Expressivist ‘&’ and ‘~’

I wanted to follow up on Jimmy Lenman’s suggestion in a recent discussion thread that there is something harder for expressivists about accounting for negation than about accounting for conjunction. I’d like to try explaining why I think that is not the case.

Jimmy describes the project of accounting for propositional logic within an expressivist framework as that of providing an ‘inferential role’ semantics for ‘~’ and ‘&’. That may be right, but inferential role semantics can take different forms.

I take it that for an expressivist, the basic project is to assign each sentence to a mental state – the mental state that it expresses. An expressivist semantics for ‘~’ and ‘&’ must assign arbitrary sentences constructed from ‘~’ and ‘&’ to the mental states that they express or are properly used to express.

So take an arbitrary sentence ‘A’, expressing mental state M. What mental state should ‘~A’ express? Well, it must express some mental state that disagrees with M, in Gibbard’s sense – the sense in which someone who believes that grass is green disagrees with someone who believes that grass is not green, but someone who wonders whether grass is green is not disagreeing with someone who wonders whether grass is not green. (This is because for any sentence ‘A’, thinking that A is being in the mental state actually expressed by ‘A’, and it has to turn out that thinking that A disagrees with thinking that ~A). It should also disagree with every mental state N that is stronger than M, in the sense that it disagrees with any state that M disagrees with. (This is because if you think that ~A, you disagree with anyone who thinks anything which implies A.) But it shouldn’t disagree with any other mental states. So if expressivism is to work at all, then for any mental state M expressed by some sentence, there must be a state M*, which disagrees with all and only the mental states N that disagree with every mental state that M disagrees with. What is this mental state? What is it like? No matter; since expressivism can only work if for each state M there is such a mental state, M*, let’s simply assume that there is, and stipulate that it is expressed by ‘~A’.

Similarly for conjunction. Take arbitrary sentences ‘A’ and ‘B’, expressing mental states M and N. What mental state should ‘A&B’ express? Well, it has to be one that disagrees with everything that M disagrees with, and also disagrees with everything that N disagrees with, but doesn’t disagree with anything else. So if expressivism is to work, there has to be, for each mental states M and N, a further state, M%N, which disagrees with all and only the mental states which disagree with either M or N. What is this mental state? What is it like? No matter; since expressivism can only work if for each states M and N there is such a state, M%N, let’s simply assume that there is, and stipulate that it is expressed by ‘A&B’.

Given an account of the mental states expressed by atomic sentences, this gives us the materials for propositional logic. We can now define inconsistency by saying that ‘A’ and ‘B’ are pairwise inconsistent just in case they express mental states that disagree with one another, that a set of n sentences is inconsistent just in case the conjunction of the first n-1 sentences is inconsistent with the nth sentence, and that an argument is valid just in case the set of the premises and the negation of the conclusion is inconsistent. This makes our logic turn out to have all of the right properties. For example, it’s easy to see that it validates modus ponens.

We can see how directly by proof from the rules for ‘~’ and ‘&’ as I stated them, but there’s a more elegant way. To see it, first notice that since our semantics for ‘~’ and ‘&’ picks out the mental states expressed by complex sentences in terms of the mental states that they disagree with, we can represent the mental states expressed by sentences in terms of sets of other mental states – the ones they disagree with. By definition, M* disagrees with all and only the mental states that disagree with every state that disagrees with M, so if M disagrees with all and only the mental states in set S, then by definition, M* disagrees with all and only the mental states in the complement of M – M’. Similarly, by definition, M%N disagrees with all and only the mental states that disagree with either M or N, so if M disagrees with all and only the mental states in set S, and N disagrees with all and only the mental states in set T, then M%N disagrees with all and only the mental states in the union of M and N – MN.

