Just a brief note indicating that I’ve uploaded a revised version of my paper on counterfactuals and modal epistemology. I first blogged about this almost a year ago, and I refer you to the previous post for an outline of the paper.

The main bilding of the university, venue for the Graduate conference

Time for the second part of my Germany report. This concerns the combination of a graduate conference and research workshop with Scott Soames, entitled ‘Meaning, Modality and Apriority’. The events took place in Cologne 17-20 May 2010. Photos from both events are up in my Gallery. I gave a paper in the research workshop, with the title ‘The Metaphysical Status of Modal Statements’ (a slightly revised draft). Soames agreed with much of my criticism, although I was perhaps a bit provocatively pushing him closer to deflationism about modality than I was entitled to — in any case he conceded that the kind of essentialist picture that I sketched in the paper is on the right lines.

Scott Soames: Truth, Propositions and Possible World States

The organisation was top notch, although it was a pity that we couldn’t stay in the same venue for both events. I enjoyed all three events, but the conference marathon started to take its toll on me already during the graduate conference. The graduate conference included seven talks with dedicated comments and they were quite good in general, although I didn’t find any of the papers extraordinary. I think that on this post I will focus on Scott Soames’ keynote lecture and the discussion at the workshop rather than individual talks.

Soames has got two new books forthcoming very soon. One of them is entitled What Is Meaning?, the other Philosophy of Language. We got excerpts of both books before the workshop, and Soames talked about related matters in his keynote lecture as well. The topic is rather less interesting for me than Soames’ work on modality and apriority, but it was interesting to get this sneak preview and I think that there is something here that I could latch on to.

I won’t go into this in much detail, but basically Soames is defending a realist account on the nature of propositions: he thinks that propositions are ‘event types instances of which are events in which agents perform cognitive acts that are inherently representational’. Soames defends the view in some detail against the traditional Frege-Russell account on one hand and a modern deflationary view of propositions on the other hand. However, he does not really elaborate what the ontological status of propositions is according to his view. I tried to get into the bottom of this by asking whether he thinks that propositions have an existence independently of the agents’ cognitive acts. There are some problems with either answer to this question. If propositions do have an independent existence, how and where exactly do they exist? Are they abstract objects? Is there a Platonic realm of propositions? If they do not have an independent existence, then it seems that propositions just come in and out of existence according to the cognitive acts of the agents, which might have undesirable consequences as well.

Soames replying to comments

Be that as it may, more needs to be said regardless of how one might answer this question. Soames, though, wishes to remain non-committal: he said that he’s happy to commit to non-existing propositions and it seemed as if he might be willing to conceive of them as abstract objects of some kind. When pushed towards Platonism, Soames becomes a little bit uneasy, as it, understandably, strikes him as mysterious. So, I think that we can ask more from Soames in this regard, and it might also be an interesting project to examine the ontological options available to him.

Another theme that came up in the workshop was Soames’ view that we can quantify over non-existents. Basically this is based on a substitutional rather than an objectual reading of the existential quantifier. The difference can be illustrated by considering the sentence ‘There is at least one thing which is F’. On an objectual reading, the sentence is true just in case some object in the domain of discourse is F, whereas on the substitutional reading the sentence is true just in case there is some true sentence of the form ‘a is F’, where ‘a’ is a singular term (this is how Lowe puts it).

My talk at the research workshop: The Metaphysical Status of Modal Statements

Now, I was rather surprised and pleased at the same time that Soames is a proponent of the substitutional reading, as I am also more sympathetic to it, as are E. J. Lowe and Kit Fine. Now, since Soames thinks that we can can quantify over non-existents, the question arises: what can we know about non-existent objects? Can we know something about their essential properties? I put this question to Soames, and he said: yes, we must be able to know something about the essential properties of non-existents. This indeed seems to be an obvious requirement, as otherwise we wouldn’t be able to individuate them. Here I am reminded of Lowe’s saying ‘essence precedes existence’. My interest in this is that Soames seems to be very close the the Lowe-Fine view of essence here, or it would at least be fairly easy to push him towards that direction, which is good news of course!

So much for that. Numerous other issues came up during the events and I really enjoyed most of the discussion. But I’d like to keep these blog posts at least reasonably brief, so this will have to do for now. I think that I will return to these two mentioned themes at some point though.

Next up: a more general, non-philosophical report of my trip to Germany, and some more photos.

