In questioning whether there exist abstract entities (abstracta) it would be helpful to have a reasoned position. Those that wish to posit such entities as well as those that wish to deny them need to give principled reasons – why do certain entities fit into our ontological categories at all? By abstract entity I mean those of two varieties: Platonic and Aristotelian. As controversial as it may be, I shall distinguish these by their ability to enter into causal relations. Platonic abstracta cannot enter into causal relations, Aristotelian abstracta can.There is then a clear and simple way to adjudicate the existence of abstracta: the Eleatic principle. This states, simply, that what is real must enter into causal processes in some way. David Armstrong has championed a view such as this, with the result that there are no Platonic abstracta but rather there are Aristotelian universals. Recent work has shown, however, that the Eleatic principle seems hopelessly inadequate: it presupposes a contentious global causal epistemic theory. I propose, however, that this charge is only half accurate: if a philosopher is a theist then he has good reasons to think the principle true – but not because of his epistemic concerns. The claim here, then, is that Armstrongian-style Eleatic sympathies can be defended if one presupposes theism.
The Eleatic Principle is an attempt to put limits to the scope of reality by having causal activity as a necessary, and not merely sufficient, criterion for being real. Following Mark Colyvan it can be formulated thus:
EP: An entity is to be counted as real if and only if it is capable of participating in causal processes.
Clearly entering into causal processes would be sufficient for being real – how else would it enter into said processes? The question of the necessity of causal participation is intended, by Armstrong and others, is intended to be a principled means to limit the range of one’s ontology and the means of sorting out ontological categories. This way of delimiting the real, however, seems to presuppose at every term a highly contentious (and probably false) global causal epistemic theory. Strictly speaking, it is a metaphysical thesis (see Armstrong’s comments on there being no good reason to posit causally inert entities given that they do no explanatory work). This metaphysical thesis is merely prejudice, however, without the epistemic thesis giving us reason to believe that all entities must enter into causal processes in order to be known. The epistemic thesis is then the most important side of EP. It runs something like the following: count no entity as real if it is a-causal, given that we would have no epistemic access to it – we cannot know about it. This global claim has two crucial setbacks. Firstly it is decidedly anthropocentric. It is our perception of causal processes that seems to set the bounds of ontology, or the limits of our imagination in conceiving causal connections. Why, however, should human abilities and intelligence be the mark of the real? Secondly, it seems to get the wrong results about clear examples (e.g. planets and stars outside our light cone do not causally interact with us – they do not cause anything we are aware of – and so would not be real). Hence, the verdict seems to be that EP requires justification via a causal theory of knowledge, which leaves out too many real entities and, further, a causal theory would be no reason for justified belief and so there is as yet no reason to believe it necessary for justified belief concerning ontological categories.
Very well and all good, but the Eleatic Stranger has at least one good response that can put EP back in play while avoiding the above-mentioned troubles. If one were a theist then EP makes good sense and has excellent reasons. For, the theist has prima facie reason to be worried about Platonic abstracta and, as such, has reason to exclude them from one’s ontology. But, seeing that the difference between the types of abstracta is some being causally interactive and others not – the latter being Platonic – if the theist has reason to exclude Platonica then the theist has reason to exclude entities incapable of participating in causal processes. Whether this a-causal nature of Platonica is what many philosophers mean by abstract entities or not is actually not vital. This is a stipulative claim: divide abstracta into the causally connected and the a-causal. It does seem, however, that at the very least Peter van Inwagen would agree with this bifurcation. The Eleaticist wants to deny the existence of the a-causal. Indeed, it will be because of their inability to enter into causal relations that the Eleaticist-cum-theist rejects them, but on entirely different principled grounds. It is key in discussions of causal idleness that one not fall into the anthropomorphic tendency of denying entities we do not enter into causal relations with – that is the lesson of the above worries. The theist, however, is not concerned with our causal relations but rather God’s. If an entity does not enter into causal relations with God then, more than plausibly, it does not exist. This argument depends upon features of God that must be defended, but I shall only give a brief sketch.
For the theist God is the absolute limiting case – and the ontological ground of all that is distinct from himself. That is one way to summarize a pair of fundamental tenets of theism: divine a seity and divine sovereignty (AS). This can be formulated in the following way:
AS: (1) God exists independently of all else distinct from himself (i.e. God does not depend on anything distinct from himself for existence), and (2) All that is distinct from God is created by God and so depends upon God for existence.
AS putatively comes into conflict with the existence of Platonic abstracta. This is so, given that these abstracta do not enter into causal relations (via the stipulation above). If there are entities that do not, indeed cannot, enter into causal relations or processes then God cannot create them. If they exist then they do so necessarily (a plausible way of understanding the existence of something that cannot be caused to be and yet exists) and are distinct, independent, and uncreated. If they were not so, then the theist runs into the problem of God creating his own nature and, hence, creating himself. Hence, taking Platonica as anything other than a-causal leads to immense bootstrapping concerns that, to date, has not been satisfactorily solved.Any theist then who is also a Platonist should be a traditional one. Traditional, or what van Inwagen calls free, Platonism, however, cannot answer the following question (which is the putative conflict with AS above):
PC: How could a necessary entity, such as Platonic abstracta, depend upon God such that God creates them?
