Hume’s Lapse?

Hume famously divided knowledge into “relations of ideas” and “matters of fact.” In more modern terminology, he divided knowledge into the analytic a priori and synthetic a posteriori. This idea is captured by Hume’s fork in An Enquiry Concerning Human Understanding:

If we take in our hand any volume; of divinity or school metaphysics, for instance; let us ask, Does it contain any abstract reasoning concerning quantity or number? No. Does it contain any experimental reasoning concerning matter of fact and existence? No. Commit it then to the flames: for it can contain nothing but sophistry and illusion.

This fork was later adopted by the logical positivists and it was noticed that it was self-refuting because this fork is neither a relation of ideas nor a matter of fact; so, by its own criteria, it is nothing but sophistry and illusion—or meaningless.

I think I spotted another lapse in Hume. In A Treatise of Human Nature, Hume says:

To form a clear idea of anything, is an undeniable argument for its possibility, and is alone a refutation of any pretended demonstration against it.

I’m not sure, but this may be the earliest form of the popular principle that conceivability is a guide to metaphysical possibility. (Some think there are counterexamples to this, so David Chalmers makes a distinction between primary and secondary conceivability to mitigate that.)

The lapse, as I see it, is that this conceivability-to-possibility principle is neither a relation of ideas nor a matter of fact, so it must be meaningless by his own lights. For the sake of argument, let’s say that it is a relation of ideas. The problem doesn’t go away because analytic a priori statements are just relations between ideas and say nothing informative about the world. Saying that something is metaphysically possible is an informative statement about the world. The better option is to say that it is a matter of fact; we’d at least be saying something substantive then. But how could it be? After all, conceiving is done from the armchair. We don’t see metaphysical possibilities anymore than we see causation.

The strange thing is that in Dialogues concerning Natural Religion (9.6), Hume says:

The words, therefore, necessary existence, have no meaning …

If necessary existence has no meaning then how can contingent existence have meaning? I suspect that Bertrand Russell may have already noticed the point that I’m making, for in his famous debate with Fredrick Copleston he says:

I don’t admit the idea of a Necessary Being and I don’t admit that there is any particular meaning in calling other beings “contingent.” These phrases don’t for me have a significance except within a logic that I reject.

I think the consistent thing for a full-blown Humean to say is that contingent existence doesn’t have any meaning either.


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William Lane Craig on Does the Vastness of the Universe Support Naturalism?

If a small universe is evidence for theism, is a vast universe evidence for atheism? I want to consider Craig’s reply to this, but before I do that I should introduce some basic concepts about the symmetry of evidence; that is, the possibility for evidence for entails the possibility of evidence against.

On likelihoodism observation O is evidence for hypothesis H over ¬H iff P(O|H) > P(O|¬H). Since P(O|H) + P(¬O|H) = 1 and P(O|¬H) + P(¬O|¬H) = 1, we can insert it into the prior formula to get an interesting result:

  • 1 – P(¬O|H) > 1 – P(¬O|¬H)
  • P(¬O|¬H) > P(¬O|H)

So, in English, O is evidence for H over ¬H iff ¬O is evidence for ¬H over H. The means that you can have evidence for a hypothesis iff you can have evidence against a hypothesis.

Craig applies this principle to an example:

David Manley was making the point that on the cozy, pre-Copernican cosmology—what C. S. Lewis called “the discarded image” of the cosmos—theism seemed vastly more probable than atheism. Like a Fabergé egg, the little universe centered on the Earth, with the spheres of the planets and fixed stars revolving about it, cried out for an explanation in terms of a Cosmic Designer. But if you agree that theism is more likely than atheism on such a view, then, Manley argued, you must also agree that a vast cosmos, such as we observe, counts against God’s existence.

Here we see Manley arguing that if a certain observation (small universe) supports theism, then ¬observation (vast universe) supports atheism. Craig agrees to this, but he softens the blow by saying:

… the degree to which the vastness of the universe increases the probability of atheism is marginal! It scarcely changes the odds at all. So while the smallness of the universe would greatly increase the probability of theism, the vastness of the universe only negligibly increases the probability of atheism.

Let’s see how he derives this conclusion. He starts with the odds form of Bayes’ theorem, which says that the ratio of posteriors = ratio of priors x ratio of likelihoods.

\frac{P(Theism|Small Universe)}{P(Atheism|Small Universe)} =  \frac{P(Theism)}{P(Atheism)} \times \frac{P(Small Universe|Theism)}{P(Small Universe|Atheism)}

Here Craig picks his numbers:

Suppose we say that P(Small Universe|Theism) = .01 and P(Small Universe | Atheism) = .0001. That reflects our conviction that given a small, pre-Copernican universe, God’s existence is much more probable than atheism. This assumes that the prior or intrinsic probability of theism or atheism is exactly the same; otherwise Manley’s argument collapses. So we’ll just assume for the sake of argument that P(Theism) = 0.5.

