Jody Azzouni
1. Introduction
Our logical practices, it seems, already exhibit “truth by convention.” A visible part of contemporary research in logic is the exploration of nonclassical logical systems. Such systems have stipulated mathematical properties, and many are studied deeply enough to see how mathematics – analysis in particular – and even (some) empirical science, is reconfigured within their nonclassical confines.1
What also contributes to the appear- ance of truth by convention with respect to logic is that it seems possible – although unlikely – that at some time in the future our current logic of choice will be replaced by one of these alternatives. If this happens, why shouldn’t the result be the dethroning of one set of logical conventions for another? One set of logical principles, it seems, is currently conventionally true; another set could be adopted later.
Quine, nevertheless, is widely regarded as having refuted the possibility of logic being true by convention. Some see this refutation as the basis for his later widely publicized views about the empirical nature of logic. Logical principles being empirical, in turn, invites a further claim that logical principles are empirically true (or false) because they reflect well (or badly) aspects of the metaphysical structure of the world. Just as the truth or falsity of the ordinary empirical statement “There is a table in Miner Hall 221B at Tufts University on July 3, 2012,” reflects well or badly how a part of the world is, so too, thePrinciple of Bivalence is true or false because it reflects correctly (or badly) the world’s structure. I’ll describe this additional metaphysical claim – one that I’m not attributing to Quine (by the way) – as taking logical principles to have representational content. Most philosophers think logical principles being conventional is
1
The families of intuitionistic and paraconsistent logics are the most extensively studied in this respect. There is a massive literature in both these specialities.
incompatible with those principles having representational content.2 I undermine the supposed opposition of these doctrines in what follows. That still leaves open the question whether logical principles do have representational content; but I also undermine this suggestion. That may seem a lot to do in under eight thousand words. Luckily for me (and for you too), most of the important work is already done, and I can cite it rather than have to build my entire case from scratch.
2. Quine’s dilemma
It’s really really sad that almost no one notices that Quine’s refutation of the conventionality of logic is a dilemma. The famous Lewis Carroll infinite regress assails only one horn of this dilemma, the horn that presupposes that the infinitely many needed conventions are all explicit. Quine (1936b: 105) writes, indicating theother horn:
It may still be held that the conventions [of logic] areobserved from the start, and that logic and mathematics thereby become conventional. It may be held that we can adopt conventions through behavior, without first announcing them in words; and that we can return and formulate our conventions verbally afterwards, if we choose, when a full language is at our disposal. It may be held that the verbal formulation of conventions is no more a prerequisite of the adoption of conventions than the writing of a grammar is a prerequisite of speech; that explicit exposition of conventions is merely one of many important uses of a completed language. So con- ceived, the conventions no longer involve us in vicious regress. Inference from general conventions is no longer demanded initially, but remains to the subsequent sophisticated stage where we frame general statements of the conventions and show how various specific conventional truths, used all along, fit into the general conventions as thus formulated.
Quine agrees that this seems to describe our actual practices with many conventions, but he complains that (Quine 1936b: 105–106):
it is not clear wherein an adoption of the conventions, antecedently to their formulation, consists; such behavior is difficult to distinguish from that in which conventions are disregarded. . . In dropping the attributes of delib- erateness and explicitness from the notion of linguistic conventions we risk depriving the latter of any explanatory force and reducing it to an idle label.
2
Ted Sider, a contemporary proponent of the claim that logical idioms have representational content, represents the positions as opposed in just this way; he (Sider 2011: 97) diagnoses “the doctrine of logical conventionalism” as supporting the view that logical expressions “do not describe features of the world, but rather are mere conventional devices.”
We may wonder what one adds to the bare statement that the truths of logic and mathematics are a priori, or to the still barer behavoristic state- ment that they are firmly accepted, when he characterizes them as true by convention in such a sense.
