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 hinted towards a project that I’ve been working on in a few previous posts to this blog, and I am now happy to finally be able to advertise the project in detail. It is an edited volume entitled Contemporary Aristotelian Metaphysics, and I have just been offered a contract for this volume by Cambridge University Press.

The volume brings together 14 new essays from leading philosophers working in, or at least sympathetic to what might be called ‘Aristotelian’ metaphysics. ‘Aristotelian’ in this context should not be taken to refer to Aristotle’s metaphysics, this is not a historical volume on Aristotle’s philosophy. The label merely refers to a certain conception of philosophy and metaphysics, perhaps best described with the idea of metaphysics as a ‘first philosophy’, that is, metaphysics as prior to science, or as a study of the most fundamental structure of reality. It should be noted however that not all the contributors necessarily commit to this type of view, but they do all take it seriously. Accordingly, to a certain extent this is a volume on the methodology of philosophy and metaphysics, although these matters will not necessarily be discussed explicitly. However, the motivation behind this volume is exactly to showcase this conception of metaphysics and to contrast it with a more deflationary conception of metaphysics (and its methods) which could perhaps be called ‘Quinean’. The list of contributors is as follows:

• Professor Alexander Bird, University of Bristol
• Professor Tim Crane, University of Cambridge
• Professor Kit Fine, New York University
• Dr. Louis M. Guenin, Harvard University
• Professor John Heil, Washington University
• Professor Joshua Hoffman, University of North Carolina
• Dr. Kathrin Koslicki, University of Colorado
• Professor E. J. Lowe, Durham University
• Professor Storrs McCall, McGill University
• Professor David Oderberg, University of Reading
• Professor Eric Olson, University of Sheffield
• Professor Gary Rosenkrantz, University of North Carolina
• Professor Peter Simons, Trinity College Dublin
• Dr. Tuomas E. Tahko, Durham University

In addition, I will write an introduction to the volume. Although this is not a volume on Aristotle’s metaphysics, many of the themes of the volume are familiar from, or inspired by Aristotelian metaphysics, specifically: ontological categories, the notion of substance, essence, identity, ontological dependence, and the ontology of species. Some of the contributions defend neo-Aristotelian accounts of the topics. Other proposed topics, which also relate to Aristotelian themes, include quantification, natural kinds, persistence, and powers. I will provide more details about the contents of the volume at a later stage.

I am hoping to get the volume together some time during summer 2010 and hopefully it will be out soon after that. I am grateful to Dr. Hilary Gaskin from Cambridge University Press for her support during the early stages of the project.

In other news, my article ‘On the Modal Content of A Posteriori Necessities’ has now been published online at Wiley InterScience. E-mail me for a pdf-offprint if you haven’t got institutional access to Theoria. Or simply download the penultimate version from my papers section.

I have been working on a paper about the notion of logical truth as a bit of a side project and it’s now at the state where I could use some input from people who know their logic better than I do (which is not much to ask). The draft is available here. I had a chat about this with Oswaldo Chateaubriand at the ENFA 4 conference in Portugal in September, and I have been reading parts of his massive book on logic since then. The book is nearly impossible to get now, but apparently there should be reprints coming out soon. Anyway, I am very sympathetic towards Chateaubriand’s conception of logic, which takes logic to be a part of metaphysics, and the key topic here is no doubt the notion of logical truth.

The purpose of the paper is to defend a metaphysical interpretation of logical truth as opposed to a linguistic one. I take my cue from Davidson’s classic paper ‘In Defense of Convention T’, where he distinguishes between absolute truth and truth in a model or relative truth. These two senses of truth can be seen to represent a metaphysical and a linguistic interpretation of logical truth and it is in my interest to see whether they can be reconciled. The notion of absolute truth is the one familiar from Tarski’s T-schema: ‘Snow is white’ is true if and only if snow is white. Truth in a model, or relative truth, instead of being a property of sentences as absolute truth would appear to be, is evaluated in terms of the relation between sentences and models, where ‘models’ is interpreted in a wide sense.

Now, drawing on the work of John Etchemendy, I propose that we can reduce truth in a model to absolute truth, when ‘truth in a model’ is defined as follows:

Once we have specified the class of models, our definition of truth in a model is guided by straightforward semantic intuitions, intuitions about the influence of the world on truth values of sentences in our language. Our criterion here is simple: a sentence is to be true in a model if and only if it would have been true had the model been accurate –- that is, had the world actually been as depicted by that model. (J. Etchemendy, The Concept of Logical Consequence, Cambridge, Mass.: Harvard University Press. (1990), p. 24.)

