In earlier posts I briefly presented both St. Augustine’s (see here) and Leibniz’s (see here) arguments for God from eternal truth. Since I find this underrepresented approach to demonstrating God’s existence both fascinating and promising, I decided to present my own Augustine-Leibniz inspired divine conceptualist argument for consideration. This is a “conceptualist” argument since its strength revolves around seeing propositions as thoughts. It is “divine” since it seeks to establish propositions as divine thoughts. By no means am I claiming originality in this general approach: I have been influenced by Alvin Plantinga, Greg Welty, James Anderson, Edward Feser, Alexander Pruss, Quentin Smith, William Lane Craig, Brian Leftow, and others. But I think my formulation and exposition of the argument has some distinguishing virtues. After presenting the argument, I offer some brief comments on the more perplexing and/or controversial premises for clarification. I close with some objections and an overview of some benefits that might accompany a successful defense of the argument. The following is, despite its excessive length (feel free to just read the argument!), only a sketch and is very much a work in progress. So I welcome any comments or criticisms.
A Divine Conceptualist Argument for God’s Existence from Necessary Truth
Premise 1: There are necessary truths (for example, 2+2=4, cats are mammals, triangles have three sides) which are true in all possible situations or, to use possible world semantics, true in all possible worlds.
Premise 2: Truth is a property of propositions which are inherently intentional, that is, they are about whether some state of affairs obtains or not.
Premise 3: Inherently intentional propositions are best understood as thoughts.
Premise 4: Thoughts require a mind.
Premise 5: So necessary truths exist as thoughts of a mind or minds.
Premise 6: A necessary being is not dependent on anything else for its existence and can’t fail to exist.
Premise 7: A contingent being is dependent on something else for its existence and could have failed to exist.
Premise 8: Necessarily true propositions are thoughts of a contingent being(s) and/or a necessary being(s).
Premise 9: There were situations in which contingent beings with minds capable of forming propositions did not exist (such as the state of our universe before life developed).
Premise 10: So necessarily true propositions, which are true in all possible situations, cannot be thoughts of contingent beings.
Premise 11: So there must be either a necessary being or necessary beings whose thoughts account for necessarily true propositions.
Premise 12: A necessarily existing mind, being independent, would be purely actual (without potentials).
Premise 13: A being with no potentials would, besides being the ground for necessary truths, be at least omniscient, omnipotent, all good, unchanging, and immaterial.
Premise 14: There cannot be more than one purely actual being.
Premise 15: A necessarily existing being with thoughts that is unique, omniscient, omnipotent, all good, unchanging, and immaterial is best referred to as God.
Conclusion: Therefore God exists.
Comments on Premise 1
Those of us who believe in truth typically maintain certain truths are contingent which means they are, to use possible world semantics, true in some worlds and false in others. For example, the sentence ‘Dwight Goodyear was born in 1970’ expresses a true proposition about me that is only contingently true since we can easily imagine possible worlds where I was never born. It seems intuitively obvious to many that there are also truths which are narrowly or broadly necessary or true in all possible worlds (for an overview of narrow and broad necessity, go here). However, some do not share this intuition so it is important to offer some reasons in defense of necessary truths and to do so in a way that doesn’t presuppose the existence of God.
One way we can do this is by considering modal logic or that branch of logic that studies reasoning which employs, among other things, necessity and possibility. For example, axiom 5 of modal logic, an axiom included in the widely accepted system of modal logic S5, states that, as Raymond Bradley and Norman Swartz nicely put it in their book Possible Worlds (Hackett, 1979), “if a proposition P is possibly true, that is, if P is true in at least one possible world then the proposition that it is true in at least one possible world will be true in all possible worlds and thus necessary” (223-224). For example, the sentence ‘Dwight Goodyear was born in 1970’ expresses, as we have seen, a proposition that is contingently true (true in some worlds and false in others) and thus possible since something is possible if it is true in at least one world. But once we have this possibility in place then, according to S5, it implies the following necessary truth that holds in all possible worlds:
Necessary truth: ‘The proposition ‘Dwight Goodyear was born in 1970′ is true in at least one world.’
That is, it is true in every world that there is a particular contingent truth about me that holds in this world. So according to S5 all possible and contingent truths imply necessary truths.
