[Warning – very long post!]
‘Quiddistic Knowledge’ by Jonathan Schaffer (Schaffer ) is a great paper. It is a model of philosophical clarity and vigour. Nonetheless, I think that nearly all of its arguments can be resisted, and that both its main conclusions are false. Here are those conclusions:
1) Necessitarianism about laws has no good motivation, is subject to devastating objections, and ‘collapses into an incoherent mess’ because the (anyway bad) motivations for it pull in different directions.
2) Scepticism about quiddities is no more plausible than scepticism about the external world.
In this post I’ll explain why I think 1) is false; 2) will have to wait for next week.
My strategy for rejecting 1) is to describe a particular necessitarian picture, and to show how it accommodates all of the genuine motivations for necessitarianism while avoiding all of Schaffer’s objections. I do not dispute that other less plausible and less well-motivated versions of necessitarianism are indeed subject to his objections, or that the various versions have not always been clearly distinguished.
The version of necessitarianism that I will defend is, in Schaffer’s terminology, modal necessitarianism. It is the thesis that the actual laws of nature hold with metaphysical necessity; that is, that they are the laws of every metaphysically possible world. Bird  calls this thesis ‘strong necessitarianism’; and it is indeed a stronger – and a more interesting – thesis than the other forms of necessitarianism that have been defended in the literature.
I will appeal to one additional premise in my defence of modal necessitarianism. It is the premise that quantum indeterminism is a part of the actual laws of nature; that is, that the actual laws are indeterministic in roughly the sort of way invoked by quantum mechanics. This assumption, while obviously not in any sense a priori, seems very likely to be true, and it is certainly not in any way in tension with modal necessitarianism. Schaffer will not, of course, be willing to grant this premise: he considers the deterministic Bohmian mechanics to be an ’empirically open possibility’. I agree that the case for quantum indeterminism is not totally conclusive, and that the appearance of indeterminism could arise from a deterministic Bohmian conspiracy, but I do think that the case for indeterminism is very strong. I am accordingly happy to make my conclusions conditional on this premise. (It should, however, be noted that I only use this premise in the course of responding to one particular argument offered by Schaffer. My other responses are independent of the question of indeterminism.)
So, on to the arguments.
Arguments for modal necessitarianism
Schaffer first seeks to undermine two arguments for necessitarianism – the argument from natural necessity and the argument from sustaining counterfactuals. He correctly notes that – if valid – these arguments count in favour only of modal necessitarianism, the version I seek to defend. So what does Schaffer think is wrong with these two arguments?
The argument from natural necessity:
1) If the relation between properties and their powers is contingent, then like charges might not repel;
2) Like charges must repel;
3) Therefore: the relation between properties and their powers is not contingent.
Schaffer diagnoses this argument as equivocating on the modal strengths of the ‘might not’ and the ‘must’ which appear in premises 1 and 2 respectively. He claims that ‘the “must” of natural necessity in 2) is a restricted necessity, and the “might” in 1) is unrestricted. Hence they are compatible.’
This objection initially seems successful. The response of the modal necessitarian will be to deny that the ‘must’ in 2) is restricted; but that is precisely what is at issue in the debate over necessitarianism, so this denial is dialectically unavailable for use in a suasive argument against contingentism.
The right course, therefore, for the modal necessitarian is not simply to deny that the ‘must’ in 2) is restricted. Rather, the modal necessitarian should deny this on the grounds that a reading of 2) as a restricted necessity makes it inexplicable why we should be interested in claims like 2). If it is genuinely possible, in the unrestricted sense, for like charges to repel, why should we care whether it is impossible in some restricted sense?
Schaffer, presumably, will seek to justify the treatment of 2) as involving a restricted necessity on the grounds that the restriction involved is an interesting and a relevant one. Even if like charges might not repel, that they repel in all the worlds which share our laws is interesting and informative if a restriction to worlds which share our laws is an interesting and relevant restriction.
