Abstract
The Platonic theist Peter van Inwagen argues that God cannot create abstract objects. Thus, the quantifier ‘everything’ in traditional statements of the doctrine of creation should be appropriately restricted to things that can enter into causal relations and abstract objects cannot: ‘God is the creator of everything distinct from himself…that can enter into causal relations.’ I respond to van Inwagen arguing that he has provided no good reason for thinking abstract objects must be uncreated. And if this is the case, then there is no good reason to think that God cannot create abstract objects.
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Notes
Subsequent reference to this essay will be made parenthetically in the text.
Van Inwagen’s claim can be understood as an application of his ‘modal skepticism’ to the question of God’s relationship to abstracta. While we can (and do) make true modal judgments in ordinary contexts (e.g., we truly judge that ‘the table could be moved two feet to the left’), we have reason to be less confident about our modal judgments when engaging in armchair philosophy about propositions remote from the concerns of everyday life. Even more so when we can’t make sense, as van Inwagen will argue, of the claim that God creates abstract objects. See van Inwagen (1997) for more on his understanding of modal judgments.
I shall deny the entailment by examining the concept of ‘necessity’ given current possible worlds semantics, whereas Swinburne denies the entailment in order to make room for the Son and Holy Spirit as created (by the Father) yet necessary beings. See Swinburne (1994, 185).
In a more recent paper, van Inwagen claims that all causal discourse is to be understood in terms of causal explanations, explanations that answer questions that begin with ‘how’ such as ‘How did Winifred die?’ or ‘How did the lion escape from its cage?’ See van Inwagen (2012).
That is, all properties are exemplified by concrete objects, or, for properties of properties, a descending chain of properties that bottoms out in a concrete object.
Assuming all concrete objects other than God are contingent beings.
See McCann (2012) where he argues that in fact God does create abstract objects by creating the concrete objects in which they are exemplifications: ‘all of creation is produced in one fell swoop, and the natures of things, along with the entire Platonic menagerie implicit in them, are created in their exemplification—that is, as manifested within the concrete reality that is the temporal world’ (2012, 201). McCann endorses a near cousin of (S1):
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(S1*) For all x, if x is an abstract object, God caused x if x is (i) a nature of a concrete object created by God, or (ii) an implication of a nature of a concrete object created by God.
I shall not pursue (S1*). It is an improvement over (S1) since it does not require a sparse theory of properties, still abstract objects are contingent on this account; hence, I set it aside.
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An attempt to refurbish this line of thinking using the tools of contemporary metaphysics and logic has been set forth in Thomas V. Morris and Christopher Menzel (1987).
Thus Davis: ‘Propositions are mental effects…propositions have parts, those parts are best construed as ideas, and their being properly related (that is, “fitted into” truth claims) requires a mental arranger…God produces [propositions]; for indeed, they are his Thoughts’ (2011, 298 & 303); And Plantinga, regarding propositions: ‘these objects can enter into the sort of causal relation that holds between a thought and a thinker, and we can enter into causal relation with them by virtue of our causal relation to God. It is therefore quite possible to think of abstract objects capable of standing in causal relations’ (1993, 121). See also Plantinga (2011, 32).
See Plantinga (1974, 44–45) where he explicates the notion of possible worlds in terms of maximal states of affairs.
For a classic treatment of the semantics of modal talk in terms of possible worlds, see Kripke (1971).
See Kit Fine (1994), where a number of cases are provided for thinking that modal facts about some object x are distinct from its essentialist facts. For example, it is possible for two philosophers to agree on all the modal facts regarding the relationship between a person, his body, and his mind (e.g., necessarily, a person just has one body and one mind, etc.) and still disagree on the essential properties of persons, bodies and minds (e.g., philosopher A thinks persons are essentially immaterial minds that happen to have bodies, philosopher B thinks persons are essentially bodies and minds are identical to brains, etc.). I shall argue that it is possible to exist necessarily (SN) without existing essentially (NN). Thanks to an anonymous referee for pointing me to the Fine article. See also McCann (2012, 235) where it is argued that essential existence doesn’t entail necessary existence.
Thanks to Paul Draper for this point.
An anonymous referee objects: ‘the conclusion of [this] argument seems to be obviously false (i.e., it seems manifestly true that if something could fail to exist, then it exists in every time).’ Response: Again, modal facts are distinct from essentialist facts—all the modal facts entail here is the existence of x in every possible world, not the existence of x at every time in every possible world. It is entirely consistent with possible world semantics to say ‘x exists in every possible world’ and to deny that x essentially exemplifies (in every possible world) the property is everlasting. A final objection: ‘x exists necessarily’ entails not (3), but (3*):
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(3*) ‘x is timeless.’
Response: This entailment is most plausible when considering abstract objects, and perhaps this is where the supposed entailment gets its force. But again, the modal facts concerning x’s necessary existence do not entail any essentialist facts regarding x’s temporal mode of being. If abstract objects are timeless, it is not due to their necessity; rather it is due to the fact that they are essentially immutable, incapable of intrinsic change. That this entailment between necessary existence and timelessness does not hold can be seen from the plausible accounts (cited above) of an essentially temporal God, a God that exists necessarily.
