Different Attitudes about Meaningfulness in Philosophy, and Their Consequences

What makes a question or a statement meaningful as opposed to nonsensical? This is a hard question, and perhaps not a very fruitful one in philosophy since the falling out of favour of verificationism. But what if we instead ask: what difference does it make whether we think something makes sense?

I have sometimes been struck by a certain kind of self-conscious, almost defiant claim of meaningfulness that can be found in work by philosophers writing after the resurgence of metaphysics in the second half of the twentieth century. You may have noticed it yourself. Often in the course of making a point, a philosopher will say something like 'Well, the question is certainly meaningful...' or 'Whether or not it is true, there can be little doubt that this is a coherent position'. 

This liberal attitude to the question of whether something even makes sense contrasts starkly, and is often expressed in reaction to, the wary attitude of other philosophers, especially earlier in the twentieth century.

Often, the liberal attitude is supported with the idea that the wary attitude depended on a discredited view - verificationism - about what it takes to be meaningful.

Both attitudes, especially when taken stridently or dogmatically, can seem stupid. The denier of meaning can seem like a shirker. Or like someone who doesn't want to play a game and justifies it by acting superior.  The denier can seem crude - like they have this stupid hammer that they wield instead of taking the trouble to understand something (or at least admitting that they can't or won't). 

But the affirmer of meaning can also seem stupid and crude. As though they are blind, perhaps even willfully blind, to subtle problems and difficulties. In the context of doing philosophy, this may seem like especially bad form, in that such problems and difficulties are just the thing that a philosopher should presumably try to be alive to.

It is quite clear that both tendencies have their pitfalls, and that both can be justified in particular cases. But the question of which attitude is right overall, or in a particular area, or in a particular vexed case even, seems peculiarly intractable, in something like the way moral and aesthetic issues can be intractable.  

I have become interested in thinking about this from the point of view of the consequences of the different attitudes, focusing on output rather than input. That is, rather than inquiring into when it is right to deem something meaningful, let us try to think about what might ensue given an attitude to the meaningfulness question. And that may then shed light back on the input question. 

A liberal attitude to the meaningfulness question can be refreshing, in that ideas and views get engaged with and clarified, in a way that they don't seem to if you're being skeptical about meaning. For example, someone who is very suspicious about the meaningfulness of the questions and views in what is nowadays called temporal ontology, e.g. whether the past and the things in it exist, is not, at least while being suspicious, likely to note certain (apparent) logical relationships between these views and others. For instance, the relationship to the question of whether true statements (perhaps of a certain kind) are all made true by some existing thing. Noticing these things seems to require that we, at least for a time, don't stand back and worry about meaningfulness, but come forward and handle these ideas - i.e. that we treat them as meaningful, and do the things that we do when we try to find out whether things are true or false.

But a warier attitude to meaningfulness can also be refreshing, leading us to take (in Wittgenstein's phrase) a wider look around. Fresh considerations may arise in this way, where from inside the meaning-granting perspective they would not. For example, someone suspicious about the way questions in temporal ontology are debated in philosophy seminars and publications may find themselves wondering what is really going on here, what is really animating all this discussion. They may think suspicious thoughts about the emotional associations of some of these ideas playing more of a role than the broadly scientific, "theory choice" mode of discussion of analytic metaphysics would suggest. And such thoughts may be fruitful. 

Understanding this better may help us avoid stupidities on both sides, making us more nimble and sophisticated. We don't have to pick a posture and stay in it forever. Even if a question or a view is ultimately dubious as regards meaningfulness - or needs to be transformed based on a better understanding of what is really at stake - taking the liberal attitude and working with the question or view for a stretch, i.e. treating it as meaningful enough, may yield insights which survive the transformation, or can be transferred to other places. And we may be more prepared to let this go on if we realise that it doesn't preclude us from taking the other viewpoint, i.e. getting suspicious and looking around more widely. And the same going the other way. One thing is that, even if the question is ultimately just really hard and not at all meaningless or in need of transformation, we may not know that, and so encouraging some suspicious minds to have a look around may be good. Another thing is that it may lead to a more subtle kind of improvement, where we may not radically reformulate our questions and views, but fold in new criteria and considerations that come from a wider look around.