Moreover, we should note that universal possibilism, the view that there are no necessary truths, appears to imply a necessary truth after all. To see this, first note that ‘It is not possible that P’ is logically equivalent to ‘It is necessary that not P.’ So if we take P to be ‘there are necessary truths’ then we would have this:
It is not possible that there are necessary truths = It is necessary that there are not necessary truths.
So claiming that necessary truths are not possible commits one to a necessary truth.
Now, it is a fact that plenty of non-theists from different philosophical backgrounds will accept this analysis. Thus it appears we can give a God-independent account of necessary truths by appealing to some fairly orthodox ideas in modal logic. If you want a few more God-independent reasons for believing in necessary truths go to my post here.
Comments on Premises 2-4
Our natural language uses the word ‘true’ as a description of something: true statements, true sentences, true beliefs, true intentions, and so on. So it seems plausible that if there are necessary truths then there exist entities that have the property of being true. Perhaps there can be, as Alexius Meinong (1853-1920) thought, non-existent things with properties. But surely it makes more sense to claim that only things that exist can bear properties. It also makes sense that entities that are necessarily true would have to exist necessarily. Alexander Pruss and Joshua Rasmussen, in their book Necessary Existence (Oxford, 2018), sum up these points nicely: “Consider the truth that 2+2=4. It’s necessarily true. But something can’t be true unless it exists. So anything that is necessarily true exists necessarily. So the object, the truth that 2+2=4, exists necessarily” (127). However, we might adopt the deflationary theory of truth and claim truth is not a property at all (for an overview of the theory with a list of objections, go here). But if we accept that truth is a property then we quickly discover one popular yet controversial candidate for truth-bearers in the philosophical community: propositions.
One plausible view of propositions starts by recognizing that they are intentional or about something. And this “aboutness” makes them the proper bearers of true and falsity insofar as truth claims are obviously about things and represent them to be a certain way. For example, the sentence ‘Augustine believed in eternal truths’ expresses in English a proposition which is about Augustine and can therefore be true or false. Now perhaps propositions can have representational properties intrinsically and independently of minds. But surely it is more natural to claim, following Franz Brentano who argued that all intentional phenomena are mental, that the intentionality of propositions shows they are mental in nature. And this, in turn, implies propositions require minds. Paul M. Gould and Richard M. Davis elaborate:
“And just as there cannot be thoughts without a thinker, ideas (which are nothing but materials for thinking) cannot exist apart from the minds that have them. But then what better explanation could there be for the orderly arrangement of ideas than the mental activity of thinkers? The obvious conclusion to be drawn here is that the things properly said to be true or false (propositions) actually result from mental activity – from the joining or separating of ideas….Thus it follows straight away that propositions are mental effects. For propositions have parts, those parts and best construed as ideas, and their being properly related (that is “fitted into” truth claims) requires a mental arranger.” (See Beyond the Control of God, ed. Gould, 58)
This view of propositions is called conceptualism which Quentin Smith defines as follows: “Conceptualism with respect to propositions is the theory that it is necessarily the case that propositions are effects of mental causes.” (Faith and Philosophy, Vol. 11, No. 1, 38). Conceptualism is to be distinguished from views that identify propositions with things which aren’t intrinsically about anything and therefore cannot be true or false (for example, sentences, abstract objects, properties, and facts). Beliefs are surely mental in nature and thus may look like promising candidates for being truth-bearers. But beliefs are best understood as attitudes towards propositions rather than being the bearers of truth and falsity themselves: if I believe 2+2=4 I have an affirmative attitude towards the proposition 2+2=4 (for an argument against the view that beliefs can be adequate bearers of truth, see my post here).
Intentionality can be a controversial topic and the above form of mental intentionality, since it is purposeful, is a form many philosophers hope to jettison from their world views which feature the non-teleological (non-purposeful) explanations of physics, chemistry, and biology. But to deny the existence of intentionality in the above sense appears to be self-defeating since the very act of denying the thesis that intentional mental states exist presupposes an intentional mental state toward that thesis. If the so-called denial is nothing but an effect of purposeless movement, akin to a set of words unintentionally formed by the falling of leaves onto the ground, then it is unclear how we are to construe it as a meaningful denial.