Craig is pointing out that if the prior probability of atheism is something small like .01 (making theism’s prior .99), then evidence from a vast universe will get drowned out anyway for our posterior probability of atheism. For the sake of argument, we’ll assume the priors for atheism and theism are both 0.5.

Plugging in Craig’s numbers it turns out the posterior ratios are

\frac{P(Theism|Small Universe)}{P(Atheism|Small Universe)} = \frac{.5}{.5} \times \frac{.01}{.0001} = 100

\frac{P(Theism|Vast Universe)}{P(Atheism|Vast Universe)} = \frac{.5}{.5} \times \frac{.99}{.9999} = .990099

So the end result is that given a small universe, theism is 100 times more probable than atheism; and given a vast universe, atheism is only slightly more probable. Craig is a happy man.

The reason this happens is because of the suspect initial numbers Craig plugs in. Why does Craig estimate P(Small Universe | Theism) = .01 and P(Small Universe | Atheism) = .0001? Those numbers look really low given the initial intuition about pre-Copernican cosmology, the Fabergé egg. That Pre-Copernican intuition should be reflected by P(Small Universe|Theism) > P(Vast Universe|Theism), which means there’s a greater than 50% chance of a small universe given Theism.

Craig hints at why he chose such low numbers:

Now I’ve read enough of the philosophical and scientific literature on fine-tuning to know that the vastness of the cosmos is not really surprising on theism. For example, John Barrow and Frank Tipler in their important book The Anthropic Cosmological Principle (Oxford University Press, 1985) emphasize that the size and age of the universe are just what we should expect to observe. For the carbon that makes up our bodies was synthesized in the interior of stars and then distributed throughout the universe via supernovae. It takes aeons for galaxies of stars to form and even more time for the carbon requisite for life to be spread abroad to become the foundation of biological life. No other element could substitute for carbon in this role. So the universe must be as old as it is for life to exist and, hence, as big as it is, since the universe is in a state of cosmic expansion since its inception in the Big Bang 13.7 billion years ago. So the size (my italics) and age of the universe are just what one ought to expect given the fine-tuning of the initial conditions of the universe (my italics), which, many have argued, is best explained through design.

It seems he’s using the fine-tuned constants, the initial conditions, and the laws (though unstated) as background knowledge. So, given that, that’s why a vast universe has such high probability on theism, according to Craig. But if we’re using that as background knowledge we need to use it for Atheism too, in which case the background knowledge does all the work and P(Vast Universe|Theism+k) = P(Vast Universe|Atheism+k) ≈ 1. The only reason the two probabilities would be different was if God performed miracles to affect the size of the universe to overrule what would naturally happen.  If the background knowledge makes the two probabilities equal then we can’t compare the hypotheses and we need to choose different background knowledge.

The intuition Manley was getting at was that, in the pre-Copernican era, “like a Fabergé egg, the little universe centered on the Earth, with the spheres of the planets and fixed stars revolving about it, cried out for an explanation in terms of a Cosmic Designer.” Let’s find more reasonable numbers for our imagined pre-Copernican:  P(Small Universe|Theism) = .8 and P(Small Universe|Atheism) = .1. Our pre-Copernican expects a small universe given theism and a vast universe given atheism.

\frac{P(Theism|Small Universe)}{P(Atheism|Small Universe)} = \frac{.5}{.5} \times \frac{.8}{.1} = 8

\frac{P(Theism|Vast Universe)}{P(Atheism|Vast Universe)} = \frac{.5}{.5} \times \frac{.2}{.9} = 2/9

A small universe would be significant evidence for Theism and a vast universe would be significant evidence for Atheism.

When evaluating the evidence, there are two questions: 1) the qualitative question of which hypothesis the evidence points to, and 2) the quantitative question of how strong the evidence is. The numbers I plugged in were subjective probabilities and will differ depending on your own personal God and atheist universe theory.  How strong the evidence is will depend on your subjective theories. I think the numbers Craig plugged in completely misconstrued the dialectic as Manley presented it, since on Craig’s numbers the pre-Copernican theist expects a vast universe! No wonder a vast universe is only negligible evidence for atheism.

The main point of this post is not so much about finding the exact numbers to plug in, but that the possibility of evidence for, entails the possibility of evidence against, a point which Craig now seems to agree with.

For some practice, let’s see how this works for other examples.

  • If successful prayer experiments are evidence for God, then unsuccessful prayer experiments are evidence against God. If unsuccessful prayer experiments aren’t evidence against God, then successful prayer experiments aren’t evidence for God. (I’ll leave out the contrapositive hereafter.)
  • If divine hiddenness isn’t evidence against God, then divine appearance isn’t evidence for God. (Surely an odd result. There must be something wrong with the antecedent.)
  • If suffering is evidence against God, then non-suffering (happiness) is evidence for God. (Notice that atheists who find the problem of evil persuasive has to admit that happiness is evidence for God.)
  • If fine-tuned constants is evidence for God, then coarse-tuned (wide-ranging) constants is evidence against God.
  • If finding intermediate fossils is evidence for common ancestry, then not finding intermediate fossils is evidence against common ancestry.