The Resurgence of Metaphysics as a Notational Convenience

Reading Jessica Wilson's interesting new SEP entry on Determinables and Determinates, the following speculation occurred to me: the oft-remarked-upon resurgence of metaphysics heralded by the work of David Lewis, D.M. Armstrong and others was driven in part by cognitive resource limitations and practicalities of notation; putting things metaphysically often lightens our cognitive loads and makes thinking and writing more efficient in many philosophical situations.

Wilson's piece is dripping with metaphysical turns of phrase, but much of what she says could be re-expressed in a conceptual or linguistic key. I think this goes for a good deal of contemporary metaphysics. However, converting metaphysically-expressed ideas and claims into a conceptual or linguistic key may make them a bit fiddlier to think and express. And if you're doing hard philosophy and need to think and express a lot of things, this extra cost is going to pile up. Sometimes, having things in a conceptual or linguistic register may make things clearer, and sometimes it may be essential. But for many purposes the metaphysical register does fine, and often has the benefit of being less resource-hungry.

Yes, some metaphysics may not be capturable in conceptual or linguistic terms, and perhaps even in favourable cases the capturing will not be complete or perfect. And there are doubtless other important things going on behind the sociological phenomenon of the resurgence of metaphysics. But maybe this is part of the story.

UPDATE: Brandon Watson (at the end of a post on Fitch's paradox) links to this post, writing: 'I'm very interested, of course, in accounts of how philosophical scenes get transformed, how ideas transmogrify, and the like. This hypothesis for the rise of analytic metaphysics makes considerable amount of sense, and is probably true.' This is encouraging!

What Are My Problems Now?

This is a follow-up to What Was My Problem?.

1. The Basis of Puzzlement about Modality

One line of investigation I would like to pursue now is into what might be called the basis of the puzzlement about modality. And as suggested by my experience of vaguely wrestling with a bunch of problems, before realizing that my strongest leading ideas for my thesis were really about some of these problems rather than others, I think this line of investigation may itself call for the distinguishing of various problems.

One locus of puzzlement about modality is the notion of metaphysical or subjunctive necessity as it applies to propositions. And one question about this notion is whether, and how, meaning comes into the picture. Also, just the question of how this notion relates to other notions, and the extent to which it can be analyzed (not necessarily in non-modal terms). Those problems are addressed, properly I hope, by the account in my thesis. But lots of what I was wrestling with at the beginning of my research remains, and does not attach specifically to the notion of subjunctive necessity de dicto; there is a lot that is puzzling about modality that my thesis does not address.

One puzzling thing which borders directly on my thesis work, and does have to do with the notion of subjunctive necessity de dicto, is the question of how this relates to de re modal constructions and quantification into modal contexts. But I have been very frustrated in my research here, and to be honest I have come to feel like it is a bit of a minor, abstruse issue compared to some of the more fundamental problems about modality (although I have no doubt that very interesting work could be done on that issue, and have a couple of ideas).

A more fundamental area I would like to work on is indicated by the question: Why is modality puzzling at all? But here too there are probably several puzzling things to distinguish. One thing I am not primarily thinking of, although it may end up becoming relevant to the problems I am grasping at, are questions about modality in an extremely general sense. For instance, the question of what unifies all uses of expressions which we call modal, or which we say are about possibility or whatever - including 'You can come in if you like', 'It could be that John is on his way', 'It is impossible for two colours to be in the same place', '"Hesperus is Phosphorus" is necessarily true', 'I can lift this weight', 'This apparatus has four possible configurations'. Also, questions about what generalizations can be made covering all or at least a great diversity of such uses, for instance about logical implication relations between them.

Rather, I am interested in trying to get at the basis of our puzzlement about what may be called objective modality. What does 'objective modality' mean? Well, one clear thing it does is exclude epistemic modals, like 'It could be that John is on his way' in natural uses. These are to be put to one side - at least initially - in the line of investigation I want to pursue. Likewise with uses of modal language having to do with permission. Within the puzzlement attaching primarily to objective modality as opposed to these set-aside kinds, important distinctions may have to be made. For instance, there may be a need to distinguish between more down-to-earth uses of modal language, for instance 'I can lift this weight', from what may be called more metaphysical uses - but not 'metaphysical' in the sense often used in modal philosophy, to mean either something like 'objective' or something a bit more specific, like picking out what I pick out with 'subjunctive'. Rather, by 'more metaphysical uses' I mean uses which are so to speak puzzling from the start. That is, where there isn't as much non-problematic, clearly useful use as in the case of 'I can lift this weight' and the like. E.g. 'The world could have been otherwise', 'Aristotle is essentially human'.

