Tuesday, 17 May 2016

Sufficient Conditions for Some Inference-Patterns Involving Conditionals

This is a continuation of the last post, which was a continuation of this article. The following three theorems show that, given a plausible assumption about the semantics of conditionals:

(1) You can't go wrong in applying hypothetical syllogism (transitivity for conditionals) so long as the set of relevant scenarios for the output conditional is a subset of that for the second input and the set of relevant scenarios for the second input is a subset of that for the first.

(2) You can't go wrong in applying contraposition so long as the set of relevant scenarios for the output conditional is a subset of that for the input.

(3) You can't go wrong in applying strengthening the antecedent so long as the same condition as in (2) is fulfilled.

Let us assume that a conditional A > C is true iff in all relevant scenarios the corresponding material conditional is true. 

I will use Sc(X) to denote the set of relevant scenarios for a conditional X .

Theorem 1. For any three conditionals A > B, B > C and A > C such that  Sc(B > C) ⊆ Sc(A > B) and Sc(A > C) ⊆ Sc(B > C), A > C will be true if A > B and B > C are true.

Proof: Take any three conditionals A > B, B > C and A > C such that Sc(B > C) ⊆ Sc(A > B) and Sc(A > C) ⊆ Sc(B > C).  Now suppose that A > B and A > C are true. Since all the relevant scenarios for A > C are also relevant for A > B and B > C, and A > B and B > C are true, the material conditionals A ⊃ B and ⊃ C will both be true at all the relevant scenarios for A > C (by the assumed semantics). Since transitivity holds for material conditionals, ⊃ C will be true at all the relevant scenarios for A > C, making A > C true (by the assumed semantics). Therefore, if A > B and A > C are true, A > C will be true.

IllustrationIf I had spoken to a cat then I would have spoken to an animal. If I had spoken to an animal I would have been happy. Therefore, if I had spoken to a cat then I would have been happy. (It is natural to think of the set of relevant scenarios for the first sentence as larger than that for the second. This could be further brought out by adding something like 'no matter what' to the first sentence.)

Theorem 2. For any two conditionals A > B and ~B > ~A such that Sc(~B > ~A) ⊆ Sc(A > B), ~B > ~A will be true if A > B is true.

Proof: Take any two conditionals A > B and ~B > ~A such that Sc(~B > ~A) ⊆ Sc(A > B). Now suppose that A > B is true. Since all the relevant scenarios for ~B > ~A are also relevant for A > B, and A > B is true, the material conditional A ⊃ B will be true at all the relevant scenarios for ~B > ~A (by the assumed semantics). Since contraposition holds for material conditionals, ~B  ~A will be true at all the relevant scenarios for ~B > ~A, making ~B > ~A true (by the assumed semantics). Therefore, if A > B us true, ~B > ~A will be true.

Illustration: (Assume for the following Q & A that it is analytic that all bachelors are men.)

Q: Do you think that, in view of the fact that we get energy from shooting men, if we don't shoot a man tonight, we won't shoot a bachelor? 

A: Of course: If we will shoot a bachelor tonight then, no matter what, we will shoot a man. And what you're asking about follows from that.

Theorem 3. For any two conditionals A > B and (A & C) > B such that Sc((A & C) > B⊆ Sc(A > B), (A & C) > B will be true if A > B is true.

Proof: (Same as for Theorem 2 but with (A & C) > B in place of ~B > ~A, (A & C)  B in place of ~B  ~A, and an appeal to the fact that strengthening the antecedent holds for material conditionals in place of the appeal to the fact that contraposition holds for material conditionals.)

(As with Theorem 2, assume for the following Q & A that it is analytic that all bachelors are men.)

Q: Do you think that we would have shot a man today if we had gone out and shot five bachelors and taken care to go for the masculine-looking ones?

A: If we had gone out and shot five bachelors, then, no matter what, we would have shot a man. So yes, of course we would have 
 shot a man today if we had gone out and shot five bachelors and taken care to go for the masculine-looking ones.

Thursday, 10 March 2016

Transitivity and Conditionals


Let us assume that a conditional A > C is true iff in all relevant scenarios the corresponding material conditional is true.

Let's leave it completely open here what makes a scenario relevant for a conditional. Let's also leave it open what scenarios are like.

