Is fragility intrinsic?

Jonathan Ichikawa suggests a disarmingly simple argument that fragility is not intrinsic; consider a fragile material object like a glass slipper. A exact intrinsic duplicate of the slipper in a world with different laws of nature might not be fragile; perhaps glass slippers are used as hammers in those worlds.

I think the first stage in responding to this is to invoke the weak nomic necessitarianism which is a part of dispositional essentialism. Any world in which there exist stable glass slippers is a world in which something extremely close to the usual laws of electromagnetism hold. But any world in which these laws (or something extremely close to them) hold is also a world in which glass slippers are fragile. This response is an instance of the argument form deployed by Bird in Bird, A. 2001. Necessarily, salt dissolves in water. Analysis 61: 267–74 – in later work, he calls it the ‘down-and-up structure of laws’.

This, however, merely shifts the question to whether an intrinsic duplicate of a glass slipper is possible which does not obey the laws of electromagnetism. It would not be made of glass (Ichikawa concedes this point in the comments, at least for the sake of argument), but nor could it involve instantiations of mass and charge – these, by weak nomic necessitarianism, obey the laws they do by necessity.

But perhaps there are possible intrinsic duplicates of glass slippers which are made of glassch, and involve instantiations of schmass and scharge. The argument could then run as follows: these glassch schlippers are not fragile, but they are intrinsic duplicates of glass slippers, so fragility is not preserved over intrinsic duplication, and fragility is not intrinsic.

The obvious place to resist this second argument is the premise that glassch schlippers could be intrinsic duplicates of glass slippers. Ichikawa seems to motivate this by the claim that both glass slippers and glassch schlippers could have atomic structure XYZ. But this still seems wrong. Glassch schlippers are made of schatoms, not atoms, so they don’t have any atomic structure at all, let alone the same atomic structure as glass slippers.

At this point, the only way I can see to resurrect the argument that fragility is not intrinsic would be to make a strongly structuralist move , and say:

1) that the identities (quiddities) of the properties involved in an object are irrelevant to that object’s structure.
2) that the structure (and only the structure) of an object is preserved under intrinsic duplication.

Now most metaphysicians would demur from at least one of these claims, and hence they can recover the view that fragility is intrinsic. But I’m tempted by both claims, since I reject quiddities altogether. Must I then say that fragility is extrinsic?

Not if I make the stronger necessitarian move of denying that schmass, scharge and therefore schlippers are possibilities. This requires a necessitarianism stronger than WNN (see my previous post for discussion of grades of nomic necessitarianism). SNN certainly permits this response. Does FNN permit it? Only if schmass and scharge do not number among the genuinely possible fundamental natural properties. If FNN is true, this is not a question we can answer on a priori grounds. So if, as I suspect, FNN is true, then whether fragility is intrinsic is a question whose answer we can only know a posteriori.

Nomic necessitarianism and counterlegal counterfactuals

One particular class of counterfactuals presents problems for (even weak forms of) nomic necessitarianism: so-called counterlegal counterfactuals, such as ‘if gravity were an inverse-cube law, then the large-scale structure of the universe would be different’ or ‘if the charge on the electron were slightly larger, then atoms would be unstable’*. These are counterfactual forms in which the antecedent is physically impossible; for example, we might say ‘If gravitation were an inverse-cube law, then the solar system could not have formed’. We assess counterlegals of this sort in the process of formulating new scientific theories, and they are frequently asserted in speculative cosmology and science fiction. However, they pose problems for the combination of SNN with any theory of counterfactuals which would ground the truth of counterfactual statements in facts about other possible worlds. According to nomic necessitarianism, there simply are no worlds at which the antecedent of a counterlegal is true; hence, counterlegals cannot be given anything like the standard possible-worlds truth-conditions. How should an advocate of nomic necessitarianism respond to this?

The simplest response would just be to declare counterlegals either trivially false or trivially true, and to say no more about them. But this is unattractive; we want to distinguish between ‘good’ and ‘bad’ counterlegals. For example, consider the following pair.

a) If gravitation were an inverse cube law, the orbit of the Earth would be unstable.

b) If gravitation were an inverse cube law, purple dragons would dance the tango.

a) sounds sensible and assertible; b) does not. If this needs any argument, it is plausible that cosmologists might appeal to a) in discussing knock-on effects of changes in the laws; but I take it to be obvious that they would have no interest whatsoever in b). We could account for this difference between a) and b) in two ways. Either we accept that the semantics of the two statements are similar – that they are both trivially true or trivially false – and give a pragmatic account of the difference in assertibility between them, or we can build the difference into the semantics of the two statements.

The latter approach involves giving a metalinguistic account of the semantics of counterlegal statements. We can interpret statements like a) as concerning our own theories; we could thus analyse a) roughly as ‘if you alter Newtonian gravitational theory so that gravitation is an inverse cube law, then the new theory predicts unstable orbits for objects like the Earth’. This account meshes naturally with the usage of counterlegal statements; they are generally considered in the context of structural relations between alternative possible theories of a particular phenomenon. It also accounts for the difference we feel between a) and b) – it is simply not true that if we modify Newtonian gravitation in the way described, the modified theory implies any particular conclusions about purple dragons.

