TTP, 6. §2.I Projectivism

Suppose we want to claim that some class of sentences that are grammatically like those of straightforwardly fact-stating, representational, belief-expressing discourse actually  have a quite different semantic function (and remember, this is going to be Weir’s line about mathematical sentences: where a fictionalist error-theorist sees a failed representation, or a kinder fictionalist sees a pseudo-representation made in a fictional mode, Weir is going to argue that mathematics isn’t in the business of representation at all). How then might we further explicate this idea of superficially representational claims which in fact have a different role?

One context in which such an idea has been developed and put to work is in the neo-Humean “projectivist” account of morals, modals, and the like, as nowadays particularly associated with Simon Blackburn. The root idea is that a judgement like ‘X is good’ doesn’t express a belief about how the world is with respect to some special property of goodness, but rather a sincere such judgement is keyed to the utterer’s attitude of approval of X. NB, it isn’t that the judgement is about the attitude; rather that it is semantically appropriate, other things being equal, to assertorically utter the judgment when you have the right attitude. Likewise, ‘E is highly probable’ doesn’t express a belief about the occurrence in the world of a special property of objective chance, but rather a sincere judgement is keyed to the utterer’s having a high degree of belief in the occurrence of event E. And so it goes.

But of course, the devil is in the details! The root idea here is equally available to the crudest expressivist: the hard work for the Blackburnian projectivist comes in explaining (a) why, despite the anchoring of the judgements in non-cognitive attitudes, it is still appropriate that they have the logical “look and feel” of cognitive judgements — i.e. can be negated, embedded in conditionals, and the like — and there’s related work to be done in explaining (b) why it makes sense to reflect “In my view, X is good, but I could be wrong” and the like. What distinguishes the projectivist from the crude expressivist is the sophisticated way in which he tries to explain (a) and (b).

Weir’s §2.I touches on the projectivist’s treatment of these matters  — but in a way that I expect is going to be far too quick for those philosophers of mathematics (surely most of them!) who aren’t already familiar with a particular strand of contemporary debate that’s mostly conducted remote from home, in meta-ethics. In particular, Weir’s constrast between earlier and later Blackburn, and the role of the idea of non-correspondence truth in his later work, will probably mystify (well, I can’t say I found it at all clear or helpful, and I start probably knowing a bit more than many logicians about these things, having Blackburn as a colleague!).

And as well as the discussion going too quickly, Weir’s discussion of projectivism is oddly framed. The full title of the section is “Projectivism in the SCW framework”, and you’ll recall that in his §1.III, the so-called sense/circumstances/world picture is exemplified in the treatment of demonstratives and the story about how the situation represented by an utterance involving “that” is co-determined by the literal meaning (or sense) of the utterance and the relevant circumstances of utterance which make a particular thing appropriately salient. But that was a story about context sensitivity in fixing what state of affairs was being represented (it is still good old-fashioned representation that is going on). The new issues raised by projectivist stories about non-representational content seem, then, to be quite orthogonal to the issues about how we need to tweak Fregean semantics to cope with demonstratives.

OK: we have a story about what is happening in the use of sentences with demonstratives and another story about sentences with “good” or “probable” (or whatever else invites projectivist treatment), and in each case the story deploys concepts (salience, pro-attitudes, degrees of belief) which are not part of the thought expressed in the circumstances. But there the similarity surely ends. Needing circumstances to help fix what is being represented is one thing; going in for non-representational thinking is surely something else, about which we need a quite different sort of story than is provided within the confines of the SCW framework as introduced in §1.III.

Still, let’s agree that Weir’s (over?) brisk remarks serve to point up that there is possibly space for, though also problems attending, treatments of areas of statement-making discourse as non-representational. And that’s perhaps all we really need for now, given that Weir has already announced in his Introduction, p. 7, that he doesn’t want to offer a projectivist account of mathematical discourse. So let’s not get unnecessarily bogged down in worries about how best to develop projectivisms.

Though let me end this instalment with a very small protest about calling projectivism a species of reductionism (rarely a helpful label, of course). Projectivism “populates the world … with certain naturalistically unproblematic attitudes or relations between humans and objects”, and in so doing does away with the need to postulate problematic properties of goodness, chance or whatever. So, to be sure, projectivism reduces ontology — but, if we want one word to describe what is happening, we are eliminating the need for the supposedly troublesome non-natural properties.

