Abstract
McFetridge (in Logical necessity and other essays. London: Blackwell, 1990) suggests that to treat a proposition as logically necessary—to believe a proposition logically necessary, and to manifest that belief—is a matter of preparedness to deploy that proposition as a premise in reasoning from any supposition. We consider whether a suggestion in that spirit can be generalized to cover all cases of absolute necessity, both logical and non-logical, and we conclude that it can. In Sect. 2, we explain the significance that such an account of manifestation of belief in absolute necessity has for the prospects of a non-realist theory of modality. In Sect. 3, we offer a sympathetic articulation of the detail that underlies the McFetridge conception of belief in logical necessity. In Sects. 4 and 5, we show that the conception so articulated will not generalize to encompass all cases of belief in absolute necessity and proceed to offer a remedy. Our proposal is based upon a distinction between two kinds of suppositional act: A-supposing and C-supposing (Sect. 6). In Sect. 7, we then explain and defend our central thesis: (roughly) that (manifestation of) belief in absolute necessity is a matter of preparedness to deploy as a premise in reasoning under any C-supposition. Finally, we indicate that there is some promise in the parallel thesis that manifestation of the treatment of a proposition as a priori is a matter of preparedness to deploy as a premise in reasoning under any A-supposition (Sect. 8).
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Notes
We depart from McFetridge’s verbatim statement of these matters in two ways. Firstly, we make propositions rather than rules the locus of necessity. Secondly, we extrapolate general principles from cases where all that is given explicitly is the application of the principle to a particular case.
In contrast to McFetridge, it would seem, there are those who hold: (a) that logical necessity is not absolute (even though it is maximal) and, more generally, (b) that there are no absolute necessities since, for any proposition, there is some supposition under which one ought not to add that proposition as a premise in reasoning from it. Thus, we suggest, Nolan (1997) and Priest (2005). Such a view is not only a formal possibility (showing that absoluteness and maximality are formally distinct), but may also have philosophical motivations. For instance, it may allow us to improve on the standard treatment of truth-conditions for counterfactuals with logically impossible antecedents and/or logically necessary consequents, by not making them automatically true (see also discussion in Sect. 7). Our project here is not to motivate such views; we just want to make clear how they would fit in our framework.
That some such account is applicable to absolute necessity in general is a view endorsed by Peacocke (1999, pp. 172–173) and, in discussion thereof, by Wright (2002, pp. 656–657). In each case, the matter is barely touched upon, but the detail of the swiftly stated claims turns out to be crucial from the standpoint of our extended discussion. Peacocke (op cit) characterizes the principles that are known to be necessary truths as those “which can be legitimately employed when reasoning within the scope of any counterfactual supposition whatsoever”. However, Wright (op cit) presents the view that “to regard a proposition as necessary is to hold that it may safely be assumed as an auxiliary premise, or rule, when reasoning about any arbitrary counterfactual—more generally, hypothetical—set of circumstances.” (The emphasis is ours in both cases). The crucial point is precisely whether the account of absolute necessity ought to proceed “more generally” in terms of any arbitrary hypothesis/supposition: Wright’s formulation suggests that it ought, Peacocke’s formulation suggests that it ought not. We shall, eventually, side broadly with the latter, although we shall also show why Peacocke’s formulation, as it stands, must be further restricted.
We note that the thesis that the inferential disposition is sufficient for belief in the logical necessity of a rule is a crucial, but implicit, lemma in the “quasi-transcendental” argument for belief in (some) logical necessity that is proposed by McFetridge (1990, pp. 153–154) and endorsed, in a significantly strengthened version, by Hale (1999).
The non-realist approach we envisage is very broad and inclusive. As indicated, it does require acceptance that the propositional surface of modal talk is in order—that we speak properly of modal beliefs, of modal truth etc.—and, as such, excludes radical (traditional) non-cognitivist positions. However, the still broad non-realism that remains is intended to encompass (for example) various positions described generically as “anti-realist” in Wright (1992) and also the quasi-realism of Blackburn (1986). For present purposes, we need not isolate any particular non-realist position within the acceptable range.
There are hints in McFetridge (1990) that he has in mind something very much along these lines: for example, in articulating the key concept that figures in his explanations as the “co-tenability” of supposition and premise (ibid, p. 151).
As a heuristic, we suggest a broadly semantic understanding of “consequence”. We acknowledge, however, that further work on the project requires serious investigation of this (potentially) very important matter.