I’ve now got a draft of my paper for the Meaning, Modality and Apriority symposium with Scott Soames. You can get it from here. The abstract of the talk is here. The paper does pretty much what I promise in the abstract: I first summarise Soames’ account of the necessary a posteriori, then I look into Alan Sidelle’s deflationary account of it, and attempt to demonstrate that these two accounts are remarkably close to each other. Hence, Soames is at a risk of sliding towards the view according to which modality is linguistic and the a priori reduces to analyticity — which is a view that he strongly opposes.

I then go on to give an analysis of what I believe is missing both from Soames’ and Sidelle’s account: an examination of the a priori, essentialist principles which are responsible for the modal content of the necessary a posteriori. Since the main example being discussed is that of water, I look into some recent work in the philosophy of chemistry, especially by Robin Hendry. I argue that we will need a detailed analysis of the nature of chemical substances, and specifically whether chemical substances have their molecular structures essentially to determine whether ‘Water is H20′ is an example of the necessary a posteriori. Hendry’s analysis of the case is a good example of how I think the essentialist account should proceed.

The upshot is that Soames is at a crossroads: either he should concede to the deflationist and adopt the view that modality is linguistic and the a priori can be identified with the analytic, or he should engage in the type of work that we saw in Hendry’s suggestion: a detailed analysis of the underlying essentialist principles. Given that Soames is one of the loudest critics of the deflationary approach, I would hope that he is more tempted by the latter option.

The paper is still in draft stage, so comments are especially welcome. I will present the paper in Cologne on May 19th.

There are still a few more days before the deadline to submit abstracts for a workshop on Scott Soames’ philosophy in Cologne, Germany this May. The conference is aptly titled Meaning, Modality and Apriority, and involves both a Graduate Conference with a keynote from Soames as well as a research workshop with Soames. The call for the graduate conference has passed some time ago, but the deadline for the research workshop is 15th March. There are only four slots though, so I expect that there will be a bit of competition for those. Anyway, since I have commented on Scott Soames’ work before, for instance in my paper ‘On the Modal Content of A Posteriori Necessities’, I thought that I should submit something. I’ve come up with an abstract for a paper in which I plan to show that Soames’ case against the linguistic account of modality supported by people like David Chalmers, Frank Jackson and Alan Sidelle suffers from the fact that his own, supposedly metaphysical story about modal statements, is remarkably close to the one offered by deflationists such as Sidelle. My abstract follows, but please don’t steal it!

The Metaphysical Status of Modal Statements
ABSTRACT

In his Reference and Description: The Case Against Two-Dimensionalism (2005), Scott Soames puts forward an influential critique of the framework of two-dimensional modal semantics and the interpretation of a posteriori necessities proposed by proponents of the framework, especially Frank Jackson (1998) and David Chalmers (1996). While I agree with much of what Soames has to say about the topic, I am concerned that ultimately both Soames and the two-dimensionalists fail to see the fine-grainedness of the metaphysical status of modal statements. This is partly due to the short-comings of Kripke’s (1980) original treatment of a posteriori necessities, and partly due to the contemporary deflationist trend, which takes modality to reduce fully to linguistic or conceptual content. The latter is familiar especially from the work of Jackson and Chalmers, as well as Alan Sidelle (2002).

On the face of it, Soames is clearly opposed to this trend, as he thinks that Kripke’s most important achievement was to break the illusion that the a priori can be identified with the analytic, and that modality is merely linguistic (Soames 2006: 307). Soames claims that any kind of interesting philosophy will not fit into this deflationary, linguistic model. I very much sympathise with this idea, but it seems to me that Soames fails to fully commit to it himself. E. J. Lowe (2007a, 2007b) has raised similar concerns about the shortcomings in Soames’ metaphysical story, but so far Soames has not replied to them in any detail (cf. Soames 2007). The closest that Soames comes to addressing the metaphysical status of modal statements are the last three chapters of his earlier book, Beyond Rigidity (2002, ch. 9-11). We are especially interested in his analysis of the difference between the following identity sentences:

[1] For all x, x is a drop of water iff x is a drop of a substance molecules of which contain two hydrogen atoms and one oxygen atom.
[2] For all x, x is a drop of water iff x is a drop of the substance instances of which fall from the sky in rain and fill the lakes and rivers. (Soames 2002: 272.)

