A Sketchy Logical Conventionalism

OpenAlex · İngilizce

Anti-realism about the foundations of logic are curiously absent from the literature. This is especially striking given natural analogies with moral anti-realism. I argue that we should reserve this view a place by showing that it gives natural explanations of various features of logic and faces fewer problems than you might think. It’s a curious fact that anti-realist views in the foundations of logic are as rare as they are. In the foundations of moral philosophy, there is a nearly straight-down-the-middle split between anti- (and near enough) realisms and stark raving realism. Moral philosophy and logic share a similar set of problematic features—they’re both intuitively normative, objective, not empirically tractable, and have intuitive functions that could be served in multiple ways. Yet few people have defended the idea that logic can be given a satisfying anti-realist treatment.1 Part of the reason for this, at least in my view, is a lingering hangover from logical positivism. Enthralled by rather silly objections to positivism, many philosophers seem to think that the whole idea that logical facts are somehow set apart from ordinary factual judgements is a non-starter. Another large part seems to be a desire to set philosophy apart from the rest of the humanities, since conventionalism and relativism about fundamental matters are widely accepted in much of the rest of the humanities. And a third seems to be the special role that logic plays as both a subject of investigation and an investigatory tool (see Woods 2019c, for instance). But whatever the historical reason is, it’s a fairly obvious fact that logical anti-realism is rather absent from the playing field.2 My goal in this essay is to start making some space for this view. As will become clear, I can hardly give a knock-down argument for it. In an often abused, but still largely true, slogan, contemporary philosophy is largely a game of costing views out, seeing what we can and cannot accept (Lewis 1983). What I hope to suggest here is that anti-realism about logic, at least the conventionalism brand thereof, can be purchased at an attractive price. In order to do so, I will start by developing a few of the features I mentioned above and then suggest why I think that realist views will struggle to capture all of them. I’ll then argue that conventionalist views will do better on this score. I’ll then develop a sketch of a logical conventionalism, paying particular attention to places where philosophers have traditionally thought such views struggle. Logic in What Sense? The very first thing we need to do is describe which sense of ‘logic’ we’re talking about here. The term ‘logic’ is used in several ways. It is sometimes used to describe the kind of proof calculus we’re taught during our undergraduate degrees. This isn’t what we’re talking about; the foundations of this aren’t especially interesting, at least when we focus on its formal implementation.3 It is also sometimes used to describe processes of correct reasoning that are relative to particular applications—such as how to correctly aggregate information from databases. This also isn’t what we’re talking about. What we’re talking about is facts like If this or that, and not this, then that and This only if that, this, so that. What makes the sort of pattern described by If that leads to inconsistency, then not that correct? What makes failing to conform to such a pattern a mistake and one that we are typically entitled to criticize? It’s these facts—facts about the correctness of various patterns of logical dependence and facts about how they ought to condition our beliefs—that we’re interested in here. It’s important not to confuse these facts with facts about how we ought to reason in the broadest sense of actually drawing inferences. This conflation is pervasive in the literature, but is one that should be avoided for reasons best articulated by Harman (1986). To give a brief flavour of these sorts of reasons, suppose we believe something and we also believe that if it, then something else. Logic by itself doesn’t tell us how to modify our beliefs to conform the correct pattern This only if that, this, so that. That might require bringing in other considerations besides those of logic. All logic can tell us is that we’re making a logical mistake if we continue to believe this and not that, along with the conditional connecting them. And that our beliefs fail to reflect a correct pattern of reasoning. So we’re interested in characterizing the sort of structural relations on beliefs that we treat as basic in having a coherent set of beliefs, in the sense of not having made any culpable mistakes.4 Having said a bit about what sense of logic we’re investigating and set it apart from some other related notions, we can now turn to articulating a few features of logic in this sense. Logic Is Normative. Our first intuitive feature of logic is clear from our characterization of what notion of logic we’re looking for. We want an account of what makes certain patterns logically correct, and thereby an account of how that entitles us to criticize someone for failing to realize or realizing a contrary pattern. The italicized words in the previous sentence indicate two senses in which logic, in our sense, is normative.5 As I’ve argued elsewhere (Woods 2018a), they are deeply connected. To see how, let’s start with the more basic notion. The first, flatter, sense