It seems indeed that once we have specified the class of models, we can define truth in a model according to Etchemendy’s suggestion, but now the problem concerns the delimitation of the class of models. A crucial question is what does the introduction of modality to this picture imply: it must be the case that the model could have been true, that is, it must be the case that the world could have turned out to be like the model depicts. Etchemendy talks about genuinely possible configurations of the world (ibid., 25), but he does not say much about the nature of the modality involved. My suggestion is that the modality in question must be metaphysical modality, as that will be the only type of modality that guarantees the needed connection to the world. I talk about this in much more detail in the actual paper.

What ties this to contemporary discussion is the question concerning the implications of the metaphysical interpretation of logical truth for the recent discussion about logical pluralism and the normativity of logic. I briefly discuss Hartry Field’s two papers about these matters, namely his ‘Pluralism in Logic’ and ‘What is the Normative Role of Logic’. I think that once the metaphysical interpretation of logical truth is adopted, there cannot be any very interesting sense of logical pluralism since the view effectively implies monism about logic, that there is a One True Logic — here I agree with Field — but according to Field, there is another question that we must consider, namely whether pluralism about logic could be seen as pluralism about the normative content of logical consequence, in the sense of epistemic normativity.

Well, epistemic normativity is something that I do not want to go into in any detail, but instead of the expressivist account that Field defends, I try to make a case for the normativity of logic which is compatible with the metaphysical interpretation of logical truth. I think that we can cash out the normative role of logic by asking how could it not be better in a normative sense to reason according to the constraints of reality? A more technical case for this can be constructed by analysing Field’s notion of genuine validity; this is something that, according to Field, a classical logician and an intuitionist, for instance, will have to share to have a debate in the first place. But if this is indeed the case, then genuine validity will have to be very close to something like a metaphysical notion of truth.

Indeed, Per Martin-Löf, the developer of intuitionist type theory, takes validity to be ‘nothing but the notion of truth or reality applied to the particular acts and objects with which we are concerned in logic’ (‘Truth of a Proposition, Evidence of a Judgment, Validity of a Proof’, Synthese 73, 1987, p. 419). So the notion of validity is fundamental, but not necessarily in the sense that Field suggests. In fact, Martin-Löf suggests that this fundamental notion of validity connects directly with what he calls the metaphysical notion of truth, as opposed to the truth of a proposition, so the case for connecting the normativity of logic and the metaphysical interpretation of logical truth is straight forward.

See my paper for further discussion.

As most of you probably know at this point, I will be visiting at the eidos Centre in Metaphysics of the University of Geneva, led by Kevin Mulligan and Fabrice Correia, for the rest of the year, or until 18th December to be precise. I arrived to Geneva a couple of days ago and I’m settling in at my place, a nice shared house, although a bit far from the centre.

I attended my first eidos seminar (not to be confused with the Durham postgraduate seminar of the same name), Problèmes de métaphysique, yesterday and I will be giving two talks at the seminar myself in December, on the 10th and 17th. My topic will be ‘Varieties of Modality’, but more about that when I’m preparing my presentations. As I understand, the seminar is supposed to be accessible to Masters students, but at least Fabrice Correia’s talk yesterday was rather technical and I suspect that most Masters students would struggle with the material. However, it happened to be on modality, or more specifically on Bob Hale’s ‘Absolute Necessity’, which is understandably of interest to me (although I last read Hale’s paper when I was an undergraduate).

In fact, there will be a workshop on Modality here on 17th November; Bob Hale will be there, and there will be talks by Fabrice Correia, John Divers and Tom Baldwin in addition. The following day there will be another workshop on The Experience of Time. Apart from these events, there will be a workshop on Intentionality in December, and one on The Epistemology of Perception already next week. These are all on top of the regular events and seminars, so looks like I will be keeping fairly busy during my time here!

I hope to fit in a bit of hiking if at all possible, I did drag my hiking gear all the way here after all. Sadly I don’t have winter gear though, so will have to remain at a lower altitude.

My only complaint is that I didn’t continue studying French! Although most people here speak English, it would be nice to be able to engage at least in casual conversations in French as well. Also, my taxi driver didn’t speak a word of English, not to mention that he was completely ignorant of the streets in Geneva and how to use GPS… Oh, actually I do have another complaint: certain restaurants in this city are outrageously expensive. A simple Ardbeg 10yo single malt cost 18 Swiss Francs, i.e. about 12 euros or 10 pounds at a bar in Carouge. But if one steers clear of these places, staying in Geneva shouldn’t break the budget.