These challenges aren’t specifically directed against the conventionality of logic but against tacit “conventions” of any sort. One challenge is concerned with making sense of when specific behaviors are in accord with the proposed tacit conventions and when they’re not. One prob- lem, that is, is this: if the conventions are explicit, we know what the conventions are – because they’ve been stated explicitly – and the behavior can be directly measured against them to determine deviations. But tacit conventions must be inferred from that very behavior, so the challenge goes, and therefore a lot of unprincipled play becomes possible because various conventions may be posited, these conventions differing in how far the practitioners’s behavior is taken to deviate from them. A second issue Quine raises is with the label “convention”; he wants to know what’s distinctive about tacit conventions that makes them stand apart from the simple “behavioristic” attribution that the population “firmly accepts them.”
So Quine’s two objections come apart neatly. There is, first, a challenge to the idea that a set of rules can be attributed to a population in the absence of explicit indications like a set of official conventions. Even if this first challenge can be circumvented, the second worry is why the set of rules so attributed to a population should be called “conventions.”3
If we concede the requirement of explicitness to Quine, we’re forced to something like the Lewis account of convention:4
A regularity R, in action or in action and belief, is a convention in a populationP if and only if, within P, the following six conditions hold: (1) Almost everyone conforms toR.
(2) Almost everyone believes that the others conform toR.
(3) This belief that the others conform toR gives almost everyone a good and decisive reason to conform toR himself.
(4) There is a general preference for general conformity toR rather than slightly-less-than-general conformity – in particular, rather than con- formity by all but anyone.
3
See (Quine 1970b) for a reiteration of the first challenge with respect to linguistic rules.
4
(5) There is at least one alternativeR0 toR such that the belief that the
others conformed to R0 would give almost everyone a good and decisive practical or epistemic reason to conform toR0likewise; such
that there is a general preference for general conformity toR0 rather
than slightly-less-than-general conformity toR0; and such that there is normally no way of conforming toR and R0 both.
(6) (1)–(5) are matters of common knowledge.
There aremany problems with this approach – indeed, it’s no exaggeration to describe condition (6) as yielding the result that there are almost no conventions in any human population anywhere. But can Quine’s chal- lenges be met? Aretacit conventions cogent?
3. Tacit conventions: Burge and Millikan. Suboptimality Since Quine’s challenges are directed towards tacit conventions of any sort, let’s look at what appears to be a less-complicated case: purportedly tacit linguistic conventions. Linguistic conventionality seem less complicated than logical conventionality if only because the intuitions that seem to accompany logical principles (ones about necessity, ones about aprioricity) aren’t present in the linguisitic case. As Burge (1975: 32) writes, “Language, we all agree, is conventional. By this we mean partly that some linguistic practices are arbitrary: except for historical accident, they could have been otherwise to roughly the same purpose.” He adds, “which linguistic and other social practices are arbitrary in this sense is a matter of dispute.” I’ll shortly show that this matters to theempirical question whether language is conventional (and in what ways) – the thing Burge tells us we all agree about.
But first, notice something important that Burge is explicit about (although he doesn’t dwell on it): there are psychological mechanisms that enable these regularities. Burge (1975: 35) writes, “the stability of conven- tions is safeguarded not only by enlightened self-interest, but by inertia, superstition, and ignorance.” He makes this point rapidly, and in passing, because he’s instead intent on undercutting the explicitness assumption for conventions: “Insofar as these latter play a role, they prevent the arbitrari- ness of conventional practices from being represented in the beliefs and preferences of the participants.”
Let’s focus on the important word “inertia.” This is an allusion to an – ultimately neurophysiological – mechanism of imitation. The point is made quite explicit some years later by Millikan when she characterizes
“natural conventionality” in terms of patterns that are “reproduced.” Crucial to the idea (Millikan 1998: 2) is that “these [conventional] patterns proliferate . . . due partly to weight of precedent, rather than due, for example, to their intrinsically superior capacity to perform certain func- tions.” That is (Millikan 1998: 3), “had the model(s) been different. . . the copy would have differed accordingly.”