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5 Responses to TTP, 6. §2.I Projectivism

  1. Alan Weir says:

    To start with the last point, I agree ‘reductionism’ is in general unhelpful (cf. p. 25) and won’t want to go to the stake for that terminology.

    On Blackburnian meta-ethics being a remote area for philosophers of maths. Well, my hope is the book won’t just be read by philosophers of maths. How am I going to get the Roman Abramovich-style luxury yacht if so? I’ll be lucky to get a duck pond paddle boat! In my rant against the cult of interdisciplinarity in the preface I alluded to the spectrum between infra-disciplinarians, like myself, who depend on more interdisciplinary philosophers of maths with strong maths backgrounds (like part III of the Cambridge maths tripos!) , who can talk to the mathmos themselves and so on. Those at my end of the spectrum surely will have some knowledge of metaethics and projectivism. As to the more specialist philosophers, yes I suppose it is difficult for me to put myself in their shoes and see how accessible things will be for them.

    But as you say the devil is in the detail. In particular, as Blackburn himself sees and makes strenuous efforts to address, having a neat idea as to how sentences might function in other than a straight representational way does not mean all will be plain sailing if those sentences are suppose to be part of a standard type language, with logical operators and the like functioning in the usual ways. This is certainly the case if all the sentences are supposed to be truth-value bearing, but difficulties also arise if one holds that the discourse merely apes truth-conditional discourse.

    Difficulties of this type as they surface in what would seem to be the easiest case for formalism- elementary school arithmetic- are the subject of chapter three and the comparison with Blackburn’s various forms of projectivism and the problems with logically complex sentences resurface in a number of places (e.g. pp. 82n., 244n.) So the devilish detail does get further treatment. I agree the difference between early and late Blackburn, between simulating truth-conditionality and genuinely having it, is not important for the argument of the book, I just wanted to do justice to the development and subtleties of Simon’s position (and record my view, which chimes of course with the overall theme, that the later ‘cognitivist’ or ‘inclusive’ truth-conditional projectivism is superior).

    Your remarks about the sense/circumstances/world trichotomy as applied to demonstratives in chapter one being orthogonal to projectivism (and more generally the concept of a non-representational mode of assertion) go much further into the heart of my project I think. The trichotomy is fairly orthodox, though there are extremists on either side, the radical contextualists and the minimalists, noted in chapter one. It looks though that my application of the picture is not so mainstream because I think the two realisations of ‘circumstance’ are not orthogonal but different determinations of the one general pattern.

    The general idea, as you say, is that an utterance of a sentence usually does not express a proposition, does not say something truth-evaluable, by dint of its Sinn or informational content alone, but requires supplementation by ‘circumstantial’ factors/parameters or such like, determined by the context of utterance. Clearly there are lots of different sub-divisions here, even in cases of context-sensitivity where the resulting proposition represents, correctly or incorrectly, a mind-independent world.

    My idea is that all these representational sub-cases are a subset of a wider class of ways in which informational content gets supplemented to yield a truth-valued proposition. In the rest of the wider class the proposition is not representational; what makes it true or false is not something independent of the cognitive make up of the utterer as is the case (matters are not so simple of course, I can make representational claims about my digestive system or mental state) with good ole-fashioned context-sensitivity. The SCW framework of course doesn’t explain how (in the ‘Circumstance’ middle of the sandwich) an assertoric truth-valued utterance can have non-representational truth-conditions- there are various stabs at that throughout the book, most particularly for mathematical utterances of course; but it can encompass the resulting account, that is my claim.

    • Peter Smith says:

      Perhaps what is showing up here is some unclarity in your (explanation of the) notion of “informational content”.

      Picture A Some indications. You say (i) Information content is “literal content” (p. 26). (ii) Synonymy is a matter of sharing informational content (p. 29). (iii) We grasp informational content by understanding the relevant fragment of language (p. 32). (iv) Informational content is, roughly, conventional meaning (p. 33).

      Now, I’d certainly say that “Marmite is tasty” has an already complete literal content, which we grasp if we know what Marmite is and otherwise understand the relevant fragment of language, i.e. if we know the conventional meaning of “tasty”. Understood in the light of those quoted indications, then, by my lights it isn’t the case that the “informational content” here needs to get supplemented by anything to yield a truth-valued proposition.