Dependence upon God such that God creates them is a causal relation – in some way that entity must enter into causal processes related to God. If this were not so then the fundamental tenet AS breaks down: something distinct from God would exist that is not dependent upon God for existence. In other words, God would not have created all that exists. Holding to Platonica thus directly violates a central tenet of theism. If there are a-causal entities then, trivially, they cannot be created by God since creation is (at least) a causal relation. Hence, if there are a-causal entities God does not exist – at least in the way required by theism.PC is a denial of AS.
It should be clear how a theist has reason to be wary of a-causal entities. Prima facie, they are antithetical to his very theism. A theist then has excellent reason to hold to an improved version of EP:
TEP: An entity is to be counted as real if and only if it is capable of participating in causal processes bottoming out in God.
This Theistic-Eleatic principle affirms that all that is distinct from God must be created – that is what is meant by participating in causal processes bottoming out in God. Casting the Eleatic principle in this light neatly avoids the worries of a causal epistemic theory since it is not us that are the measure of ontology. The limiting reason to believe in something is the limiting case: God. Hence, there is a way out of the simple stipulative prejudice that Armstrong falls into with his appeal to naturalism in science, a point made by Alex Oliver when he notes that such naturalism requires the epistemic argument that is so repugnant. Notice further that Aristotelian abstracta are not affected by these worries – they canenter into causal processes. As such they can be created, not worrying the theist, and are at least in principle causally accessible to mankind.
What this allows then is that the best way to be an Armstrong-type Eleaticist is to be a theist. This has some immediate benefits, such as the ability of properties to come into existence (one way would be through being created). By placing the limiting reasons to believe in something in God rather than in our limited causal epistemic framework we have good reason to deny an entire class of entities: namely, the Platonic ones. Abstract entities, if they do exist, are Aristotelian in nature. This TEP approach avoids both problems with EP; it is neither anthropocentric nor does it cause us to deny such obvious existents as stars outside of our light-cone. A further immediate benefit then is the realization that naturalism is not enough for delimiting the real – although a ‘naturalism’ combined with TEP, such that one can keep inference to the best explanation of the commitments of the best scientific theory, seems entirely compatible. The measure of the real, then, is fundamentally: could God have created it. This does not answer every question of ontology but at least it makes credible sense out of the plausible intuition that reality is not lazy. As Graham Oddie puts it, characterizing Armstrong, “respectable entities work for their living, and there is no social security.”Given theism, explanation of ontology does involve causation – but causation in relation to God and not us.
Armstrong, David. A Combinatorial Theory of Possibility. Cambridge: Cambridge University Press, 1989.
Colyvan, Mark. “Can the Eleatic Principle be Justified?” Canadian Journal of Philosophy 28, no. 3 (1998): 313-336.
Girwarnauth, Samuel. “No Platonism Given Theism: God and the Problem of Abstract Objects.” Forthcoming?
Gould, Paul. “The Problem of God and Abstract Objects – a Prolegomenon.” Philosophia Christi 13, no. 2 (2011): 255-274.
Oddie, Graham. “Armstrong on the Eleatic Principle and Abstract Entities.” Philosophical Studies 41 (1982): 285-295.
Oliver, Alex. “The Metaphysics of Properties.” Mind 105 (1996): 1-80.
van Inwagen, Peter. “God and Other Uncreated Things.” in Metaphysics and God, ed. Kevin Timpe. London: Routledge, 2009, 3-20.
 Whatever one wants to call abstract, the claims made herein should fit.
 See Peter van Inwagen, “God and Other Uncreated Things.” in Metaphysics and God, ed. Kevin Timpe. London: Routledge, 2009, 8. There may also be concerns of abstracta being within or without of space-time, but I set these aside as less important.
 Mark Colyvan, “Can the Eleatic Principle be Justified?” Canadian Journal of Philosophy 28, no. 3 (1998): 314.
 David Armstrong, A Combinatorial Theory of Possibility. Cambridge: Cambridge University Press, 1989, 8.
 Alex Oliver, “The Metaphysics of Properties.” Mind 105 (1996): 8.
 Where ‘a-causal’ means not capable of participating in causal processes.
 See Mark Colyvan, “Can the Eleatic Principle be Justified?, 6, 14.
 Seeing as how both Socrates and Plato seemed to be theists themselves, this also has the nicety of fitting historically.
 Samuel Girwarnauth, “No Platonism Given Theism: God and the Problem of Abstract Objects.” Forthcoming, 2.
 For a discussion of the various options for the Platonist, including the option of created Platonica, see Samuel Girwarnauth, “No Platonism Given Theism: God and the Problem of Abstract Objects,” 4-9.
 See Gould, Paul. “The Problem of God and Abstract Objects – a Prolegomenon.” Philosophia Christi 13, no. 2 (2011): 255-274, for an excellent discussion of the bootstrapping problem caused by non-traditional Platonisms.
 Of course, by theism here I mean classical theism.
 Alex Oliver, “The Metaphysics of Properties,” 8.
 At least, they can by stipulative definition.
 Graham Oddie, “Armstrong on the Eleatic Principle and Abstract Entities.” Philosophical Studies 41 (1982): 286.