The deep incoherence of strong necessities

ABSTRACT

Modal rationalism is the claim that for all p, if it is ideally conceivable that p, then there is a metaphysically possible world, W, in which p is true. This will be true just if there are no strong a posteriori necessities, where a strong necessity (for short) is a proposition that is conceivably false, but which is true in all metaphysically possible worlds. But are there any strong necessities? Various alleged examples have been proposed and argued over in the literature, but there is no consensus on whether any is genuine. In this paper, I aim to move the debate forwards by proving that there are in fact no strong necessities. I argue that there are no strong necessities because they are impossible; they are impossible because the very notion of a strong necessity is – despite prima facie appearances – ultimately incoherent. Thus, I argue, it is an a priori truth that there are no strong necessities, and that modal rationalism itself is true.

KEYWORDS:

• Modality
• modal rationalism
• a posteriori necessity
• metaphysical necessity
• conceivability

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 Such worlds are also usually centred, in the sense that statements at the world are evaluated from the point of view of a particular subject at a particular time and place in the world. This allows us to assign contents to statements containing indexical expressions.

2 One might take issue with my implication that a secondary intension contains, as proper parts, a primary intension and a link to a world considered as actual. To be fair, this is not how it is normally put. 2Dists will often state simply that the 2-intension of ‘water’, for example, is H₂O. Whilst I think this is perfectly legitimate shorthand, it is not technically correct. Strictly speaking, the 2-intension of ‘water’ is not H₂O itself, but rather the function that picks out H₂O (if anything) at any world considered as counterfactual.

A 2-intension requires us to perform one operation (represented by the 1-intension) on a world considered as actual, and then to apply another operation that has as inputs any world considered as counterfactual and the output of the first operation. Thus a 2-intension is in effect a set of instructions, roughly:

Take the 1-intension of ‘water’; apply it to {world considered as actual}; determine what object the 1-intension picks out at {world considered as actual}; at any {world considered as counterfactual}, look for this object; if you find it, then it is the extension at {world considered as counterfactual}; if you do not find it, then there is no extension at {world considered as counterfactual}.

3 One possible line of objection to this definition (I am grateful to an anonymous reviewer for this point) is that it would make an instance of strong necessity trivially impossible. Since – as we shall see later – ideal epistemic possibility is defined in terms of conceivability, the requirements placed on strong necessities – that they must on the one hand have necessary 1-intensions as well as necessary 2-intensions, yet on the other be conceivably false – are mutually inconsistent at the outset, or so it is argued. However, I think this is too quick, for two reasons. First, while I think the required combination of epistemic necessity and conceivable falsehood is ultimately incoherent, I do not think this is a trivial matter. As I will consider in Section 7, there is a prima facie case that some p might be conceivable but not epistemically possible. And if that were the case, then not-p would be epistemically necessary yet conceivably false. Second, the charge of triviality – if it applies at all – only applies as far as ideal epistemic possibility is concerned. Yet – as I will consider in Section 6 – a modal dualist will argue that ideal epistemic possibility does not entail metaphysical possibility. And, while I will argue that this too is ultimately incoherent, it is not clear that it is trivially so.

4 To clarify, I am not hereby conceding that these cases cannot be explained in terms of the deflationary 2D analysis. The point is just that if there are strong necessities, then they are not susceptible to the 2D analysis (since, by definition, they are not susceptible to any such deflationary account), and that the listed examples are claimed by their advocates as examples of strong necessities. But, of course, I deny that there are any strong necessities, and therefore I deny that these cases are truly examples thereof. And so, by my own lights, I do not rule out the possibility that the deflationary 2D analysis may work for some of these cases, just as it does (in my view) for the standard Kripke cases.

As a matter of fact, I think that the standard 2D account does work for some of the cases listed here, namely the indexical truths and essential properties of individuals. This does require that our concepts of individuals – such as Hesperus and David Papineau – have 1-intensions with something like a descriptive content. So I have to deny direct referentialist accounts of meaning, even for proper names (and indeed indexicals). But this is an argument I am content to make (although obviously it is beyond the scope of the paper to go into detail on that argument).

5 By inconsistency, I just mean a logical contradiction. Now, it may be objected (I am grateful to an anonymous reviewer for this point) that this makes it trivial that a paraconsistent logic cannot be correct. I take this point, and will bite the bullet: I do indeed think it is trivial that a paraconsistent logic cannot be correct. However, if this seems too quick, then I would make two points in mitigation: first, that it may not be trivial whether or not any particular logic is in fact consistent; second, that this need not prevent us from engaging in non-trivial deductive reasoning using paraconsistent logics, just as we engage in non-trivial reasoning employing imaginary numbers, or from necessarily false hypotheses that are assumed to be true just for the purpose of reductio ad absurdum.