Some may be worried about this characterization of conventional pat- terns.5 As I understand the characterization, for it to work we need to sharply distinguish between the patterns being conventional because they are proliferating partly due to the weight of precedent, and the patterns instead only being thought to be conventional because they’re thought to involve arbitrariness in our choice of a course of action. On the one hand, we can simply be wrong – thinking that arbitrariness is involved when it isn’t. On the other hand, there can be “arbitrariness” without our realizing it: there are other model-options we don’t know about, which, were they in place, would have been imitated instead.
Consider the venerable practice of rubbing two sticks together to start a fire.6
A tribal population may simply fail to realize that banging rocks together will work instead. Their practice ofrubbing sticks to start a fire is conventional despite their failing to realize this. Imagine, however, that they live where there are no such rocks, and where, presumably, there are available no other ways to start a fire. Then the practice isn’t conventional. Suppose (after many moons) the tribe migrates to an area where suitable rocks are located. Because of a change of location, a practice that wasn’t conventional has become conventional. (More generally, technological development can induce conventionality because it creates practical alter- natives that weren’t there before.) There is a lot of work to do here (much of it empirical) detailing more fully the notion of “genuine practical alternatives” – what sort of background factors should be seen as relevant and which not – but the need for hard empirical work isn’t problematical for this characterization of tacit convention.
Another worry. Many people believe (and some believe correctly) that some of their practicesP are optimal. They engage (imitate) those practices (so they believe) precisely because they think these are optimal practices and not because of the weight of precedent. Conventional or not conventional? Well, beliefs about optimality aren’t relevant; only the
5
Epstein (2006), for example, is worried. My thanks to him for conversations (and email exchanges) about this topic that have influenced the rest of this section.
6
efficacy of P ’s optimality to the spread of the practice through the population is relevant. Suppose alternative suboptimal practices would not have spread through the population, if instead they were the models, precisely because their suboptimality would have extinguished the prac- tices (or the population engaging in them). Then P isn’t conventional. Otherwise it is. Superior optimality, of course, can be why a practice triumphs over alternatives. It’s an empirical question in what ways the optimality of a practice relates to its popularity, but I’m betting that superior optimalityrarely counts for why a practice P spreads through a population.7 If a practice has enough optimality over other options to make its superior optimality efficacious in its spread, then it isn’t conven- tional. On the other hand,some superior optimality clearly isn’t enough to erase conventionality. Therefore: How much superior optimality is required to erase conventionality is an empirical question, turning in part on how muchdamage a suboptimal practice will inflict on its population, how fast this will happen, how fast this will be noticed, and so on. These empirical complications, although of interest, don’t make the notion of tacit convention problematical.
One point in the previous paragraph must be stressed further because I seem to be definitively breaking with earlier philosophers on convention- ality on just this point. This is thatroughly equivalent optimality is invari- ably built into the characterization of conventionality: the alternative practices that render a practice conventional are ones that are reasonably equivalent in their optimality – this is built into Lewis’ approach by condition (3), that others conforming to such alternatives would give people “good and decisive” reasons for engaging in them as well – this is false if the alternative practices are suboptimal enough. It seems built into Millikan’s approach – at least when conventional patterns serve functions – because alternatives should serve functions “about as well” (Millikan 2005: 56).
Unfortunately, as Keynes is rumored to have pointed out in a related context, in the long run we’re all dead. Anthropology reveals that seriously suboptimal practices are quite stable in human populations (and, to be
7
Is it conventional that we cook some of our food and don’t eat everything raw? I think it is. Is the alternative suboptimal? There is controversy about this, but I think it is: I think this is why the alternativeeventually died out among our progenitors (after thousands of years, that is). On the other hand,some of the reasons for why the alternative died out (the greater likelihood of food poisoning, the inadvertent thriving of parasites in one’s meal, etc.) have been – presumably – eliminated by technical developments in food processing. So the practice of eating all food raw needn’t be as suboptimal as it once was.