      To be sure, the projectivist gives a certain account of what it is for “Marmite is tasty” to have that conventional meaning; it isn’t a matter of “tasty” being conventionally used to represent a property “out there” in the world, but being used to express a certain pro-attitude. But (thus understood) the projectivist story on Picture A plays its part in explicating the kind of literal conventional meaning “Marmite is tasty” has, the content which it shares with synomyms across languages etc.; it doesn’t have a role in getting us from the conventional meaning to a determinate message (in the way that the talk about context, salience, etc. does in getting us from the conventional meaning of “That is green” to a determinate message about a particular thing).

      Picture B But you also say that (v) informational content is “cognitive content” (p. 26), and that could suggest a different picture. On this picture, as far as cognitive content fixes things, “Marmite is tasty” has incomplete content Marmite is …; and now we need something else to give us a complete truth-evaluable proposition — this time not anchorage in “objective” context (as in the story about demonstratives) but anchorage in, as it were, “subjective” context, the attitudes of the speaker (as in the projective story about “tasty”). You comment also seems to suggest that it is Picture B that you are thinking in terms of.

      Well two comments. First, given the quoted indications (i) to (iv), it is — to say the least! — forgiveable if readers take “informational content” as in Picture A, and then see the projectivist story as a story about informational content a.k.a. conventional meaning (not a stort about how to supplement that content).

      Second, why — if it is your picture — prefer Picture B to Picture A? I can see why someone of Wittgensteinean cast of mind might be unhappy with trying to shoehorn every “ingredient of meaning” in the broadest sense into one of two categories. But if we are going to play this regimentation game, why (B) “information content = representational/cognitive content” vs other ingredients, rather than (A) conventional (“dictionary”) meaning vs contextual ingredients? — especially as the other ingredients for you are such a very mixed bag.

      • Alan Weir says:

        I accept both Picture A and picture B! (I have a minor quibble with picture B, I’m not keen on saying informational content is representational/non-representational. I don’t think the distinction applies best there. The informational content of utterances like ‘Marmite is tasty’ and ‘7+5=12’ I certainly wouldn’t say is representational, for, according to me, these sentences are typically used to make assertions with no representational content. Perhaps ‘cognitive content’ was misleading if suggesting representation, ditto ‘cognitivist projectivism’.)

        I think the four indicators you cite as Picture A are compatible with picture B because I don’t think they entail that ‘Marmite is tasty’ is semantically complete. Knowledge of the conventional meaning of the terms will not enable me to know the truth-conditions (or correctness conditions if you don’t have a relatively deflationary view of truth) of an utterance of the sentence. I’m not thinking here of irrelevant, for our purposes, factors like tense or the possibility that somebody has named their pet pig ‘Marmite’. Rather, that what makes it true or false is determined, in part, by the pro-attitudes (and correctional dispositions), vis a vis food and drink, of the utterer- not the hearers or anyone else; that much is part of what we grasp when we grasp its meaning in the language in general. But then to know its truth conditions we need to know who the utterer is and that is not supplied by the conventional meaning.

        Who the utterer is, and thus whose internal attitudes partly determines the truth value will often be obvious, just as the referent of ‘that’ in ‘that is green’ might be obvious, but this is an additional element of the determination of truth conditions (whether it is true or false is a further matter of course, determined by the actual likes of the utterer and the nature of Marmite, the latter surely an incomprehensible ‘something we know not what’). It won’t always be obvious though, even to the utterer : what if we are communicating by typing sentences which appear on the screen in the lecture hall and it is not always obvious which token sentence is produced by which participant?

        So I don’t think the situation is so different from ‘that is green’ or ‘I like Marmite’. (‘Seeing the projectivist story as a story about informational content’- that looks to me like crude expressivism: ‘Marmite is tasty’ is synonymous with ‘I like Marmite’.)

        However ‘incomplete’ or my appeal to ‘supplementation’- this is perhaps not the best way to put it (nor need non-representationality bring in the relativism evident in the projectivist example). For it’s not that the informational content and the metaphysical content are two separate ingredients, like two distinct and unrelated meanings of an ambiguous term which have been conjoined by an accident of etymology. To grasp the informational content will require mastering the practices which determine the metaphysical content: locating the salient F (whether or not one can reflect on what salience is) if trying investigate if that F is a G; searching for a proof or refutation if trying to figure out if every even number is the sum of two primes.