(That something like the above is true for counterfactual or subjunctive conditionals seems more widely accepted than that something like it is true for indicatives, so the following will be most widely acceptable as an observation about the logic of counterfactuals. I think it probably applies to indicatives too. That it holds on the assumption of the above schematic semantics seems to me to be almost beyond dispute.)

In their 2008 paper 'Counterfactuals and Context', Brogaard and Salerno attempt to block a famous counterexample to transitivity for counterfactuals (cf. Lewis , p. 33) with the proposal that to have conditionals for which different scenarios are relevant figuring in the same argument is illicit.

But an inference from A > B and B > C to A > C will be truth-preserving as long as the set of relevant scenarios for the second is a subset of that for the first, and the set of relevant scenarios for the third is a subset of that for the second. (Note I don't say 'proper subset': they could all be the same set, but that's a special case.)

Illustration: If I had spoken to a cat then I would have spoken to an animal. If I had spoken to an animal I would have been happy. Therefore, if I had spoken to a cat then I would have been happy. (It is natural to think of the set of relevant scenarios for the first sentence as larger than that for the second. This could be further brought out by adding something like 'no matter what' to the first sentence.)

(This post builds on this.)


Brogaard, Berit & Salerno, Joe (2008). Counterfactuals and context. Analysis 68 (297):39–46.

Lewis, David K. (1973). Counterfactuals. Blackwell Publishers.

Wednesday, 9 March 2016

Five Objections to Sider's Quasi-Conventionalism About Modality

In a recent post I described Sider's quasi-conventionalism about modality, which in my view takes an important step forward with respsect to necessity de dicto but is mistaken in other ways. (My account of necessity de dicto shares a structure with it.) Here I give five objections to Sider's view.

None of these take the form of counterexamples. As Merricks (2013) observes:
[...] Sider’s general approach—as opposed to specific instances of that approach—is immune to counterexample. For suppose that Sider lists the “certain sorts.” You then come up with an absolutely compelling example of a proposition that is necessarily true and not of a sort on the list. Sider need not abandon his overall approach to reducing necessity. Instead, he could just add a new sort to the list to accommodate that example. Or suppose you come up with an absolutely compelling example of a true proposition that is not necessarily true and is of a sort on the list. Sider could just expunge that sort from the list.
1. Necessity does not seem disjunctive or arbitrary (at least, not to this extent).

This is an objection centering on our intuitive grasp of the concept of necessity de dicto. It seems like this is a notion we can grasp, with the help of Kripke’s characterizations as supplemented in this post. Now, when we grasp this idea, it seems we are grasping a single, unified concept: necessary truths could not have been otherwise, no matter how things had turned out. This just doesn’t seem like a disjunctive matter, and nor does it seem like the sort of thing we make one way or the other with any kind of arbitration - although of course there are unclear or borderline cases, which we may perhaps make stipulations about to some extent.

This is not a knock-down objection, of course. Sometimes philosophy can reveal things to be other than they might seem. But I think it is hard to deny, if we are willing and able to grasp the concept of necessity de dicto and careful to hold in abeyance any of our pet theoretical proclivities which may suggest otherwise, that the notion does seem more unitary and less arbitrary than Sider’s theory would have us believe. And I propose that that should count as a mark against Sider’s theory.

Furthermore, insofar as appearance really is different from what Sider says the reality is when it comes to necessity, there is some explanatory work for Sider, or more generally the would-be quasi-conventionalist, to do here: why the discrepancy? As far as I know, no answer has yet been given.

2. The ersatz substitute worry.

A starting point for this worry is the unapologetically ad hoc nature of Sider’s successive extensions of the toy version of his approach that he begins with (where the “certain sort” of propositions he takes as “modal axioms” are just the mathematical truths). This process seems to be one of going back and forth between a growing list of types of propositions, the list at the heart of an increasingly disjunctive account, and our grasp of the real modal notion of necessity. This gives rise to the worry that all we are doing is building an ersatz substitute for the real notion, by looking at the extensional behaviour of the latter and stipulating this behaviour into the account. No matter how far we pursue this strategy, the disjunctive notion we are building will remain fundamentally different in character from the notion whose behaviour we are modelling with it. Supposing that what we want from an ‘if and only if’ style account of necessity de dicto is not some substitute for that notion, but a biconditional which gives us insight into the notion itself, Sider’s approach will never satisfy.