Taking this latter option does result in a kind of dualism in our interpretation of counterfactuals. Counterfactuals with genuinely possible antecedents will have a different metaphysical status to counterlegals – they will have different truthmakers, or different correctness-makers if you prefer. Furthermore, it need not always be clear whether a given counterfactual is a counterlegal or not. Take the claim ‘if the Higgs boson had been discovered last year, scientists would have celebrated.’ Since we do not know whether the Higgs boson is a (genuinely) possible existent, we do not know whether it would have been (genuinely) possible to discover it last year. Here we have an example of a counterfactual which may or may not be a counterlegal. According to the proposal under consideration, it will either have truth (or correctness) conditions derived from properties of other worlds, or it will have metalinguistic truth (or correctness) conditions. We will not in general be able to know which kind of conditional we are using.

Alternatively, we can take the former line, giving a) and b) the same semantics but locating the difference between them in pragmatic considerations. This might, for example, involve allowing all counterlegals to be trivially true. We could then go on to explain the assertibility or otherwise of counterlegals in terms of metalinguistic phenomena – whether or not our best theory predicts the consequent if it is modified to include the antecedent. Both the semantic and pragmatic approaches can thus account for the felt difference between ‘good’ and ‘bad’ counterlegals along metalinguistic lines.

An objector might press the objection from counterlegals, by pointing to the need for dualism in our analysis of counterfactuals as an undesirable feature of nomic necessitarianism. But a tu quoque response is available here; even if we reject nomic necessitarianism, we still cannot give a uniform philosophical account of counterfactuals. Certain counterpossible conditionals are problematic whether or not we accept nomic necessitarianism: conditionals whose antecedents are logical or mathematical falsehoods. Supposing that there are necessarily-existent abstract objects (among them numbers), consider the counterfactual statement ‘if there were no abstract objects, then there would be no numbers’ and ‘if there were no abstract objects, trees would levitate.’ We would like to be able to give an account according to which the first counterfactual is superior to the second, despite there being no possible world in which the antecedent holds. These conditionals will already require metalinguistic considerations, whether they are eventually located in semantics or pragmatics. Once we take this on board, then clarifying the details of the semantic theory starts to look more like a job for empirical linguistics than a job for metaphysics.

The upshot of this is that whichever semantic theory of counterlegals we end up with, we will need to recognise a metaphysical difference between two types of counterfactual – counterlegals and counterfactuals with possible antecedents – which does not correspond to any surface semantic difference. This need not be any cause for concern. We can explain why there is no surface semantic difference between the two – it is simply because we cannot always tell when we are discussing genuine possibilities and when we are not. Unable to reliably distinguish between genuine possibilities and only apparent possibilities, we ended up using the same form of language for each. As science progresses and rules out more and more apparent possibilities, we are better able to distinguish the two types of counterfactual and to recognise a metaphysical distinction between them. Although the proportion of counterfactuals falling on each side of the dividing line is altered once we adopt nomic necessitarianism, rejecting nomic necessitarianism does not allow us to dispense with the division altogether.

* It may be, as discussed above, that the charge of electrons could have been determined by an indeterministic process in the early universe. In this case, nomic necessitarianism would have no special problems dealing with this ‘counterlegal’, as the antecedent would only be locally physically impossible. The counterfactuals which cause problems for nomic necessitarianism are those with globally physically impossible antecedents. Plausibly, the example involving gravity is just such a counterfactual.

Spacetime in Everettian QM

(some of this is adapted from a comment I posted at Theories ‘n Things)

How should we think about spacetime in Everettian quantum mechanics? If we adopt the Saunders-Wallace multiple-utterance proposal as a way of accounting for uncertainty (and hence probability) in EQM, we still have a choice. Either we treat spacetime the same way as we treat material objects (in which case spacetime doesn’t literally fission, and there is exactly one object in each spatio-temporal location even counting by identity) or we treat it as a common background to all the branches (in which case it literally fissions, and material objects are literally collocated on a grand scale). This choice is exactly the choice of whether spacetimes diverge or branch.

If we go the latter way, we need to count by world-indexed identity if we want to say that there is exactly one object in a particular spatio-temporal region. But we don’t need to count by world-indexed identity to say (for example) that there is only one cat on the mat, or only one table in this room: the cat, mat, table and room are all branch-bound objects. So then the semantics of ‘there is one table in this room’ and ‘there is one table in this spatio-temporal region’ would be structurally different. This seems good reason to consider the alternative route.

If we go the former way, what remains of the notion that reality is branching? The answer is simply that branches branch. But this can all get very confusing. I’ll try to clear this up a bit by reiterating how everything’s supposed to fit together. This is my current preferred take on things, which presupposes supersubstantivalism, for reasons I’ll discuss below.

