Logical Possibility: Its Nature and Value

Strictly and Broadly Logical Possibility

A distinction may be made between logical modalities narrowly and broadly conceived.68 Thereby, strict logical possibility involves the absence of formal

contradiction. Broadly logical possibility, in turn, arises from the meanings of non- logical terms, rather than just the logical constants.69 Both conceptions involve meaning: the distinction arises from the locus of the meaning at issue in each case.70 There is no strict formal contradiction involved in a supposition to the effect that bachelors may be married. The meanings of noun phrases are irrelevant to strictly logical modalities. In accordance with the integral role of logical modalities in the practice of reasoning from suppositions, logical possibility is unrestricted in that even broadly logical impossibilities may be strictly logically possible.

Strictly logical possibility is more liberal than broadly logical possibility. I am motivated to attach some importance to the distinction partly by a desire to avoid the conflation of substantive and merely logical modalities. Such conflation might arise from extensionalist views of meaning, as embodied, for example, in Putnam (1975, 215-271).71 Given the recognition that the meanings of non-logical terms have a determining influence upon broadly logical modalities, the danger is that the extensionalist will be tempted to let extensional factors impinge upon the determination of those modalities. As we have seen, Putnam (1975, 233; contrast 1983, 63-64) has succumbed to this temptation, as have other philosophers of essentialist persuasion.72 I do not retract my commitment that logical modalities,

69 On my account, this precludes neither broadly logical impossibilities not reducible to contradictions nor logical necessities not reducible to logical truths.

70 Cf. Wiggins (1979, 156 nt. 27):

logical truth is...forced upon us by the meanings of the logical constants. By this criterion not even ‘all bachelors are unmarried’ qualifies. Because logical necessity in the useful and strict sense is exigent, the species of possibility which is its dual is hopelessly permissive.

The distinction is implicit in Quine (1980, 20-24); cf. Romanos (1983, 109). As should already be clear, Plantinga’s excessive conception (e.g., 1974, v, 1-2), mistakenly intended to include the necessity pertaining to essential attributions, of ‘broadly logical necessity’ is rejected on my account.

71 Putnam (1975, 227) comments that ‘“meanings” just ain’t in the head’. As should be clear from my approach to logical modalities, the extensionalist has no monopoly on the thesis of the objectivity of meaning.

72 According to Seddon (1972, 483):

One move is to argue that although the statement that ‘A bar of iron floats on water’ is not explicitly self-contradictory, it is implicitly so, for we are saying that a mineral with a specific gravity of less than one (i.e. it floats), has a specific gravity in the range 7.3-7.8 (i.e. it is iron), and this is a contradiction, and is therefore logically impossible.

This move is adopted by Rasmussen (1977; 1983). I take the contrary view, deeming matters concerning real definition entirely irrelevant to considerations regarding the logical modalities.

broadly or narrowly conceived, are non-substantive. I urge that the intensions of ordinary names for concrete objects, but not their extensions, bear upon the determination of broadly logical modalities.73 This is consistent with the conceptualist realist approach to essence and modality de re that I adopt. So far as concerns the logical modalities, facts about the natures of concrete entities and deictic-nomological restraints upon conceiving of such entities are irrelevant. So far as concerns the modalities, reference to concrete natures bears only upon the objective non-logical modalities. Allowing extensional factors to impinge upon logical possibility, I will suggest, undermines the utility of the notion.

Given that only intensional meaning is admissible as a determinant of broadly logical modalities, it may be suggested that there is no need to place much emphasis on the distinction between strictly and broadly logical modalities. The extensionalist has been warded off: the threatened conflation of substantive and merely logical modalities is no longer immanent. However, the distinction has additional value in that it accords well with the considerations relating to reasoning from suppositions to which I have alluded. It allows for situations in which a reasoner may lack the relevant epistemic background pertaining to broadly logical modalities (i.e. the reasoner may lack knowledge of the relevant intensions: this accords with the Fregean thesis of the objectivity of sense). Benardete (1962, 346 n. 3) suggests that there ‘is no contradiction, in the strict formal logical sense, in asserting that some ideas are made of tin, yet that freedom from self-contradiction does not suffice to make the thing logically possible’.74 However, Benardete’s claim is at best arbitrary, if not question-begging. If a construction is grammatically well-formed and declarative, i.e., if we are really dealing with a statement, and if that statement embodies no formal contradiction, then it is logically possible in the strict sense. In view of the objective status of logical modality it is not surprising that logical impossibilities may escape detection and can even be believed.75

Logical Possibility: Elimination, Revision, Conservation

73

Cf. Strawson (1966, 225).