Something of this worry is even suggested by what Sider says about family resemblances, rehearsed in the previous post as point (6). The quasi-conventionalist could simply insist that each of the items on their list of the types of propositions which count as modal axioms is there as a brute fact - that’s just how the notion of necessity works. But, Sider says, the quasi-conventionalist ‘need not be quite so flat-footed’, and is ‘free to exhibit similarities between various modal axioms, just as one might exhibit similarities between things that fall under our concept of a game, to use Wittgenstein’s example’. This move, offered as an optional extra for the quasi-conventionalist, is plausibly in tension with the way Sider’s successively extended accounts are formulated. Just as the concept of a game - allowing for the sake of argument that it is a family resemblance concept - is plausibly not actually captured by any particular disjunction, but is as we might say inherently open-ended, it is also plausible that we should admit that the real “certain sort” or “modal axiom” notion doing the all-important work in Sider’s account - allowing for the sake of argument that it is a family resemblance concept - is not captured by any particular disjunction either.

This of course suggests a variant of Sider’s approach, where it is held that the “modal axiom” notion is a family resemblance concept, and admitted that any definite, disjunctive list of types of propositions could only yield, when plugged into the overall account, an ersatz substitute for the notion of necessity de dicto. This variant is not, or at any rate less, vulnerable to the the ersatz substitute worry. But it is not clear whether it could really satisfy a philosopher who wants insight into the notion of necessity de dicto, let alone a philosopher with Sider’s motivations. For instance, can it really claim to be modally reductive? It might on the contrary seem that the family resemblance notion in question should be counted as thoroughly modal. Furthermore, it may seem to yield an account which is insufficiently insightful - essentially all we are now getting is (Schema) itself, together with the pronouncement that the condition C is given by a family resemblance concept. Is there nothing more which can be said? Relatedly, the question now arises: is it after all true that the notion in question is a family resemblance concept? What reason have we to believe that? (I will suggest, somewhat ironically given that I am on the whole much more admiring of Wittgenstein’s philosophy than Sider is, that it isn’t true. The notion playing this ‘condition C’ role, i.e. the notion which when combined with the notion of truth yields a notion playing Sider’s “modal axiom” role, can be defined in terms of a single necessary and sufficient condition.)

3. No iteration?

When Sider says early on in the modality chapter of his (2011) that the account he offers will be partial, there is a footnote to this remark which runs as follows:
(16) For example, the account defines a property of propositions that do not themselves concern modality, and thus is insufficient to interpret iterable modal operators.
This raises the question: how come, faced with this failure of coverage, Sider doesn’t simply make the same move with modal statements as he does with analyticities, “metaphysical” statements, and natural kind statements - namely include them expressly in the account?

Perhaps the answer is that this would threaten the account’s claim of reductiveness. For it seems that in order to include modal statements on the list, we need the concept ‘modal’.
The question then becomes: is ‘modal’ modal? If it is, Sider’s account is in serious trouble: it cannot, as a matter of principle, handle iterated modality. For remember, it is supposed to be modally reductive. And if iterated modality is a real, legitimate thing, then what use is a theory which gives us - by design - some extensionally correct answers but cannot handle this whole class of cases? It seems such a theory could give us an ersatz substitute for modality at best (to recall the above objection by that name). Its failure, if it is a failure, to be extendable to a salient class of cases should perhaps suggest to us that it is on the wrong track.

So, is ‘modal’ modal? It is an interesting question, and suggests interesting analogous questions about other kinds of concepts. One reason to think it is, is that we don’t seem to have a general way of saying what ‘modal’ means which doesn’t work by way of example. We seem to need examples of modal notions - necessity, or contingency, or possibility, or impossibility, or some combination of them - to do the job. To be sure, we could be said to be mentioning rather than using these notions in our explanations of ‘modal’, but is that any help? Don’t we need to use them in some broad sense in order to mention them in the appropriate way?

Another way out which may occur to the reader is to somehow delineate the modal statements using notions which are distinct from ‘modal’ and the like, but which fortuitously give the right extension. I am pessimistic about this. For a start, I can’t think of any good candidate notions. Furthermore, even if there were notions around which could do the job, wouldn’t using them for this purpose play further into the ersatz substitute worry described above? In particular, it seems like this strategy, while it may help Sider’s account deliver extensionally correct answers, would take the account (even) further from the real meaning of modal expressions, or the real nature of modal notions.