Here we expand in response to a point raised by a referee. There is—of course—an important kind of reasoning wherein we (aim to) form an unstable set {S, P}, from stable S and stable P, and then discharge S in order to conclude on the basis of premise P, that not-S. (Note also the distinct and not strictly relevant case, in which we form unstable {S, P}, “discharge” P, and conclude on the basis of S that not-P; then we are not using P as a premise.) So our understanding of (LN1) and (LN2), since it is based on the norm of stability-preservation, does not speak to every case in which X believes P logically necessary and adds P as a premise in reasoning from S. Our proposed articulation of the McFetridge condition, in imposing the constraint that {S}, and then {S, P}, should be stable, restricts (in effect) the account of the manifestation condition of belief in logical necessity to consideration of the kind of reasoning that is aimed at establishing what is true-in-S, or what is the case according to S. But what, then, justifies that restriction? Our response is that there is no further justification. We contend that we have isolated a feature (norm) that allows articulation of the McFetridge condition in a way that (we will argue) succeeds in providing a necessary and sufficient condition for manifestation of belief in logical necessity. It does not detract from, or otherwise bear on, the effectiveness of that condition that the norm in question does not hold sway in (other) inferential contexts in which a proposition believed logically necessary might be deployed for other purposes—in particular, in contexts where discharge of an initial supposition is intended or enforced. Our account suffices to isolate the phenomenon of belief in absolute necessity (we claim), without aiming to encompass its full richness, and only the former is required in the context of the dialectic. We do not deny that it might be distinctive of belief in absolute necessity that when P is taken to be absolutely necessary it can be used in a kind of reductio to “rule out” the supposition S and so arrive at the belief that S is absolutely impossible. If that is so, then an account, in the spirit of ours but aiming, more ambitiously, to encompass the full richness of belief in absolute necessity, might have to enrich the ideas of stability and the aim of the relevant forms of reasoning, so that it is overall stability (achieved by rejecting S) rather than stability within a supposition, and whether S can be “ruled out” as well as what is true according to S, that are at issue. We do not take the exploration of such delicate issues to be crucial to the dialectic of this article. For one thing, it would be unhelpful as an account of the inferential role of belief in absolute necessity to focus on interactions with other clearly modal beliefs; those interactions should eventually be explained once the inferential role has been characterised in relation to suppositional reasoning that is not itself aimed at modal belief.
The proper complement of the attitude of belief that is logically necessary that P is that of non-belief-that-it-is-logically-necessary-that-P, and the latter admits of various agnostic sub-cases (e.g. complete agnosticism about necessity, or believing in non-impossibility but being no further opinionated). We cover those cases by pointing out that, in any case that encompasses agnosticism about the logical impossibility of P, preparedness is eliminated by awareness of risking (not being able to rule out) the dissipation of stability as it occurs in cases where one has belief in logical impossibility: similarly, mutatis mutandis, for any case that encompasses agnosticism about logical contingency.
We must distinguish our present concession that our recent justification of (LN1+) and (LN2+) relies on classical logical principles from the contention that (LN1+) or (LN2+) apply only to reasoners who adhere to such principles. The latter contention is far from evident, and we are strongly inclined to resist it. For our theses are intended to be tolerant of heterodox views about all sorts of matters as long as variations from the orthodoxy on one side (convictions about logical consequence, conditions of stability etc.) are matched by variations on the other (beliefs about logical necessity). Thus, see n2 above. We fully accept that the cases of variously non-classical logicians call for far more extensive consideration of the justification and formulation of the conditions than we offer here. And we signal again our reliance on an unspecified notion of logical consequence (see n10 above). However, we also seek permission to put aside such an enormous package of under-explored issues, pleading that the present treatment has already gone much further in exploring the underlying issues from a classical standpoint than has previously been attempted.
See Blackburn (1986). We emphasize here that it is no part of our present concern whether any kind of necessity is co-extensive with any kind of inability to conceive or inability to make anything of. We are presently concerned only with the (canonical) psychological circumstances that prompt such belief, and while an account of justification might be constructed out of those resources, we do not claim that the obtaining of these circumstances is inevitably justificatory of such belief, far less what “makes it true”.
To forestall misunderstanding, in our usage, one and the same proposition may be the object of A-supposing and the object of C-supposing. An A-supposition (C-supposition) is a propositional attitude of A-supposing (C-supposing) that P. We also note, following a referee’s suggestion, that some suppositions may be neither determinately A-suppositions nor determinately C-suppositions yet may (nonetheless) be fit for inferential purpose (taken either way), e.g. suppose the rationality of the square root of 2….
We intend here—as throughout, and as an instance of our official metaphysical neutrality—to be neutral with respect to realist versus non-realist conceptions of talk of possible worlds.
The formulation of Peacocke (1999) is as per our slogan, and our explanation here will justify why we say (in n3 above) that that formulation will not do as it stands.
To point out absence of commitment in these respects is not, of course, to express opposition.
See the final part of Sect. 2 above.
The notion of treating a proposition as a priori may sound initially odd, but we hope to convince the reader in what follows that this is exactly what is at issue in certain discussions of a priority—in particular, that of Quine (1951).
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Acknowledgments
Earlier versions of this article were presented at the University of Geneva, the University of Glasgow, and at the Centre for Metaphysics and Mind at the University of Leeds; we are grateful to audiences on those occasions and to our colleagues at Leeds for helpful feedback. We are particularly grateful to Jose E. Gonzalez and Bob Hale for detailed comments on earlier written versions, and to Daniel Nolan and Graham Priest for help with understanding their views. The final version of this article also benefited substantially from excellent comments and suggestions from an anonymous referee for this journal.
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Divers, J., Elstein, D.Y. Manifesting belief in absolute necessity. Philos Stud 158, 109–130 (2012). https://doi.org/10.1007/s11098-010-9674-1
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DOI: https://doi.org/10.1007/s11098-010-9674-1