1) At the fundamental level, there is just the universal state.
2) Decoherence picks out an approximate basis to decompose the universal state, approximately defining an emergent branching structure.
3) Pick out big-bang-to-heat-death histories from this emergent branching structure and call them branches.
4) Pick out parts of branches and call them branch segments. Branch segments are common to multiple branches.
5) Ordered pairs [branch segment,branch] are identified with spacetime regions. A special case of this is when the branch segment is the whole branch; the spacetime region [branch x, branch x] just is the spacetime of branch x.
6) Via supersubstantivalism, subregions of a spacetime are identified with objects and agents.

So on this account spacetime and ordinary objects do not branch, but the underlying emergent branching structure does. This is my preferred set-up at the moment; but I imagine many people will baulk at the supersubstantivalism. Why is it needed? Consider another way of setting it up which appeals to a more orthodox view of spacetime:

1-4) unchanged
5) Ordered pairs [branch segment,branch] are identified with spacetime regions. A special case of this is when the branch segment in question is the whole branch; the region [branch x, branch x] is the spacetime of branch x.
6) For some spacetime regions there is a material object occupying that region.

The problem I have with this is that material objects only come in at the final stage. What we have in stages 2-5) is a new kind of entity being extracted from an already-accepted layer of ontology. But in stage 6 a new kind of entity is introduced in a different way; material objects are just stipulated to occupy particular regions of spacetime. But the hypothesis made in 1) is that the quantum state is the only fundamental existent, so these material objects must be emergent from it somehow. But the non-supersubstantivalist story doesn’t give us any picture of how this works.

We could switch things around as follows:

1-4) unchanged
5) Ordered pairs [branch segment,branch] are identified with material objects. A special case of this is when the branch segment in question is the whole branch; the material object [branch x, branch x] is the mereological sum of all objects realized by branch x.
6) For every material object there is a spacetime region which that material object occupies.

But this looks even less good. Not only do spacetime regions now seem to float free from the underlying ontology just as material objects did in the previous version, this version doesn’t even seem to get us unoccupied spacetime regions.

Perhaps all this isn’t so much of an argument as a restatement of the intuition motivating supersubstantivalism. Accepting two different kinds of entity (objects and regions) related by a primitive ‘occupation’ relation doesn’t add any extra explanatory power to supersubstantivalism, rather it makes things more mysterious. We are faced either with the problem of explaining where material objects come from, given a spacetime, or the problem of explaining where spacetime comes from, given material objects. Just calling the relation between the two ‘occupation’ won’t cut any ice in a naturalistic picture.

Easy possibility

Tim Williamson has made use of a notion of ‘easy possibility’ in his modal account of knowledge – some event is an easy possibility if it could easily have happened. Where did this notion come from? It seems plausible that ‘event x could easily have happened’ is an anthropomorphic generalization from ‘person p could easily have performed action a’. I’m going to briefly explore the consequences of this.

Easiness is at least a partially normative concept; as well as circumstances, competence plays a role in deciding whether a is easy for p. So consider an exceptionally competent archer – if a clear path to a target at 20 metres distance is available, he will always be able to easily hit it. An incompetent archer in exactly the same circumstances would not find it easy to hit the target. So easiness of an action is (obviously) agent-relative. But when we use the phrase ‘could easily have happened’, which agent is it relativized to?

It’s easy (apologies for the pun!) to see that it can’t be any contingent agent. We can apply the notion of easy possibility to particle-interactions well before any life existed: it could easily have been that more interactions occurred in the first nanosecond of the universe than actually did occur in the first nanosecond. An idealized human agent won’t do either. If an idealized human agent were around in the early universe, they would die before having the chance to tweak any particles. It looks like we’re going to have to wheel in God.

If God was the relevant agent, it would give a pretty satisfying reductive account of easy possibility. Something could easily have happened if it would not have required much effort for God to change things so that it happened. Maybe the idea is that God would only have had to alter the position of a particle one millionth of a micro-metre, and more interactions would have occurred in the first nanosecond than actually did occur.

Why not take this as a conceptual analysis of the notion of easy possibility? Event e could easily have occurred iff it would have been easy for God to change things so that e occurs. Obviously ‘easy’ is a vague term, but then so plausibly is the extension of easy possibility; no problems there. I think this looks like the bare bones of a good analysis. Indeed, I think it’s a worryingly good analysis for the friend of easy possibility; through the association with an idealized agent, it casts doubt on whether easy possibility has a place in naturalistic modal metaphysics.

Grades of nomic necessitarianism

Some have claimed recently that the laws of nature are necessary truths. What does this claim amount to? It can’t just mean that they hold in any naturally possible world, if natural possibility is analysed a la Lewis in terms of a restricted space of metaphysically possible worlds – otherwise, it would be trivial. This is what I think Kit Fine is getting at in his paper ‘The Varieties of Necessity’ (Fine 2002). (See this post for my objection to the way that Fine uses this point.)

