On Family Resemblance Concepts

I want to clarify some aspects of the celebrated Wittgensteinian idea of a family resemblance concept.

Are all family resemblance concepts such that no single feature is shared by all the things to which the concept applies?

Some of Wittgenstein's formulations, and explanations based upon them, would suggest an affirmative answer. But I think that a more general, useful notion of a family resemblance concept should not require this.

It should disqualify a concept for family resemblance status that some feature happens to be common to all the things that fall under the concept. It may be that this feature does not sufficiently characterise the things as falling under the concept. That is, just because you can give necessary conditions for the application of a concept, does not mean its application is not based on the kind of criss-crossing network of similarities that Wittgenstein has us imagine. This passage gets it right:

we extend our concept of number as in spinning a thread we twist fibre on fibre. And the strength of the thread does not reside in the fact that some one fibre runs through its whole length, but in the overlapping of many fibres. (PI §67)

This makes it clear that there may still be a single fibre running through the thread. It's just that that alone isn't responsible for the strength of the thread.

Are all concepts which do not admit of non-trivial analysis in terms of necessary and sufficient conditions family resemblance concepts?

It seems to be a necessary condition on family resemblance concepts that they do not admit of non-trivial analysis in terms of necessary and sufficient conditions. But it doesn't seem to be a sufficient condition. That is, it seems that there are concepts which do not admit of this sort of analysis and yet are not what we would think of as family resemblance concepts. For example:

• Certain primitive, i.e. undefined, concepts in theoretical use are not family resemblance concepts. For example, the concept of a lever (insofar as it isn't defined).
• A concept that is undefined but very closely tied to experience, e.g. the concept of red.
• Concepts which by design only apply to one thing, such as the concept of God - or, for that matter, just your concept of some particular person you know. (The whole idea of 'individual concepts' is a bit neglected though, and may not strike the reader as being in good standing.)

These do not seem to count as family resemblance concepts, because while they do not admit of non-trivial airtight definitions, there does not seem to be the sort of heterogeneity among the things that they apply to that characterises family resemblance concepts as discussed by Wittgenstein.

This last category, however, invites another question...

Diachronic family resemblance concepts?

It would seem that the concept of a particular person can't be a family resemblance concept in the sense of many different things falling under it not because of a common feature but because of overlapping similarities, because at most one thing does fall under it. But if we consider the individual through time, we start to see the possibility for something like the family resemblance idea applying to the concept of a particular person.

Is 'family resemblance concept' a family resemblance concept?

I think there's potential for a negative answer. At least, it seems to me we can give a precisified version of the idea that is not itself a family resemblance concept. On the other hand, perhaps such a thing would fail to capture the idea in full.

Against Inherently Representational Anything

Soames, in his fascinating recent work Rethinking Language, Mind, and Meaning, begins by posing a problem for the study of meaning and language as developed by philosophers and logicians in the Twentieth Century.

For propositions to play the theoretical roles assigned to them - such as being the primary bearers of truth, being the objects of propositional attitudes like belief and desire, being the contents of mental and perceptual states, and being the meanings of some sentences - they, Soames says, must be inherently representational. That is, they must impose conditions on the world off their own bat, so to speak. 

But, argues Soames, the sorts of things that traditionally play the proposition role in modern theories do not seem to be inherently representational. Soames provides 'reasons to believe that no set-theoretic construction of objects, properties, world-states or other denizens of Plato’s heaven, could ever be inherently representational bearers of truth conditions in this sense' (Rethinking, Ch. 2).

This leads Soames to his new theory of propositions, on which they are cognitive acts of a certain kind. ('Suppose, however, we start at the other end, taking it as an uncontested certainty that agents represent things as being certain ways when they think of them as being those ways' (Rethinking, Ch. 2).) For example, the proposition that snow is white, on Soames's theory, is the act of predicating whiteness of snow. These cognitive acts, according to Soames, are inherently representational, which means that they could be able to play the role of propositions. 

(Soames says that, at bottom, it is language users that represent things as being certain ways, and they do this by performing cognitive acts, which acts may derivatively be said to represent. But although, in this way, they represent in a derivative sense, they do so inherently - and that is the crucial point for Soames, that makes cognitive acts fit to play the role of propositions.)

I am very heartened to see Soames realising that his earlier, broadly Russellian conception of propositions won't do and looking for an alternative. But his cognitive acts seem a bit mysterious to me. In this note I won't try to refute Soames's new theory of propositions, but let me say something briefly about what worries me. It's not so much that I think that there's no such thing as the cognitive act of predicating whiteness of snow, but I don't feel like this is the sort of thing that is fit to play the sort of basic explanatory role that Soames wants it to play. It feels too much like a black box containing important workings for that. Treated as something basic, it feels occult or magical. (Wittgenstein in the Investigations seems very concerned to avoid positing mental goings-on that are meant to play this kind of foundational role in explaining representation. This has influenced me and I think there's something right about Wittgenstein's conviction that this is not the way forward.)

There is another conception of propositions, on which they are sentences (of a certain kind) in use (or a certain kind of use). For instance, in the Tractatus Wittgenstein said that a proposition is a propositional sign in a projective relation to the world. (In a recent paper I sketch an account of propositions that treats them similarly.)

(Of course, it is nice to be able to say what two synonymous sentences in different languages have in common, and often it is said that they 'express the same proposition'. On the present approach, they may be said to have the same use, the same meaning. But ultimately it is not just the use or the meaning that represents - it is a sign in use, a sign with meaning, that does this. The "proposition" or "statement" or whatever you call it that two different sentences express is an abstraction from the particular propositions that are alike in meaning.)