These observations make it easy to represent the mental states expressed by the sentences of an arbitrary modus ponens argument, ‘A’, ‘~(A&~B)’, ‘B’. If ‘A’ expresses M which disagrees with all and only the mental states in S, and ‘B’ expresses N which disagrees with all and only the mental states in T, then ‘~(A&~B)’ expresses (M%N*)*, which disagrees with all and only the mental states in (ST’)’, ‘~B’ expresses N*, which disagrees with all and only the mental states in T’, and ‘A&~(A&~B)’ expresses M%(M%N*)*, which disagrees with all and only the mental states in S(ST’)’. So the argument is valid just in case M%(M%N*)* and N* disagree with each other. The way to check and see whether two mental states disagree with each other, however, is to see whether the sets of mental states that they don’t disagree with are non-intersecting. But the set of mental states that N* doesn’t disagree with is just T, and the set of mental states that M%(M%N*)* doesn’t disagree with is just (S(ST’)’)’, which is equivalent to S’(ST’), which is equivalent to (S’S) (S’T’) – that is, equivalent to S’T’. But this set is clearly non-overlapping with T. QED.

Those familiar with Gibbard’s view will see its close affinities with the one I’ve just presented. I think the one I’ve given is more intuitive. The main differences consist in that instead of picking out mental states in terms of the classes of all mental states that they disagree with, Gibbard picks them out in terms of the classes of all hyperdecided mental states that they don’t disagree with, and that Gibbard picks them out purely in terms of their inferential properties, and I’ve merely allowed that they are some states which have those inferential properties, allowing that there may be distinct states which have the same inferential properties. (This allows that believing A&B may be a different state from jointly believing A and believing B, which disagrees with all of the same mental states.) Those familiar with Horgan and Timmons’ view will also see the similarities. The main difference consists in that I’ve appealed to Gibbard’s notion of disagreement in order to spell out the ‘inferential properties’ of the mental states expressed by complex sentences, and skipped the details of how their account of the states expressed by basic normative sentences works.

So what does this show? I think it shows that defining ‘inferential roles’ for ‘~’ and ‘&’ within an expressivist framework is not the hard part. Within an expressivist framework, strictly speaking what we want is not inferential roles for sentences containing ‘~’ and ‘&’, but inferential properties for the mental states expressed by sentences containing ‘~’ and ‘&’, which we can understand in terms of characterizing them in terms of their disagreement-relationships. I think the foregoing exercise shows that it’s easy to stipulate such inferential properties, such that if there really are mental states that have those properties, then an expressivist semantics can get off of the ground.

The problem, as I understand it, is not that an expressivist semantics can’t work, provided that there are mental states with the requisite inferential properties. The problem is why we should think that there really are such mental states, if expressivism is true. An ordinary cognitivist can tell us what mental state is expressed by ‘murder is not wrong’, and why it disagrees with the mental state expressed by ‘murder is wrong’. It is the belief that murder is not wrong, which disagrees with the belief that murder is wrong, because belief is the kind of attitude that always disagrees when its contents are inconsistent. The expressivist view that I’ve just outlined, on the contrary, says only that ‘murder is not wrong’ expresses that mental state, whatever it is, which disagrees with all and only the mental states that disagree with everything that the state expressed by ‘murder is wrong’ disagrees with. But it has no answer to what mental state that is, or why it disagrees with those mental states and no others. The deep problem with such an account, I think, is not that it is formally inadequate, but that it is non-constructive, and hence unexplanatory.

16 Replies to “Expressivist ‘&’ and ‘~’

  1. Hi Mark,
    I’m not clear enough what you think the problem is now. Your thought is, even supposing for argument that thus sort of inferential role semantics works, that still leaves us with a mystery about how to understand the psychology. But, assuming that very thing for argument’s sake, I can’t see what the objection is going to be with identifying the mental states associated with a non-atomic sentences with a complex inferential dispositions whose structure is just isomorphic with the inferential roles specified in the semantics?
    Jimmy
    Jimmy

