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Exclusion and Sufficient Reason

Published online by Cambridge University Press:  23 June 2010

N. M. L. Nathan
N. M. L. Nathan*
Affiliation:
University of Liverpool University of Birmingham
*
N.M.L.Nathan@Liverpool.ac.uk
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Abstract

I argue for two principles by combining which we can construct a sound cosmological argument. The first is that for any true proposition p's if ‘there is an explanation for p's truth’ is consistent then there is an explanation for p's truth. The second is a modified version of the principle that for any class, if there is an explanation for the non-emptiness of that class, then there is at least one non-member of that class which causes it not to be empty.

Information

Type
Research Article
Information
Philosophy , Volume 85 , Issue 3 , July 2010 , pp. 391 - 397
Copyright
Copyright © The Royal Institute of Philosophy 2010

Two principles. The first, which I call Sufficient Reason, says that for any true proposition p, if ‘there is an explanation for p's truth’ is consistent then there is an explanation for p's truth. The other one I call Exclusion. It says that for any class, if there is an explanation for the non-emptiness of that class then there is at least one non-member of that class which causes it not to be empty. Taken together, these are powerful principles. With minimal assistance, they entail a large conclusion: there is a single, conscious, non-material, eternal, omnipotent, uncaused cause. Are they, then, both true? Exclusion Principle must I think be modified. But that hardly matters if, as I later argue, Sufficient Reason principle should be preserved intact. For from modified Exclusion and Sufficient Reason the same large conclusion can be derived with the same minimal assistance. We have here the engines of a sound cosmological argument.

Could this argument help to show that God exists? You might think not: it is an entity whose existence the argument seeks to prove, and God is not an entity but, rather, Being itself, or, even, what is ‘beyond being’.Footnote 1 I doubt though that even on these far from obviously intelligible conceptions of divinity the argument would lack all interest. Even if they are not divine, still superhuman entities are not beneath our notice.

Combine, to begin with, Sufficient Reason and Exclusion in its pristine form. The class of non-conscious beings is non-empty, and, given Sufficient Reason principle, this has an explanation. But by Exclusion Principle there is an explanation for this explanandum only if there is at least one conscious being which causes there to be at least one non-conscious being. By parallel reasoning we can conclude that there is at least one non-material being which causes there to be at least one material being, at least one eternal being which causes there to be at least one being whose existence has begun or will end, at least one omnipotent being which causes there to be at least one non-omnipotent being, and at least one uncaused being which causes there to be at least one being which was caused to exist. If we are not to multiply entities beyond necessity we should however postulate just one rather than more than one conscious being which causes there to be non-conscious beings, just one non-material being which causes there to be material beings, and so on. And now, appealing again to considerations of simplicity, we can identify the one conscious cause of non-conscious beings, with the one non-material cause of material beings, and with all the other beings whose existence we have used our two principles to infer. There is, then, a single conscious, non-material, eternal, omnipotent, uncaused cause.

Schopenhauer's stricture may now come to mind. Are we not treating Sufficient Reason as a hired cab, to be conveniently dismissed as soon as we have reached our destination? Whatever being we postulate to explain the non-emptiness of some class, will there not by Sufficient Reason be an explanation for the existence of this being, and hence yet another causally efficacious being, whose existence will in turn have an explanation, and so on, ad infinitum? I think not. Sufficient Reason says, not that if p is true then p has an explanation, but that if p is true and it is consistent to suppose that p has an explanation, then p has an explanation. Consider the class of caused beings. To explain its non-emptiness we postulate a single causally efficacious uncaused being. But Sufficient Reason does not require us to suppose that there is an explanation for the existence of this uncaused being because ‘there is an explanation for the existence of an uncaused being’ is not consistent. There is, admittedly, no inconsistency in supposing that there is an explanation for the existence of a conscious cause of non-conscious beings or of a non-material cause of material beings. But we have agreed in the interests of simplicity to say that both the one conscious cause of non-conscious beings and the one non-material cause of material beings are the same being as the one uncaused cause of caused beings. And if it is inconsistent to say that there is an explanation for the existence of an uncaused being then it is equally inconsistent to say that there is an explanation for the existence of an uncaused being which is conscious and non-material.

But there are other difficulties. Consider another explanandum: the non-emptiness of the class of conscious beings. Why should we not also infer that there is a single non-conscious being which causes there to be at least one conscious being, and identify this non-conscious cause with the uncaused cause of caused beings? Our uncaused cause of caused beings has however already been identified with the non-material cause of material beings, and it is hard to see how a causally efficacious non-conscious being can be anything but material.