Comments on Premises 6 and 7
Premises 6 and 7 offer definitions: a necessary being is not dependent on anything else for its existence; a contingent being is dependent on something else for its existence. These definitions have the potential to get us into deep metaphysical waters. But Richard Taylor, in his book Metaphysics (Prentice Hall, 1992), offers a helpful elaboration which I think makes these premises plausible:
“A being that depends for its existence upon nothing but itself and is in this sense self-caused, can equally be described as a necessary being; that is to say, a being that is not contingent, and hence not perishable. For in the case of anything that exists by its own nature and is dependent upon nothing else, it is impossible that it should not exist, which is equivalent to saying that it is necessary. Many persons have professed to find the gravest difficulties in this concept, too, but that is partly because it has been confused with other notions. If it makes sense to speak of anything as an impossible being, or something that by its very nature does not exist, then it is hard to see why the idea of a necessary being, or something that in its very nature exists, should not be just as comprehensible. And, of course, we have not the slightest difficulty in speaking of something, such as a square circle or a formless body, as an impossible being. And if it makes sense to speak of something as being perishable, contingent, and dependent upon something other than itself for its existence, as it surely does, then there seems to be no difficulty in thinking of something as imperishable and dependent upon nothing other than itself for its existence.” (107-108)
Comments on Premise 12
Premise 12 introduces the concepts of potentiality and actuality and states that a necessarily existing mind would be purely actual or lacking in potencies. This is plausible since if it was partially potential then it would lose its necessary or independent existence in at least three ways: (1) its existence would be dependent upon the existence of its potential/actual parts thus making it contingent; (2) it would be composite and this composite would require a cause upon which it would depend making its existence contingent; and (3) it would be dependent upon external factors for the actualization of its potentials making it contingent upon them. Of course, we would have to accept the reality of potential and actual parts which are often construed as metaphysical parts along with distinctions like form/matter, essence/existence, substance/accident, and genus/species. The belief in metaphysical parts is certainly more controversial than the belief in physical parts. But I think in this case the distinction is warranted based on how the concept of potentiality, far from being some antiquated notion, can help us make sense of various dispositional analyses in both philosophy and science (as Barbara Vetter’s Potentiality: from Dispositions to Modality makes clear; for a summary and review, go here). Indeed, we may, as Aristotle points out in an important passage from his Metaphysics (Book Theta, Chapter 3), land ourselves in absurdity if we deny the existence of potentialities:
“There are some who say…that a thing can act only when it is acting, and when it is not acting it cannot act, e.g. that he who is not building cannot build, but only he who is building, when he is building; and so in all other cases. It is not hard to see the absurdities that attend this view. For it is clear that on this view a man will not be a builder unless he is building (for to be a builder is to be able to build), and so with the other arts. If, then, it is impossible to have such arts if one has not at some time learnt and acquired them, and it is then impossible not to have them if one has not sometime lost them (either by forgetfulness or by some accident or by time; for it cannot be by the destruction of the object, for that lasts for ever), a man will not have the art when he has ceased to use it, and yet he may immediately build again; how then will he have got the art? And similarly with regard to lifeless things; nothing will be either cold or hot or sweet or perceptible at all if people are not perceiving it; so that the upholders of this view will have to maintain the doctrine of Protagoras [at Metaphysics 1007b20–22 Aristotle attributes to Protagoras the thesis that “it is equally possible to affirm and to deny anything of anything”]. But, indeed, nothing will even have perception if it is not perceiving, i.e. exercising its perception. If, then, that is blind which has not sight though it would naturally have it, when it would naturally have it and when it still exists, the same people will be blind many times in the day – and deaf too. Again, if that which is deprived of potency is incapable, that which is not happening will be incapable of happening; but he who says of that which is incapable of happening either that it is or that it will be will say what is untrue; for this is what incapacity meant. Therefore these views do away with both movement and becoming. For that which stands will always stand, and that which sits will always sit, since if it is sitting it will not get up; for that which, as we are told, cannot get up will be incapable of getting up. But we cannot say this, so that evidently potency and actuality are different (but these views make potency and actuality the same, and so it is no small thing they are seeking to annihilate), so that it is possible that a thing may be capable of being and not be, and capable of not being and yet be, and similarly with the other kinds of predicate; it may be capable of walking and yet not walk, or capable of not walking and yet walk. And a thing is capable of doing something if there will be nothing impossible in its having the actuality of that of which it is said to have the capacity. I mean, for instance, if a thing is capable of sitting and it is open to it to sit, there will be nothing impossible in its actually sitting; and similarly if it is capable of being moved or moving, or of standing or making to stand, or of being or coming to be, or of not being or not coming to be.”
