the notion of truth by conventionbecoming vacuous or applicable to all obvious truths.

This has been the merest sketch of the role that rules of inference couldpotentially play in a full implicit conventionalist theory of logic. It hardly needsto be said that, even given the notion of a linguistic rule of inference with whichto work, the task of constructing a full conventionalist theory of logical truthsis non-trivial.45 There are many points at which the theory may yet falter.However, all that is relevant for our purposes is that Quine’s complaint, thatthe notion of an implicit convention or a linguistic rule of inference doesn’tgive the conventionalist the resources to adequately single out the logical truthsfrom other obvious or supposedly a priori truths, is simply false. Whateverthe ultimate merits of implicit conventionalism, given the notion of a rule ofinference, Quine’s complaint about implicit conventionalism is dead in the water.

What should Quineans say in response? Perhaps the modern day Quineanhas a recourse that can be found in Quine’s own reactions to the Chomskianparadigm shift in linguistics? After the revolution in linguistics spearheaded byChomsky, Quine had several occasions to address the new paradigm and discusswhether or not it refuted his behaviorist approach to language. He was opento accepting Chomsky’s arguments that more than traditional behaviorism’smechanisms were needed to explain language learning:

It may well turn out that processes are involved that are very unlikethe classical process of reinforcement and extinction of responses.This would be no refutation of behaviorism, in a philosophically sig-nificant sense of the term; for I see no interest in restricting the term

45For more on this, see my (2014a).

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’behaviorism’ to a specific psychological schematism of conditionedresponse.46

In this way, Quine seems to allow for the use of linguistic rules in explaininghuman linguistic competence. However, in a slightly later and more thoroughdiscussion of contemporary (circa 1970) linguistics, Quine raised a number ofcriticisms of types of implicit rules posited by linguists based on the differentways that rules can relate to behavior.

In his later discussion, Quine distinguished between a rule R fitting speakerbehavior—where fit is simply a matter of true description—and rule R guidingspeaker behavior—where guiding is a matter of cause and effect. Significantly,Quine claims:

. . . behavior is not guided by the rule unless the behavior knows therule and can state it.47

Combining his complaints, Quine can be seen as arguing that rules are onlyexplanatory when they play a role in guiding behavior. He is aware that thelinguistic rules posited by Chomsky and others were implicit and didn’t fitneatly into his dichotomy between fitting and guiding, but he rejected these rulesbecause, he claimed, they went beyond the evidence. He argued that all of ourevidence for rules of grammar can, at best, determine which strings of symbolsdrawn from the lexicon of our language count as sentences. If this is right, thenany proposed grammar that produces the same set of grammatical sentencesfrom the lexicon is as good as any other vis-à-vis the empirical evidence. Beyondthis, it is simply a matter of choosing the pragmatically best grammatical theory.

We can imagine a similar Quinean argument concerning rules of inference.This imagined Quinean claims that the evidence only allows for us to determinethe set of valid inferences in our language, but beyond that there is no fact aboutwhich rules are being followed. The first point to make in response is that evenif this complaint is correct, identifying the set of valid inferences in our languagesuffices to determine the logical truths in our language (since the set of validinferences will determine the set of sentences provable from the empty premiseset). This means that given the valid inferences of the language, we can recover(and thus explain) the logical truths in the language (if such there be). This isto say that Quine’s criticisms of linguistic rules don’t undermine the use of theserules to found conventionalism once we have admitted, in addition to rules of

46Quoted from Quine (1968).47Quine (1970), page 386.

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grammar, rules of inference. So by Quine’s own lights, implicit conventionalismseems admissible as a theory of logic.

The second point to make in response is that despite my concession to Quinefor the sake of argument, we do have the resources to distinguish which rules ofour language are basic and which are derived in exactly the manner I sketchedabove, viz., a basic rule is simply accepted, whereas a non-basic rule is acceptedonly after a derivation from the basic rules has been found or the existence ofsuch a derivation accepted. This allows us to distinguish the basic from thenon-basic rules using simply the gross dispositions of language users, evidencethat Quine himself, arch-behaviorist, allowed and relied upon. So this meansthat by Quine’s own methodological lights, the implicit conventionalist has theresources to single out some valid rules in our language—perhaps includingmodus ponens and conditional proof—as the basic rules that constitute ourlanguage/linguistic competence. So even if two sets of rules determine exactlythe same set of valid inferences for the language, the Quinean argument forunderdetermination doesn’t go through in this case, because the data Quineallows suffices for breaking the tie in this kind of case.