It seems to me that this fundamental logical move of treating propositions not as things by themselves, as it were, but a certain kind of thing in a certain kind of context is very important, and constitutes the right way to avoid the twin pitfalls of having propositions be things that don't themselves represent, and of having them be explanatorily basic cognitive acts. 

Admittedly, sentences in use can't just be slotted in to all the roles Soames delineates without further ado. For instance, we probably don't want to say that if you believe something - perhaps without even representing it to yourself linguistically - the thing you believe is a sentence in a particular use. Soames's theory may have an advantage over my approach here in having this one kind of thing - propositions - playing all of these roles (although I doubt it, since Soames's theory has predictions which sound like category-mistakes, such as that one may 'perform a proposition', propositions being acts according to this theory). But I think that ultimately such a theory with one single sort of thing playing all these diverse roles will not be attractive overall, and that we may have to refine the picture somewhat of how these things like sentence meaning and the objects of belief relate to each other. I am focusing for now on linguistic meaning.

Sentences in use, you might say are 'inherently representational': but the whole idea of inherence doesn't really fit here. The whole point is that sentences are not inherently representational, but used in certain ways, they are. If you want to treat the sentence-in-use as a sort of thing by itself, then this is a kind of abstraction. Such a logical construction may be useful, but the resulting entity is not explanatorily basic: underneath, you have the sentence and you have all the stuff about how it is used. And so, at the base level, you don't have anything inherently representational.

This approach fits naturally with the ideas of representing and of a representation. Fundamentally, a representation itself is just a concrete thing - like a drawing or a sentence. And it represents not inherently, but by being used in a certain way. People represent things as being certain ways by putting representations to use.

This approach also furnishes a kind of explanation of the feeling of occultness or suspiciousness in theories which posit inherently representational entities in their explanatory base: they feel unsatisfactory because they hide the contextual rabbit in the hat of some posited object. If we are forced to treat this object as basic, we can never see under the hat.

References

Haze, Tristan Grøtvedt (2018). Propositions, Meaning, and Names. Philosophical Forum 49 (3):335-362.

Soames, Scott (2015). Rethinking Language, Mind, and Meaning. Princeton University Press.

Wittgenstein, Ludwig (1922). Tractatus Logico-Philosophicus. Routledge & Kegan Paul.

Notes on Modality II - "Deserving the name", the grandeur of the idea of metaphysical modality, &c.

I want to explore a 'no clear best deserver' view of the - very inchoate - role that the distinction between (metaphysically) necessary vs. contingent truths is supposed to play.

The idea is that once you drill down in the borderlands, you see that there are different ways of going.

So no clear best deserver. But also: it's not clear that anything is a good enough deserver.

The 'no clear best deserver' hypothesis raises questions: why wouldn't everyone agree? Why would this be news?

One reason might be that there really is a best desever. Or that it seemed like there was a clear best but on further reflection there are competitors and it's not clear that any one has the edge. But I think there's more to say about why this might be news. There is something very natural about thinking that there is some single distinction here. There is a strong inclination to think that there some one major, fundamental distinction between the truths that could have been otherwise and the ones that couldn't. 

So if there is a sense in which this is not so - or if we want to be circumspect about it - we could try to tell a positive story about how this comes about.

Also, it is important to remind ourselves that the strong inclination I am speaking of may not be universal, or even normal. (Think of people who encounter this philosophical discourse, feel vaguely skeptical, maybe kind of interested but not particularly compelled, don't sign up for any view in particular, or flirt with some unusual view (an undergrad fellow student of mine defended the view that all truths are necessary in a course essay), and simply move on with their lives and don't ever really think about the matter, except as something some people are concerned with.)

But, at the same time: it's not just some specific problem in some particular subliterature. Versions of it, or closely related things, come up in philosophy at many times and places. And I have the feeling that it springs from a kind of root that also gives rise to certain philosophical thoughts and frames of mind that all sorts of people have.

So, how might it come about? Perhaps: Some kind of drive towards systematic understanding run rampant. Desire to see world as mechanism with discrete states. And the point isn't that that's naive, or probably not true after all, or something like that. But one issue here may be: why should there be one clear best way of seeing the world that way? 

It is possible to get into a frame of mind where it seems like there must in some sense be a single or primary set of facts about the possible states of the world, if there really is a world at all. It is like Wittgenstein's demand for substance, for eternal objects, in the Tractatus. It can seem like if the thing you're demanding weren't so, there would be no world at all, or nothing would be true.

There's something here I want to say in connection with this 'no clear best deserver' idea, along the lines of: how little is said when the idea of metaphysical modality is introduced! How could there be enough specific information there - in phrases like 'really could have been that way' - to narrow things right down to a particular, clear distinction!  It feels completely "lay", really quite free of theory (but of course you can theorise about 'really' or formulate it in terms of 'some fundamental sense' and then theorise about that).

But on the other hand, isn't that a bit fallacious? Can't specific, detailed things come out of arrangements of ordinary, quite general concepts? And don't, for example, specific seeds produce specific trees, despite being so small?

So this thought needs to be stated carefully. There's not some general rule here that's being appealed to. Still I think there's a point here, a way to see something  - a way to break the grip of something.

The words and associated ideas we're using here are quite flexible things, on reflection. 'Things', 'really', 'could'.

You might say there's a kind of naive level of "buying into" the idea of this one major distinction between contingent and necessary truths. Just not thinking about it too much. But then if you've thought about it and seen it threatened or scoffed at or considered uninteresting, but still want to pursue it - OK, now you're after something. Now you have a dream, I feel like saying.

I think, awkward as it is to talk about, there is really no getting away from the fact that there's something fantastic about the idea, something grand. '"How things really could have been" - what could be more interesting than that?!'

* * *

Consider Kripke's suggestive remark at the end of Naming and Necessity about leaving open the extent to which metaphysical modality will turn out to be closer to physical than suspected.