        But a) the conditions encapsulated in the metaphysical content do not form part of the informational content b) they pertain not to matters external to the linguistic practice but to internal matters- the attitudes of the speakers, the calculi and proof procedures of the speakers, c) excise, as it were, those practices- imagine the speakers become transmuted into disembodied intelligences, or becoming incapable of deriving anything- and the sentences lose all their current meaning, including informational content. (A Cantor or hard-line platonist about a given area of maths will disagree of course, holding that the theses can be perfectly meaningful and indeed true or false, even if nothing, or nothing that humans could grasp, could prove or disprove them.)

        • Peter Smith says:

          Ah. Until I read on to §2.III, I hadn’t really picked up how you construe projectivism as always(?)/typically(?) a form of relativism — rather extremely so, in the case of “tasty”, it seems, if only the speaker’s attitudes really count. I don’t agree about “tasty”, but let that pass. The main point is that I think you are running two things together.

          In the abstract, it surely could be the case that a judgement “X is G” is both semantically complete, but such as to be apt for a projectivist treatment. (If we think that genuine morality as opposed to other normative judgement is characterized, inter alia, by caring that everyone agrees, maybe moral judgement would be non-relative like this. But anyway, it is enough that the abstractly described situation is surely possible.) In this sort of case, at any rate, the projectivist story is just a story about literal content/conventional meaning, yes?

          OK, now take a case “X is H” which is apt for a relativized projectivist treatment. Then, context maynow play its part in fixing whose attitudes are relevant. But still, the rest of the projectivist story for the relevant judgements (and all the hard work) will come in spinning the bit of the yarn which is constant across contexts, i.e. the bit about what kinds of attitudes matter, how they are keyed to snapshot dispositions, what kind of correctional practices matter etc. etc. And this, the major part of the projectivist story, deals with the conventional meaning of “X is H”, constant across contexts. That’s why I’d still say that projectivism (the core contentious part of the theory) is still best thought of as a novel way of explaining the conventional meaning of a class of judgements, even granted that in some cases context is needed to complete the story about what is said.

          You’re saying context can matter (but of course!). I’m stressing that buying into forms of projectivism as a departure from classic realist semantics is a whole different ballgame from tweaking the Fregean story into the SCW story, raising quite different issues. You seem to think that recognizing the need to make the SCW tweak should soften us up for the big departure: I think the cases are just too different. Others can decide how big a disagreement that really is!

          • Alan Weir says:

            Thanks for all that Peter, I’m finding it very helpful. Perhaps we are just chopping up conceptual space differently; perhaps I’ve packed too much into the ‘circumstance’, the very sort of complaint against Frege and his notion of Sinn I endorsed (p. 26).

            But I don’t think relativism is essential to incompletion or need of supplementation. The terms may suggested that informational content can get supplemented in different ways yielding propositions with different truth-conditions but though I think that’s true in the projectivism case it isn’t always true.

            At one point in the book I suggested critical talk about fiction has absolute truth values but I’d agree, as per earlier posts, that different groups of readers could ‘fill’ out the story of different texts, or groups of texts (or texts plus factual data) they are comparing in incompatible ways. One group agrees Holmes is a smarter detective than Taggart, another Glaswegian group says no way.

            But mathematics is a case I give in the book (Ch. 4 §II.3) of non-representational semantics completing or supplementing the informational content, but without relativism. True ‘3+1=0’ doesn’t have an absolute truth value: are we working in standard arithmetic, arithmetic mod 4, or to a different modulus (or some more abstract algebra or whatever)? But surely this is a case of ambiguity of informational or literal content. To make a determinate claim it has to be made clear, if it isn’t from the context, what theory we are working in. The ambiguity passes tests for ambiguity of the sort mentioned by Cappelen and Lepore (p. 108).