  2. Hi, Jimmy.
    The semantics that I gave picked out the mental states expressed by complex sentences in terms of their ‘inferential roles’, which I understood in terms of the set of mental states that they disagree with, in Gibbard’s sense of ‘disagree’.
    It didn’t guarantee that anything actually filled those roles, however, much less explain, given expressivist-friendly assumptions, why there is always guaranteed to be a state that fills them – which amounts to an existential hypothesis with infinitely many cases.
    You seem to be offering a proposal about what fills those roles – namely, dispositional states which are, in some yet-to-be-filled-out sense, ‘isomorphic’ in structure to the inferential roles that I specified. That’s great – if you think that an expressivist account isn’t complete until an answer to what fills those roles is offered, then you’re agreeing with me. That’s what I meant by saying that the problem with the kind of view I presented isn’t that it is formally inadequate; it is that it is non-constructive and hence unexplanatory.
    But now you have to tell me why the dispositional states that you’re going to specify really do disagree with the right other mental states in order to fill the roles that I specified. And this has to operate under the constraint, mind, not only that they turn out to disagree with the right states, but that they turn out to not disagree with the wrong states. This is the crux of the problem Mark van Roojen discusses in ‘Expressivism and Irrationality’.
    The problem with any set of dispositions that you specify, however, is that for whatever explanation you give of why they amount to states that disagree with the right other states, I’ll be able to generalize your explanation to explain why they also disagree with some states which they shouldn’t disagree with.
    That’s why Gibbard (as I read him) and Horgan and Timmons don’t actually tell us what states fill the kinds of roles that I specified – they stop in the same place that I did in my post. My point is that as long as you stop there, there aren’t any problems, but it’s not really an acceptable place to stop.
    It is, however, intelligibly an inferential role semantics – it specifies ‘inferential roles’ corresponding to each complex sentence. And it doesn’t have any greater problem with ‘~’ than with ‘&’ – they work on precisely the same principles.
    (The motivation for my approach to expressivist semantics in Being For is that it can offer a constructive answer to the question of what mental states fill these roles that can explain why they fill the roles by appeal to cheap, expressivist-friendly assumptions, and without overgeneralizing.)

  3. Hi, Mark. My question is mainly about the overall dialectic. I’m not sure whether, at bottom, the question is similar to Jimmy’s, so I’ll just state it in my own way.
    Here’s how I understand the dialectic. We have some data: We understand complex sentences that contain ethical sentences; (the best explanation for this ability is that) natural languages are compositional; and ethical sentences stand in various logical relations to others sentences of a language. So, everyone, especially expressivists, has a challenge, a point which has been hammered home by Geach/Frege:
    Challenge: Provide a semantic theory that (i) explains how we understand complex sentences (including those containing ethical sentences) on the basis of understanding their component sentences, connectives, and the syntactic combinations of these, (ii) for an entire natural language, and that (iii) preserves, for each sentence of that language (including ethical sentences), all of the logical relations we intuitively think they have.
    I take it that your post is showing how expressivists can have (ii) and (iii), but at the expense of (i). (An implication of the theory you provide on behalf of expressivists is that we cannot really understand the mental state expressed by complex sentences, and so we have no good reason to think there are such states.) I take it that Jimmy (with Hale/Unwin) wants to show that even if expressivists can have (i) and (iii), they can’t have (ii), since there is some (disambiguated) sense of a negated, ethical sentence for which expressivists cannot provide a semantics (since expressivists have no way of accounting for the kind of mental state that is expressed by a certain kind of negation). A couple of weeks ago, I tried to show how simple noncognitivists (I won’t call them ‘expressivists’ in this post) could have (i) and (ii), but it looks like they can do so only at the expense of (iii).
    So, in terms of the dialectic, I’m thinking that the main problem is not with either of (i), (ii), or (iii). The main problem is accounting for (i)-(iii) together. So, could you say more about the sense in which you think that the “deep problem” for expressivists is in accounting for (i), and not for (i)-(iii) together?

  4. Hi, Dan.
    That’s fair; I don’t know that I disagree with you. That’s a nice way of pulling apart different ways in which things can break down, although I was thinking of the main problem with (i) differently from you. The main thing that I emphasize in Being For is that the project of expressivist semantics is all about (i) building a constructive semantics which (ii) works for an entire natural language and (iii) predicts all of the right semantic properties for complex sentences. There I argue that given certain assumptions, you can do this for a language with the expressive power of the predicate calculus, but you run into increasingly problematic difficulties as you try to extend it to a language with constructions like modals and binary quantifiers like ‘most’.
    I don’t really want to insist that (i) is the real sticking point, but I do think that it is the main sticking point for the most sophisticated expressivist views on the table, in which I include both Gibbard and Horgan and Timmons, and perhaps Blackburn’s 1988 view, depending on how you interpret it – of which the view in my post was supposed to be a straightforward version.
    And I also think that it is a particularly perspicuous way of understanding how expressivists need to approach the problem. If an expressivist semantics works by assigning sentences to mental states, and for any sentence ‘A’, to think that A is to be in the mental state actually expressed by ‘A’, then the disagreement-conditions that I stated are really conditions of adequacy on any expressivist account, and so the problem of providing an expressivist semantics reduces to the problem of finding role-fillers for the roles that I stated.