To cope with this difficulty, we can distinguish between A-conscious beings, which are always directly aware of themselves, and B-conscious beings, which are at least sometimes conscious but not always directly aware of themselves. Human beings are B-conscious beings, and our principles allow us to infer that there is a single non-B-conscious being which explains the non-emptiness of the class of B-conscious beings. Nothing now prevents us from identifying this non-B-conscious being both with the uncaused cause of caused beings and with the non-material cause of material beings. A causally efficacious non-conscious being may have to be material. But a causally efficacious non-B-conscious being may perfectly well be non-material. A non-B-conscious being is either never conscious or always directly aware of itself. It is, in other words, either never conscious or an A-conscious being. It it is never conscious it may have to be material. But if it is an A-conscious being it may be non-material. Considerations of simplicity do indeed positively require us to make the double identification, and thus to assume that it is an A-conscious being that is the non-B-conscious cause of B-conscious beings and the non-material cause of material beings. Can we sabotage this reasoning by inferring the existence of a single B-conscious being which explains the non-emptiness of the class of A-conscious beings? No, because without the reasoning just outlined we do not even know that the class of A-conscious beings is non-empty.

The most serious difficulty is, however, yet to come. It is that taken together our principles prove too much. Since something exists and there are no unicorns, the class of non-unicorns is non-empty. So, given our two principles, there is at least one causally efficacious unicorn which causes there to be non-unicorns. How can we avoid such absurdities? As I will later argue, Sufficient Reason should be left alone. We must, then, modify Exclusion.

There is I think something clearly right about the general idea which underlies the Exclusion, namely that to explain why there are any F's at all we must appeal to the causal efficacy of something which is not an F. The unicorn example shows that if we want to combine this idea with Sufficient Reason then we shall have to restrict the permissible values of F. But, given that Exclusion got something right, we must be careful not to overdo the restrictions. A first step would be to distinguish between purely and partly negative properties: to be a non-unicorn is to have a purely negative property, while to be white and a non-unicorn is to have a conjunctive property which is only partly negative. We could then go on to modify Exclusion so that it no longer applies to classes defined in terms of purely negative properties but still applies to classes defined in terms of properties which are only partly negative. This gives us:

E* For any class which is not defined in terms of a purely negative property, if there is an explanation for the non-emptiness of that class, then there is at least one non-member of that class which causes it not to be empty.

Since the class of non-unicorns is defined in terms of a purely negative property, the conjunction of E* and Sufficient Reason will not commit us to the absurd conclusion that if there are any non-unicorns then there is also at least one causally efficacious unicorn. Since to be white and a unicorn is to have a conjunctive property which is only partly negative, E* together with sufficient reason will allow us to conclude white non-unicorns then there is a causally efficacious entity which is either non-white or a unicorn. But this is a conclusion which is odd rather than absurd.

How will our cosmological argument be affected if it is E* rather than unmodified Exclusion that we combine the Sufficient Reason? The class of B-conscious beings is defined in terms of a property which is partly but not purely negative property: a B-conscious being is not defined simply as a being which not always directly aware of itself, but rather, as a being which, as well as not being always directly aware of itself, is, positively, sometimes conscious. The class of material beings is not defined by an even partly negative property. Nor is the class of caused beings. Nor is it inconsistent to suppose that the non-emptiness of any of these three classes has an explanation. We can then use Sufficient Reason and E* to infer that there is at least one non-B-conscious being which causes there to be B-conscious beings, at least one non-material being which causes there to be material beings, and at least one uncaused being which causes there to be caused beings. As before, considerations of simplicity allow us to infer that there is a single, A-conscious, non-material, uncaused cause. Can we infer as well that this being is omnipotent and eternal? Since ‘not omnipotent’ is a purely negative property we cannot employ our two principles to deduce from the non-emptiness of the class of beings that are not omnipotent that there is at least one omnipotent being. And since ‘not eternal’ is also purely negative, there is a similar obstacle in the way of deducing that there is at least one eternal being from the non-emptiness of the class of beings that are not eternal. To solve the problem we substitute for ‘not omnipotent’ the partly positive ‘powerful but not omnipotent’, and for ‘not eternal’ the partly positive ‘temporally located but not eternal’.

Why should we accept the two principles here applied? As already noted, E* attempts to preserve as much as possible of the plausible general idea that to explain why there are any F's at all we must appeal to the causal efficacy of something which is not an F. That seems a sufficient recommendation. But what of Sufficient Reason? Natural theologians and other metaphysicians do often insist that something more or less like it is a presupposition of all scientific or common sense enquiry.Footnote 2 This seems unsatisfactory. To presuppose a proposition is indeed not necessarily even to believe it. It can be merely to assume its truth for the purposes of some action or general policy. I end by sketching out an argument for Sufficient Reason. In this argument I refer to the principle as SR.

Let M stand for ‘it is logically possible that’, Ep for ‘there is an explanation for the truth of p’, and H for the negation of SR. SR says that for any true p, if MEp then Ep. So H says that for some p, p & MEp & not-Ep, and we can take, as a witnessing instance of H, H*: q & MEq & not-Eq. We now have the following argument for not-H*, and hence for not-H and for SR.