One possible strategy remains to be considered: accepting that ‘modal’ is modal and simply giving up the claim to full modal reductivity. From one angle, this seems not unreasonable; the way that ‘modal’ introduces modality, assuming it does, into the account, seems quite special and different from the way modality would be introduced if a notion of possibility or necessity were directly used. So perhaps there is room to claim that a broadly Siderian quasi-conventionalist account involving the notion of ‘modal’ as an unreduced modal element could still constitute a theoretical advance. I have no knockdown objection to this, but I do want to suggest that once this concession is made, other objections, such as the first two considered here - (i) that necessity does not seem as disjunctive or arbitrary as quasi-conventionalism would have us believe and (ii) the ersatz substitute worry - become all the more acute; I am not sympathetic with the following sort of move, but you might try to argue that biting those bullets is worth it if we get in return a complete reduction of modality, with its attendant payoff in eliminating puzzlement and vindicating certain sorts of metaphysical visions, but you can’t do that anymore under the present strategy. Indeed, the whole spirit of the quasi-conventionalist approach seems to be in tension with allowing such a modal element into the mix.

In sum, there is reason to suspect that iterated modality, and the failure of any existing version of Sider’s approach to cover it, poses a serious threat to Sider’s approach in general.

4. Reductivity a bug, not a feature.

Essentially this objection is raised against Sider’s theory by Merricks (2013). The objection is simply that, if we have reason to think that a modal notion like that of necessity de dicto cannot be reduced to non-modal notions, or if we just intuitively feel that to be right, then we should on that score alone be suspicious of Sider’s theory, since it purports to give a reduction. In making this objection, Merricks cites an argument he gives elsewhere (namely in Chapter 5 of his (2007)) for the conclusion that such modal notions indeed cannot be reduced to non-modal ones.

5. Questionable motivation.

As we said at the outset, Sider’s account is partly motivated by general puzzlement about modality, and partly by a metaphysical vision. Both these facets of the motivation can be made the focus of criticism. The following is not supposed to constitute a sharp, incisive objection, but rather to cast some doubt on these general features of Sider’s approach.

Regarding general puzzlement: yes, modality is puzzling to philosophers. But perhaps this puzzlement is not to be treated exclusively by means of reduction (or, for that matter, by ‘if and only if’ analysis whether modally reductive or not). Indeed, pursuing reduction can even be seen as pursuing an easy way out - albeit one which may be impossible in principle. Perhaps the only real way forward, with parts of our puzzlement at least, is, rather than trying to reduce modality to non-modal terms, to work on our way of looking at modal concepts themselves, using philosophical methods other than reductive analysis. (One method which comes to mind is the method, due to Wittgenstein, of imagining simplified language games and comparing and contrasting them to ours. In the Brown Book some steps are taken towards doing this with modality, but only cursorily. I mention this to give a particularly concrete and well-known example of a possibly helpful method, but this is just one among many - I do not mean to suggest it could suffice all by itself.) Non-modally-reductive accounts of necessity de dicto such as mine do not face this criticism, since they do not aim to clear up all of our puzzlement about modality, or even just some core of it, by means of an ‘if and only if’ style analysis. Nor to they aim even to point the way to such a clearing up. By being less ambitious on that front, they offer a more realistic hope of genuine theoretical progress on our understanding of de dicto modal notions - how they relate to other notions both modal and non-modal.

Regarding the metaphysical vision: it is beyond the scope of this post to criticize Sider’s Hume-influenced, Lewis-influenced metaphysical vision head-on. But we may note that, insofar as there may be grave problems with this sort of metaphysics for all we know given the present state of philosophical inquiry - nothing of the sort may be tenable, ultimately - there may also be problems with a highly ambitious approach to modality which is in service of this sort of metaphysics. More generally, perhaps there is reason to be dubious of any approach to modality based upon a metaphysical vision. One reason may be that the vision is, so to speak, too antecedent to modal considerations: perhaps one should let modal considerations shape one’s approach to metaphysical questions, rather than trying to explain modality (away, if you like) in terms of an approach to metaphysical questions which had its appeal quite apart from, or even in spite of, modal considerations. Another reason may be that the best way to make theoretical progress on the notion of necessity de dicto is to keep sweeping metaphysical visions out of it. We may do better to instead treat our topic along broadly logical lines. One way this may help is that it might free us up to throw a wider variety of conceptual resources at the problem - for instance, semantic notions or other modal notions which may seem problematic against some special metaphysical backdrop but are actually quite in order.