It's remarkable how little investigation or facing up there has been to the issue of how such a thing might be decided. (Williamson talks about 'detailed theoretical investigation' but I can't help but feeling that this is a kind of mirage, like how Russell and the early Wittgenstein palmed off the question of what the logical atoms will turn out to be.)

Decades later, we seem to just have different viewpoints - some rationalists who are far from thinking it coincides more with physical possibility than you might think, and others who are captured by the idea of empirical insight into hard limits (due to what seems to me a kind of misinterpretation of the necessary a posteriori, but working out where the stand offs there lie would be good).

The picture I have now is this: there's a certain inchoate role, inchoate requirement or job description for this idea of the ways things really could have been (metaphysically), and then it recedes into the background when we look at cases and theories. But this needs to be scrutinised more, and this will shed light on skepticism about the notion, and on different positive views.

I don't mind if you settle on a best deserver and are happy with it, but I will want to be clear that this is what is happening, and be wary of an alternative way of thinking about the matter as something which has been investigated and a view found correct. <-- Inadequate, but there is an important feeling here that I don't want any smoke and mirrors.

A large part of the worry is: that this process of coming to rest upon a choice of best deserver gets misrepresented as investigation into how things could have been. A failure to distinguish between getting to a concept and investigating what it applies to. But there are dangers with this hypothesis too.

'Philosophers framed the question of how things really could have been, and detailed philosophical research has led to a convergence on the view that this turns out to be a matter of ...'

In terms of what we want from the term, what gives it its life and feeling of importance - this is so easy to write off as a trifling, preliminary thing. Almost indecent to talk about. But it is very important. And it's amazing how far it reaches, so to speak. 

A Dialogue on Mathematical Propositions

I wrote the following dialogue as an antidote to the dogmatism I felt myself falling into when trying to write a paper about a priori propositions. The characters A and B are present-day analytic philosophers. Roughly, A represents the part of me which wanted to write the paper I was working on, and B represents the part which made trouble for the project.

A: I've got a view about a priori propositions I'd like to discuss with you. I don't think you're going to like it.

B: Intriguing! I'll try to put up a good fight.

A: Good. Still, you won't just defend the opposite view no matter what, will you? I'm certainly going into this ready to modify my view, if not to completely relinquish it.

B: Sure. No, I won't just set myself up as an opponent debater. Let's try to give each other as much ground as our philosophical consciences allow, and see if we can agree on some things.

A: OK, great. So, here's the view: what is special about a priori propositions, which enables them to be known independently of experience, is that they have their truth values essentially. They do not reach outside themselves to get their truth values, but carry them within as part of their nature.

B: OK. Interesting use of the notion of essence. I'm used to associating views which tie a priori propositions' truth or falsity closely to meaning with more deflationary attitudes, not with philosophers who make positive use of metaphysical notions like that of essence.

A: Exactly. That's one of the exciting things about my view, I think. It brings out the fact that that sort of tight connection between meaning and truth value can be posited without embracing any problematic conventionalist or deflationary attitudes about essence or meaning.

B: I think you have a point there. A meaning-based view of a priori truth doesn't need to be deflationary or conventionalist. Still, I think it's wrong. Your view overlooks the fact that a priori propositions, or many of them at least, are about something, and we often have to inquire into that something to know them. When mathematicians discover new truths, they don't sit and try to get insight into the essences of the propositions they are wondering about. They try to get insight into the things that the propositions are about, like numbers, or sets, or graphs.

A: That is true, but does not affect what I am saying. Look, the a priori truths of mathematics either have their truth essentially, or accidentally. And if they really had to reach outside themselves for their truth, then they would only be true accidentally. And in that case it should be possible to depict those very propositions reaching out but getting the opposite truth value. But you can't even begin to imagine a situation where someone has expressed what is actually an a priori truth, but which in that situation is a false proposition. And it's not like the case of propositions whose instantiation vouchsafes their truth, like 'Language exists'. Instead, their truth is of their very essence. Now, we all agree that an a priori truth can have its actual truth value, but what would it look like for it to have the other one? The onus is on you to flesh out an answer here, and it seems to me that nothing you could say on this point would satisfy.

B: I do not dispute that I couldn't really flesh out a description of a situation where the same a priori proposition gets the opposite truth value, but I don't think I have to be able to. I can still maintain that these a priori truths do not have their truth off their own bat, due to meaning alone. The source of their truth lies in what they are about. However, unlike with empirical truths, what they are about is rigid and unmoving - necessarily the way it is. So it is no real objection that I cannot depict a situation in which their source of truth or falsity yields them a different truth value, since that is just because their source is necessarily the way it is. That doesn't make their source any less of a source.

A: So you are saying that the meanings of these a priori propositions are out there in a rigid, unmoving space of possible meanings, and that they get their truth or falsity from an equally rigid, unmoving space of mathematical objects. But since all this stuff is rigid, unmoving, and necessarily the way it is, it seems to me that your talk of sourcing is just empty talk. The very idea of sourcing seems dubious here. Granted, you may seem to have an advantage in the fact that our knowledge of these truths must have some source. But the sourcing you are talking about is all going on in Plato's Heaven. It does nothing to explain how we get the knowledge. So you might as well not posit it.

B: You are trying to cast aspersions on my talk of sourcing, but I want to suggest that what you are saying is, on examination, more dubious than what I am saying. You are no nominalist, no denier of the independent existence of mathematical objects. Right?

A: Sure. I mean, I think when people object to claims like 'Mathematical objects exist independently', they are perhaps bothered by something that really should bother them. But I do think that understood properly, such claims do make a sound and correct point.