Presumably, (1) is metaphysically necessary, while (2) is contingent. Soames takes a point from Nathan Salmon (2005), which I believe to be of crucial importance for this analysis: what makes (1) a metaphysical necessity, if anything, is the underlying assumption concerning chemical substances, namely, that they have their molecular structures essentially (Soames 2002: 273). Now, Soames goes on to ask ‘What exactly are substances, and how do we arrive at our modal intuitions (pretheoretic beliefs) regarding them?’ (ibid.). This is of course where one ought give the metaphysical story, but the story that Soames gives is remarkably close to the one familiar from the deflationists. Soames describes how we introduce a natural kind term such as “water” with the intention that it is a ‘substance term’, i.e. applies to everything that shares the molecular structure in the original sample that we decided to call “water”. However, we do not need to know what that structure is when we introduce the term, all that matters is that we intend to use the notion in a way that respects the original intuition. We may subsequently learn more about the substance in question, e.g. that water is H2O, but this is the point where the metaphysical story about (1) ends (cf. Soames 2002: 273-275).

Soames goes on to refine the account somewhat, but this picture is effectively what he ends up with. Now, it seems that we could sum up Soames’ account roughly as follows: ‘Nothing counts as water in any situation unless it has the same deep explanatory features (if any) as the stuff we call “water”’, which I have quoted from Sidelle (2002: 319). But as Sidelle argues, this is an analytic principle concerning the linguistic usage of the the term “water” rather than a metaphysical a priori truth! The way Soames sometimes puts this is almost exactly as in the passage quoted from Sidelle:

‘”Water” was stipulated to designate whatever underlying physical characteristic it is that is shared by (nearly) all members of the class of paradigmatic water-samples that explains their most salient features – the fact that they boil and freeze at certain temperatures, that they are clear, potable, and necessary to life, etc.’ (Soames Forthcoming: 7).

According to Soames, when this stipulation is combined with our empirical information about water, it follows that water is necessarily H2O. So, it seems that Soames has given us little more than what the deflationary picture offers, and hence we are still at risk of identifying the a priori with the analytic and reducing modality to linguistics. In fact, Soames explicitly opts for a linguistic analysis rather than a metaphysical one, although he claims that this helps us to narrow down ‘the range of feasible ontological alternatives’ (ibid., 1).

In addition to an inquiry into Soames’ account of modal statements, I will offer a more detailed analysis of the metaphysical assumptions associated with modal statements and argue that the metaphysical story is much more fine-grained than Soames suggests. The elements of the metaphysical story are indeed already familiar from Salmon (2005), but there is much more to be said about e.g. the status of chemical substances, and it seems to me that Soames does not do justice to Salmon, who did recognize the complexity of the underlying metaphysical story (p. 176 ff.). Relying on recent work in the philosophy of chemistry (e.g. Hendry 2006, Needham 2008), I will attempt to give a more satisfactory account about the underlying metaphysical assumptions concerning chemical substances. We will see that there are some good reasons to think that the assumption according to which chemical substances have their molecular structures essentially may even be mistaken.

The upshot is that although Soames is on the right lines in challenging the deflationary approach to modal statements, his own account fails to fully accommodate their metaphysical status.

References:

• Chalmers, D. (1996) The Conscious Mind: In Search of a Fundamental Theory (Oxford: Oxford University Press).
• Hendry, R. F. (2006) ‘Elements, Compounds, and Other Chemical Kinds’, Philosophy of Science 73, 864–75.
• Jackson, F. (1998) From Metaphysics to Ethics: A Defence of Conceptual Analysis (Oxford: Oxford University Press).
• Lowe, E. J. (2007a) ‘Does the Descriptivist/Anti-Descriptivist Debate Have Any Philosophical Significance?’, Philosophical Books 48, 27-33.
• Lowe, E. J. (2007b) ‘A Problem for A Posteriori Essentialism Concerning Natural Kinds’, Analysis 67.4, 286-92.
• Needham, P. (2008) ‘Resisting Chemical Atomism: Duhem’s Argument’, Philosophy of Science 75, 921–31.
• Salmon, N. U. (2005) Reference and Essence, 2nd ed. (New York: Prometheus Books).
• Sidelle, A. (2002) ‘On the Metaphysical Contingency of Laws of Nature’, in Conceivability and Possibility, ed. T. S. Gendler & J. Hawthorne (Oxford: Oxford University Press), pp. 309-336.
• Soames, S. (2002) Beyond Rigidity: The Unfinished Semantic Agenda of Naming and Necessity (Oxford: Oxford University Press).
• Soames, S. (2005) Reference and Description: The Case Against Two-Dimensionalism (Princeton: Princeton University Press).
• Soames, S. (2006) ‘The Philosophical Significance of the Kripkean Necessary Aposteriori’, Philosophical Issues 16: Philosophy of Language.
• Soames, S. (2007) ‘The Substance and Significance of the Dispute Over Two-Dimensionalism’, Philosophical Books 48: 34–49.
• Soames, S. (Forthcoming) ‘What are Natural Kinds?’, Philosophical Topics.