Comments on Premise 13
Some divine conceptualist arguments seek to only demonstrate a necessarily existing omniscient mind. But premise 13 attempts to establish other characteristics commonly associated with God in light of the connection between necessary existence and pure actuality. Of course, the nature of these characteristics and their relation to pure actuality would require an extensive defense. But the basic ideas are as follows: an independently existing and fully actual mind would (1) be omniscient (would know all true propositions) since any lack in its knowledge would imply the existence of potentials it doesn’t have; (2) would be omnipotent (would be able to do anything logically possible) since any lack in power would imply potentials or dependencies it doesn’t have; and (3) if being bad or evil is a privation or deficiency of goodness, then this being, having no potentials, deficiencies, or privations, would be all good (for my three post series on the privation theory of evil go here). Moreover, if change and material existence are inseparable from potentials then this being, which has no potentials, is (4) immaterial and (5) unchanging as well.
Comments on Premise 14
Premise 14 states there cannot be more than one purely actual being. There are various ways we can defend this premise. Here are a few:
(1) If there were more than one purely actual being then the same class of necessarily true propositions would exist in each of those minds. After all, each of these beings, not lacking anything, would know all the truth there is to know. But this multitude of classes would undermine the objectivity of truth which requires that for every proposition humans think there is only one such proposition (e.g., the Pythagorean Theorem). This reason harmonizes well with the argument’s emphasis on propositions and truth.
(2) Leibniz claimed there are necessary truths that are the outcome of relating other necessary truths together. After all, “these necessities can be combined, any one to any one, because any two propositions can be connected to prove a new one, when the means of joining them have been added” (see Leibniz: The Shorter Texts, 182). If we maintain, as we did above, that minds are necessary to establish propositional relations, then perhaps we can infer one being as the means for joining necessary truths together. As Leibniz put it in his work On the Ultimate Origination of Things: “Moreover, it [the ultimate source for the reality of eternal truths] can be sought in but one source, because of the interconnection among all these things [necessary truths]” (Hackett, 45). Robert Merrihew Adams, in his book Leibniz: Determinist, Theist, Idealist (Oxford, 1998), explains Leibniz’s position
“According to Leibniz’s argument, for any plurality, P, of (necessary) truths or natures, there necessarily exists a necessary truth, T, grounded in a relation, R, among all the members of P; in order to sustain T in being there must eternally and necessarily exist at least one mind that understand R. But a mind that understands R must be one that understand the members of P, a mind “in which [the idea of] the nature of the circle, the square, and the others is,” if those are the natures in which T is grounded; understanding all that, it will presumably be a mind that understands T itself. The conclusion of this argument is that for any plurality, P, of (necessary) truths or natures, there eternally and necessarily exists at least one mind that understands all the members of P” (182).
(3) It is simpler to posit one purely actual mind rather than many thus satisfying the principle of parsimony (entities are not to be multiplied beyond necessity).
(4) To distinguish more than one purely actual being would require that they be different and difference is grounded in what things lack (I can distinguish a red car from a black car because the red lacks black and the black lacks red). But a purely actual being lacks nothing. Therefore any claim that there is a multitude of purely actual beings must be mistaken: the so-called plurality would actually be the same in accordance with Leibniz’s Law (if, for every property F, if object x has F if and only if object y has F, then x is identical to y). Edward Feser, in his book The Last Superstition, provides a helpful elaboration: “[I]n order for there to be two (or more) purely actual beings, there would have to be some way of distinguishing them, some feature that one of them had that the other lacked…For to lack a feature is just to have an unrealized potentiality, and a purely actual being, by definition, has no unrealized potentialities. So if we said, for example, that one purely actual being was more powerful than another, and that that is what distinguished him from the other one, then we’d be saying in effect that the other purely actual being had failed to realize his potential for power as fully as the first had – which makes no sense given that we’re talking about a purely actual being, with no potentials of any sort” (97-98).
(5) And if we accept the distinction between essence and existence as implying real metaphysical parts then we can argue that this distinction wouldn’t apply to a completely actual being without parts. Such a being would just be its essence. But this would imply that such a being couldn’t be a particular example of an essence like a particular scalene triangle is an example of the essence of a triangle. Thus a purely actual being must be unique and can’t be one among others like a scalene triangle is one among others with the same essence. William Vallicella puts the point nicely: “God is necessary because he is simple and not because he exists in all metaphysically possible worlds. And while one may say that the simple God is or exists, God is not an existent among existents or a being among beings, but Being (esse) itself in its prime instance and in this respect different from every other being (ens). Unique in all these ways, God is uniquely unique. He is not unique as one of a kind, but unique in transcending the distinction between kind and member of a kind. God is unique in his very mode of uniqueness. The simple God, we could say, differs not only in his attributes, but also in his very ontological structure, from any and all created beings.” (see the introduction to his Stanford Encyclopedia of Philosophy entry on “Divine Simplicity” here).