That concludes our list of objections or worries. For two further objections, see Merricks (2013).

I think the cumulative effect of the objections canvassed above should be for us to regard Sider’s theory as highly problematic. But note that none of these objections threaten (Schema). This raises the question: what if these were a more soberly motivated, more theoretically satisfying (Schema)-embodying account available? Some other candidate for the condition C in (Schema) which avoids these objections?

Merricks, Trenton (2007). Truth and Ontology. Oxford University Press.
Merricks, Trenton (2013). Three Comments on Writing the Book of the World. Analysis 73 (4):722-736.
Sider, Theodore (2003). Reductive theories of modality. In Michael J. Loux & Dean W. Zimmerman (eds.), The Oxford Handbook of Metaphysics. Oxford University Press 180-208.
Sider, Theodore (2011). Writing the Book of the World. Oxford University Press.
Sider, Theodore (2013). Symposium on Writing the Book of the World. Analysis 73 (4):751-770.

Saturday, 5 March 2016

Forthcoming in The Reasoner

My paper 'Against the Brogaard-Salerno Stricture' is forthcoming in The Reasoner. It is about the logic of conditionals, and derives from this blog post. The final draft is available at PhilPapers. Here is a post building on it.

Friday, 26 February 2016

Fifth Anniversary of Beginning Sprachlogik

February 24 this year marks the fifth anniversary of the first Sprachlogik post.

Thanks to everyone who has been supportive of the blog!

Saturday, 13 February 2016

Sider's Quasi-Conventionalism About Modality

Starting in his (2003), and in an unpublished draft from around the same time which is not to be cited, Theodore Sider has proposed a theory of necessity de dicto called quasi-conventionalism. The most up to date version can be found in his (2011) and his replies to a symposium on that work. It states necessary and sufficient conditions for a proposition to be necessary, but as we will see, one of the key concepts involved has been left open-ended, so the account is to be regarded as partial. The account is supposed to reduce necessity de dicto to non-modal notions, and to be extendable to de re modality.

What makes Sider’s account so worthy of discussion from my point of view is that it takes what I believe to be an important step forward with respect to the task of giving an account of necessity de dicto. The step forward is that it embodies a certain structure, which my account shares. Abstracting from the details of Sider’s account, the shared structure can be expressed in the form of a schematic analysis as follows:

(Schema) A proposition is necessary iff it is, or is implied by, a proposition which is both true and meets a certain condition C.

(Sider, as we shall see, does not quite use his schema, but his analysis can easily be re-expressed so as to conform to it.)

So, Sider’s view takes, as I will argue, an important step forward. But it also has grave defects. Considering Sider’s view, then - seeing that it instantiates the suggestive and appealing (Schema), and seeing what is wrong with it - offers a nice way of leading up to and motivating my own account, which I will give in the next chapter. (This is not the way I actually arrived at my account, but it could have been.)

Two of SIder’s main starting points seem to be: (i) the desire to find a way of reducing modal concepts to non-modal concepts, and (ii) a hunch that conventionalist theories according to which necessities are true by convention were on to something: roughly, that convention should play some key role in the analysis of necessity. Regarding (i) and the underlying motivation for it, there are two interrelated strands here: one is a relatively theory-neutral feeling that modality is mysterious, or cries out for explanation, but this then plays into the second strand, which is emphasized in his (2011): a desire for an account of the “fundamental nature of reality”, “reality’s fundamental structure” - an account that “carves nature at the joints”.

Sider argues that it was always a mistake to try to account for necessary truth by means of the idea of truth by convention: the idea is of dubious coherence, and in view of necessary a posteriori truths especially, would not seem to line up with the idea of necessary truth anyway. But that doesn’t mean convention can’t play a crucial role in, not truth-making, but necessity-making, or accounting for the necessity of necessary truths. (I make the analogous point, with the meanings or natures of propositions in place of convention, in arguing for my account.) Part of the motivation and attraction of truth by convention theories of necessity, Sider allows, was their promise of shedding light on the epistemology of logic and mathematics. The theory of modality Sider is offering makes no claim to do that. But so what? Who says the place to look for insight into the epistemology of logic and mathematics is in a theory of modality?