B: OK, fine. And so, it seems to me that if you are saying that a priori truths about these objects have their truth essentially and off their own bat, you are positing a kind of harmony between the meanings and what they carry inside them on the one hand, and the mathematical objects on the other. But this harmony seems dubious. It cries out for explanation. Why should it exist? Coming around to the proper view, that the propositions are about the mathematical objects, and therefore the mathematical objects' being the way they are is the source of these propositions' truth values, the difficulty disappears.

A: I don't see how the harmony you complain about is particularly strange or objectionable. Don't parts of mathematics mirror and reflect each other in weird and wonderful ways? Since we accept that, it seems that it's not particularly costly to acknowledge that the meanings of mathematical truths are also part of this crystalline structure. Crucially, it seems less dubious than your sourcing talk - more of a piece with things we already acknowledge. And it seems to me that your view overdoes the analogy between mathematical and empirical truths, leading to confusion.

B: Do you see any positive value in your view? Or is it all about stopping that over-assimilation?

A: Well, perhaps my view helps with the problem of how we get mathematical knowledge. It seems to me an easier problem to say how we get in touch with meanings, than to say how we get in touch with things like numbers and sets. Our talk and thought instantiates meanings, I want to say, even if the meanings themselves are abstract, like numbers and sets.

B: But there are also "instantiation relationships", arguably more straightforward, between, say, numbers and piles of apples.

A: Hmm. Well, I don't know, I'll have to think more about that - but perhaps stopping the over-assimilation is enough. What value do you see in your view, anyway?

B: When I think about what is fundamentally wrong with your view, apart from my complaints about it being mysterious and ill-motivated, it seems to me that, in your effort to block the over-assimilation of mathematical and empirical propositions, you bring about another over-assimilation. Namely, between mathematical propositions which can be hard to discover the truth about, and what you might call paradigmatically analytic propositions - propositions where it really does seem that the way to know the truth about them is just to have insight into their meanings. Those propositions may perhaps be said to have their truth values essentially, since they don't seem to say anything substantial about anything, whether their subject matter be empirical or mathematical. And your view wrongly depicts substantial mathematical propositions as being like them. My view has the virtue of avoiding that over-assimilation. It may be that the over-assimilation you worry about is also a problem, but it should be combated in a different way.

A: Well, I am - or at least have been, up to having this conversation - inclined to think the corresponding thing about the over-assimilation that you are worried about. Positing a mysterious sourcing relationship between mathematical propositions and mathematical objects seems like a crude expedient. But I must acknowledge that the over-assimilation that bothers you is also a problem.

B: OK. So, it seems we can both agree that our respective views may have some power to prevent a certain over-assimilation, a different one in each case. And perhaps we can also agree that each of our respective views, when adopted, may increase the danger of falling into the over-assimilation targeted by the opposite view.

A: Hmm. I suppose we can both agree about that.

B: Now, isn't this worrying? I mean, where does it leave us? We have a question: Do mathematical propositions have their truth values essentially, intrinsically, inherently, off their own bat - or do they not? And it seems like our opposing answers have opposing strengths and opposing weaknesses. I feel the weakness of your view much more acutely, but I can't deny that your feeling that my view might be a somewhat crude expedient makes some sense as well.

A: I'm glad you're staying true to your intention of not just defending your view tooth and nail. Now it's starting to look like both our views have some merit, but that these merits crowd each other out. I am beginning to think that perhaps both our views can be said to suffer from crudeness on that score. We are both inclined to use a certain picture to ward off the over-assimilation which has most bothered us. And the pictures conflict, or at least seem to. Now, could it be that if our views were made clearer, these pictures could be seen to apply in different ways, so that there is no inconsistency in using one in its way, and the other in its way? The task then would be to clarify the difference between these two ways of using what appear to be conflicting pictures.

B: That is sounding more and more reasonable to me as a diagnosis of what's going on in this case. How Wittgensteinian! And to be honest, the Wittgensteinian-ness of this view worries me a bit, since this sort of approach, to this sort of problem, seems like it will turn many people off right away. If we are to try to resolve our difficulties this way, and if we expect the resolution to be given a fair hearing, I suppose we will also have to be careful to defend our resolution from objections which lump it together with features of Wittgenstein's views which people don't like.

A: I agree that is a worry. And it may be even worse than you are suggesting. What if the things people don't like and have turned their back on include this very power to resolve our difficulties!

B: Well, I see what you're saying. People are invested in a certain way of doing things, and in defending views of a certain type. And those ways of doing things may come naturally, at least to people with a certain background (including us), so that one slides back into them. But I think we may just have to try to give the naysayers about this method plenty of credit, and allow that there are serious problems with the sort of resolution we're talking about now. After all, why wouldn't there be? It could be that it's very promising, and still ultimately our best hope, but that there are serious difficulties with it which, in our desire to resolve our present issue, we aren't currently alive to.

A: I suppose I'm on board with what you're saying. As exciting and powerful as this approach may seem now, we must beware of coming off as if we think there's a silver bullet, a simple solution we've already got here. And I think that comes out more clearly when we come back from talking about pictures and consider the question, framed in terms of 'essence' or 'intrinsic' or what have you. Something about the idea of pictures makes us quite willing to allow different applications. Ambiguities, if you like. But it seems as though people, ourselves included, may be inclined to take a certain attitude to words like 'essence' and 'intrinsic', such that the word analogue of the move where we say 'These pictures appear to conflict, but if you look at their application, you see it's only an apparent conflict' seems less appealing. There is a feeling that with such words that for each there is a big, important, single job that they should be doing.