Another approach is called for. Plausibly, the necessity of laws of nature involves at least the claim that Bird in Nature’s Metaphysics calls ‘weak nomic necessitarianism’ (WNN) – the claim that fundamental natural properties have their nomological role essentially, and obey the same laws of nature in every world in which they exist.

Bird describes the thesis of strong nomic necessitarianism (SNN), which goes beyong WNN by adding the further proviso that all fundamental natural properties exist at all worlds (call this claim APAW). To a lot of people this looks too strong. Bird intends APAW to rule out an objection to the necessitarian position which alleges that, while it might be that gravity is necessarily (approximately) an inverse-square law and necessarily acts between masses, there is another possible force, fravitation, just like gravitation in every way except for being an inverse-cube law and acting between schmasses. An acceptance of the possibility of such alien properties (and of alien laws of nature which the alien properties necessarily obey) seems to vindicate the contingentist intuition. But then APAW starts to look like an ad-hoc move to preserve necessitarianism as an interesting and substantive position.

Compare the situation with the debate about alien fundamental natural properties in connection with modal realism. The argument that Lewis finds compelling for the existence of alien natural properties is that it seems parochial to assume that our world is maximal in terms of its inventory of fundamental natural properties. If (as appears intuitively possible) some worlds lack some of the properties found in the actual world, why might the actual world not lack some of the properties found in other worlds? This line of objection tells against the principle APAW which makes SNN stronger than WNN. A more direct line of objection against APAW is the possibility of subtraction itself – it is judged intuitively possible that there could have been no mass, but APAW entails that mass exists at all worlds.

One response to these worries would be to distinguish between existence of a property at a world and instantiation of a property at a world. We could say that mass exists at some worlds but is not instantiated there, and that there are might or might not be unknown properties which exist at the actual world but are uninstantiated here. The problem with this response is that it once again seems to give up on the core of the necessitarian view. Nothing in the picture rules out schmass and fravitation as existent but uninstantiated, and the contingentist can reasonably point to this as vindication of their view. Given that the distinction between instantiation and existence doesn’t help us find a stable form of nomic necessitarianism, I will henceforth assume that they are co-extensive to simplify the rest of the presentation.

Given the problems with APAW mentioned above, it is not surprising that SNN is treated with suspicion by most metaphysicians. But I think that there are ways to uphold necessitarian principles in a non-trivial form without being forced to assert the speculative-looking claim APAW that all natural properties exist in all worlds. One claim we could use to bolster WNN would be the claim that there are a finite number of possible fundamental natural properties. Call this claim FP. While FP is still compatible with our world being maximal in terms of fundamental natural properties, it does not entail this conclusion, avoiding the parochialism objection which afflicts APAW. Indeed, it is compatible with FP that no world be maximal in the sense of containing all natural properties. Maybe two fundamental natural properties exclude one another, for example.

Call the conjunction of WNN and FP Finite Nomic Necessitarianism, or FNN. FNN entails that the actual laws of nature are necessary in that they necessarily apply to the natural kinds which actually exist but it allows for a further sense in which they are necessary – that no world contains any law which is closely similar but still distinct from a given actual law. The actual law may be the only possible law of its type, relating properties of particular types.

This characterization of FNN is obviously very general – but I think it shows there is conceptual room for a brand of nomic necessitarianism in between Bird’s WNN and his SNN. Indeed, there could be many different strengths of this in-between necessitarianism, depending on the details of structural similarities within the set of possible laws. From this perspective, SNN and WNN are different ends of a spectrum, rather than exhaustive exclusive alternatives.

McKitrick on manifestations

Another talk at the powers conference which grabbed my interest was by Jennifer McKitrick, on the metaphysical status of disposition-manifestations. The central debate is about which of two kinds of thing we should take the manifestation of a disposition to consist in. Are manifestations particular events, the ‘net results’ of the activation of dispositions, or are they instead partial contributions to the ‘net result’? McKitrick was defending the line that manifestations should be thought of as events; Mumford is the main author to have taken the opposing view.

A couple of examples are useful here. Consider the case of a boat pulled along a canal by two horses. Each horse exerts a force at an angle to the canal, but the direction in which the boat accelerates is along the canal. Each horse has the disposition to accelerate the boat, but what are the manifestations of these dispositions? Is the boat’s actual acceleration along the canal the manifestation of each disposition, or is each disposition manifested separately in some contribution to the boats actual acceleration? McKitrick was arguing for the former conclusion, which involves making the relation between particular disposition and particular manifestation many-one, rather than the one-one relation envisaged by Mumford.

One strand of McKitrick’s argument was epistemological. We cannot in general directly observe the individual contributions made by particular dispositions to the net result of a transition, but we want to say that we individuate dispositions by their manifestations. This leads to a tension; unless manifestations are events, either dispositions are individuated by something other than their manifestations, or we have problems individuating dispositions.