honest, a cold hard look at our own practices reveals exactly the same thing). Evolution takes areally long view of things – even the extinction of a population because it engages in a suboptimal practice may occur so slowly that the conventional fixation of that practice can occur for many generations, at least.8 How suboptimal a practice can be (in relation to alternatives) is completely empirical, of course, and turns very much on the details of the practices involved (and the background context they occur in); but optimality comparisons should play only a moderate role in an evalu- ation of what alternative candidates there are to a practice, and therefore in an evaluation of whether that practice is conventional and in what ways. (This will matter to the eventual discussion of the conventionality of logic: that alternative logics are suboptimal in various ways won’t bar them from playing a role in making conventional the logic we’ve adopted.)
One last additional point about conventionality that I’ve just touched on in the last sentence. This is that it isn’t – so much – entire practices that are conventional, but aspects of them that are. “Minor” variations in a practice are always possible, minor variations that we don’t normally treat as rendering the practice conventional because we don’t normally treat those variations as rendering the practice a different one. There are many variations in how sticks can be rubbed together, for example. How we describe a practice or label it (how we individuate it) will invite our recognition of these variations as inducing conventionality or not. It’s conventional to rub two sticks together in such and such a way, but not conventional (say) to rub two sticks together instead of doing something else that doesn’t involve sticks at all (in a context, say, where there are no rocks). How we individuate “practices” correspondingly infects how and in what ways we recognize a practice to be conventional; but this is hardly an issue restricted to the notion of tacit convention, or a reason to think the notion has problems.
4. Empirical evidence for tacit conventions
More than a serviceable notion of tacit convention is needed to respond to Quine. Recall his worry aboutevidence, that “in dropping the attributes of
8 A nice example, probably, is the arrangement of the lettered keys on computer keyboards. No doubt
the contemporary distribution of letters is suboptimal compared to alternatives; it’s clearly an inertial result of the earlier arrangement of the keys on typewriters – which was probably also suboptimal in its time and relative to its context at that time. I’m not suggesting, of course, that keyboard conventions are contributing to a future extinction event – although I have no doubt that a number of conventions that we currently use are doing precisely that.
deliberateness and explicitness from the notion of linguistic convention we risk depriving the latter of any explanatory force and reducing it to an idle label.” As it turns out, and this is an empirical discovery, for conventional patterns to even bepossible for a human population requires neurophysio- logical capacities and tendencies in those humans. These are currently being intensively studied, and preliminary results reveal how human children have a capacity to imitate that’s largely not shared with other animals.9 The recently discovered mirror-neuron system is crucial to this capacity (but is hardly the whole story). My point in alluding to this empirical literature is to indicate how a systematic response to Quine’s challenges has emerged: Not only is a decent characterization of tacit conventionality – as noted above – now in place, but an explanation of the capacity for imitation that underwrites tacit conventions in this sense (and one that goes far beyond sheer behavioral facts about “firm accept- ance”) is also emerging due to intensive scientific study.10
Of course, Millikan (and Burge) seem to largelyassume that language is “conventional” in the appropriately tacit sense. But this (on their own views) should be an entirely empirical question – patently so now that the neurophysiological mechanisms of imitation are being discovered. It’s an empirical question, for one thing, whether these mechanisms (mirror neurons, etc.) are involved in language acquisition – more specifically, it’s an empirical question how they’re involved in language acquisition. Imagine (instead) that something like Chomsky’s principles and param- eters model is at work in language acquisition.11
Then the picture is this: the child starts language-acquisition with a massive prefixed cognitive language-structure which is multiply triggered to a final state by specific things the child hears. Imagine (what’s surely false, but will make the principle of the point clear) that there are (say) only three thousand and seventeen human languages that are possible, so that the child has only to hear a relatively small number of specific utterances for that child’s
9
See the introduction to (Hurley and Chater 2005a&b) for an overview of work as of that date. See