is simply that there’s a notion of correctness associated with logic. This is a normative notion, but it’s normative in a completely flat sense. Nearly every notion is normative like this, including oddball notions like ‘correct 9/11 truther reasoning’ and `correct according to Calvinball’. As you might expect from such an encompassing notion, that logic is normative in this sense doesn’t go very far. It’s just one possible system of rules among many; what of it? In Woods (2018a), I pointed this out that from any notion of correctness*, we could induce an associated ‘ought’ in terms of how closely we or the world or what have you are correct*. So, for our purposes here, we can easily have a large collection of logical oughts, corresponding to various collections of patterns. But note again that this doesn’t go very far; from the fact that we can make sense of oughtclassical and oughtintuitionistic, it doesn’t follow at all that we have any reason or normative pressure to do what we ought in either sense. We would need a further reason to conform to these notions of correctness. In order to get something closer to the second sense of normativity, one which licenses criticism, we need an account of how to activate or put in force one of these notions of logical correctness. This need not be anything more than the fact that one or the other of these notions of logical correctness has some worldly validity, but something needs to close the gap between there being a flat notion of correctness and a more oomphy or robust kind of normativity that would license criticism and the like. Logic Is Objective. Our second intuitive feature of logic is its objectivity. Logic is not supposed to be relativized to individuals or cultures; arguments don’t become correct by being articulated in different cultures; and so on. Logic is about what follows from what and why, period. We already made part of this point above, when we took instrumental notions of logical correctness off the table. These notions, useful as they are, are meant to be derivative of facts about the application and logic itself (and perhaps a bit of maths). That is, if we want to know how to reason with databases, this should be determined by facts about databases, such as the fact that they often contain benign inconsistencies that we’d like to contain, and logical facts about what would happen if we reasoned the usual way with them (Belnap 1977). But our most basic or canonical notions of logical correctness aren’t themselves derivative in this way; that would be flatly circular. This point was made by Quine (1936). Moreover, they’re not themselves relative to circumstance. They’re supposed to be above this kind of relativity; logic is characteristically formal and, consequently, free of worldly interference. If something is logically correct, it’s correct everywhere, no matter what that is like. The above is mere sloganeering, of course. But it’s familiar sloganeering and thus forms part of our collection of intuitive features to respect. We have to start somewhere with our investigation; (theoretical) folk intuitions seem the best place to do so. So a proper account of logical correctness and its grounds should pay some respect to them. We can put a bit more flesh on what we mean here. As emphasized by Crispin Wright, disputes about logical correctness don’t seem faultless; they don’t see to be cases where two participants to the dispute can have perfect access to all information about the dispute and make no errors, and yet come to different views. And as David Lewis emphasizes, we can fairly refuse to engage our opponents about logical matters even when we have defences against their challenges. So we seem to be permitted to be epistemically about our logical which is an obvious to logic as Lewis Logic Is in of the previous two our third feature is that logic isn’t an We don’t and accept our logical by any kind of but rather engage in ordinary with the subject of our also being part of the at least this seems to be how we go about making about which logic to accept and how to our one logic against and I’ve some of this feature (Woods but I with Quine in the We do our logical in much the way we our we do ordinary notions of in which of logic we should and which we should on This to looking at various of a how this or that would the of and to This feature is made even more by looking at the of contemporary with it. The in the previous of various and those from both contemporary and those from of the that and has to have at least a of to it. from the above, what this It to the that when how our logic should in terms of our logic or to accept a different one make of notions like the of a logic, its its how much information it and so on. these features of a particular logic we an and we see how to in our to by various that we need to our particular account when our logic, since many of the above and so deeply to our Moreover, this leads to feature which is in with the features so far. Logic Is The feature is perhaps the most of on logic in the of has to suggest that the of logic aren’t That is, that we have about which logic we can the of logic and its normativity, this is especially can we criticize other people for something different but to the we put it can logic be if there could be more than one way we could do it? It’s to that this is the If we our third that we ought to which logic to accept or to our in of various we need to that there can be in