This leads to the wider question of how, since – by my own lights – necessarily false propositions are logically contradictory / not ideally conceivable, and paraconsistent logics are necessarily false, we can engage in non-trivial deductive reasoning using them. The problem is particularly acute, since I must, on the one hand, allow the possibility of non-trivial deductive reasoning from necessarily false premises whilst, on the other, maintain that such premises – unlike consistent ones – do not constitute real possibilities. And by what rule, on my account, are consistent possibilities deemed legitimate, and paraconsistent ‘schmossibilities’ deemed improper?

In outline, my view is that logical consistency is a minimal requirement of any objective alethic possibility – there is no way things can be such that a logical contradiction is true – and therefore mere prima facie conceptions should be understood to represent the mere appearance of possibility. And the mere appearance of a possibility is not a modal entity in its own right, any more than a mirage is a type of lake. The real question, then, is how we can engage in non-trivial deductive reasoning involving mere prima facie conceptions. In outline, I think the answer is that mere prima facie conceptions can contain semantic components that are themselves internally coherent, and these semantic components can be employed in deductive reasoning, even though they are combined in such a way that the overall prima facie proposition is inconsistent. Of course, there is more to be said; but it is beyond the scope of this paper to give a full account of these issues.

6 I am grateful to an anonymous reviewer for this point.

7 This means that logical necessity is trivially absolute in this sense, since what is logically necessary will be logically necessary with respect to any given set of facts. But does this mean that metaphysical modality, which is supposed to be absolute, must itself be nothing more than logical modality? No, because logical modality is a purely formal set of constraints on what is possible and what is necessary. But when logical modality is combined with semantic content, the result is ideal epistemic modality – and this (so I argue) is what must constitute metaphysical modality, if metaphysical modality is to be absolute.

8 Even where it succeeds, this strategy raises wider questions about how necessarily false propositions – which, by modal rationalist lights, are inconsistent and not ideally conceivable – can be used in non-trivial counterfactual reasoning. If it is not ideally conceivable that, say the square root of 2 is rational, then what are we doing when we assume, for the purpose of a reductio proof, that it is rational? We do not want this assumption to be vacuous, and we do not want any inferences from it to be merely trivial. I have outlined some possible answers to these questions above, but it is beyond the scope of this paper to address them in full.

9 I am grateful to an anonymous reviewer for this point.

10 I am grateful to an anonymous reviewer for this point.

11 Mallozzi (2023) also considers the claim that even ideal epistemic possibility is not absolute. The idea is that ideal epistemic possibility is just what is logically possible given the facts about meaning – in much the same way that physical possibility is just what is logically possible given the fundamental physical facts – and is therefore restricted relative to the broader space of logical possibilities. However, my own view is that this is a false comparison. The reason is that meanings are needed to define a real possibility in the first place; correct logical form, on its own, is not sufficient. So we should not think of the facts about meanings as a constraint that can be added to a basic type of possibility in order to produce a more restricted one – in that respect, they are not like the fundamental physical facts. Rather, meanings – along with formal logical constraints – are a necessary component of any scenario that is even a candidate for possibility.

12 And I think that this is the question that we ought to be interested in. Suppose that modal dualism is true, and there are thus metaphysical modalities that are grounded in the a posteriori nature of things. In this case, as I have argued, it will be epistemically possible that the metaphysical modalities could have been other than they actually are. So consider the following: could God, if God exists, have caused the metaphysical modalities to have been other than they actually are? If modal dualism is true, then the answer is surely ‘yes’. But what we ought to be interested in is the modalities that would bind even an omnipotent God. It is widely accepted by theologians and philosophers of religion that it does not count against God’s omnipotence that God cannot do the logically impossible, such as making a stone too heavy for God to lift. But, if modal dualism is true, then the metaphysical modalities will not be binding in this way.

13 I am grateful to an anonymous reviewer for suggesting this (prima facie) possibility.

14 Of course, this does not mean that we cannot suspend disbelief, or have some combination of propositional attitudes that involves the endorsement of p and not-p at the same time. I can know perfectly well that p is false, or even that p is impossible – and yet still consider, counterfactually or per impossible, the scenario that p is true. But this is not the same as thing as thinking that p and not-p, and it certainly does not mean that it is ideally conceivable that p and p is impossible.