74 Interestingly, and in contrast, a similar example, ‘the sound of a trombone is blue’, was offered by Russell (1940, 170) as ‘perhaps’ a logical possibility. Such examples, called ‘selection errors’ by syntactic theorists after Chomsky (e.g., 1965), are described by Wolfram (1989, 33) as occurring where ‘the wrong sort of property or activity is predicated of the subject’. That description is suggestive that substantive metaphysical considerations have some sway here. There is a marked difference between selection errors and unquestionably ill-formed constructions (such as Wolfram’s example, ‘Cats blows the wind’ (1989, 32)), in that the former, but not the latter, clearly admit of internal negation. I see no reason for deeming selection errors either logically impossible or meaningless: I admit them as logical possibilities. Cf. Hodges (1977, 154) who deems them false.

Entrenched abuses of the notion of logical possibility and purported difficulties concerning its definition or its discernment have led some philosophers to regard it with some suspicion. Various positions, including revision of the notion and denial that logical possibility is any kind of possibility at all, have been adopted. Occasionally philosophers have appeared to advocate the elimination of the notion. I believe that such positions have arisen through the tendencies to too closely associate the very notion with the aforementioned abuses and to view metaphysical considerations concerning substantive possibility as a threat to the notion of logical possibility without bearing in mind the question as to what that notion is actually

for. The tendency to revise the notion in light of one’s metaphysics is also manifested in work which is not motivated by suspicion of the notion. We have already seen this is the case of Putnam, who (at one time) allowed (purported) facts about the natures of actual existents such as water to delimit logical possibility. Similarly, Plantinga (1974, v, 1-2 and passim) proposes a notion of ‘broadly logical necessity’, intended to be implicated in the expression of substantive modal attributions de re,76 without ever asking what the notion of logical possibility is actually for, and without addressing the legitimacy or otherwise of his own usage. I view Plantinga’s proposal as both revisionary and, like his attempt to explicate essence and modality de re in terms of modality de dicto, misguided. I will briefly survey and criticize the views I reject. This will serve to substantiate my own position, which I take to be conservative.77 (Philosophers whose interests are primarily metaphysical ought to bear in mind the question as to the value of the notion of logical possibility so as not to be misled into providing a distorted account of its nature or adopting an unduly hostile attitude towards the notion.)

Eliminativism about logical necessity is not viable so neither is eliminativism about logical possibility. It is worth noting that many accounts critical of the notion of logical possibility make no mention of its correlative. I take this to substantiate my suggestion that such accounts have tended to allow their own metaphysical commitments with regard to real possibility, and their attendant anti-empiricism, to cloud their philosophical judgment: surely, one who seeks to revise or banish logical possibility has either to revise by the same lights, or to deny the centrality to the notion of deductive consequence and the whole practice of philosophy of, its correlative. Neither course is tenable.

76 Cf. Plantinga (1970, 475), ‘a possible world is a state of affairs that could have obtained if it does not. Here “could have” expresses, broadly speaking, logical or metaphysical possibility.’ It is not clear that Plantinga takes ‘logical’ and ‘metaphysical’ to mark any distinction here. On my account, many states of affairs which could not have obtained nonetheless constitute logical possibilities.

77 I take it that the notions of logical necessity and logical possibility are not pre- philosophical. It may be suggested that there is no historically continuous notion of logical possibility at play, but various shifts from one notion of logical possibility to another: cf. Hacking (1975, 334-335). In so far as a core notion of logical necessity has persisted since ancient times this suggestion can be regarded as harmless to the case I will present. That there is such a core notion is suggested by McFetridge (1990, 136) after Aristotle, Prior Analytics, 24b19-22.

Antipathy to the reckless applications to which empiricists have attempted to put the notion of logical possibility has led anti-empiricists to reckless views on that notion. For example, Cook (1994, 155) depicts ‘the idea of “logical possibility”’ as something which ‘burdens us’ if we adopt ‘the Humean view of causation’. Given the indispensability of logical necessity we can hardly agree that its correlative is burdensome. The point is, rather, that the notion has been abused and that we must recapture clarity by rending the notion free of the legacy of that abuse. It is the abuse which is burdensome and which is up for elimination, not the notion.78 Cook charges that ‘the idea of “logical possibility”...leads...to a peculiar view of the way in which philosophy is to construct and deal with examples’, i.e., that the notion has a detrimental effect upon philosophical methodology. The distinction I have defended between conceiving of (de re) and conceiving that (de dicto), affords the view that the ‘leading’ about which Cook is concerned comes about through historical accident, and through confusion, rather than being internal to the very notion of logical possibility. By the lights of the distinction, merely logically possibilities have significant bearing on neither our epistemology where matters a posteriori are concerned nor our substantive metaphysics.

Some philosophers (Rinaldi (1967, esp. 97); Seddon (1972, esp. 481); cf. Toulmin (1958, 169-172); Mason (1988, 11)) have claimed that ‘logical possibility’ is a misnomer which fosters confusion. According to Seddon (1972, 481),

we all know that it is not possible for a bar of iron to float on water...if we insist that it is nonetheless logically possible, we invite the comment that we are using the word ‘possible’ in a very odd way, and that we will need good reasons for such a striking departure from ordinary usage. I doubt that good reasons are forthcoming.