  5. I wonder if the expressivist could approach the problem from another direction. It’s true that Blackburn wants to start from the attitudes taken as basic and then build up an account of the moral language on that basis. But, I wonder if the expressivist could work at the same time from the other direction, i.e., the utterances and the discipline they show.
    This is going to be very vague but I wonder if the expressivist could begin from the inferential roles of the simple sentences and use them to attribute the right kind of conative mental states to people. I have in mind some version of Davidson’s principle of charity. Using that principle, we seem to be forced to think that people express with their utterances mental states with content that would make the rational and such that they are not making simple logical mistakes. Given this assumption and which utterances people make and accept and the way they behave, the expressivist could assign people mental states with the right sort of inferential properties such that these states would disagree with just the right class of other mental states to make the people rational and free of logical mistakes.

  6. Hi, Jussi – that’s great, provided that there really are mental states that have the right inferential roles. The problem is that expressivism is competing with ordinary cognitivism, which easily predicts that there are mental states with all of the right properties, because they are just beliefs with different contents. So it might be true that there are mental states that play the right roles, but only because cognitivism is true. (I think Jamie has explained this particularly well.)
    That’s why it’s not fair game for expressivists to rely on intuitive confidence that there is something it is to think that murder is not wrong – which disagrees with all and only the mental states that disagree with everything that thinking that murder is wrong disagrees with. If there’s no respectable expressivist-friendly way of picking out what this mental state is, then that’s evidence that expressivism gives us no explanation of why there really is such a state, and hence that expressivism is inferior to cognitivism, which not only predicts that there is always a state to correspond to the negation of an arbitrarily complex sentence, but also explains why that state has the right disagreement relations to other mental states.

  7. Hi Mark, Continue to suppose arguendo the semantics works. So we have an account of the meaning of NOT-P in terms of some inferential role for negation IN. So a sentence expresses NOT-P iff it has inferential role IN(P). Then we say that a thought is the thought that NOT-P iff that thought has inferential role IN(P) where that is a matter of the thinker having the inferential dispositions D(IN(P))of which IN(P) amounts to a specification.
    “But now you have to tell me why the dispositional states that you’re going to specify really do disagree with the right other mental states in order to fill the roles that I specified.”
    Well because they have D(IN(P)) and that disagrees with the right stuff because we are assuming for the sake of argument that IN(P) suffices to nail negation. You say:
    “The problem with any set of dispositions that you specify, however, is that for whatever explanation you give of why they amount to states that disagree with other states, I’ll be able to generalize your explanation to explain why they also disagree with some states which they shouldn’t disagree with.”
    Well the explanation I give is that the state with inferential role D(IN(P))is the state with content specified by IN(P) and as such it disagrees with everything that is inconsistent with that and if you then ask me what I think inconsistency is I’ll refer you back to the semantic story whatever that is. And it’s hard to see how that could then give the wrong answers without that falsifying the semantic story we were supposing arguendo to be in good shape. I can’t see how it could be the case that D(IN(P)) could fail to nail negation but IN(P) succeeds. Thus e.g. it’s a constraint the specification on IN(P), at the SEMANTIC level, that it capture the consistency of NOT-P with other sentences with which it is perfectly logically consistent but with which it is apt to conflict at the level of pragmatics. That as I recall was the difficulty Mark vR raised in E&R and its not a difficulty that as far as I can see can be quarantined off so as to infect only the psychological story and not the semantic one.