Quine’s worries about linguistic rules of grammar don’t carry over to lin-guistic rules of inference in a way that blocks implicit conventionalism. Likethe grammatical rules that he was wary of, linguistic rules of inference don’t fitfirmly into either the “mere fitting” or “guiding” category. They aren’t simplydescriptions of the actual linguistic behavior of speakers, since they extend be-yond all observed and actual linguistic behavior and apply to novel cases. Andwhile they aren’t behavior guiding in the manner suggested by Quine—whichrequired explicitness—speakers, even without formulating the rules explicitly,accept corrections toward the rules, frown upon deviations from the rules, etc.,and so the rules are behavior guiding in a less demanding sense. In short: theseimplicit rules of language use, in a manner similar but distinct to other linguisticrules of language, both fit/describe and guide our linguistic behavior, thoughthey don’t just merely do either.

Quine’s view, that implicit rules cannot do useful, explanatory, theoreticalwork, is an implausible fringe view. Quine claims that once explicitness isremoved, you are left with nothing. That is just false. Whether or not implicitconventionalism can be maintained, implicit linguistic rules, including implicitlyfollowed rules of use or inference, would do useful theoretical work just as surelyas their cousins in phonology, morphology, and grammar. In addition, thereasons Quine offered for skepticism about the explanatory worth of these more

25

familiar linguistic rules (a) don’t carry over to rules of inference and (b) evenif they did, wouldn’t block an implicit conventionalist theory of logical truth.Quine’s challenge for the implicit conventionalist has been met on both basicscientific grounds and on methodological grounds that Quine himself accepted.

V Coda

Quine’s super-task and regress arguments together defeat any version of explicitconventionalism, but they fail to defeat implicit conventionalism—a point thatQuine himself realized more clearly than some who have endorsed his arguments.Against the implicit conventionalist, Quine raised a different problem: implicitconventionalism is explanatorily idle, since it amounts to nothing more thanrestating the behavioristic fact that simple logical truths are obvious. Againstthis charge I have pointed out that (i) the modern scientific study of languageand mind posits various kinds of syntactic rules to explain human verbal be-havior and linguistic capabilities and argued that the same considerations thatlead to the positing of rules of phonology, morphology, and grammar apply alsoto the positing of inference rules; (ii) with these rules posited, there is an obvi-ous difference between sentences that follow from the rules alone (conventionaltruths) and those that do not.

The implicit logical conventionalist can maintain that for any logical truth�, the truth of � in our language is explained by �’s being provable solely on thebasis of the linguistic rules of inference of our language, as modeled in naturaldeduction systems for formal languages. In this sense, the rules of our language,by themselves, fully explain the truth of � when � is a logical truth. This basicapproach cannot be extended as is to any form of mathematics that includeseven basic arithmetic, since by Gödel’s incompleteness theorem, no theory ofarithmetic meeting certain basic constraints (consistency, recursiveness) will besuch that either � or p¬�q will be provable for every sentence � in the language;yet according to our intuitive picture of mathematics, for each sentence � either� is true or p¬�q is.48 Still, there is no formal obstacle to applying this version ofimplicit logical conventionalism to semantically complete logics, such as classicalsentential logic and first-order logic.

Conventionalism is a much maligned view, and it is often thought to be un-tenable for fundamental reasons. One of the most popular holds that since anysentence S is true just in case there is some proposition p and S means that

48See Gödel (1931).

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p and p, that if our conventions could make it the case that S were true, thenour conventions would have to make it the case that p, but that’s absurd. Howcould our conventions make it that either it is raining or not raining? Do theyhave the powers of God? This argument is very widely believed, but I have ar-gued elsewhere that it is fundamentally flawed.49 The other canonical, folkloricrefutation of logical conventionalism comes from Quine and has been analyzedhere. We saw at the outset that influential philosophers still point to Quine’sdiscussion as definitive, but I have argued that this argument, too, is funda-mentally flawed. Whatever the merits of logical conventionalism, understoodimplicitly, neither Quine nor anyone else has refuted it. Yet?50

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