One way forward in this line of investigation would be to look critically and closely at philosophers' attempts to give a sense of the puzzlement about (objective) modality, often as a preliminary to some account or a survey of accounts. For instance, Sider's remarks on the subject in 'Reductive Theories of Modality'. But I think it will also be important to look within, so to speak, and keep seriously asking myself 'What is it that puzzles me about this?'.

2. Propositions and Meaning, Language Systems, and Our Expectations

Another line of investigation I would like to pursue has to do with the account of propositions and meaning sketched in chapter 6 of my thesis. That account appeals to a notion of an expression's internal meaning, cashed out in terms of the expression's role in the language system to which it belongs. This may raise questions about the nature of the system, and how we should think of it and describe it. In my thesis, I tried to remain quite open about this, emphasizing that I was offering a sketch, and that different fillings in of the detail here may be possible.

It was hard to avoid striking a false note here. For I do not think this is the whole story about my sketch, and the middle-Wittgenstein idea about role-in-system which it takes over; it may not be quite right to just think about it as a sketch of a theory, where some aspects are not filled in. For the very idea of what needs filling in, and how, should I think be scrutinized. It is not that I am advocating quietism, or defeatism, about questions about the 'language system' I appeal to. But I think that some of our expectations here may be in need of examination.

A curious thing happens in this territory - it is easy to become disoriented, and wonder what the problem was and what is needed now. Maybe sometimes in philosophy, as we solve problems, they slip from our grasp. Sometimes there is a strange feeling where we wonder something like: how could there be a solution here which is given in mere words? How could that ever do? We feel we still need to be taught something, or shown something. Could it be something practical, so to speak? I.e. something we could get through practice?

In the new year, I intend to use this blog to try to make some inroads into these and related problems.

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. 

Illusory Explanatory Benefits in Philosophy

This post was prompted by a recent blog post of Wolfgang Schwarz's. See also a recent post of Alexander Pruss's.

“The difficult thing here is not, to dig down to the ground; no, it is to recognize that the ground that lies before us is the ground” - Wittgenstein (Remarks on the Foundations of Mathematics, VI 31, p.333).

I think we are often dogged, when doing philosophy, by a tendency to give credence to false theories on the grounds that they provide an explanation of something, when really the explanation is a pseudo-explanation, and where nothing of the kind is required if we see things aright.

In such situations, the false theory gives us something to say about some fact which resembles a real explanation, but gets us nowhere, and charmed by the idea that here we have an explanation where before there was none, we think better of the false theory. But having an explanation where before there was none is only a virtue if the explanation is a real one - if it actually helps us understand something, and does not merely have the form of an explanation.

A recent blog post by Wolfgang Schwarz called 'Magic, worlds, numbers and sets' contains an interesting example of this. It begins as follows:

'In On the Plurality or Worlds, Lewis argues that any account of what possible worlds are should explain why possible worlds represent what they represent. I am never quite sure what to make of this point. On the one hand, I have sympathy for the response that possible worlds are ways things might be; they are not things that somehow need to encode or represent how things might be. On the other hand, I can (dimly) see Lewis's point: if we have in our ontology an entity called 'the possibility that there are talking donkeys', surely the entity must have certain features that make it deserve that name. In other words, there should be an answer to the question why this particular entity X, rather than that other entity Y, is the possibility that there are talking donkeys.

It might be useful to consider parallel questions about mathematical entities.'

The example I want to concentrate on here is the one about mathematical entities, coming right after this passage. The post goes on to explore all kinds of weird stuff about Lewis, and I am not responding to it as a whole - I am just helping myself to something which occurs early on in the post, and using that as a vivid illustration of the particular failure mode in philosophy that I am trying to isolate and warn against.

