05 / 06

Necessary Beings by Bob Hale

William Lane Craig

Used by permission of Philosophia Christi 18 (2016): 246-51.


Bob Hale is one of the most important Platonists writing today. The unintended interface of his rich metaphysical theory of modality with theism is briefly explored.

Bob Hale undertakes to provide an account of the ontological foundations of modality with the technical rigor, thoroughness, and clarity characteristic of his work.  While Hale takes modality to be fundamental and irreducible, still he thinks that a good deal can be said by way of explaining the modalities of modal truths.   He defends what he calls an essentialist theory of modality, according to which metaphysical necessities have their source in the natures of things, and metaphysical possibilities are those left open by the natures of things (p. 253).

The book may be briefly summarized as follows:  In the long opening chapter “Ontological Preliminaries” Hale lays out his neo-Fregean approach to ontology, which prioritizes language as a guide to ontological categories and ontological commitment.  In the next two chapters Hale criticizes attempts to reduce or discount modality in favor of non-modal notions. In chapter 4 “Absolute Modality” Hale explains his fundamental modal notion of absolute necessity counterfactually:  a proposition p is absolutely necessary iff p would be the case no matter what else were the case.  In chapters 5-6, we discover that logical necessity is a species of absolute necessity.  The source of logical necessity is, not the meaning of words or concepts, but the natures of certain logical entities like conjunction and negation. Similarly, non-logical absolute necessities can be explained in terms of the natures of non-logical entities.  For example, arithmetic truths owe their necessity to the nature of the natural numbers together with the natures of the relevant properties, relations, and functions. Once it is recognized that an explanation of necessity may appeal to the natures of non-logical as well as logical entities, there is no limit to the kinds of entities to whose natures such an explanation may appeal.   For example, “Anything red is colored” is necessary in virtue of the nature of the property being red. The nature or essence of a thing (in the widest sense) is simply what it is to be that thing, what distinguishes that thing from every other thing.  So an essentialist explanation of necessity is one which holds that it is necessary that p because q, where q is a proposition which is true in virtue of the nature of some entities. 

In chapter 7 necessary beings—properties and numbers—are introduced.  Hale rejects as unsatisfactory the explanation that some entities exist necessarily just because it belongs to their nature to exist.  Rather objects like numbers exist necessarily in virtue of the existence of certain properties which themselves exist necessarily.  Hale argues that it belongs to the nature of a pure property (a property which is the semantic value of a predicate involving no singular terms) that it exists if it is possible that a suitable predicate exists and that since what is possible is necessarily possible, pure properties exist necessarily.  After an excursion into higher order logics in chapter 8 Hale turns in chapter 9 “Contingent Beings” to a defense of the position that some things exist contingently. In order to resist the Barcan Formula and Converse Barcan Formula, which lead, notoriously, to necessitism, the doctrine that no contingent beings exist, Hale makes the interesting move of adopting a negative Free Logic, which by rejecting the classical inference rules of Universal Instantiation and Existential Generalization, avoids the derivation of the Barcan formulae.  Hale does not advocate the use of an existence predicate in order to salvage revised versions of UI and EG, as do many Free Logicians; rather he stipulates that the classical rules hold only in the case of existence entailing contexts F(t), where t is a singular term.  For example, while “Pegasus is mythical” is not existence entailing, “Aristotle is philosopher” is.  So “Something is a philosopher” follows.  In chapter 10 Hale rejects the use of possible worlds in favor of possibilities and offers responses to those who for various reasons defend the truth of disjunctions without true disjuncts, a section relevant to the claim of some open theists that the Principle of Bivalence fails for future contingent propositions.  Finally Hale wraps up the book with a chapter on modal knowledge, in which he defends, against modal sceptics, our ability to grasp the essences of things, whether a priori or a posteriori.

There is a good deal to interest the philosopher of religion in Hale’s book.  His attempt to ground modalities ultimately in the nature of things contrasts sharply with Brian Leftow’s recent defense of theistic activism to ground non-logical necessary truths, as well as with what Leftow calls “deity theories,” which would ground modalities in God’s nature (God and Necessity, OUP, 2013). Deity theories technically fit Hale’s definition of an essentialist theory of modality (pp. 150-2), since they, too, ground necessities in the nature of some things, namely, in the nature of God. 

Theistic theories could be seen as extending Hale’s theory.  Hale simply stops once he has grounded a necessity in a non-divine thing’s nature. These constitute a base class of necessities which admit of no further explanation.  Hale explains,

If the aim were to explain (absolute) necessities in such a way as to leave no necessity unexplained, it could indeed be accomplished only by providing, for a sufficiently rich base class of necessities, explanations which themselves make no appeal to any necessities at all–that is, it would have to give a reductive explanation of at least some necessities, in which the explanans invoked only non-modal facts.  But. . . I do not believe that can be done, and I do not see essentialist explanations as a doom-laden attempt to do it.  Any true proposition about the nature of a thing–that it is true in virtue of X’s nature that j(X), say–is indeed necessary.  But its necessity cannot be explained.  It cannot be explained by appealing once again to the nature of that very thing, for that would be viciously circular; it cannot be explained by appealing to the natures of any other things, for that would both undermine the claim that j(X) is true in virtue of X’s nature, and be viciously regressive; and it cannot be explained in any other way. . . .