Firstly, if you haven’t seen my previous post, go there now and leave a comment. I’m hoping to get some feedback about what people would like to see on this blog. In the meanwhile, here is another post in the ‘Work in Progress’ series. This time a survey article of sorts based on the lectures that I gave in Geneva last December, entitled ‘Varieties of Modality’. I was hoping to get this published somewhere like Philosophy Compass, but it seems that I entered the party a bit too late, as they are not intending to commission any more modality stuff at this time. It may be difficult to find a home for this, as it is really a survey article, although I do entertain some rather wild ideas towards the end of the paper…

The question that I pursue in the paper is how many different kinds of modality – different realms of possible worlds – are there? Philosophers commonly talk at least about metaphysical, conceptual, epistemic, logical, physical, mathematical, biological, technological, normative and natural modality. It is not always clear how these different types of modality are related, or whether some of them are more fundamental than others. The relationships between metaphysical, conceptual and logical necessity and possibility are particularly interesting. The paper is a survey of our options in this regard. We can distinguish four approaches which are currently widely discussed: the Kripkean approach, the conservative approach, the conceptualist approach, and the essentialist approach. The differences between these approaches are best described by comparing their takes on the distinction between metaphysical and conceptual modality. The Kripkean approach holds that this distinction is genuine and that we are dealing with two different kinds of modality. The conservative approach, which is familiar for instance from Bob Hale’s work, challenges the role of metaphysical modality and suggests that logical necessity is the most fundamental type of modality, it is absolute. The conceptualist approach, most forcefully argued for by Frank Jackson and David Chalmers, also questions the distinction and suggests that metaphysical modality can be fully accounted for in terms of conceptual modality. Finally, the essentialist approach, defended especially by Kit Fine, suggests that conceptual and logical modality can be seen as species of metaphysical modality. I will also consider an alternative approach based on the essentialist approach, which takes metaphysical modality to be absolute in Hale’s sense.

You can download the paper for the survey bits, but what’s this crazy alternative approach..? Well, if we take the cue from the essentialist approach and consider logical and conceptual necessity as subspecies of metaphysical necessity, as Kit Fine suggests in his ‘Varieties of Necessity’ (2002), then I think we already have the tools for something a bit more radical. Firstly, we can rule out all extra-metaphysical possibilities — that is, possibilities such as water being XYZ, when we consider water to be essentially H20 — as pseudo-possibilities. What this means in practice is that there is no stronger type of necessity than metaphysical necessity; in fact, metaphysical, conceptual and logical necessity would all seem to be equally strong. But I think that we can go even further, and indeed that we must go further if we wish to maintain that conceptual and logical necessity are useful notions at all: otherwise it seems that we might just as well talk only about metaphysical modality. But if we reserve the notion of metaphysical modality to those modal truths which are not true in virtue of either the definitions of concepts or the laws of logic, and similarly for conceptual and logical modality, we get a rather surprising picture about the relationships between different kinds of possibility:

Metaphysical, Logical, Conceptual, and Physical Possibility

What makes this interesting is that, according to the line suggested above, the picture for necessity is exactly the same. This is obviously a rather strange and seemingly contradictory result, but there may be a way to accommodate it. The idea is that only metaphysical modality is fundamental, but there is still use for the notions of conceptual and logical modality exactly in the same sense as there is use for the notions of physical or biological modality. So, according to this picture, different subspecies of metaphysical modality should be considered as concerning the natures of specific subsets of the set of all things. Hence, conceptual modality concerns things that are possible or necessary in virtue of the natures of concepts, and only them. Specifically, although it would commonly be considered that something like ‘It is possible to travel faster than light’ is conceptually possible, according to this picture this is not strictly correct: the possibility of travelling faster than light is not ruled out by the natures of concepts, but nor do the natures of concepts make it possible to travel faster than light. For something to qualify as a conceptual possibility, it has to be made possible by the nature of concepts in this positive sense. A similar analysis applies to logical possibility.