We have already seen that the premises of my argument, while they introduce sensible ideas, definitions, and principles, nonetheless include controversial topics like the existence and nature of necessary truths, the nature of propositions, the nature of necessary and contingent being, the existence and nature of potency and actuality, and the nature of the divine attributes. Moreover, we can raise plenty of questions: How can God’s thinkings be propositions? Aren’t propositions those things which are thought rather than being thoughts themselves? If we think that God’s thoughts, like our thoughts, are concrete (capable of causal efficacy) then how can they be multiply-instantiable? If we don’t think they are multiply-instantiable then how would God’s thoughts be accessible to us so that we can express them and have attitudes towards them? Aren’t thoughts private? And if we can access God’s thoughts is there something heretical in the idea that we are doing so? If we think God has infinite propositions then how can we reconcile this rich mental life with the doctrine of divine simplicity? If God knows all propositions then does God think false propositions and immoral thoughts? If God is the ground of necessarily true propositions – say, the laws of logic – don’t we have to presuppose the existence of God as we formulate a divine conceptualist argument thereby begging the question? Could it be that propositions can be intentional but not mental in nature? Could it be that propositions are truth bearers but not representational? Could it be that propositions are not truth bearers and that truth is not a property at all? And if we think that true propositions don’t exist independently of God as objective things then do we run the risk of making truth arbitrarily grounded in God’s mind? Couldn’t God make 2+2=5 as easily as he could 2+2=4? If not, why exactly?
It appears we can find plausible and even convincing responses to many of these objections. I offer some responses in the benefits section and the comments section below. You can also consider plenty of responses in this paper in which Greg Welty and James Anderson respond to objections to their divine conceptualist argument here; in this downloadable paper in which Greg Welty responds to criticisms raised by William Lane Craig in chapter 5 of his book God Over All: Divine Aseity and the Challenge of Platonism (Oxford, 2016); and in chapter three of Edward Feser’s book Five Arguments for the Existence of God in which he responds to objections to his Augustine-inspired divine conceptualist argument (to name just a few resources). But clearly the above objections and others besides collectively pose a serious challenge to any defender of the argument. And we must keep in mind other related issues that are bound to arise such as how a necessary being relates to a contingent world, what we can really know about such a being, the evidential problem of evil, the hiddenness of God, and so on.
A Rationally Acceptable Argument for Some
I think it is safe to say my argument is not a rationally compelling deduction whose premises will be accepted by all rational persons upon consideration. Perhaps it has the potential to be rationally acceptable given a more thorough defense of the premises and a set of adequate responses to the above objections. Quentin Smith defines rational acceptability as follows: “An argument A for a thesis T is rationally acceptable (an no more) to x if and only if (1) A is not a rationally compelling F proof of T and there is no is no rationally compelling proof of not-T, (2) A appears sound to x even after x has considered possible objections to A and considered A’s relations to other relevant arguments which he accepts or rejects, and (3) x is rational with respect to A” (Faith and Philosophy, Vol. 11, No. 1, 47).
Here is a brief overview of some of the benefits that may come to those who find the argument rationally acceptable:
(1) We can make sense of the intuition that there are true propositions that are mental, intentional, and unchanging. In his dialogue On Free Choice of the Will (Macmillan, 1964) St. Augustine wrote: “If truth were equal to our minds, it would be subject to change. Our minds sometimes see more and sometimes less, and because of this we acknowledge that they are mutable. Truth, remaining in itself, does not gain anything when we see it, or lose anything when we do not see it” (67). If true propositions were to reside in our changing minds then truth would change which is absurd: our estimations of the truth change, not the truth itself. But, as Augustine pointed out, if truth resides in God’s mind then it can be as unchanging as the unchangeableness of God.