            Once a mathematical theory is fixed and the sentence has a determinate literal meaning it has a unique truth value but if we ever got a good metatheory which accounted for the literal content it would need supplemented by an account of what makes the sentence true, an account which appeals to workings which are not part of the literal content. The existence of concrete proofs or refutations , in fact- though in this case (unless we learnt our arithmetic from Principia Mathematica) just basic rules drilled into us (pretty literally in my case as a nipper) at school. This isn’t part of the literal content, ‘3+1=0’ isn’t synonymous with ‘there is a (one-line) proof of ‘3+1=0’ and a platonist can grasp the sentence perfectly correctly whilst believing one and not the other (substitute something more complex in this case, GCH say).

            So I think we have a substantive disagreement over ‘the major part of the projectivist story …. is still best thought of as a novel way of explaining the conventional meaning of a class of judgements’. ‘Is beautiful’ isn’t synonymous with some specification of aesthetic attitudes, a realist about beauty can believe ‘that is beautiful’ and disbelieve ‘that excites such and such responses in me’ etc.

            If relativity of truth isn’t essential to the sort of semantic incompleteness and need for supplementation I appeal to, what doesn’t need supplemented?! Take an ‘eternal sentence’ in Quine’s phrase like ‘everything is composed of mereological atoms’ (tenseless ‘is’). Now if we ever did manage to get an account of what it is to understand the literal meaning of such a sentence it sure as hell would include a lot more content than is in that meaning. So in what sense is there no need for supplementation in a metatheoretic account of the meaning of this eternal sentence?

            Something like this: such an account of the informational content will at minimum explain what the referents of the expressions are (or if you think predicates refer to properties, what their extensions are) how the logical operators work, how these combine to yield truth conditions. Once that is done, there is no other mechanisms in play which determine truth-conditions.

            If platonism is right about ‘3+1=0’ there is no need for supplementation there either. The singular terms have referents, as do the function terms and identity predicate (or extensions), we have an explanation of how their combination is true just in the circumstance that the first added to the second referent yields the third. All these semantic relations are part of the conventional meaning of the words just as with the mereological claim:- minimally reflective speakers take it as default that the singular terms stand for objects, predicates are true or false of objects and so forth.

            But if platonism is wrong and my account is right, we have to appeal to semantic relations and linguistic practices not part of the literal content in order to explain how the sentence gets its truth conditions. (So the ‘incompleteness’ is not something one can neutrally agree exists, not something that is part of conventional linguistics, dealing as it does with literal content). A reflective and thoroughly competent speaker may not believe these mechanisms- inferential practices in my view- are part of the meaning, she may be an ardent platonist.

            So maybe I should present it this way. We start with a paradigm of representational meaning: names refer to external objects, predicates to properties, the truth functional operators operate in their standard ways etc. This is how we account for the truth-conditions of factual talk except most of it is context sensitive, so we have to supplement the account of how literal meaning includes referential relations and the like, with saturation, assignment or whatever, of values for context-sensitive terms before we get a proposition apt to be truth or false. The extra stuff may not be in the literal content, the ‘metaphysical contents’ spelling out the extra stuff are not synonymous with the tangent sentence, behave differently in modal contexts and so on.

            But this feature: extra stuff not part of the literal content, also applies to sentences used to make non-representational assertions, because the grounds for truth are internal to the speakers or their sets of linguistic practices (cf. my clauses i), ii) iii) in my last paragraph above)- as in projectivist, perhaps fictional, and I claim most relevantly for the book, mathematical cases. Sometimes these grounds induce a relativism, sometimes not.

            Do we have two different kinds of ‘extra stuff’ here: firstly the factors which fill out context-sensitivity to yield a fix proposition, secondly the factors which link words to the world in ways very different from standard referential semantics, in a non-realist way. Or are they both sub-species of a more general extra-sense type?

            I think it’s verging on the terminological here what way you go. The important point is- does the existence of extra truth-condition determining factors beyond literal content provide a way into a non-realist semantics, for taste or probability talk, critical judgements about fiction, mathematics; a way which allows at least those not vehemently opposed to deflationistic approaches to truth to get the naturalistic benefits of projectivism whilst quickly disposing of Frege/Geach, to handle the tricky cases the Meinongian points to- ‘Holmes is more famous than any actual detective- without pledging allegiance to the baroque Austrian? And to get truth in mathematics, without platonistic ontology. That’s the non-terminological, and of course far from trivial, aspect it seems to me.

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