Another line of argument was metaphysical. Mumford gives us no clear general account of what the manifestation of a disposition consists in. In the case of the two horses towing a boat, it looks like he would say that the manifestations of the two individual dispositions to accelerate the boat are two individual ‘virtual’ acceleration vectors, which sum to the actual acceleration vector.

In discussion, Kit Fine emphasized some interesting properties of these virtual effects: only in combination with other virtual effects do they condense into a real, observable event. He was very inclined to recognise these virtual vectors as genuine (albeit peculiar) entities, admitted into our ontology for their explanatory power. If we’re prepared to be as ontologically generous as Fine, I think McKitrick’s arguments can be resisted. The manifestations of dispositions on this view are sui generis virtual effects; their postulation is justified in the same way as the postulation of unobservable theoretical entities like quarks.

A variant on this view would be to say that in certain scenarios, virtual effects can be directly observed. We certainly feel the push of the wind when we walk in a gale, even though we can resist this push and not fall over. It could be said that what we are feeling is a virtual effect, and hence that such effects can after all be observed; the line of thought is similar to the idea that we can observe singular causation directly. I think some delicate issues in philosophy of mind and action are likely to be raised here, so I’d like to try and skirt this debate by focussing on fundamental natural properties. I don’t think anyone is likely to say that we can observe directly the gravitational forces exerted on one proton by a distant pair of protons; but this kind of interaction is a paradigm of combination of virtual effects. If we have to accept virtual effects into our ontology at all, we will have to accept fundamental unobservable virtual effects as well as the more homely and potentially observable macroscopic virtual effects that feature in the common examples.

So it looks like the friend of virtual effects can postulate an inferential route to knowledge of them, perhaps combined with non-inferential knowledge of a macroscopic subset, defusing McKitrick’s epistemological objection. But a metaphysical strand of objection remains; perhaps these virtual effects are simply too strange to be admitted into our ontology. McKitrick pressed this line by challenging the audience to produce a clear account of what the virtual effects amount to, for example in the case of the boat pulled by the horses.

I thought I’d have a go at explaining virtual effects a little. A helpful example is the case of a train which is moving through a station. At the same time, I’m walking along the train with an equal and opposite velocity, so that I remain stationary relative to the platform.

McKitrick’s way of explaining this is that I have a disposition to change position* relative to the platform when I walk, but also a disposition to change position relative to the platform (in the opposite direction) when the train moves. These two dispositions cancel out, such that each of them is manifested in the same result; me remaining stationary.

On the virtual effect picture, there is a clear sense that can be given to the virtual effects. One virtual effect is my change of position relative to the train; the other virtual effect is the train’s change of position relative to the platform. The dispositions that both the train and I have are manifested directly in these virtual effects. In special relativity, change of position relative to an inertial reference frame is a genuine physical quantity, so in this case at least physical meaning can be assigned to virtual effects. The case obviously generalizes straightforwardly from macroscopic trains to microscopic particles.

However, to give an account of virtual effects applicable to the boat case, we have to complicate matters a bit. If we replace motion in the train case with acceleration, so that the train starts to pull out of the station just as I start to walk along it, then the virtual effects end up being accelerations relative to an accelerating frame. Arguably, in special relativity accelerations relative to accelerating frames are not genuine physical quantities, since accelerating frames are non-inertial.

Here however we can appeal to general relativity; an acceleration relative to an arbitrary frame of reference is a genuine physical quantity in general relativity. Here’s how I would then suggest explaining the boat case. In a frame of reference accelerating in the direction of one of the net forces applied by one of the horses, the boat really is accelerating in the direction of the force applied by the other horse. When we move to the correct non-inertial frame, we can see what was a virtual effect in another reference frame. Virtual effects in one reference frame are genuine physical effects in other frames.

McKitrick’s defence of manifestations as effects amounts to a pair of arguments against the virtual effect picture, and it looks like these arguments are inconclusive. We can get epistemological access to virtual effects through standard scientific inferential procedures, and we can identify them with genuine physical quantities by making use of varying frames of reference. The upshot is that both accounts of manifestations are still on the table. One traditionalist at the conference was overheard to remark that it looked like this was a thoroughly boring debate about terminology – that we have a stable conception of manifestations as effects, and another stable conception of manifestations as virtual effects, and that we use sometimes one conception and sometimes the other. I’m not sure whether this is right, but it’s food for thought.

* In combination, Jennifer said she didn’t like thinking of motion as a disposition to change position. But this is just the introductory case; skip to the acceleration case if you like.

Does dispositional essentialism need natural necessity?

I’ve been lucky enough to have a world-class conference on my doorstep over the last three days – Anna Marmodoro organized everything really well, and it was great to hear Alexander Bird, Kit Fine, EJ Lowe, Stephen Mumford, Ernest Sosa and others in full flow. Over the next week or so I’ll be discussing a few of the suggestions raised there in this blog. Let’s begin with natural necessity.