My account of logical possibility is already equipped to deal with Seddon’s remarks since it maintains that it is not the case that it is logically possible for a bar of iron to float on water since this conflates modality de re and de dicto. When logical possibility is used, as is appropriate, to qualify a dictum, the difficulties alluded to by Seddon are avoided. This involves no deviant use of the word ‘possible’. In addition, the notion of logical possibility is technical. There is no reason why it should comply with ‘ordinary usage’. Once we have a clear view of how the notion of logical possibility should properly serve us the difficulties which Seddon purports to present are entirely avoided. As long as it is clear, as I have recommended, that logical possibility talk is not just about genuinely possible

78 Mason (1988, 11) writes that the notion of logical possibility ‘has some uses...but in most circumstances it is a notion which (as Hume would say) we should commit to the flames’. This is an injudicious comment, since a notion is either up for elimination or not. The point is to discriminate between the legitimate and illegitimate applications of the notion. It is the latter which must be expunged from our philosophical practice, not the notion itself. This is in line with the tenor of Mason’s discussion.

states of affairs (i.e. ways the world could be), there is no need to be so extreme. We need only bear in mind that logical possibility qualifies dicta rather than concrete entities. Logical possibility is a variety of possibility, it is just that it is distinct from concrete possibility: there is no misnomer involved.

On my account, both empiricists and essentialists have been guilty of failing properly to observe demarcations between logic and metaphysics where modalities are concerned.79 I have sought to maintain a clear distinction, certainly in practice, and I hope also in theory, between merely logical modalities and substantive metaphysical modalities. In the words of Rasmussen (1983, 537), I claim that ‘confusion results from using “it is logically possible that” in reference to beings in rerum natura’. Unlike Rasmussen, I take this to be a sufficient condition for confusion.80Rasmussen’s actual, and in my view subversive, intention is to use the word ‘logical’ in reference to the natures (essences) of concrete objects. Thus, he seeks to restrict logical possibility in a manner akin to that displayed by Hacking’s Kripke. As we have seen, a similar view is entailed by some of Putnam’s work, and is implicit in Plantinga’s category, intended to encompass essentialist modalities for concreta, and taken up by Davies (1981, 187- 201), of ‘broadly logical possibility’. My account conserves logical possibility, abandoning the pretension that logical possibilities involve reference to concrete entities. Rasmussen, Putnam, and Plantinga seek to uphold the pretension and revise logical possibility.81 We can distinguish between the extensional/real-

79 Compare the case of the attendant failures to afford due recognition to the de re/de dicto distinction and to the form of essentialist claims.

80 Rasmussen’s weaker claim is that

confusion results from using ‘it is logically possible that’ in reference to beings in rerum natura, solid iron bars, cats, etc., but retaining a sense to the term ‘logical’ that confines the object of analysis to the [nominal] definition of the entities in question and not their respective natures. (1983, 537)

81 It is with good reason that I tar Plantinga and Putnam with the same brush as their less- renowned contemporary: all three philosophers give accounts of logical modality and modality de re which allow extensional factors pertaining to real essences to impinge upon the logical modalities. In a remark reminiscent of Putnam’s extensionalism, Rasmussen (1983, 533) complains that ‘appeals to “meaning”...do not constitute some special access to what is and is not logically possible for beings in rerum natura’. What this indicates, however, is the inappropriateness of the idea that logical possibility does so relate to concrete entities, rather than the need to revise the notion of logical possibility, relativising it to substantive considerations concerning the natures of real existents in the concrete realm. I take Rasmussen’s view to be the most misguided of the three, e.g., since, unlike Putnam and Plantinga, his account of concepts and logical possibility at least fails to explain how we can reason using concepts which lack extension and perhaps fails to allow for this. Rasmussen’s remark (1983, 515) that ‘concepts...are inherently relational and are necessarily of or about something other than themselves’, conjoined with his thoroughgoing extensionalism, suggests that only that which is instantiated can feature in our reasoning.

essential and intensional/nominal-essential aspects of concepts, which leaves room for the claim that logical possibilities relate at best to the latter. An essentialist view of concepts need not restrict logical possibilities in so far as we distinguish between de re and de dicto conceiving. On the account I have offered, after Wiggins, it is inconceivable for a solid iron bar to float on water, since an entity which can float on water does not have the persistence principle of a solid iron bar. Any conceiving going on can therefore not be conceiving of an iron bar. Nonetheless the logical possibility of the statement that an iron bar floats on water is in no way undercut. The restriction on conceiving de re is in virtue of metaphysical necessity de re: there is no such restriction on conceiving de dicto. Claims about the natures of concreta are not founded upon de dicto, or logical, necessities.82 The accounts of Rasmussen, Putnam and Plantinga show no awareness that there is logical room for the position I adopt according to which, for example, it is impossible for iron bars to float on water but logically possible that iron bars float on water.83 My account, unlike those I brand revisionary, respects the utility and the formal and a priori nature of the logical modalities.