B: I think you're right. But again, I think you may be overplaying people's resistance. Yes, there will be people who just get turned off at the suggestion that such words should be understood as having various quite important roles to play. But probably, with many of the sort of people you have in mind, you must admit that they are willing to countenance such things as long as you keep things relatively clear and definite. I mean, if you start banging on about how complex and multifaceted it all is with these words, then yes, that will turn people off, because it sounds defeatist. It sounds like shirking hard and maybe very interesting work. But these sorts of people - and let's face it we're among them a lot of the time when we aren't just talking but trying to write papers - are quite willing to distinguish certain senses of weighty-seeming words, using little subscripts for example. So we shouldn't be too discouraged.

A: Yes, I suppose that's right. So, we should be ready to float the idea that our different pictures each having a role to play, but that just giving the picture and saying 'That's how things are' is a bit crude until we clarify and distinguish the application of the picture in each case. And we should be ready to try to take exactly this approach when it comes to our difficulties as posed in philosophical jargon, but be on guard against defeatist or wishy-washy sounding attitudes. I confess I'm worried about the extent to which this is possible. I mean, maybe once we try, we will find that the distinctions we might want to make by putting little subscripts on words like 'essence' tend to fall apart in our hands, or that possibilities multiply very quickly. But on the other hand, I must admit we haven't seriously tried yet. And maybe there is some progress to be made in that way, even if it does give out and get confusing again in a way similar to our original disagreement. So we should keep working on this.

B: Agreed.

A: I think I'm pretty worn out for now, though. And I suspect there are further problems with your view that I haven't brought out.

B: Same here, on both counts.

A: I hope we can find what it takes to continue soon.

B: So do I.

The Pre-Kripkean Puzzles are Back

Yes, but does Nature have no say at all here?! Yes.

It is just that she makes herself heard in a different way.

Wittgenstein (MS 137).

Modality was already puzzling before Kripke - there’s a tendency for the potted history of the thing to make it seem like just before Kripke, philosophers by and large thought they had a good understanding of modality. But there were deep problems and puzzles all along, and I think many were alive to them.

There is a funny thing about the effect of Kripke’s work which I have been starting to grasp lately. It seems like it jolted people out of certain dogmas, but that the problems with those dogmas were actually already there. The idea of the necessary a posteriori sort of stunned those ways of thinking. But once the dust settles and we learn to factor out the blatantly empirical aspect from subjunctive modality - two main ways have been worked out, more on which in a moment - the issue comes back, and those ways of thinking and the problems with them are just all still there.

(When I was working on my account of subjunctive necessity de dicto, I thought of most pre-Kripkan discussions of modality as irrelevant and boring. Now that I have worked that account out, they are seeming more relevant.)

What are the two ways of factoring out the aposterioricity of subjunctive modality? There is the two-dimensional way: construct “worlds” using the sort of language that doesn’t lead to necessary a posteriori propositions, and then make the truth-value of subjunctive modal claims involving the sort of language that does lead to them depend on which one of the worlds is actual.

This is currently the most prominent and best-known approach. However, it involves heady idealizations, many perplexing details, and various questionable assumptions. I think the difficulty of the two-dimensional approach has kept us in a kind of post-Kripkean limbo for a surprisingly long time now. Except perhaps in a few minds, it has not yet become very clear how the old pre-Kripkean problems are still lying in wait for us. I have hopes that the second way of factoring out will move things forward more powerfully (while I simultaneously hope for a clearer understanding of two-dimensionalism).

What is the second way? It is to observe that the subjunctively necessary propositions are those which are members of the deductive closure of the propositions which are both true and C, where C is some a priori tractable property. (On my account of C-hood, the closure version of the analysis is equivalent to the somewhat easier to understand claim that a proposition is necessary iff it is, or is implied by, a proposition which is both C and true. On Sider’s account of C-hood this equivalence fails.)

My account of subjunctive necessity explains condition C as inherent counterfactual invariance, which in turn is defined using the notion of a genuine counterfactual scenario description. And it is with these notions that the old-style puzzles come back up. Sider’s account has it that C-hood is just a conventional matter - something like an arbitrary, disjunctive list of kinds of propositions. (Here we get a revival of the old disagreements between conventionalists and those who were happy to explain modality semantically, but suspicious of conventionalism.)

What are these returning puzzles all about? They are about whether, and in what way, meaning and concepts are arbitrary. And about whether, and in what way, the world speaks through meaning and concepts. Hence the quote at the beginning, and the quote at the end of this companion post.

Are Meanings 'Individual Things'? An Important Unclarity in Lycan

I have recently been enjoying some of Lycan's papers, as well as his Philosophy of Language: A Contemporary Introduction. In Chapter 5 of the latter he writes:

In stating the foregoing meaning facts, I have at least half-heartedly tried to avoid “reification” of things called meanings; that is, talking about “meanings” as if they were individual things like shoes or socks.

'Like shoes and socks' how, though? The problem is: what does this mean?

Lycan then introduces the idea of 'entity theories':

Philosophers have made an issue of this. Let us use the term “entity theory” to mean a theory that officially takes meanings to be individual things.

And he goes on to contrast such theories with - you guessed it - 'use' theories, with the later Wittgenstein as the paradigm.

I think this is an unclear and misleading contrast. It is unclear what it takes to be an 'entity' or an 'individual thing'. The examples of shoes and socks may suggest that this notion is something like that of a physical object, or a 'concrete particular'. But that can't be right, as Lycan wants to count Fregean sense theories, or Moore's theory of propositions, for instance, as 'entity theories', but Fregean senses and Moorean propositions are not supposed to be physical, concrete things. Also, how are we to know what is official and unofficial? That distinction seems fishy here.

This contrast is misleading, I think, because it may suggest that the idea that meanings - or an aspect of them at least - should be thought of as roles in language systems, or uses of signs, commits one to some dark doctrine about these roles or uses not being 'individual things'. Which, as I have suggested, has no clear meaning. This may then marginalize this sort of role/use idea about meaning, for example by making it look as though it is automatically in contradiction with any technical semantic theory which maps expressions to entities of some sort.