This justification depends on an adequate contingentist treatment of laws of nature. This, I submit, we do not have. I am essentially convinced by van Fraassen  that all extant contingentist theories of laws fall prey either to the ‘inference problem’ (given knowledge of the laws, why is it rational to draw inferences from them about unknown events) or to the ‘identification problem’ (how do we acquire knowledge of the laws anyway?). Humean theories that have the laws supervene on total history face the identification problem; Humean theories that have the laws supervene on past history face the inference problem; and arguably non-Humean accounts such as those due to Armstrong  face both problems.
I cannot consider possible contingentist lines of response to the inference and identification problems here. My conclusion is conditional: as long as there is no satisfactory contingentist account of the knowability and rational relevance of the laws of nature, there can be no contingentist explanation of why we should invoke a form of necessity restricted to worlds in which the actual laws in the semantics for assertions like 2). And if the best semantics for assertions like 2) does not involv e a modality restricted to worlds in which the actual laws hold, then there is no equivocation between the modalities in 1) and 2), and the argument from natural necessity stands.
The argument from sustaining counterfactuals:
4) If the relation between properties and their powers is contingent, then there is nothing that guarantees that charges repel in any other possible world;
5) In the nearest possible world, like charges repel;
6) Therefore: the relation between properties and their powers is not contingent.
Schaffer’s response to this argument is to deny that the consequent of 4) is in contradiction with 5). He argues that although there is no guarantee that charges repel in some arbitrary possible world, there can be a guarantee that charges repel in the nearest possible world if fixity of laws is partly constitutive of nearness.
The reason this response fails is that it makes it inexplicable why we should be interested in the counterfactual construction thus constituted. It is certainly open to Schaffer to postulate, along with Lewis, that fixity of laws is an important ingredient in closeness for some logical construction counterfactual*. But unless we can explain why the counterfactual* construction is of interest and use to us, we have no reason to think the counterfactual construction that we use in ordinary discourse is the counterfactual* construction. And since, in light of the inference problem and the identification problem, it seems that the contingentist cannot explain why fixity of the laws is an interesting condition, and hence that the contingentist cannot explain why we should be interested in a counterfactual construction which incorporates it into closeness.
Until a contingentist account of laws can be given which solves the inference and identification problems, the fixity-of-laws condition is unmotivated as an element of counterfactual closeness. The contingentist can give no explanation of why the nearest worlds are always worlds which share the laws of the actual world, and consequently can give no explanation of why laws of nature play a role in sustaining counterfactuals.
In contrast, the modal necessitarian has a straightforward explanation of why the nearest worlds are always worlds with the same laws as the actual world; it is that all worlds have the same laws as the actual world. The argument from sustaining counterfactuals is thus sustained.
Arguments against modal necessitarianism
Taking himself to have punctured the two arguments just described, Schaffer moves on to providing arguments against necessitarianism. He gives five such arguments: from modality, from counterfactuals, from propositions, from conceivability, and from recombination. There is a common form to these arguments: in each case, Schaffer argues that the best philosophical theory of the topic in question relies essentially on contingentism. There is also a common form to my replies: in each case, I will argue that the contingentist theory Schaffer provides is inferior, or at least not clearly superior, to the necessitarian alternative.
The argument from modality:
The contingentist analyses natural necessity as a restricted form of necessity. According to Schaffer, only this theory ‘can assimilate natural necessity to the general pattern of restricted necessities found across the historical, epistemic, deontic and conventional necessities.’
The necessitarian response to this argument is straightforward – it is not at all clear that natural necessity should be assimilated to this general pattern. There are obvious differences between natural necessity and the restricted forms of necessity Schaffer mentions;
(Note that the analyses of epistemic and deontic necessity are by no means universally accepted. According to the strategy that analyses epistemic necessity as a restricted necessity, all metaphysically necessary truths are epistemically necessary; but we lack knowledge of many metaphysically necessary truths of mathematics and of logic. And according to the strategy that analyses deontic necessary as a restricted necessity, ought implies can – it will never be the case that we ought to do something that is metaphysically impossible. Such problems cast significant doubt on the analyses of these forms of necessity as restricted.)
