Thursday 1 October 2015

An Account of Necessity as an Attribute of Propositions

I hope to say more about this in future, making the account more perspicuous and better defending it, but it is high time I made a blog post about it. My view that this account is correct has been stable since 2012. It fits with my account of propositions and could also be adapted to various other conceptions of propositions and meaning (but not all).

(Added October 2016: my most up-to-date treatment of this topic can be found in Chapters 1 and 5 of my PhD thesis. This is an early, undeveloped attempt.)

Some related posts:

A proposition is necessary iff it is, or is implied by, a proposition which is both inherently counterfactually invariant and true.

A proposition is inherently counterfactually invariant iff, if it is held true, it is held fixed across counterfactual scenario descriptions, i.e. its negation does not appear in any counterfactual scenario descriptions.

(I say 'its negation does not appear in any' rather than 'it appears in all' because counterfactual scenario descriptions don't normally deal with everything - are not normally maximal.)

Whether or not a proposition is inherently counterfactually invariant is a matter of the internal meaning of that proposition.

When I speak of 'counterfactual scenario descriptions', I mean not just those actually produced, but those which can be produced. Thus there is an unreduced modal element in my analysis of de dicto necessity.

Not everything which we could call a description of a scenario, where the scenario in question does not in fact obtain, counts as a counterfactual scenario description. If we say, for example, 'Perhaps things are actually such that ...', what goes in the blank is not to be counted as a counterfactual scenario description, even if it is a description of a scenario which does not obtain. Rather, I am talking about descriptions which, so to speak, describe a scenario as counterfactual - e.g. 'Things could have been such that ...'. This is like the distinction two-dimensional semanticists emphasize, between considering a scenario as actual vs. considering it as counterfactual. When a description is made of a scenario which is being considered as counterfactual, then that is a counterfactual scenario description.

We must distinguish between genuine and non-genuine counterfactual scenario descriptions. In the case of the latter, we may always say that the meaning of at least one of the expressions involved is being violated or departed from. For example, if we suppose that 'Cats are animals' is necessarily true, and yet speak loosely of a counterfactual scenario in which there are robot (and thus non-animal) cats. Here we can either say that we are using 'cat' in a different meaning entirely, in which case the counterfactual scenario description may be genuine, or are beginning with the primary meaning but, as it were, stretching it, in which case we have a non-genuine counterfactual scenario description. Another example: if Euler had squared the circle, he would have been famous for it. The description in the antecedent of what Euler does should be regarded as a non-genuine counterfactual scenario description. I take this notion as primitive, and think it is vague.

Note that it is not the case that a counterfactual scenario description is genuine iff the scenario it describes is metaphysically possible, and so it would be a mistake to think that counterfactual scenario descriptions play more or less the same role as "possible worlds" do in some other accounts. For instance, if I believe that Hesperus is not Phosphorus, then if I talk about a case in which 'Hesperus had been Phosphorus', this will be a non-genuine counterfactual scenario description, even though it is metaphysically possible, indeed actual, for Hesperus to be Phosphorus. Likewise, if I - again, believing Hesperus not to be Phosphorus - talk about a situation in which Hesperus and Phosphorus are distinct, this may be a genuine counterfactual scenario description, even though it is metaphysically impossible for Hesperus to be distinct from Phosphorus.

It cannot be denied that the notion of a genuine counterfactual scenario description, and in turn that of inherent counterfactual invariance, have much of the character of the notion of necessity de dicto. Still, as we have just seen, they behave quite differently. So it is anything but trivial to see that we can put these notions together with those of truth and implication to yield a statement of the conditions under which a proposition is necessary de dicto.

We may also delineate the inherently counterfactual scenarios in another way: they are those which are such that it is a priori that they are necessary if true. I do not think we should think of this as giving the content of the notion, however. It is another way to get a handle on the relevant class of propositions, which may help us to get the notion.

To see why closure under implication is required, consider any disjunction of a necessary truth with a contingently true or false proposition. Such a disjunction will of course be necessary, but it will not be inherently counterfactually invariant, since it can be held true by holding the contingent proposition true and the necessary one false.

My analysis gets the right answer on such a case, since the proposition will be implied by a proposition which is both inherently counterfactually invariant and true - in the simple disjunction case, the necessary disjunct. However, note that the relevant implier will not always be a part of the proposition in question: consider 'Everything is either such that it is either not a cat or is an animal, or such that it is either less than 100 kilograms in weight or not in my room'. This is in fact necessarily true, since all cats are animals and that is a necessary truth (or so I'll assume - the particular example doesn't matter). But you might hold it true if you disbelieve that all cats are animals, by believing that nothing in the speaker's room weighs more than 100 kilograms. If that is how you held it true, you would let its negation appear in counterfactual scenario descriptions - namely, descriptions of scenarios in which I have something heavy in my room.

Again, it is very important to see that counterfactual scenario descriptions do not act as "possible worlds" in my account. One easy way to see this is to consider someone who falsely believes a proposition whose negation is necessarily true a posteriori. Examples: 'Hesperus is not Phosphorus', 'Cats are robots', 'Hesperus is Mars'. Such a person will be in a position to produce counterfactual scenario descriptions involving these propositions, despite them being not only false but impossible. My account filters these out from being classed as necessary by means of the truth requirement.

To get a better grip on the role the notion of inherent counterfactual invariance plays in my account, compare Sider’s account on which there is something list-like and arbitrary at the core of the notion of necessity de dicto. The account is given in Writing the Book of the World, but is also rehearsed briefly in ‘Symposia of Writing the Book of the World’ (which has the benefit of being freely available at

According to this account, for a proposition to be necessary is roughly for it to be a logical consequence of a certain class of propositions, the “modal axioms”. Modal axioms come in different sorts, including mathematical truths, analytic truths (under a certain conception of analyticity), “laws of metaphysics”, and “axioms of a metaphysical semantics”. The account is a highly “defl ationary” one in that no metaphysically deep condition is given to unite all the modal axioms. They are given by a mere list (mathematical truths, analytic truths, …), which is selected, so to speak, “by us rather than by the world”—perhaps by linguistic convention.
Once you realize that the “modal axioms” Sider is talking about are all truths, you can see that his account shares a structure with mine: a proposition is necessary if it is or is a consequence of a true proposition fulfilling come condition C. Realizing that something of that form is correct is an important step. And I think my account is preferable to Sider’s because I have something more substantive to say about what the condition C is, such that it is in not in any relevant sense arbitrary whether a proposition has it or not: it is inherent counterfactual invariance. (Of course, if the notion of necessity de dicto seems arbitrary or conventional to you, you might prefer Sider’s account. I discuss that account and offer objections to it here.)

One of the attractive things about my account, I think, is that it does not try to reduce necessity de dicto to non-modal notions. For one thing, that may not be possible. For another, it seems it isn't necessary for an informative analysis of necessity de dicto. By not trying to reduce the modal to the non-modal, my account has more of a chance of being true and insightful. Also, it seems to me to be attractively simple and elegant, while still having enough structure, and involving the hitherto unfamiliar but natural notion inherent counterfactual invariance, so that it is understandable why it was not immediately obvious once the notion of necessity de dicto was clearly isolated by Kripke.

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