  8. Hi Mark,
    I think the discussion so far answered my (as usual too cryptic) question. My initial reaction to your post was, Well, why not start with a semantics of, literally, ‘Boo for that’ and ‘Hurray for that’, (or similar such sentences). Whatever that semantics is, it doesn’t seem to be cognitivist. And whatever mental state would be assigned to “Boo for that”, it seemed to me, at least as far as I understood the proposal, to disagree with all and only the mental states that disagree with everything that the mental state assigned to ‘Hurray for that’ disagrees with (I think I put that the right way). And so although there might be handwaving on the part of expressivists, it’s not that they’re entirely without some direction to go it for an answer to your challenge.
    But I think this suggestion has already been discussed.

  9. Jimmy,
    You write
    Well the explanation I give is that the state with inferential role D(IN(P))is the state with content specified by IN(P) and as such it disagrees with everything that is inconsistent with that and if you then ask me what I think inconsistency is I’ll refer you back to the semantic story whatever that is. And it’s hard to see how that could then give the wrong answers without that falsifying the semantic story we were supposing arguendo to be in good shape.
    I’m not sure I see this. While I agree that if the psychological story does not work out the semantic one won’t either (because there will be no psychological states for the relevant sentences to express if there are not the right sort of psychological states), I don’t see how the semantics helps us with showing why the relevant states are inconsistent or not in the first place. The idea was, we explain the inconstistency of the sentences expressing the states by explaining the inconsistency of the states they express and the semantics tells us which sentences express which states. But we still need/want a story about why these states are inconsistent with just the ones they are supposed to be for the account to work, and I don’t yet see that just referring back to the semantics helps with that.
    Or am I really confused about the dialectic here?
    PS, I find the new format particularly confining when I’m composing an answer and the comment box contains only 4 words across and ten lines down. I like to be able to see what I’ve just written to tell if I’m making sense. I find the same thing a bit problematic when reading, but not as much.

  10. Mark, The focus of my scepticism was t’other Mark’s thought that we can envisage a circumstances where the semantics is all sorted and hunky-dory but a psychological difficulty remains. As you don’t disagree about that, I’m not sure we do disagree about all that much. But I guess I am taking it that inconsistency is fundamentally a semantic rather than a psychological notion.

  11. Hi, Jimmy.
    I think we might be misunderstanding each other. As I tried to indicate, I think that the kind of semantics that expressivism requires, involves assigning sentences to mental states – so the semantics works only if there are such mental states so to be assigned.
    Why is it, you might ask, that expressivism must understand the semantics of complex sentences by assigning them to the mental states that they express? As I argue in Expression for Expressivists, it’s because they understand the semantics of atomic sentences in terms of the mental states that they express, and so they can get a univocal treatment of the logical connectives only if they take the same kind of arguments.
    So suppose that we grant that. In my original post, I didn’t just assume that we had an expressivist semantics that would work. I showed that it is easy to do expressivist semantics in this way, if we just help ourselves to the existence of mental states with the right properties. Conditional on there really being such mental states, with the arbitrary disagreement properties that I used to pick them out, it’s easy to account for propositional logic in our semantics.
    The problem, I meant to be saying, was that this existential assumption requires a lot to discharge. The problem wasn’t that we can get the semantics to work, but there will still be a problem with the psychology. The problem was that the semantics works only conditionally on assumptions about the psychology, and that that’s what’s really difficult about giving a constructive expressivist semantics. I think this is pretty much what Mark van Roojen said in his comment, as well.
    That’s why I don’t think you get any free story about the psychology out of the semantics – you need the story about the psychology in order to discharge the existential hypothesis the semantics requires – one which, by the way, didn’t specify any dispositions that you could appeal to in order to define the dispositional state. But if the existential hypothesis is true, then in a sense, the semantics is complete already, though as I pointed out, I think it is non-constructive and non-explanatory.

  12. Thanks Jimmmy. I think you’re right we’re mostly in agreement (and Mark S is right that I’m really saying what I took him to be saying.) I even agree that inconsistency is really at base semantic and not psychological. But then I’m a skeptic about the ultimate success of the logic of attitudes approach. I take it as essential to the LOA approach that they think the order of explanation goes the other way round.

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