In his (2011), Sider labels his account ‘Humean’. Here is his first pass at expressing it there:
To say that a proposition is necessary, according to the Humean, is to say that the proposition is i) true; and ii) of a certain sort. A crude Humean view, for example, would say that a proposition is necessary iff it is either a logical or mathematical truth. What determines the “certain sort” of propositions? Nothing “metaphysically deep”. For the Humean, necessity does not carve at the joints. There are many candidate meanings for ‘necessary’, corresponding to different “certain sorts” our linguistic community might choose. (Sider 2011, p. 269.)
The role of convention in Sider’s account, then, lies in distinguishing this “certain sort” - or “certain sorts” (Sider switches as this point to the plural):
Perhaps the choice of the “certain sorts” is conventional. Convention can do this without purporting to make true the statements of logic or mathematics (or, for that matter, statements to the effect that these truths are necessary), for the choice of the certain sorts is just a choice about what to mean by ‘necessary’. Or perhaps the choice is partly subjective/projective rather than purely conventional. (p. 270.)
As can be seen at the end of this last quote, Sider has some uncertainty about whether the choice of the “certain sorts” is ‘purely conventional’. We will not get deeply into Sider’s ideas of ‘conventional’ and ‘subjective/projective’ here. It is enough for our purposes that the “certain sorts” are, for Sider, ‘not objectively distinguished’ (p. 270). Or again in different words:
The core idea of the Humean account, then, is that necessary truths are truths of certain more or less arbitrarily selected kinds. (p. 271.)
At this point Sider introduces a refinement, and it is this that will allow us to see how Sider’s account embodies (Schema) above:
More carefully: begin with a set of modal axioms and a set of modal rules. Modal axioms are simply certain chosen true sentences; modal rules are certain chosen truth-preserving relations between sets of sentences and sentences. To any chosen modal axioms and rules there corresponds a set of modal theorems: the closure of the set of modal axioms under the rules.[footnote omitted] Any choice of modal axioms and modal rules, and thus of modal theorems, results in a version of Humeanism: to be necessary is to be a modal theorem thus understood.[footnote omitted] (“Modal” axioms, rules, and theorems are so-called because of their role in the Humean theory of modality, but the goal is to characterize them nonmodally; otherwise the theory would fail to be reductive. [...]) (p. 271.)
Then, getting more specific with a preliminary proposal:
A simple version of Humeanism to begin with: the sole modal rule is first‐order logical consequence, and the modal axioms are the mathematical truths. (Logical truths are logical consequences of any propositions whatsoever, and so do not need to be included as modal axioms.) (pp. 271 - 272.)
At this point, we can see how Sider’s account, or type of account, will embody (Schema); his notion of ‘modal axiom’ combines the requirements of truth and being of a “certain sort” (or one of “certain sorts”), and the main point of the ‘modal rules’ seems clearly to be to draw out implications of the axioms. So, separating the truth and “certain sort” requirements again, we can with little or no distortion put Sider’s preferred type of account into (Schema):

(SiderSchema) A proposition is necessary iff it is, or is implied by, a proposition which is both true and is of a more or less arbitrarily selected “certain sort”.

The presence in the account of implication (or something like it) is in my view an important and laudable feature. It is perhaps not sufficiently emphasized by Sider, and has been glossed over in subsequent discussion of his view. For instance, Merricks (2013) glosses Sider’s account as saying that ‘Sider reduces a proposition p’s being necessarily true to: p is true-and-mathematical or true-and-logical or true-and-metaphysical or…’. The importance of implication (or something like it) in (Schema) and views embodying it is made clear in my recent post on my account.

After giving his preliminary version of Humeanism, Sider goes on to consider a series of worries, responding with ‘a combination of refinement and argument’ (p. 272.) He never arrives at a definitive proposal, but aims to develop his strategy sufficiently to justify his general approach.

I think we have already gotten a pretty good sense of Sider’s approach, but I want more or less to complete the exposition of Sider’s approach before, in my next post, moving on to objections, none of which are among the worries Sider considers. So before moving on to objections, I will now briefly convey six further points which emerge in Sider’s responses to the worries.