I suggest that the real point in this neighbourhood, regarding a role/use conception of meaning, is not that on such a conception, meanings aren't entities, or individual things - whatever that means - but that they are, speaking loosely, 'things' in a quite particular, easy to misunderstand sense. In Wittgensteinian terms, the grammar of expressions like 'the meaning of that utterance' must be attended to, and our understanding of it not simply modelled on that of expressions which function very differently, say, 'the bearer of that name' or 'this shoe'.

Reference

Lycan, William G. (1999). Philosophy of Language: A Contemporary Introduction. Routledge.

Quine's Poor Tom Revisited: Against Sayward

UPDATE (Nov 2019): I have recently published a paper on this topic, 'Quine's Poor Tom', in the European Journal of Analytic Philosophy.

I have recently come back to the argument in section 31 of Quine's Word and Object. In a post just over four years ago I criticized the argument for a use-mention shift with regard to a principle which, on an opaque reading of 'believes', is a reasonable thing to require of a good logician, but which, on a transparent reading of 'believes', is not a reasonable thing to require of a good logician.

In Quine's argument as he stated it, the principle is introduced in terms of belief in sentences, which all but forces an opaque reading. But then when it is applied in the argument, Quine has semantically descended to a 'believes that' construction, and applies the principle in such a way as would only be legitimate if it is given the transparent reading.

The principle as originally stated runs as follows:

(Acumen) [P]oor Tom, whatever his limitations regarding Latin literature and local philanthropies, is enough of a logician to believe a sentence of the form ‘δp = 1’ when and only when he believes the sentence represented by ‘p’. (Quine 1960, p. 148.)

In that-clause form it runs as follows:

(AmbigThatAcumen) Tom believes that δp = 1 when and only when Tom believes that p

(For the definition of the 'δp = 1' construction see my original post, but it can be read as 'The truth-value of "p" = 1' without going far wrong.)

Sleigh's (1966) objection makes the same point that I made towards the end of my original post, namely that the (AmbigThatAcumen) is only a reasonable assumption on an opaque reading, whereas its transparent reading is needed for the argument. He did not note that Quine's originally stating the principle in terms of belief in sentences all but forces us to give it an opaque reading at that point in the argument.

Widerker (1977) and Sayward (2007) criticized Sleigh's objection. I did not engage with these papers in my original post. In this post, I would like to refute Sayward's criticism. I think this can be done more or less conclusively.

Widerker's objection is less easily dealt with, and leads us into some interesting territory. I am currently working on a paper where I try to sort out the whole mess, and try to draw a metaphilosophical lesson.

One of the most important things I did not appreciate earlier is that Quine in his argument does give us what is needed for a good argument for his ultimate conclusion, namely that it will not do to treat belief transparently always. Once we see this, what is so objectionable about his argument may start to look more like a matter of presentation.

The way Quine presents things, I would like to say, is not perspicuous, and cultivates an air of paradox. (Quine makes it look like he has shown that if we treat belief transparently always, and if Tom has good logical acumen and believes one true thing and one false thing, then he believes everything.) I think this is philosophically bad, and so presumably did Sleigh. But it is interesting to note that what originally looked more like a dry, logical error (so to speak) may be more effectively criticized in this way - as a matter of non-perspicuous, philosophically bad presentation, rather than the commission of a definite logical error which flouts a principle we could get the supporter of Quine's argument to agree to. (Compare on the one hand the attempts of "cranks" to show that Cantor's diagonal proof was unsound, and on the other hand Wittgenstein's more sophisticated criticisms. I have blogged about this matter elsewhere.)

Sayward's criticism is simply that Sleigh has left it unargued that (AmbigThatAcumen) on its transparent reading is an unreasonable thing to require of  a logician - put differently, the criticism is that Sleigh has left it unargued that (AmbigThatAcumen) on its transparent reading does not express a form of logical acumen. He writes:

So if Sleigh’s point is to carry much weight it must take the form of a claim that no logical acumen, or at least none at all widely shared, is expressed by [(AmbigThatAcumen) read transparently]. But so far as I can see that simply goes unargued in his paper. Indeed, so far as I can see the paper contains no argument that the logical acumen to which Quine referred is not expressed by [(AmbigThatAcumen) read transparently]. It is simply and baldly asserted. (Sayward (2007), pp. 57 – 58.)

This objection can be convincingly rebutted. Firstly, it gets the dialectic wrong. Quine, for his argument to be plausible, needs his hypothesis about Tom's logical acumen plausibly to be about some genuine kind of logical acumen. I think it is perfectly fair to point out that this only seems to be so if we take the hypothesis opaquely, in which case it doesn't support the argument. This is already a good objection, in my judgement, without any further argument that it is not the case that (AmbigThatAcumen) read transparently – contrary to appearance – does express logical acumen after all.

Admittedly, this appearance may not be universal. This leads us to a second, stronger, point against Sayward's objection: Sleigh does give an argument that no logical acumen is expressed by the transparent reading! Sayward's claim that he does not do so is a sheer mistake. The argument comes at the end of Sleigh's note and runs as follows (except I have, for ease of reading, removed the subscript notation which he applies to singular terms to disambiguate between transparent and opaque, and simply put bracketed specifications of the intended reading next to 'believes' instead):

Obviously, (4') does not express the idea of Tom's acumen. Consider: 

(9) Tom believes [transparent] that [δp] = 1. 

and 

(10) Tom believes [opaque] that [2­ - 1] = 1. 