And there is independent reason, as argued above, to think that the conception of natural necessity as a restricted necessity is problematic; it is that it renders it inexplicable that we should be interested in the particular restriction which corresponds to natural necessity.
Kit Fine  has pushed an alternative argument for the conclusion that natural necessity is not best seen as a restricted necessity; this argument maintains that the laws of nature themselves should be ascribed natural necessity, but that the ‘restriction strategy’ renders the natural necessity of the laws simply as truth relative to themselves. Since every truth is true relative to itself, Fine argues that this renders the natural necessity of the laws ‘cheap and trivial’. I will not attempt to adjudicate on how successful this argument is; but, if it is found convincing, it provides a further reason not to conceive of natural necessity as a restricted necessity.
The modal necessitarian picture can still accommodate restricted modalities, of course; it is just that the restrictions are placed on a space of possible worlds which only includes worlds in which the actual laws hold.
I conclude that the strategy which analyses natural necessity as a restriction of metaphysical necessity is not clearly superior to the necessitarian alternative, which simply identifies natural necessity with metaphysical necessity. This undermines Schaffer’s argument from modality.
The argument from counterfactuals:
Schaffer argues that the best semantic theory of counterfactuals requires that we recognise possible worlds containing miracles: small violations of the actual laws. Miracles of this sort are selected for by the Lewisian criteria for nearness of possible worlds set out in Lewis ; they allow the closest antecedent world(s) to match the actual world exactly up to some time, and then to smoothly diverge in such a way as to make the antecedent true. Without worlds containing miracles, if the laws are deterministic then the closest world in which an antecedent which contradicts actuality holds would be one in which the initial state of the universe is different. Miracles therefore allow determinism and our intuitive judgments about counterfactuals to co-exist: we do not have to accept that, if the laws are deterministic, then had I scratched my nose just now the state of the universe at the big bang would have been different.
I agree that this argument spells trouble for the modal necessitarian who wants to reconcile deterministic laws with the denial that, were things to differ from actuality in any way, the initial state of the universe would have differed. However, even holding fixed our intuitive judgments about counterfactuals, this is not a natural position for the modal necessitarian to adopt. Rather, the best form of modal necessitarianism will hold that the actual laws involve quantum indeterminism, and hence that the laws of all possible worlds are indeterministic.
The claim that quantum indeterminism holds at all possible worlds allows the modal necessitarian to account for counterfactuals without worlds involving miracles. There are two ways this can be done. Either the modal necessitarian can replace miracles with highly unlikely but still lawful quasi-miraculous quantum fluctuations, and preserve the rest of the Lewisian semantics for counterfactuals unchanged; or the modal necessitarian can adopt a modified semantics which makes no appeal to miracles at all. While I will make no attempt to provide such an alternative semantics here (I venture an initial proposal in my doctoral thesis), and the obstacles which must be overcome in providing one are significant, I am optimistic that this can be done. The main advantage of such an account would be that it would not render true counterfactuals like ‘if I had scratched my nose just now, a highly unlikely quantum event would have had occurred’. But, more modestly, the modal necessitarian can resist the argument from counterfactuals simply by adopting the modified Lewisian semantics which replaces miracles by quantum quasi-miracles.
Of course, relying on quantum indeterminism makes the acceptability of modal necessitarianism hostage to empirical fortune. But I am happy to accept the risk that future developments will reveal that the world is deterministic, since I take that revelation to be extremely unlikely.
The thought that miracles are not needed for the best account of counterfactuals is an unfamiliar one. That is because work on counterfactuals tends to take for granted that, whether or not it they are an open epistemic possibility, deterministic laws are a metaphysical possibility, and we must allow for the truth of our ordinary counterfactual judgements to be preserved in deterministic worlds. That is, work on counterfactuals tends to presuppose contingentism. But this is just a sociological observation; it does not amount to any kind of argument for contingentism.
If modal necessitarianism is correct, then the best semantics for counterfactuals will not involve worlds containing miracles. And if quantum indeterminism is a part of the actual laws, then the best necessitarian semantics for counterfactuals is at least as good as the best contingentist semantics. So Schaffer’s argument from counterfactuals has no force against the modal necessitarian who accepts quantum indeterminism.