(Before that, some sidenotes on the possible worlds case. The case is difficult, in part because there are various different ways of understanding 'possible worlds' in philosophy. We have some on which they really exist, some - perhaps for this reason closer to ordinary language - on which, apart from the actual world, they do not. We have some on which they are all the same sort of thing as the real, actual world, and some on which they are not. But on a lot of these, I too have sympathy for the idea that there is nothing here to explain. However, I think putting the point in terms of an emphatic identification of possible worlds with ways things might be missing the mark - for there are reasons due to Stalnaker in 'Possible Worlds' and elaborated on by Yablo in 'How in the World' for thinking that possible worlds are not to be identified with ways at all.

Secondly, regarding the point about an entity called 'the possibility that there are talking donkeys' (which of course need not be thought of as maximal or world-like) having to have certain features in virtue of which is deserves that name: perhaps that isn't so wrongheaded, but why can't the answer be along the following lines?: yes, one such feature is that, in this possilibity, there are donkeys. Another is that, in this possibility, they talk - or at least some of them do.)

To continue quoting:

'Mars has two moons, Phobos and Deimos. So here is a fact about the number 2: it is the number of moons of Mars. Following Lewis, one might argue that any account of numbers should explain in virtue of what the number 2 has this property. If we have numbers in our ontology, surely it can't be a brute fact that precisely this one is the number of moons of Mars.

The von Neumann construction of numbers gives a plausible answer to the Lewisian challenge. Here the number 2 is identified with the set { {}, { {} } }. This set has two members. The set of moons of Mars also has two members. And that is why 2, i.e. { {}, { {} } }, is the number of moons of Mars. In general, a von Neumann cardinal n is the number of Xs iff there is a one-one map between the members of n and the Xs.

By contrast, consider a primitive platonism about numbers on which the numbers are irreducible extra entities, distinct from sets, sticks, Roman emperors, and everything else. I do think the Lewisian objection has some bite here. One of the Platonic entities, call it X, is supposed to be the number 2. But what makes it the case that X, rather than Y, is the number 2, and thereby the successor of 1, and the number of moons of Mars? How come our label '2' picks out X rather than Y?

There seems to be an argument here for reducing numbers to sets.'

I want to criticize the line of thought indicated here. Firstly, regarding the idea that an account of numbers must explain in virtue of what the number 2 has the property of being the number of moons of Mars: aren't we being misled here by a phrasing which puts the focus on 2 instead of Mars? Intuitively, it is not an intrinsic feature of 2 that it is the number of moons of Mars, but an extrinsic one.

It is indeed plausible that it can't be a brute fact that the number 2 is the number of moons of Mars, but it doesn't follow from this that an account of numbers is the place to look for the explanation. Rather, the explanation we feel the lack of is that of, as we would more naturally say, the fact that Mars has two moons. And so I suggest, the apparent non-bruteness of the fact in question lies in its being explicable in astronomical terms. It seems like there is, whether or not we are able to figure it out, a story to tell about the formation of the planets and their moons which explains why Mars has two of them. I don't think there are any good reasons to believe that, with such an explanation on board, we would have further explaining to do as to why the number 2 is the number of moons on Mars. (Indeed, from a practical standpoint the idea seems ridiculous. But perhaps a practical standpoint isn't everything.)

I say 'I don't think there are any good reasons' above - but is that really the point? What force does my argument have? I am doing two things: firstly, I am suggesting that there is potentially a kind of bait and switch going on in our getting to the point of feeling that we need an account of numbers that explains why the number two is the number of moons of Mars: the fact calls for astronomical explanation, but if we consider the matter abstractly, we may just feel that it needs some explanation, and then the weird explanation involving the von Neumann construction is wheeled in.

Secondly, I am proposing that there is no explanatory gap between 'There are 2 Fs' and '2 is the number of Fs'. But at this point my arguments give out. Indeed, I think the best approach at this point is to stop arguing for the correct viewpoint, and switch to trying to trace the origin of the incorrect viewpoint. And I think in this case it lies in our misunderstanding expressions like '2 is the number of Fs', due to their superficial resemblance to expressions which work in a different way. (This is, it must be noted, is not at all to say that there is no such thing as the number two, or that it doesn't really have such properties as being the number of moons of Mars.)

Raisins at Dawn #2

Topics this time include: false thoughts, psychological impossibility, metaphilosophy, losing the use of a concept as it gets problematized or worked on, interdefinability as a sign of non-basicness, intuitionism, and the Russell-Copleston debate.