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John Pollock explicitly defends this intuition in his (1984, 151–153). I am not here endorsing a counterfactual account of causation. Rather, I am asserting that a causal claim will be vacuous, and so defeated, were this entailment denied. On the other hand, a counterfactual analysis of causation will reduce causal dependence to counterfactual dependence. I am simply reporting the pre-philosophical intuitions of many philosophers, as summarized by James Woodward (himself an anti-reductionist regarding causation):
The suggestion I want to make is that to the extent that commonsense causal judgments are unclear, equivocal, or disputed, it is better to focus directly on the patterns of counterfactual dependence that lie behind them—the patterns of counterfactual dependence are, as it were, the ‘objective core’ that lies behind our particular causal judgments, and it is such patterns that are the real objects of scientific and practical interest (quoted in John Carroll (2010, 292)).
See David Lewis (1973) and Robert Stalnaker (1968). Matthew Davidson (1999, 283) explicates the Lewis-Stalnaker semantics for counterfactuals as follows (where ‘>’ is used for counterfactual implication):
‘A counterfactual (p > q) is true in the actual world if and only if (i) p is necessarily false or (ii) a world where (p&q) is true is closer to the actual world than any world where (p & ~ q) is true.’
Granted, (S3) does not obviously satisfy C1, so it would need to be filled in a bit, but minimally, satisfying C2 gets us going in the right direction.
In Leftow (1988), Brian Leftow also has provided an alternative semantics for so-called counterpossibles such as (5) and (6) (i.e., counterfactual conditionals with impossible antecedents). Recently, Leftow defended this earlier paper against objections from Richard Brian Davis in Leftow (2006). However, in the years since he wrote the 1988 paper, Leftow’s view of abstract entities has changed considerably. He now is inclined toward anti-Platonism and fictionalism about worlds and hence doesn’t employ the null-world semantics that he originally offered (and recently defended against charges of semantic collapse from Davis) in articulating his own current views on counterpossibles. Still, a Platonic theist could employ his so-called null-world semantics if desired.
Some think the second strategy the only possible way to explicate the causal dependency between God and abstracta. For example, after an extended discussion of the possibility of employing a counterfacutal analysis of causation to God’s creating abstracta, Matthew Davidson states, ‘if any reductive analysis of causation would capture the causal relationship between God and abstracta, it would be a counterfactual analysis…But, since not even [a counterfactual analysis] works as a reductive analysis, it seems that no reductive analysis of the causal dependence of abstracta on [God] can be given’ (Davidson 1999, 286). So too Scott Davison: ‘I am inclined to think that no counterfactual with impossible antecedents express important metaphysical connections, and hence (for reasons of systematicity and convenience) that all of them are vacuously true. In part, this is because I can’t think of any way to characterize the purported asymmetric “connection” between antecedent and consequent which would distinguish the “good” from the “bad” counterfactuals with impossible antecedents’ (Davison 1991, 491). See also Ernest Sosa and Michael Tooley (1993) for discussion of the difficulties in providing a reductive analysis of causation.
Typical arguments for anti-reductionism involve (1) detailing the repeated failures of reductive analysis, (2) the fact that there is a sparse base of non-causal concepts that can be employed in providing a reductive analysis, and (3) the case of preemption. See John Carroll (2010).
Van Inwagen (2012) remains unimpressed by contemporary attempts to define causation. Still, he thinks causal explanations are possible and that such explanations depend essentially on causal verbs. If this is not an endorsement of anti-reductionism, it is (minimally) consistent with it.
Objection: If God is the creator of all free abstract objects, then universal possibilism is true. If triangularity is created by God, then triangles could have been other than they are. Response: The objection is based on a mistake, that of thinking we can speak sensibly of possibilities with respect to free abstracta prior to God’s creation of such entities. But, if God is the creator of free abstracta, then prior to God’s creative activity there was nothing to be said about triangularity or any possibility regarding it. See McCann (2012, 211), Leftow (2012, 272–98), and Morris and Menzel (1987, 168–72).
Granted, there are other issues looming in the background that would need to be addressed in articulating a robust doctrine of God’s creation of abstract objects, including providing an explication of eternal creation—for in the case of God creating everlasting abstract objects, the cause is not temporally prior to its effect. This topic would require another paper, but for now let me state that many contemporary philosophers working on the metaphysics of causation agree that causation need not involve reference to the relation of temporal priority. Indeed contemporary discussions of causal asymmetry deal routinely with cases in which cause and effect are simultaneous and, we are told, physics takes seriously the possibility of backwards directed time travel and the accompanying backwards directed causation. See John Carroll (2010), ‘Anti-reductionism,’ and Michael Huemer and Ben Kovitz (2003).
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Acknowledgments
I wish to thank Richard Brian Davis and an anonymous referee for many insightful comments of an earlier draft of this article.