Given (10), (9) is true provided the sentence represented by 'p' is true. But we cannot infer from this that Tom believes the sentence represented by 'p' even if every singular term in 'p' is taken transparently and even if Tom is overflowing with logical acumen. (Sleigh 1966, p. 93.)

Clearly this is an argument, so Sayward is just wrong in saying that Sleigh doesn't offer one. I think it's a perfectly good argument, too – although I think it was unnecessary to make 'believes' in (10) opaque and (as I hope to make clear in the paper I am working on and perhaps a future post here) this makes Sleigh more vulnerable to Widerker's criticism.

Finally, I think we can give a more straightforward argument that the transparent reading does not express any sort of logical acumen. To rewrite the principle with an explicit disambiguation:

(TransparentThatAcumen) Tom believes [transparent] that δp = 1 when and only when he believes [transparent] that p.

Now, let us plug in some truth for 'p' which not everyone with logical acumen knows – say, 'Quine was born in 1908':

Tom believes [transparent] that δ(Quine was born in 1908) = 1 when and only when he believes [transparent] that Quine was born in 1908.

Now, substituting '1' for the co­extensive 'δ(Quine was born in 1908)', we get

Tom believes [transparent] that 1 = 1 when and only when he believes [transparent] that Quine was born in 1908.

This is plainly not something we should require of a reasoner. Using 'of' language to induce a transparent reading, so that the point reads more intuitively: a reasoner may not believe, of Quine, that he was born in 1908. They may not have any beliefs about Quine at all. Obviously, they should not in that case – by the 'only when', which is essential to Quine's argument – fail to believe, of 1, that it is equal to 1. But we obtained this wrong result just by substituting co-extensive terms in an instance of (TransparentThatAcumen). Therefore (TransparentThatAcumen) does not express any sort of logical acumen. Rather, it seems like something we definitely shouldn't conform to.

The above, I think, completely diffuses Sayward's criticism.

References

- Quine, W. V. (1960). Word and Object. The MIT Press.

- Charles Sayward (2007). Quine and his Critics on Truth-Functionality and Extensionality. Logic and Logical Philosophy 16:45-63.

- R. C. Sleigh (1966). A note on an argument of Quine's. Philosophical Studies 17 (6):91 - 93.

- David Widerker (1977). Epistemic opacity again. Philosophical Studies 32 (4):355 - 358. 

An Account of the Analytic/Synthetic Distinction

Some of the intuitive characterisations given, in the last post, of the notion of internality of truth-value – such as 'internal meaning determines truth-value' - sound a lot like a common post-Kantian way of characterising or defining analyticity, namely as 'truth in virtue of meaning'. This raises the question of whether the class of a priori truths is the class of analytic truths, and the question of whether there are, or should be, distinct notions here at all. My answers to these questions will be No and Yes respectively.

The aim here will be to try to clarify an interesting notion of analyticity which is conceptually and extensionally distinct from all the notions of truth a priori identified in the last post (internality of truth, non-Twin-Earthability of truth, Chalmers' epistemic two-dimensionalist account, and traditional conceptions). It is distinct from, but builds on, our internality conception of the a priori.

The account I will give of this notion is inspired by Kant's account of the analytic-synthetic distinction in the Critique of Pure Reason, as well as Wittgenstein's remarks on the synthetic a priori and concept-formation in the Remarks on the Foundations of Mathematics.

It is well known that Kant's definition, or principal explication, of 'analytic' and 'synthetic' is given in terms of subject and predicate:

In all judgments wherein the relation of a subject to the predicate is cogitated (I mention affirmative judgments only here; the application to negative will be very easy), this relation is possible in two different ways. Either the predicate B belongs to the subject A, as somewhat which is contained (though covertly) in the conception A; or the predicate B lies completely out of the conception A, although it stands in connection with it. In the first instance, I term the judgment analytical, in the second, synthetical.

Since modern logic and philosophy of language has taught us not to regard every proposition as being composed of a subject and a predicate, this definition can't be adequate for us. But it is suggestive, and even moreso are some of the other things Kant says about the analytic-synthetic distinction. He says of analytic and synthetic propositions respectively that 'the former may be called explicative, the latter augmentative'. And consider this elaborated version he gives of his main question, that of how synthetic a priori knowledge is possible: 'If I go out of and beyond the conception A, in order to recognize another B as connected with it, what foundation have I to rest on, whereby to render the synthesis possible?'.

The idea that synthetical judgments are 'augmentative', that they 'go out and beyond' 'conceptions', can, I think, be generalized or abstracted from Kant's discussion in such a way that it does not depend on construing all propositions as being of the subject-predicate form. And we get a hint of how to do this from the following passage about the syntheticity of the proposition '7 + 5 = 12':

We might, indeed, at first suppose that the proposition 7 + 5 = 12 is a merely analytical proposition, following (according to the principle of contradiction) from the conception of a sum of seven and five. But if we regard it more narrowly [my emphasis], we find that our conception of the sum of seven and five contains nothing more than the uniting of both sums into one, whereby it cannot at all be cogitated what this single number is which embraces both. The conception of twelve is by no means obtained by merely cogitating the union of seven and five; and we may analyse our conception of such a possible sum as long as we will, still we shall never discover in it the notion of twelve. We must go beyond these conceptions, […]

This regarding-more-narrowly will be the key for us. We said above that a proposition is a priori iff it contains its truth value, i.e. iff its internal meaning determines its truth-value. Our idea now is that a proposition is analytic iff its internal meaning regarded more narrowly in a certain way – or iff a certain sort of part or fragment of its internal meaning – determines its truth-value. And so the next task is to try to clarify what characterises the aspects of internal meaning we are restricting our attention to here.