Well, this doesn’t really do justice to the idea, and I’m not quite sure that it even works, but the survey of other approaches that precedes this alternative picture in the paper might motivate the approach somewhat. There’s also a lot more to say about the status of logical modality here and I do go into it in some detail in the paper. If the idea is at all feasible, it would seem to require revamping modal logic as well — that’s something that I will not attempt.

I’ve been in Geneva for about three weeks now, and I’ve got another three weeks left. Time has gone past quickly and I’ve been neglecting work a bit, but it doesn’t mean that I haven’t been doing philosophy. It’s about time that I start thinking about the two talks that’ll give here in December though, and since they are on modality, I thought I might make a few remarks about the topic. There will be a lighter post very soon with some photos from a hike that I did last weekend, but today it’s just hardcore philosophy I’m afraid!

Bob Hale (Sheffield): Possibilities

As it happens, about a week and a half ago we had a workshop which was exactly on modality (and the experience of time), namely the sixteenth eidos workshop. The first day was dedicated to modality, and it was certainly the more interesting for me, and the second was on the experience of time. I’ve posted photos from the workshop here. Although all the talks were interesting, Fabrice Correia’s was closest to my own research, so I will make a few comments relating to his talk ‘On the Reduction of Necessity to Essence’ here.

Those familiar with the topic will know that this will have something to do with Kit Fine’s influential paper ‘Essence and Modality’. The topic that I wish to bring up does not concern this exactly, but rather the hierarchy of different kinds of modality, specifically, metaphysical, conceptual, and logical modality.

Correia’s presentation of Fine’s view included one principle which I found problematic, namely the monotonicity principle, which says that if A is true in virtue of the nature of X and X is a subset of Y, then A is true in virtue of the nature of Y. According to Correia, this has the following consequence for Fine’s view: logical necessity is at least as strong as conceptual necessity, which is at least as strong as metaphysical necessity. The key here is the interpretation of ‘strong’. I had a chat with Correia and at first I thought that I must understand it differently from him. Bob Hale, who was also the workshop, defined ‘strong’ in his 1996 paper ‘Absolute Necessities’ as follows:

One kind of necessity, [box1], may be said to be stronger than another, [box2], if ‘[box1]p’ always entails ‘[box1]p’ but not conversely. Assuming the usual relations between necessity and possibility, this relationship will obtain if and only if [diamond1] is weaker than [diamond2], i.e. ‘[diamond2]p’ always entails ‘[diamond1]p’ but not conversely. I shall also say that [box1] is at least as strong as [box2] if the first half of this condition is met, i.e. ‘[box1]p’ always entails ‘[box2]p’.

Now, if I’ve understood correctly what Hale means by at least as strong as, and Correia says that he means it in the same sense, then saying that logical necessity is at least as strong as conceptual necessity, which is at least as strong as metaphysical necessity amounts to this: if p is logically necessary, then p is conceptually necessary, and if p is conceptually necessary, then p is metaphysically necessary. This is something that some people might indeed want to say, but in my understanding it is not what Fine wants to say, or what I want to say, or indeed, so I thought, what Correia wants to say.

Fabrice Correia (Geneva): On the Reduction of Necessity to Essence

Why is this? Well, if this were the case, then it appears that all logical necessities are metaphysically necessary, i.e. all things that are true in virtue of all logical concepts are also true in virtue of the nature of all things. This may seem fine, but it is incompatible with a certain intuitive understanding of necessity. What I mean is that, for me at least, something being necessary entails that it is true throughout the modal space. And the modal space, according to the Finean picture, is metaphysical modality (we may here ignore normative and natural modality, which Fine distinguishes from metaphysical modality). We can of course divide the modal space into smaller, proper subsets of metaphysical modality, which is what we do when we talk about logical and conceptual modality, but if we then say that something is logically necessary, we mean that it is true throughout the proper subset of metaphysical modality which concerns logical concepts. Now, we can certainly say that all logical necessities are a proper subset of metaphysical necessities, but it is misleading to say simply that all logical necessities are metaphysically necessary. How could this be when logical modality only concerns a proper subset of metaphysical modality — it can make no claims outside its designated realm.