On Tuesday afternoon, Markus Schrenk and Stephen Mumford gave two parts of a very interesting ‘Nottingham paper’ on the relation between power and necessary connection. The written version of Markus’ paper is here. Very briefly, they argued that necessary connections between (token local) events should be carefully distinguished from powers, and that we should believe in the latter but not the former.

The master argument is based on the idea that any causal chain can be interfered with, so no episode of singular causation or disposition-manifestation occurs with natural necessity. The way the conclusion was stated was that they were denying natural necessity, although rescuing powers, causation, natural possibility, forces, tendencies, and so on.

What does their denial of natural necessity amount to? Their target notion of necessary connection is a relation between events – so it looks like all it takes for there to be no naturally necessary connections in the world is that for each actual transition from cause to effect or from disposition to manifestation, that transition could have (naturally) possibly not occurred. A token cause, considered by itself, does not necessitate any particular effect, since the intrinsic specification of the cause does not exclude the possibility of interfering environmental factors. This claim seems plausible – so maybe there is indeed no natural necessity to the relation between local token events. This, I think, is interpreted as a partial vindication of the Humean denial of necessary connections.

A different candidate sort of natural necessity is the conservation of charge. In conversation afterwards, Mumford suggested that he wanted to take this form of necessity as a Kripkean metaphysical necessity. The idea would be that electromagnetic interactions form a natural kind, and that it is part of the constitution of this kind that all such interactions conserve charge. So although there is metaphysical necessity in the picture, we still haven’t found any non-trivial natural necessity (unless, of course, we follow Bird and Edgington in identifying natural necessity and metaphysical necessity).

However, natural necessity does re-enter the picture when we look beyond particular pairs of localised events, at the bigger picture. Consider ‘maximally conditional’ natural necessity – specify a past light cone, and the effect follows with necessity if the underlying physics is deterministic. If the underlying physics is indeterministic, instead we get probabilities for effects following with necessity. Either way, there is at least one non-trivial form of natural necessity. This point was raised a few times in discussion, by Jennifer McKitrick and then by John Heil and Galen Strawson. Mumford’s reply, which seemed to appeal to Anscombe’s heterodox view of determinism, wasn’t enough to leave me satisfied.

So although Schrenk’s and Mumford’s rejection of necessary connections between token local events is plausible, and their distinction between necessary connections and powers is attractive, I think the dispositional essentialist should resist their headline claim that natural necessity is non-existent.

Analysing physical modality

Here’s a draft of a short paper making a few simple points about the analysis of physical modality. The abstract is as follows:

I discuss some general conditions on accounts of modality, and argue that the Lewisian condition of ‘Plenitude’ is misleading and ill-motivated. I then apply the resulting set of criteria to the case of the analysis of physical modality, arguing that the Lewisian ‘restriction strategy’ for analysing physical modality leaves important work undone.

The draft is here. Any comments extremely welcome!

Edit: Made some minor changes after discussing my objection to Fine’s argument with the man himself.

Edit again: Updated the draft again. Not that anyone’s reading this!

Four-dimensionalism

In the last MLE seminar of term we discussed some extracts from chapter 5 of Sider’s Four-dimensionalism. John and Frank moaned about the way Sider sets the debate up – John in particular was keen to emphasize that it’s possible for a three-dimensionalist to adopt eternalism and to assert the existence of temporal parts. His view is that there is no ‘endurance/perdurance’ or ‘3d/4d’ debate – what we actually have are four or five pretty much orthogonal debates, and a myriad of potentially defensible combinations of views.

We agreed that Sider’s argument against what he calls the ‘worm view’ in favour of his ’stage view’ is pretty weak. The crucial example goes by analogy: imagine we have to cross a wiggly road several times, and wonder how many roads we have to cross. This is meant to be analogous to the problem of how to count people prior to personal fission. Lewis has a way of counting (‘tensed identity’, which counts shared worm-segments rather than total worms) which is meant to explain how there is a sense in which there is only one person present prior to fission, and a sense in which we have to cross multiple roads to get to our location even when those roads are segments of a larger road. Sometimes we count by tensed identity, sometimes by timeless identity. (For a vigorous contemporary defence of this view, see this paper by Saunders and Wallace.)

Sider’s claim is that we should reject Lewisian tensed identity, since (allegedly) the claim that we contextually switch between different ways of counting is undesirable and unmotivated. But Sider has to posit an equally undesirable switch between our referring to stages and our referring to worms to explain the same kind of phenomenon. His final view is an ‘ambiguity view’ on which context determines whether the reference of our terms are worms or stages – but we retain a single, tenseless, way of counting. But this switching of reference would have to be a fairly substantial piece of hidden semantic structure, and it’s not at all clear that it’s less problematic than Lewis’ multiple ways of counting.