To do this, we will use the notion of concept- or conceptual-structure-possession, and the notion of understanding. We will not need to involve considerations of knowledge, judgement, being-in-a-position-to-see-that, or anything like that. (Later, we will consider how what we say may shed light on accounts which do involve such considerations.)

As a first approximation, we will say that a proposition is analytic iff the bits of conceptual structure – the part of its internal meaning - one must possess in order to understand it, determines its truth-value. (This involves a terminological departure from the possibly more common procedure of regarding analyticity as implying truth – we say that an analytic proposition can be true or false, just as we say an a priori proposition can be true or false. This has the nice feature of giving us a simple division among propositions in general, not just truths, so that we can say that for propositions in general, being analytic is just not being synthetic, and vice versa.)

We can make this definition easier to handle and more memorable by giving it in two parts:

The meaning-radical of a meaningful expression consists in the bits of conceptual structure, i.e. the part of its internal meaning, one must possess in order to understand it.

A proposition is analytic iff its meaning-radical determines its truth-value.

(As an added bonus, we now have the general concept of a meaning-radical, which we can apply to sub-propositional expressions as well as propositions, and perhaps also to super-propositional expressions such as arguments.)

Consider the fact that we can come to believe false arithmetical propositions - for example on the basis of miscalculation, or misremembering, or false testimony - and that we can apply them.

Contrast the case of a paradigm analytic proposition, such as 'All bachelors are unmarried'. (To get around the irrelevant problem that in English 'bachelor' very arguably doesn't mean 'unmarried man', let us just suppose that it does mean exactly that.) To be sure, someone can assent to the sentence 'Not all bachelors are unmarried', and dissent from 'All bachelors are unmarried', but in such a case we would say that they don't understand this latter as we do – they don't understand our proposition 'All bachelors are unmarried'. So they don't believe – and here we are using words with our meanings kept intact – that not all bachelors are unmarried.

Kant says that we can become 'more clearly convinced' of the syntheticity of arithmetical propositions 'by trying large numbers'. Let us now, therefore, try to illustrate the notion of a meaning-radical, and in turn that of analyticity, by considering an example of a false arithmetical proposition involving numbers larger than 7, 5 and 12. Say '25 x 25 = 600'.

Despite being false a priori, the proposition '25 x 25 = 600' is something we can mistakenly believe and apply while still understanding it correctly (in some suitably minimal, and natural, sense of 'understand'). We have – wrongly – made a connection between our conception of the product of 25 and 25, and our concept of 600.

Why do we say that we understand the proposition in its ordinary sense and are wrong, rather than saying that we are operating in a different system, in which the sentence '25 x 25 = 600' is true, and that we (therefore) don't understand the proposition in its ordinary sense? It is not hard to see what sorts of things make it that way. If we worked it out on a calculator, or calculated it again ourselves, we would unmake the connection. Such developments would show that we did understand the proposition correctly (i.e. in its ordinary sense).

(Suppose an illegal move is made in chess, say that someone moves their king into check (so that it need not be immediately obvious that it is an illegal move). If the maker of this move can easily be brought to accept that their move was illegal, we can maintain that they understand how to play chess and were playing it according to the ordinary rules, but playing wrongly. If they cannot, then either they simply do not understand chess, or are insisting on playing according to deviant rules.)

The fact that in the case of the false belief that '25 x 25 = 600', there is this other option here, if I may put it that way, of saying that we are operating in a different system – an option which we will have to reject because of many things about how things are, so in that sense not an option, but still something which makes sense – shows that there is a possible system, compatible with the meaning-radical of '25 x 25 = 600', in which that sentence holds. That is, the meaning-radical of '25 x 25 = 600' – that bit of conceptual structure – can be incorporated into a larger structure wherein the concept of the product of 25 and 25 (although we might not want to call it that anymore) is connected to that of 600 in such a way that the sentence '25 x 25 = 600' is true. It will have a different internal meaning from our proposition '25 x 25 = 600', despite the system it belongs to incorporating the meaning-radical of our proposition. This is what makes '25 x 25 = 600' synthetic.

On this picture, the full internal meaning of a concept or proposition-meaning may involve connections which do not have to be made in order to understand it.

So, a proposition is analytic iff it has its truth-value in virtue of the bits of conceptual structure someone has to possess in order to understand it. That is, iff the bits of conceptual structure one must have in order to understand it cannot be embedded in a context such that the proposition-radical of that proposition gets a completion such that the resulting proposition has a different truth-value from the proposition in question.

More briefly, a proposition is analytic iff its meaning-radical determines its truth-value.

All a priori propositions, then, on the account I am giving here, will be such that their internal meanings determine their truth-values. But analytic propositions have the further property that their radicals determine their truth-values, whereas the radicals of synthetic a priori propositions can be incorporated into both true propositions and false ones.

A Complication

One complication: perhaps there is a mistaken assumption of uniqueness built into my talk above of the meaning-radical of a proposition. The bit of conceptual structure one must possess in order to understand it. Perhaps one and the same proposition can be understood from more than one angle, as it were, in which case it may be better to talk about multiple meaning-radicals – distinct bits of conceptual structure all of which individually and minimally suffice for understanding.

This gives rise to a choice: if that's how things are, should we call the analytic propositions those which are such that all their meaning-radicals determine their truth-values? Or those which have at least one meaning-radical which determines their truth-value?

I do not want to try to settle the issue of whether we should recognize a possibility of multiple radicals. Furthermore, I have no opinion about which use of terminology is best, in case we should – perhaps it just doesn't matter. If we use 'analytic' for the first, we may say 'weakly analytic' for the second. Or, if we use 'analytic' for the second, we may say 'strongly analytic' for the first. Or we might make 'analytic' mean 'either strongly or weakly analytic'. Or drop it entirely, and always specify 'strong' or 'weak'.