The argument from propositions:
Schaffer’s argument from propositions is straightforward. He assumes that propositions can be identified as sets of worlds such that p is true at w, and that there are contentful propositions involving actual properties under alien laws. An example which is meant to underwrite this latter assumption is that ‘a misinformed scientist might believe that like charges attract’.
Here is the way Schaffer formalizes the argument:
7) If the relation between properties and their powers is necessary, then there is no contentful proposition that like charges attract;
8) There is a contentful proposition that like charges attract;
9) Therefore: the relation between properties and their powers is not necessary.
Schaffer suggests that the necessitarian will reject 8). I agree that rejecting 8) is an option for the necessitarian, though I do not think it is the only option – 7) could also be rejected. But I take particular issue with Schaffer’s claim that the only way for a necessitarian to reject 8) is to say that the supposed proposition that like charges attract is the proposition that like schmarges schmattract, where schmarge and charge are distinct properties governed by distinct laws. As Schaffer correctly points out, this response calls for nomic or causal necessitarianism – the modal necessitarian will deny that there is any such property as schmarge or any such possible behaviour as schmattraction. And, as Schaffer correctly argues, the response lacks independent motivation; he also argues that charge and schmarge cannot be epistemic duplicates.
The way that the modal necessitarian should respond to the argument from propositions is by drawing an analogy with mathematical necessities. Consider the analogous argument:
7a) If the relation between numbers and number-theoretic truths is necessary, then there is no contentful proposition that 1+1=3;
8a) There is a contentful proposition that 1+1=3;
9a) Therefore: the relation between numbers and number-theoretic truths is not necessary.
Nobody will be willing to accept this argument. But reasons for rejecting it may differ.
Some will say that there is indeed a contentful proposition that 1+1=3 – it is just that it is necessarily false. Saying this requires a theory of propositions more fine-grained than the propositions-are-sets-of-worlds theory. (I am assuming that the null proposition, true at no world, is not ‘contentful’ in Schaffer’s sense.) Such people will reject 7a). But if 7a) is rejected then there seems no reason to uphold 7); and the argument from propositions fails.
To give it any chance of success, we must bolster the argument from propositions with the assumption that the best theory of propositions is indeed the propositions-are-sets-of-worlds theory. But even given this assumption, the argument can be resisted by the modal necessitarian. For given that theory of propositions, the modal necessitarian will deny 8), for the same reason that proponents of the propositions-as-sets-of-worlds theory must deny 8a).
Schaffer’s motivation for 8) is equally motivation for 8a). A misinformed mathematician might believe that Fermat’s Last Theorem is false. But according to the propositions-as-sets-of-worlds theory, interpreting this mathematician as believing a contentful proposition is impossible. If Schaffer’s argument from propositions were correct, by parity of reasoning we would have to reject the necessity of the truths of mathematics. Since the truths of mathematics are undeniably necessary, the modal necessitarian can accordingly resist the argument from propositions.
The argument from conceivability:
Schaffer’s argument from conceivability maintains that the link between conceivability and possibility is an indispensable part of modal epistemology, and that the modal necessitarian ‘is committed to a complete collapse of any conceivability-possibility link’. He formulates the ‘argument from conceivability’ as follows:
10) If the relation between properties and their powers is necessary, then it is inconceivable that like charges attract;
11) It is conceivable that like charges attract;
12) Therefore: the relation between properties and their powers is not necessary.
Schaffer expects the response from the necessitarian that 11) is false; that when we take ourselves to be conceiving that like charges attract, we are in fact conceiving that like schmarges schmattract. He correctly maintains that this response is not available to the modal necessitarian, but only to the causal or nomic necessitarian, and quite rightly criticizes it as lacking independent motivation.