how various logical are. And a of the that this is the various of between various of our logic to with and many of with logic all seem to more or on a with respect to intuitive of So it seems we can have a different logic. it’s that two very different to that and those which conditional on a with respect to how they various of It’s on to see any robust reason to one way to the So if we one such we should that we could have for the other our that might be as a reason to think that of these is But that seems this the of logic. And some of our do seem a bit We could a but we could have it in an way by making different But of if logic is not in any obvious So our second and feature are in given the facts I’ve just with this Moreover, our first feature licenses for that the feature are So our collection of features of logic leads us fairly a Yet all of these features seem to part of how logic intuitively What ought we to This seems to out for an anti-realist a similar to by two intuitive features of moral have a be and an to them. This that moral if they would have to be very are not familiar or with like that. Moreover, of the problems that is supposed to and how they have in various places that our moral and are a bit we easily could have This leads to develop an of there are no moral but we as if there and more or for to do what we We might think that the of features I’ve just mentioned a similar If logic is normative, objective, and then we would need to a very kind of in the world to it. It would have to have a certain be at it would have to be worldly and the for and yet our best of it are deeply to our and of the and we could easily have something different the to which we put logic I cannot here give you a reason to logic an anti-realist This is a where a realist can their in the and that it just be the that the world is than we think. And how to other than by ordinary But I do think I can give reasons to the of and what I’ll now What kind of there’s a brief or two with logical these have not obvious reason for this is that we have no better idea how to develop an account in the logic than we do in the moral where we get to logic as To my there any to develop an of logical this seem on the whole to be a bit itself isn’t a view of the foundations of something so much as a So this my conventionalism about logic. If we at the features above, conventionalism seems to actually be a rather natural for how to these off with the of logic. of any conventionalist view, with Lewis is the fact that we could in have the that the system is supposed to in a different That is, there should be to the way we do That is in the logic we could have much We could the by what we can or how we And so on. that this is an not that we are to be by the collection of features I’ve put that conventionalism is a natural to the problems these features give But so I’ve only how this for one now at the that our are deeply to particular features of our role in the it’s no that our of what our are This people to the idea that logic is to us a in to people that we know what our are. But could be further from the and the All are at least Yet in of these cases is it obvious to any of us what all the are. We need and to us such And these themselves some of an in such To put it rules of are the least of more we accept certain of and which we accept is itself a rather on cases like with as is objective, in one sense, and not in It’s in the sense that we treat it as on of their when they’re in the for you to off in my even if you in a And it’s not in the sense that I as do that we could have places and the a to how we get along in the world we other of Moreover, it’s to our notions of logic in when we them. This point is often made with to moral we that we could have a different set of moral doesn’t force us to all of moral That would having as part of our moral a any set of will But we and should more than And are of developing correctness that are with and I’ve argued elsewhere that it’s and criticism, and our desire to that our of (Woods In it’s what the gap mentioned above, between there being a system of or patterns and that system of or patterns being or as I’ve described it as being in I’ll more about this but we can that a system of or logical patterns is in force for us if we treat of them as to criticize and more or desire to such patterns It seems clear that this is of our logical at least for those of us in the of might think that this kind of thing has a different when with the idea that there’s a of criticism to many folk that being is just a way of being moral in the So being is when it’s The with this view, as I pointed out in Woods is that we can all the moral from being and still be with the sense that we’re entitled to criticize someone for being a lingering of to being even when it doesn’t do any so I’ve So all in conventionalism like a for our foundations of logic. It a of logical many are in the sense. is are is and so is It a and important with It for our of logical and patterns to with what makes them the And it that there could have other we So why this view more I think this is the it’s given was I cannot develop a of the conventionalist of logic here, I’ll sketch the of such a view. I’ll then go a few objections you might of We can start off by that come in many like the rules of are fairly and easily by looking at the of the the game like are a of and particular Logic is to somewhere in it’s if a an it to and our logical This is