  1. (1) H*

  2. (2) For all p, if p then either MEp or not-MEp

  3. (3) Either MEH* or not-MEH*   from (1) and (2)

  4. (4) Not-MEH*

  5. (5) If H* then MEH*

  6. (6) Not-H*   from (1), (3), (4), (5)

Why (4)? If MEH* then ME (q and MEq & not-Eq). Explanation is dissective: necessarily if there is an explanation for a conjunction there is an explanation for each of the conjuncts. So if MEH* then M(Eq and Enot-Eq). But explanation is factive: Ep entails p. So if MEH* then, absurdly, M(Eq and not-Eq).

Why (5)? H* has three conjuncts: q, MEq, and not-Eq. So if not-MEH*then either (i) not-MEq, or (ii) not-ME MEq, or (iii) not-ME not-Eq. If H* then (i) is false: MEq is an actual conjunct of H*. So if H* and not MEH* either (ii) or (iii). If H* then (ii) seems false. If, as H* says, MEq, it should be possible to explain the truth of this just by describing how Eq is possible. (iii) also seems false. If there is no explanation for the truth of q, then it is at least possible that the explanation for this explanatory void is that although the truth of q is not explained by the creative action of a god or superhuman being still the action of such a being explains why the laws of nature lack the scope for there to be a nomological explanation for q's truth.Footnote 3,Footnote 4

References

1 While Aquinas often says that God's nature is his own being, suum esse, he also often says that God is ipsum esse. For references see Kretzmann, Norman, The Metaphysics of Theism (Oxford: Oxford University Press, 1997), 127, n 14Google Scholar. Kretzmann thinks that when Aquinas says that God is ipsum esse, being itself, he is suggesting that God is nothing but existence, and is open to the objection that nothing subsistent could be just existence, that a merely existent substance is too thin to be possible. (The Metaphysics of Theism (Oxford: Oxford University Press, 1997), 127) The objection is developed by Hughes, Christopher, On a Complex Theory of a Simple God (Ithaca: Cornell University Press, 1989)Google Scholar, ch.1. Gilson seems by contrast to think that though we cannot conceive of being as anything other than the being of something, of an existent, the reality is otherwise, and it is just because the reality is otherwise that God is unknowable. The unknowability of God is based on the fact that ‘the intellect is not able to represent to itself the quiddity of the act of esse except under the form of the existent that it causes to exist.’ (Gilson, E., ‘Propos sur l'être et sa notion’, in Piolanti, A. (ed.) San Tommaso e il pensiero moderno (Citta Nuova: Roma, 1974), 16Google Scholar). To say that God is ‘beyond being’ is perhaps to say that ‘God exists’ is in some sense reducible to the fact that ethical requiredness, itself not existent, is nevertheless creative, or to the fact that when there was nothing its being better for there to be something itself ensured that something came to be. John Leslie develops a doctrine on these lines in ch. 8 of his Universes (London: Routledge, 1989).

2 For example, Kretzmann attributes to Aquinas, and himself accepts, a cosmological argument which requires the principle ‘Every existing thing has a reason for its existence either in the necessity of its own nature or in the causal efficacy of some other beings.’ This he calls (PSR2). Here is his justification for believing (PSR2). ‘Not only the history of science but even a fundamentally rational, attitude toward ordinary reality presupposes (PSR2). And since there is no ordinary existing thing about which we could tolerate the blithe announcement that there simply is no reason for its existence, rationality forbids our abandoning the principle when the existing thing in question is extraordinary or all-pervasive a thing such as the universe, or matter.’(‘Aquinas's Disguised Cosmological Argument’, in Jordan, J. and Howard-Snyder, D. (eds.), Faith, Freedom and Rationality (Lanham: Maryland, 1996), 200Google Scholar).

3 Gale and Pruss have constructed a cosmological argument which employs S-PSR Necessarily, for every contingent proposition, p, if p, then there is an explanation for p. And, as evidence for S-PSR, they cite W-PSR Necessarily, for every contingent proposition, p, if p, then it is logically possible that there is an explanation for p, See M. Gale, Richard and Pruss, Alexander R., ‘A new cosmological argument’, Religious Studies 35 (1999), 461–476CrossRefGoogle Scholar. On plausible assumptions, W-PSR entails S-PSR: see Oppy, Graham, ‘On “a new cosmological argument”’, Religious Studies 36 (2000), 345–353CrossRefGoogle Scholar. Is W-PSR true? That seems doubtful: see Daley, Kevin and Clifton, Rob, ‘Insufficient reason in the “new cosmological argument”’, Religious Studies 37 (2001), 488–90Google Scholar, Gale, and Pruss, , ‘A response to Oppy, and to Davey and Clifton’, Religious Studies 38 (2002), 89–99CrossRefGoogle Scholar, and Oppy, , Arguing about gods (Cambridge: Cambridge University Press, 2006)CrossRefGoogle Scholar. My SR is, needless to say, not the same as W-PSR. For another cosmological argument, different from the one I have defended, but employing a principle which does seem to be the same as PSR*, see Pruss, ‘A restricted Principle of Sufficient Reason and the cosmological argument’, Religious Studies 40 (2004), 165–179.CrossRefGoogle Scholar

4 Thanks to Graham Oppy for comments on a previous version.