The problem for Sider becomes vivid when we consider objects going out of existence. While Benazir Bhutto was alive, our talk about her (according to Sider) referred to the stage of her co-present with our utterance. But now that she’s been assassinated, our talk about her now refers to the whole spacetime worm of her life. Sider presumably wouldn’t want to say that, supposing that she died midway through an utterance of ours which refers to her twice, that the first occurrence refers to a stage and the second to a worm. But I’m not sure how he can easily avoid saying something problematic here. Sider concedes there is a worry:

Sentences involving counting of the non-timeless variety, for example ‘there is one person in the room with me now’, receive a stage-theoretic analysis, as do certain sentences to be discussed below, since this analysis makes the best sense of our intuitions about those sentences. But in cases like that of timeless counting, a worm-theoretic analysis seems required. The concession perhaps makes the stage view a little less attractive since, arguably, candidate semantics that postulate this sort of ambiguity or indeterminacy seem, other things being equal, weaker than candidates that do not. Nevertheless, the stage view’s advantages outweigh this defect.

There is just no argument given for the final claim, that this defect is less problematic than the Lewisian ‘two kinds of counting’ story. Sider argues that ‘the evidence doesn’t require Lewis’ explanation’ – but it does require it if we wish to avoid an ambiguity in the semantics at the level of reference. At best, there is a stand-off between Sider and Lewis here. Perhaps some input from empirical semantics would help resolve it?

Deterministic Chance

We had a thoroughly successful MLE seminar today on the subject of objective chance in deterministic worlds. Lewis influentially insisted that deterministic chance was simply incoherent – that the only objective chance in such worlds could be 1 or 0. This conclusion seems fairly intuitive, but it doesn’t give a satisfying account of the chanciness of the special sciences. Classical statistical mechanics, in particular, presupposes determinism at the lower level, but produces probabilistic predictions. It doesn’t feel right to say these chances are ‘merely’ epistemic, as Lewis does.

So there’s been lots of work in recent years to rehabilitate the idea of deterministic chance. Barry Loewer in particular has treated making sense of deterministic chance as a precondition of making sense of chance. Schaffer has recently defended the Lewisian line, and his paper was the one under discussion.

One worry I initially had was that Schaffer’s presupposition that information about the laws of nature is admissible is incompatible with the Humeanism about laws he advocates. This worry ends up just being equivalent to the problem of undermining futures which led Lewis to the ‘new principal principle’. Although I think this remains a decisive argument against Humeanism, it’s not relevant to the main aims of Schaffer’s paper, so I’ll say no more about it.

There were some worries about how far the ‘platitudes’ about objective chance (which Schaffer appeals to in arguing that the best chance-candidates in deterministic worlds are 0’s and 1’s) are really platitudinous. We ended up satisfied that FP is platitudinous, but unconvinced by CTC – in fact, CTC seems false, as the following example suggested by John indicates:

I kill lots of Napoleon’s soldiers while they’re making their way to Waterloo. Wellington charges, and overwhelm’s Napoleon’s forces. My actions altered the chance of Wellington’s victory, but the actions were not temporally located between the cause (Wellington’s charge) and the effect (Wellington’s victory), as the CTC requires.

EDIT: this misunderstands either the CTC or John’s example. See Schaffer’s comment below.

Frank objected to the ‘Big Bang’ argument against the compatibility of IR and initial deterministic chances, on the grounds that in a Big Bang cosmology there is no first instant – time has the structure of an open set. We wondered, inconclusively, whether we could take a limit instead. EDIT: But as Schaffer points out in the comments, those who don’t believe in a first instant won’t be able to appeal to initial deterministic chance anyway.

Now to the main issue I want to discuss. Can the ‘objectively informed but still epistemic’ chances which Schaffer discusses count as objective chances? Lets consider three kinds of these ‘objective epistemic chances’ – chances in a poker game, chances in classical statistical mechanics, and chances in Bohm’s version of quantum mechanics.

In the poker game, what the next card will be is fixed from the start by the way the deck is shuffled. But this doesn’t mean that there aren’t correct and interesting probabilities that an experienced player can calculate and use to his advantage. These probabilities presuppose ignorance of the order of cards in the deck, but that ignorance is part and parcel of the game of poker. Playing within the rules, the poker-chances play the role of objective chances; it’s only when we go beyond the game, and ask for information inadmissible according to the rules (the actual order of cards in the deck) that the poker-chances are trumped by the underlying deterministic mechanism.

Now consider classical statistical mechanics. Here, the future evolution of a system is fixed by its microstate, but we typically know only its macrostate. While we are ignorant of the microstate a system is in, the CSM statistical chances play the role of objective chances, but were we to be informed of the exact microstate the chances would become superfluous – we could use the deterministic mechanism to work out the future evolution of the system with certainty.

Similarly, in the Bohmian case, the actual future is fixed by the precise positions of the Bohmian corpuscles. But (assuming an equilibrium distribution of these corpuscles) it’s impossible for us to measure these precise positions. The information is inaccessible to all intents and purposes, so the Bohm-chances play the role of objective chances. Unlike poker, it’s physically impossible to obtain the information which would trump the Bohm-chances.