(2) We can account for how truth is something that exists independently of us which we discover rather than create: propositions are God’s thinkings which exist independent of human minds. In his book Actuality, Possibility, and Worlds (Continuum, 2011) Alexander Pruss elaborates: “If propositions are thinkings, then any necessarily existent proposition will have to, thus, be a thinking by a necessary being, and if God is the only necessary being, then it will have to be one of God’s thinkings. On orthodox views of propositions, all propositions are necessarily existent, and it is in any case plausible that at least the necessarily true propositions should exist necessarily. Thus, if the propositions are thinkings, they can only be God’s thinkings (209). Greg Welty provides a helpful elaboration as well: “Our mental tokens think God’s thoughts after Him, because they are attitudes to His thoughts (whether we are aware of this or not). The contents of our mental tokens are the (adverbially characterized) contents of divine mental tokens” (Beyond the Control of God, 187).” So according to this theory some of God’s thoughts are propositions and we can have attitudes to those propositions. We do not think these propositions the way God does: his first-person perspective on his thinkings is, of course, necessarily his and his alone. What we have are third-person perspectives on his thoughts. Likewise, God cannot have our first person perspectives and must adopt a third-person perspective on our thoughts. But the crucial thing to understand is that the propositional content of God’s thinkings is the same for both God and us.
(3) This shared content makes communication about the same propositions possible which seems to be required if we are going to have objective truth and avoid the pitfalls of relativism.
(4) We can make sense of the intuition that there are indeed an infinite number of truths. After all, God’s mind is omniscient and would know, for example, an infinite number of necessarily true mathematical propositions.
(5) We can understand how necessary truths can be relevant to us and our world by appealing to God’s intentionality and creative power. In Actuality, Possibility, and Worlds Pruss writes: “As for the question of how the propositions represent the world, the answer is that they do so by virtue of the intentionality of the divine mind” (210). He then connects this intentionality to God’s creative powers and truth: “Granted, propositions expressing modal truths are ideas in the mind of God. But what, we asked, makes these propositions true? The answer is that they are made true by the capabilities of the God whose action guiding ideas they are and by those beings that he might have created. What makes it true to say that it is possible for there to exist a world with unicorns is that the idea of such a world is an idea in the mind of an all-powerful God capable of acting on it and creating such a world” (222). Here Pruss is working with a common sense account of modality deriving from Aristotle who saw possibility as grounded in the prior actual powers of real beings. So, for example, the modal proposition “It is possible that Dwight Goodyear can paint a picture on August 15, 2023” would, if true now in 2020, be true because I have the ability to paint a picture on that day. But why should we delimit possibilities to those grounded in the actual powers of things in this universe? Isn’t it the case that possibilities far outrun such powers? After all, it certainly seems possible that the universe could have been 22 dimensions or, perhaps, that there might have been no universe at all. If we agree then we might find a theistic ground for global possibilities and possible worlds attractive. Pruss explains: “It is here that combining the Aristotelian account with Leibniz’s theistic story would solve the difficulties. On this combined account, there would be a God outside the universe…who has in his mind ideas of all kinds of possible worlds. We get to retain Leibniz’s intuition (very much in the Aristotelian spirit) that propositional-type entities can only exist in minds. But what we now add is the fact that this God is not just all-knowing but all-powerful. He is capable of putting his divine ideas into action. He can produce a 22-dimensional universe, not just think about one” (216).
(6) We can understand how there is an interrelated system of propositions since all truth is interrelated in God’s unique mind.
(7) Lastly, we can avoid having to posit, as a contemporary Platonist who is committed to the existence of abstract entities must, an infinite number of abstract entities to account for the infinite plenitude of truths independent of human minds. This is a boon for at least three reasons. First, abstract entities, as we have seen, don’t have intentionality and thus cannot be true or false insofar as they are not about anything at all. Second, how can we be causally connected to necessary truths if they are abstract entities with no causal efficacy? As Paul Benacerraf nicely put it: “To Platonism, necessary truths’ ontology is independent of thought and language and causally inert. As inert, it cannot affect us; as independent of thought and language, our access to these is not access to it. So we have no good account of how we could know necessary truths if they have Platonic ontologies: we can have an acceptable modal epistemology only by sacrificing Platonism” (see the second edition of Philosophy of Mathematics, edited by Benacerraf and Putnam, 403-420). And third, by positing one God with an infinite number of ideas we can reduce the number of ontological kinds to which we are committed. For example, instead of having minds, bodies, and abstract objects in our world view we can just have minds and bodies. So even if, somehow, one could make sense of abstract entities as causal agents with intentionality, we could still argue that divine conceptualism is preferable since simplicity is widely embraced as a desirable property of any explanation.