part of what we do as We also our account of correct logical patterns to more and more of natural for on what follows from the or those I just said that our logical are But to I what it is to accept a system of as a matter of what in a sense of my I here in a sense. That of in the of individuals to such patterns of both as to their and as of criticism which and various forms of pressure So we accept a system of or in force for we have to criticize of patterns of as to our and as of criticism for both and To flesh this out a something like This pattern is in force for us the system of it, but that when we something like someone if then and as something to and as grounds for of we aren’t all very at such or even But when it’s that someone has a pattern like this, we do to be to criticize and we do it as something to be at least in Yet this isn’t to get us even in we don’t have of the It’s here that we need to make sense of a notion of We of our logical and so we to on and when So to put the view more a system of logical is in force for us when we have to to and to criticize folk for being or where the of these terms is set by what those we view as would be to treat as This is a much more account of what it is for a system of to be in force for that we need not a pattern as a way of being or in order to have the It can be more than that. We also might just when argue that this or that has made the most important is that we the or grounds for And this be so most of us don’t have to have the to which we should But we are to to on this the the and treat what they would criticize and as what we should criticize and And in logic, as in we are if not The in and what we should do our logical by of best with our to the of logic a coherent of the and as our third feature of logic And just as do with and do with In Woods I having and to and the point of to a system of I still think this is more or now a bit on the of the point of view to This is important it’s what to the fact that we are to criticize when they our logical even when we know that they don’t to them. We are simply not that about logical and this is by the fact that when we the point of view to other don’t seem in the and this is a much But this be especially logic is so fundamental to the way that we see our it so deeply our various that seeing a different way is if not We simply do not have the to our logical in and to do so in a That would require nearly all of our beliefs and their of logic is the of the of the this is something just most of our then do we logic at it of how arguments about which logic to accept typically start at an nearly our logical to develop this a few on the and off showing how we can our on the world our This be even a of what would have to that it’s nearly this of it’s no that it’s what a different system of logical would like. And thus it’s completely that we’re to criticize those our even are since simply don’t seem possible to us in our That isn’t to we more and This is much and largely what we do when we about logic. And it’s the sort of that we can actually make sense It’s not a bit of it, to get the of of an with logic when it to most fundamental logical and where it it’s where we start when we’re more in logic. the more we get so the more we’re to two and treat as something but not what we much as we’re to treat on the as it a few as with and even when logical are as in this they’re still And they still give us reasons to this in would more space than I have (see Woods for how to develop such a view, So we have what we we have a to to made sense of our of ordinary in a logic, and how we can that we could have way it. That is, to sketch a account of how logic could be which the features I’ve fact much to be but for this will to give you a brief I but note one fact that should make developing this kind of logical anti-realism more If you note that the view I give above makes sense, and is of or not logic has any realist We do our logical making of terms like and We do have to being in these and to criticize for being in them. And we do have so could further that these are they actually the logical the that why As I at the close of Woods that, of or not there are logical there will be logical then we should a bit at the idea that we need more than the what would they do besides our about how we in the of philosophy have large of our being a suggest that we should such and what could be more of a than a set of worldly logical facts that doesn’t any role in how or why we criticize other people for being objections here. The first, is to I’ve argued has the to And even there are of this in other like and normativity, it’s (Woods this is true, I don’t think it the I’ve given above for developing a conventionalist to the foundations of logic. This is a special in to logic, no matter what the foundations of logic for the but at the of So this isn’t much of an at the of the I think. The second mentioned above, is that it could be that logic is only in the sense that there’s a collection of that share a and this is some free at the conventionalist if you not much of a I have to if I could you that there’s that much conventionalism in logic, be a already a for But there are problems for this view. no to or and for logic. And we be to not confuse what like us will on with any sort of that those are the kind of we should on. The point further of but that will have to for I hope all we should be developing a conventionalist whatever it will come to