This points to a notion of admissible information which is, roughly speaking, relative to the rules of the game. In poker, the rules make the information about the order of cards in the deck inadmissible; finding out the order would allow us to dispense with the poker-chances, but amounts to cheating. In CSM, the in-practice impossibility of finding out the exact microstate of a system would allow us to predict its evolution with certainty. In Bohm theory, finding out the exact position of the particles would allow us to dispense with the Bohm-chances, but this is physically impossible.

Looked at this way, Lewis’ and Schaffer’s inability to accept deterministic chance arises from a fixed criterion of admissibility. But sticking to absolute admissibility seems unmotivated. The original account of admissibility given by Lewis was, by his own admission, not a rigorous one; but he allowed all historical information to be admissible (except in pathological cases, such as cyclical time). This immediately gives the game away; if historical information is admissible, so is information about the deck of cards when playing poker, so is information about the microstate when doing CSM, and so is (physically inaccessible) information about the exact position of corpuscles when doing Bohmian mechanics. So where is Lewis’ argument that historical information is always admissible? I don’t think there is one – he offers it as a proposal. However, this proposal makes it impossible to think of poker-chances, CSM-chances, and Bohm-chances as genuine chances; so there is good reason to reject his proposal.

Schaffer’s argument against deterministic chance goes via the six platitudes. The kind of deterministic chances we get out of relativizing the admissibility relation are what he calls ‘deterministic macro-posterior chances’; he claims that such chances cannot validate the ‘principal principle’, the ‘realization principle’, or the ‘lawful magnitude principle’. I’ll take these in turn.

The principal principle connects credence with chance. Schaffer envisages someone who knows that (for example) the CSM-chance of an outcome is 1/2, but also knows the exact microstate of the universe and hence knows that the ‘newtonian chance’ of the outcome is 0. Obviously, such a person should set her credence by the newtonian chance, and not by the CSM chance. But the natural explanation of this is not that CSM chances are not genuine chances, but that they can be trumped by knowledge of lower-level chances; these lower-level chances are inadmissable relative to CSM. In cases where there is no information inadmissible relative to CSM available to the agent, the CSM chances do play the correct role in the principal principle. So this objection fails once we relativize admissibility.

The realization principle says that, if the chance of an event at time t at world w is non-zero, there are worlds which match w perfectly up to t, and which share its laws, in which the event occurs. Schaffer argues that a believer in deterministic macro-posterior chance will be committed via the RP to worlds existing which are ruled out by the deterministic micro-laws. The response here for a believer in macro-posterior chance is to deny that the correct version of RP involves a perfect match up to t. He should instead say that the correct version of RP involves only a perfect match as regards all admissible information up to t. This principle reduces to Schaffer’s version if all historical information is admissible; but if only some such information is admissible then the new RP no longer poses any problem for deterministic macro-posterior chances.

A similar move rescues deterministic macro-posterior chance from the conflict Schaffer adduces with the Lawful Magnitude Principle. This says that if the chance of event e at time t at world w is x, then the laws of w entail that if the occurrent history up to t is H, then the chance of event e at time t at world w is x. This is just to say that chances are lawfully projected magnitudes. Schaffer argues that CSM chances will not be projected by the underlying deterministic laws. This is quite right – but the underlying deterministic laws are not the right ones to consider. The relevant laws are the CSM laws, which do project CSM chances. Similarly, the history which appears in the history-to-chance conditional should be a macro-history, not a micro-history, or we bring in information inadmissible by the lights of CSM.

The upshot of all this is that relativizing admissibility avoids the three objections Schaffer has to deterministic macro-posterior chances. His objections boil down to the single objection, that macro-chances can be trumped by knowledge of micro-chances – but if we relativise admissibility, this is no surprise, since micro-chances are inadmissible relative to the theory which produces macro-chances.

So we have two options – accept relativized admissibility, and allow both macro-chances and micro-chances to count as objective chance. Then the same world can contain chances of just 0 and 1 at some levels, as well as non-trivial chances at other levels. Or we stick with absolute admissibility and are forced to say that in deterministic worlds there are only trivial chances.

One interesting upshot of relative admissibility is that we can have chances of 0 and 1 in indeterministic worlds. Suppose, as Bohmians sometimes do, that there is an indeterministic micro-micro-dynamics underlying the deterministic Bohmian mechanics; there could then be non-trivial chances at the fundamental level, only trivial chances at the level of the corpuscle motions, and non-trivial chances again at the level of observable phenomena. This kind of picture should actually fit nicely with Schaffer’s denial that there has to be a fundamental level; but I have to think more about this.

Comments more than welcome!

(I should note that the proposal to relativize admissibility has a lot in common with a proposal of Luke Glynn’s, which (following Hajek) takes chances to be fundamentally conditional on histories (where histories could be either fundamental histories or special-scientific histories). I’m not yet sure whether the two proposals are equivalent, but they are in a very similar spirit.)