So, I believe that what has happened here is that in the end Correia and myself share the same Finean picture about modality, indeed it seems as much from my discussions with him. However, the monotonicity principle causes unfortunate connotations. At the very least, we should not use Hale’s notion of strength here, as it is apt to drive us towards the problematic reading of the relationship between logical and metaphysical modality.

John Divers (Leeds): The Acquisition of (Warranted) Belief in Absolute Necessity

Quite independently of this confusion, there is a further problem here concerning metaphysical necessities which are not logically necessary, e.g. the proposition ‘all cats are animals’, as tt would seem to be the case that the proposition ‘cats are demons’ is logically possible, but not metaphysically possible. So in the Finean picture, there seems to be no room for such propositions. Correia did not offer much in terms of an answer to this problem, but my own solution is to simply exclude them from the modal space: they are pseudo-possibilities. Of course more needs to be said about the modal epistemology behind this picture, namely, how do we know which possibilities are pseudo-possibilities. I’ve said something about this in my previous post about Counterfactuals and Modal Epistemology, but I’d better not go into the topic here…

Another update will follow soon!

I have uploaded a new paper to my Work in Progress section. The title is Counterfactuals and Modal Epistemology. Basically this is a paper criticising Timothy Williamson’s account of modal epistemology, familiar from his recent book The Philosophy of Philosophy. Williamson claims that the epistemology of metaphysical modality is a special case of the epistemology of counterfactuals. I have two problems with his account, one concerns the basis of what he calls ‘background knowledge’ and ‘constitutive facts’, one concerns his use of imaginability or conceivability as an epistemic tool. Take one of Williamson’s examples:

You are in the mountains. As the sun melts the ice, rocks embedded in it are loosened and crash down the slope. You notice one rock slide into a bush. You wonder where it would have ended if the bush had not been there. A natural way to answer the question is by visualizing the rock sliding without the bush there, then bouncing down the slope. You thereby come to know this counterfactual:

[CF] If the bush had not been there, the rock would have ended in the lake. (T. Williamson, The Philosophy of Philosophy, Oxford: Blackwell, 2007, p. 142.)

According to Williamson we come to know counterfactuals like (CF) with the help of our imagination. However, we are immediately faced with a problem: how are we supposed to choose the correct scenario given that our imagination can come up with the wildest of scenarios, such as ‘the rock rising vertically into the air, or looping the loop, or sticking like a limpet to the slope’ (ibid., 143). Williamson’s reply goes as follows:

You do not imagine it those other [irrelevant] ways because your imaginative exercise is radically informed and disciplined by your perception of the rock and the slope and your sense of how nature works. The default for the imagination may be to proceed as ‘realistically’ as it can, subject to whatever deviations the thinker imposes by brute force: here, the absence of the bush. Thus the imagination can in principle exploit all our background knowledge in evaluating counterfactuals. (T. Williamson, The Philosophy of Philosophy, Oxford: Blackwell, 2007, p. 143.).

The idea is presumably that our imagination will be restricted by our knowledge of the laws of nature so that we will omit scenarios that are physically impossible. There are some problems already here, but let’s focus on just one: what about scenarios that are physically impossible but metaphysically possible? More generally, if our background knowledge concerns the actual world, how can we restrict our imagination regarding scenarios that do not concern the actual world? It seems that Williamson does not even consider cases like this, but unless he implicitly assumes that the laws of physics are metaphysically necessary, then he must somehow be able to distinguish between physical possibilities and physical impossibilities which are metaphysically possible.

The figure on the right illustrates the situation. We are interested in the distinction between the left and the right half of the circle, i.e. between what is conceivable & metaphysically impossible, and what is conceivable & metaphysically possible. An example of the first could be that water is XYZ (if water has its actual molecular structure by necessity), an example of the latter could be a rock floating above a lake. Some further qualifications are needed though: the relationship between what is conceivable & metaphysically impossible, and what is conceivable & metaphysically possible is of course intransitive – the two are mutually exclusive – but the relationship between what is conceivable & metaphysically possible, and what is conceivable & physically possible is transitive, as everything that is physically possible is also metaphysically possible.

Obviously, there is an overlap between what is conceivable and what is metaphysically possible, but given that there is also an overlap between what is conceivable and what is metaphysically impossible, the previous overlap does not amount to very much. In fact, it seems clear that there will be a greater overlap between conceivability and metaphysical impossibility, due to the virtually infinite range of scenarios that we can imagine. Thus, when we compare the space of conceivable & metaphysically impossible scenarios to the space of conceivable & metaphysically possible scenarios, the previous will certainly dominate. If we hope to use conceivability as a guide to metaphysical possibility, we should somehow be able to distinguish between the two.