  1. Logical consequence must be non-modal: Sider wants his account to avoid modal notions, so modal characterizations of logical consequence are out. Remaining options include primitivism about logical consequence, something Sider calls the “best system” account of logical truth (which he describes in section 10.3 of his (2011)) extended to an account of logical consequence, and model theoretic approaches.
  2. Analytic truths added as axioms: Sider holds that analytic truths should come out necessary, and proposes to that end that each analytic truth be added as a modal axiom (p. 274). This move is unapologetically ad hoc. (You might worry, as I do, that some examples of the contingent a priori should count as analytic, in which case not all analyticities are necessities. But perhaps there are different notions of analyticity which may give different results here. In any case let’s set this aside.)
  3. “Metaphysical” statements added as axioms: again, modulo some fuzziness about what it takes for a statement to count as metaphysical - the gloss Sider uses is ‘truths about fundamental and abstract matters’ (p. 275) - true metaphysical statements are to be added as axioms. Again this is unapologetically ad hoc, or treated as a brute fact: ‘What justifies their status as modal axioms? This is just how the concept of necessity works. Such propositions have no further feature that explains their inclusion as modal axioms.’ (p. 275)
  4. A new class of ‘natural kind axioms’: another unapologetically ad hoc addition, this time to accommodate the necessity of natural kind type examples of the necessary a posteriori, e.g. ‘Water is H20’. I refer the reader to (pp. 282 - 283) for details.
  5. Contextual variation of the “outer modality”: it is conventional wisdom that modal talk in the wild should be understood as being about a contextually variable space of possibilities. This is often combined with a picture of an outer, unrestricted space of possibilities which does not vary. Sider suggests, as ‘more attractive’ (p. 281), that even the outer space is contextually variable - that ‘there can be contextual variation both in the modal axioms and the modal rules’ (p. 281).
  6. Family resemblances (maybe): on (p. 288) Sider rehearses his (by now familiar) attitude to necessity thus: ‘Why are logical (or mathematical, or analytic, or …) truths necessary? The Humean’s answer is that this is just how our concept of necessity works.’ But then he turns around and suggests (pp. 288-289) that ‘a Humean need not be quite so flatfooted. [...] [The Humean] resists the idea that there is a single necessary and sufficient condition for being a modal axiom. Nevertheless, she is free to exhibit similarities between various modal axioms, just as one might exhibit similarities between things that fall under our concept of a game, to use Wittgenstein’s example. Doing this would help to show that the Humean concept of necessity is not utterly arbitrary or heterogeneous.’ This no doubt helps the plausibility of Sider’s account in a way, but may also play into the hands of an objector, as we shall soon see.

This completes our exposition of Sider’s theory. In the next post we will consider some objections.


Merricks, Trenton (2013). Three Comments on Writing the Book of the World. Analysis 73 (4):722-736.
Sider, Theodore (2003). Reductive theories of modality. In Michael J. Loux & Dean W. Zimmerman
Sider, Theodore (2011). Writing the Book of the World. Oxford University Press.
(eds.), The Oxford Handbook of Metaphysics. Oxford University Press 180-208.
Sider, Theodore (2013). Symposium on Writing the Book of the World. Analysis 73 (4):751-770.

Tuesday, 26 January 2016

Indicative Modality is Not Epistemic

Philosophers today frequently identify indicative modality with apriority, or at least identify it as an epistemic notion.

For instance, the abstract for a recent talk by Greg Restall (currently available at his website) refers to 'subjunctive (metaphyisical) and indicative (epistemic) modalities'.

Even Chalmers in his admirable piece on the tyranny of the subjunctive, which might be expected to resist this tendency, bites the bullet here. Witness:

(a) Indicative necessity is "merely epistemic".
    [Answer: So? Before 1970, almost everyone thought necessity was tied to the epistemic (cf. Pap's book). Kripke *argued* that necessity and epistemic notions came apart, by appeal to the subjunctive, but one can't simply presuppose it.]

This is a mistake. Indicative modality is not epistemic. A proposition is subjunctively necessarily true when it could not have been false, no matter what. A proposition is indicatively necessarily true when it cannot be false, no matter what.

I see no reason to think we need to understand this latter notion by appealing to anything to do with knowledge or a knowing subject. The idea is rather that an indicatively necessary proposition is true by its very nature, or has truth as an internal property.

It may be that a proposition is a priori iff it is indicatively necessary (or maybe the two categories are almost but not completely aligned). I once proposed something like this as an analysis of the concept of apriority. While this may still be an instructive result, shedding light on apriority and indicative necessity both, I no longer think it should be thought of as giving the content or intension of the notion of apriority. That should be left as a concept which has to do with knowledge or knowability, and indicative necessity recognized as an interesting, and non-epistemic, concept in its own right.

This point is just a continuation of Kripke's work in distinguishing concepts of propositional typology which have typically been conflated.