It is clear, though, that the modal necessitarian ought to respond to the argument from conceivability by rejecting 10). Whether it is conceivable that like charges attract depends on us, and on our conceptual apparatus. Whether the relation between properties and their powers is necessary depends not at all on us, or on our conceptual apparatus, but on the properties and powers themselves. 10) is prima facie highly implausible.
Schaffer does in fact go on to provide additional support for 10). In a footnote he argues that ‘conceivability sees to be our main guide to knowledge of what is possible. This suggests that it is preferable to restrict conceivability rather than reject it outright, on pain of modal skepticism.’ This motivation for the conceivability-possibility link may be persuasive to the contingentist (who faces notorious difficulties when it comes to modal epistemology, and who might thus be driven to embrace a problematic epistemology rather than give up on the project altogether) but it is totally unpersuasive for the modal necessitarian.
According to the modal necessitarian, we gain knowledge of what is (unrestrictedly) possible by engaging in empirical scientific enquiry. No special epistemology is required for modal truths; and the problematic conceivability-possibility link need play no special role. The argument from conceivability is accordingly totally impotent against modal necessitarianism.
The argument from recombination
Schaffer’s final argument against necessitarianism runs as follows:
13) If the relation between properties and their powers is necessary, then some combinations of charge and acceleration would be impossible;
14) All combinations of charge and acceleration are possible;
15) Therefore: the relation between properties and their powers is not necessary.
As should be obvious, the modal necessitarian will deny 14), and maintain that not all combinations of charge and acceleration are possible. This need not be in conflict with the principle of recombination (as Schaffer states it, that if x and y are distinct existences, then there is a possible world with just x, a possible world with just y, and a possible world with x and y). That is because, for the modal necessitarian, charge and acceleration are not distinct existences.
Schaffer anticipates this necessitarian response, and argues that it ‘preserves the letter of recombination, but dashes its spirit.’ The argument for this conclusion involves the supposition that the laws are deterministic. For reasons discussed above, the necessitarian need not allow this supposition; the best form of necessitarianism has it that the laws are necessarily quantum-indeterministic. However, even granting this supposition, Schaffer’s rebuttal of the necessitarian response fails.
The rebuttal starts with the observation that ‘every actual existence is a correlate of a common cause: the Big Bang’ and argues that, if necessitarianism and determinism are true, that entails that ‘zero recombination of actual existences is allowed. The world has become an indivisible Parmenidean unity, the essential outpouring of the initial singularity. This is not a minor restriction on recombination, but rather an unprecedented rejection of any recombination of actual elements.’
This argument fails because it neglects that the necessitarian may allow that the actual initial conditions of the universe are contingent, even if the actual laws are necessary. Schaffer recognises this option in a footnote, but dismisses it as a route to reclaiming recombination: ‘Perhaps sometimes this is possible. But, I suspect, it will still drastically limit recombination of actual elements, far beyond what intuition permits.’ He also complains that it renders recombination an a posteriori matter. I find it difficult to be worried by this line of thought. The necessitarian will typically be unmoved by appeals to intuition about what is possible; their modal epistemology is scientific and a posteriori, not intuition-based and a priori. And in any case, Schaffer has not provided any argument that the restriction on recombination which determinism and modal necessitarianism jointly produce is as extensive as he suspects it is. And finally, for a necessitarian who rejects determinism, the argument has no force. I conclude that the argument from recombination is unpersuasive.
I have replied to Schaffer’s objections to the two arguments for modal necessitarianism that he discusses, and have shown how his arguments against necessitarianism lack any force against a modal necessitarian who take quantum-mechanical indeterminism to be a part of the actual laws. In the process, I have highlighted the advantages of the necessitarian modal epistemology over the contingentist modal epistemology. I conclude that modal necessitarianism remains a tenable and attractive account of the modal status of laws of nature.
Armstrong, D. . What is a law of nature?
Bird, A. . ‘Strong necessitarianism: the nomological identity of possible worlds’
Fine, K. . ‘The Varieties of Necessity’
Lewis, D. . ‘Counterfactual dependence and time’s arrow’
Schaffer, J. . ‘Quiddistic Knowledge’.
van Fraassen, B. . Laws and Symmetry.