The point of the essentialist theory is not, then, to provide a reductive explanation of any necessities. It is, rather, to locate a base class of necessities– those which directly reflect the natures of things–in terms of which the remainder may be explained.  The kind of explanation it offers, then, is . . . one which exhibits the class of necessities as structured in a certain way, by identifying some necessities as basic or fundamental, and the rest as dependent, inheriting their necessity, ultimately, from necessities in the base class (pp. 158-9, my emphasis).

It seems to me that such a theory is perfectly compatible with a similar non-reductive grounding of the necessities about the natures of things in God’s nature or will.  A theistic theory simply goes one step further than Hale’s.  I see no reason to think that such a theistic theory would undermine the grounding of certain necessities in things’ natures by providing a grounding for truths about those natures; nor need such a theistic account be viciously circular, for it will also involve a base class of necessities which cannot be further explained.

Early in the book we find this intriguing footnote:

One reader for the Press thought that the complete absence, in a book on necessary beings, of any discussion of God at least noteworthy, if not regrettable.  The little I have to say on the matter is that it is, I hope, obvious that the kind of argument I give for the necessary existence of general properties and numbers does not lend itself to a proof of His necessary existence (p. 5).

That argument, as mentioned above, comes in chapter 7.  What strikes me as curious is that Hale’s argument there seems very similar to modal ontological arguments for God’s necessary existence.

In asking how the essentialist theory can explain the necessary existence of certain objects, Hale says,

I think it would clearly be unsatisfactory for the essentialist to try to explain this by claiming that it simply belongs to the nature of certain objects to exist–that whereas the nature of aardvarks, say, leaves it open whether there are in fact any aardvarks, it belongs to the nature of natural numbers to exist. . . . This claim is uncomfortably reminiscent of the notorious ontological argument for the existence of God. Even if there is no outright incoherence in the idea that existence can be part of a thing’s essence, this is a desperate move–it amounts to an invitation to accept necessary existence as a brute inexplicable fact (pp. 175-6).

Hale is evidently thinking of non-modal versions of the ontological argument, which infer that because God is by definition a necessary being therefore He must exist.  These versions of the argument are now defunct and have been replaced by modal versions, to which Hale’s argument for the necessary existence of pure properties bears a striking resemblance.  He offers a modal argument for the existence of pure properties based on the possibility of a predicate for which the property is the semantic value.  He explains,

It is sufficient for the existence of a pure property that there could be a suitably meaningful purely general predicate.  Given that the relevant kind of possibility is absolute, it follows that if it is indeed possible that there should be a suitable predicate, that is itself necessarily so—i.e. it is necessarily possible.  But if that is right, then the existence of any pure property or relation is always a matter of necessity (p. 167).

Thus, “The essentialist does not claim that existence is simply and irreducibly part of what it is for something to be a pure property or relation.  What he claims is that a pure property or relation just is, by its very nature, one for the existence of which it is sufficient that there could be a suitable predicate. . . .” (p. 176).

But doesn’t the natural theologian do something similar?  He does not infer God’s existence from the fact that necessary existence properly belongs to maximal greatness.  Rather he argues that it is sufficient for God’s existence that maximal greatness is possibly exemplified.  It seems to me that Hale’s argument just is a sort of modal ontological argument for properties.  The theist can say that the explanation of God’s necessary existence is that His nature is such that if it is possible then it is instantiated.

In any case, even if there were no explanation forthcoming of God’s necessary existence, that would not justify Hale in ignoring God as a candidate for a necessary being.  For it seems that God fits very nicely with Hale’s characterization of what it is to be absolutely necessary.  God exists would be true no matter what else were the case.  Therefore, God’s existence is absolutely necessary.

My personal interest in Hale’s book is his Platonism and its implications for God’s unique aseity.  Hale’s espousal of negative free logic shows that he takes first-order quantifiers to carry existential commitments.  So are we to think that all these abstract objects like the nature of conjunction and the nature of natural numbers really exist?  I think that the answer is, no.  For Hale has a very thin concept of existence.  Hale is quite forthright about his espousal of a lightweight Platonism that does not presume to make metaphysically heavy commitments.  The book’s opening chapter is quite helpful in this regard.  In section 1.12 on “The bearable lightness of being” Hale makes clear that it is sufficient for the existence of properties and objects in his sense that one can discriminate between the ontological categories under which things should be classified.  He explains,

The abundant conception of properties might just as appropriately be described as deflationary, or metaphysically lightweight. It takes as sufficient for the existence of a property what one might reasonably see as the bare minimum required to distinguish properties from entities of other categories–a condition which things of the appropriate sort, depending on the level of the property, may or or may not meet, either contingently or as a matter of necessity.  Briefly, properties are ways for things to be–ways things could be or, on the most abundant conception, could not be.

Modulo the small but important extra demand that (actual or possible) singular terms figure in some true atomic contexts, the conception of objects I am defending is equally deflationary or metaphysically lightweight.  In parallel with the abundant conception of properties, it takes as sufficient for the existence of an object what one might reasonably see as the bare minimum required to distinguish objects from entities of other categories–the possibility of being an object of identifying or individuating thought or reference (pp. 39-40).

On this lightweight view the Fountain of Youth is an object, since it is or can be an object of individuating thought or reference and so is not a property or relation.  Such an object therefore exists—not in a metaphysically heavy sense but in being the semantic value of a singular term.  The existence of abstract objects in this lightweight sense seems to me to pose no challenge at all to God’s being the sole ultimate reality.

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