Now consider Williamson’s analysis of ‘gold is the element with atomic number 79′:

If we know enough chemistry, our counterfactual development of the supposition that gold is the element with atomic number 79 will generate a contradiction. The reason is not simply that we know that gold is the element with atomic number 79, for we can and must vary some items of our knowledge under counterfactual suppositions. Rather, part of the general way we develop counterfactual suppositions is to hold such constitutive facts fixed. (T. Williamson, The Philosophy of Philosophy, Oxford: Blackwell, 2007, p. 164.)

Williamson seems to provide a partial answer to the problem, for supposedly we can dismiss the conceivable but metaphysically impossible scenario of gold having some other atomic number than 79 with the help of ‘constitutive facts’, i.e. background knowledge that we do not vary when considering counterfactual scenarios. This enables us to distinguish between conceivable metaphysical impossibilities and metaphysical possibilities. But this solution will not work in all cases: it only works in cases where we are dealing with metaphysical necessities, such as ‘gold is the element with atomic number 79’. This is because in cases where we are dealing with mere metaphysical possibilities we should be able to vary many more, if not all items of our knowledge under counterfactual suppositions: in cases such as the rock sliding down a slope the possibilities for variation are much greater – even the laws of physics may be varied unless it is assumed that they are metaphysically necessary, which is something that Williamson does not argue for. Be that as it may, unless there are some metaphysically necessary conditions that serve as clear candidates for constitutive facts that should be held fixed, such as the fact that elements have their atomic number by necessity (if this is indeed the case), then there are no obvious reasons to decide which items of background knowledge should be held fixed.

There’s more to say about all this, see the actual paper for the details. One approach that might help Williamson is to draw on Kit Fine’s suggestion according to which metaphysical modality is a special case of essence. Accordingly, metaphysical modality could be grounded in the essences of the entities it concerns. But even if he did go this way, it seems that Williamson has left the most crucial part of the story untold.

A paper of mine with the above title has been accepted for publication in the Swedish journal Theoria. It’s an old journal and not at all bad, although not really world class either. Wiley-Blackwell acquired it recently. Anyway, I thought it would be appropriate as Kripke’s latest paper was recently published there. There’s also a paper by Nick Zangwill in a recent issue. My paper was under review for quite a long time (since October 2008), and I have thought about the matters that I discuss in this paper in more detail. In the light of that, this paper is really just an introduction. However, it is 7,000 words long in any case, so I couldn’t have extended it much more. I’ve posted a copy of the paper here. Grab it now if you’re interested, because I will have to take it down when it appears in print. Wiley-Blackwell insists that the paper will not appear on a personal home page until 24 months after the publication. Obviously I can still e-mail it to people.

The purpose of the paper is to demonstrate that the classic Kripkean story about a posteriori necessities omits a couple of important things. The primary case that I analyse is the classic ‘Water=H20′. Basically I argue that the a priori principle that the modal content of this identity statement is grounded in has not received sufficient support. The a priori principle that I am referring to is that compounds such as water have their molecular structure by necessity, i.e. that it is part of the essence of compounds that they have the very molecular structure that they do. While this might seem like an obvious thing, it is far from clear how we are supposed to come to know this a priori principle. I discuss this in some detail in the paper, but more recently I’ve learned about some peculiar cases, such as so called non-stoichiometric compounds or Berthollides, as they are sometimes called. These are compounds which at least seemingly violate the law of definite propositions, namely they are compounds which do not always contain exactly the same proportions of elements by mass and would hence seem to cause problems for the a priori principle that compounds have their molecular structure by necessity. There is some interesting chemistry behind this, I recently had a chat about this with Robin Hendry; he has got a couple of papers about the problems concerning water. As to Berthollides, they do not seem to have been discussed in any detail in philosophical connections. I got a couple of references from another philosopher who knows his chemistry, Paul Needham (see his ‘Resisting Chemical Atomism: Duhem’s Argument’, Philosophy of Science, 75: 921-31, 2008), but this appears to be something that philosophers haven’t really picked on yet. Anyway, I plan to look into this matter in some more detail when I’ve got some time. This is also core content for the book that I am supposedly working on, so I will extend on this there at the very latest.