The above examples only speak on the qualitative (or binary) nature of evidence. The quantitative aspect will depend on your priors and particular theory. If you’re wondering about the quantitative aspect for any of these examples, plug in your own numbers to the odds form of Bayes’ like I did in the vast universe example. Elliott Sober explains in his paper (p. 16) that the reason why not finding an intermediate fossil is negligible compared to the support gained from finding an intermediate fossil is because of the low probability of finding a fossil. (He goes through the math in the paper.) Evolutionists need not worry.


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William Lane Craig, presentism, Zeno’s paradox, and the Kalam

I have been puzzled by how Craig’s Aristotelian solution to Zeno’s paradoxes is consistent with presentism. I finally got around to reading the part of his book that explains this. If I am understanding his view correctly, it seems that his Aristotelian solution comes at the cost of (1) giving up on presentism, and (2) giving up on the supporting premise for the second premise of the Kalam cosmological argument. The Kalam, Craig says, depends on the A-theory of time where temporal becoming is real; presentism—the view that only the present exists—is the most popular version of A-theory.

What is the Aristotelian solution to Zeno’s paradox?

… before Achilles could cross the stadium, he would have to cross half-way; but before he could cross half-way, he would have to cross a quarter of the way; but before he could cross a quarter of the way, he would have to cross an eighth of the way, and so on to infinity. Therefore, Achilles could not arrive at any point. Zeno’s paradox is resolved by noting that the intervals traversed by Achilles are potential and unequal. Zeno gratuitously assumes that any finite interval is composed of an infinite number of points, whereas Zeno’s opponents, like Aristotle, take the interval as a whole to be conceptually prior to any divisions which we might make in it. Moreover, Zeno’s intervals, being unequal, add up to a merely finite distance. By contrast, in the case of an infinite past the intervals are actual and equal and add up to an infinite distance.[1]

Craig makes two points here. First, against those who argument for actual infinities based on Zeno’s paradox, that there is a disanalogy between the infinities in Achilles’ case and the case with an infinite temporal past. Second, and more relevant, the Aristotelian solution is to take the whole to be conceptually prior to the parts. Think of a length of 1 meter. That meter is not composed of points; rather, the whole meter exists prior to the points, and any points within the meter are merely a result of our conceptual divisioning, our thinking of it. Furthermore, conceptual divisions don’t entail an actual infinity, because we can only go through the process of conceptually specifying a potential infinity.

What puzzled me was: How could this Aristotelian view be applied to presentism, given that, on presentism, only the present exists and the future and past do not exist. The question for Craig is: In the past 13.7 billion years, do we traverse an actual infinity of points? For the Aristotelian solution to work—for the whole to be prior to the parts—the whole has to exist. The Aristotelian solution couldn’t work because the only thing we could be conceptually dividing is the present instead of the whole 13.7 billion years. So, at this point, the Aristotelian solution does not seem to solve Zeno’s paradox applied to past time.

To see how Craig would reply, we need to go into his book A Tensed Theory of Time: A Critical Examination. A natural question arises for presentism: What is the extent of the present? Craig goes over three options: (1) instantaneous, (2) atomic, and (3) non-metric. I’ll go through each in turn.

Instantaneous present
An instantaneous present has been criticized “because a concrete object can no more exist with zero duration than with zero breadth and length” (Williams 1951). The idea is that it is puzzling how something with zero duration can exist. (Objectors think this isn’t problematic as they think that space is composed of an uncountably infinite number of extensionless points. The cosmological singularity, if real, would be an example of an extensionless point.)

Craig criticizes the instantaneous present view because of Zeno’s paradoxes of motion and plurality. Consider Zeno’s paradox of motion, given the continuity of time:

… let us suppose … that the basic parts of time are instants. In order for the present instant to elapse it must be succeeded by another. But there is no immediate successor to the present instant. Before the succeeding instant can become present, an infinite number of succeeding instants will have to become present first. … For no instant can immediately succeed the present. The present would therefore exist as the nunc stans of the classical doctrine of eternity, not the nunc movens of A-theoretic time. (Craig 2000, p.235-6)

and Zeno’s paradoxes of plurality:

If we conceive temporal becoming to proceed instant by instant, the length of time between some past event or moment and the present could never increase, since the lapse of durationless instants adds nothing to the interval between the past instant and the present instant. But then there is no “flow” of time at all, and we are left again with the nunc stans of the present instant, never able to recede into the past. The doctrine of the instantaneous present is thus incompatible with objective temporal becoming. (Craig 2000, p.236)

In sum, Craig sees two problems for instantaneous presents: (1) there cannot be ‘motion’, and (2) there cannot be duration since adding a series of zeros is still zero.

Consider how instantaneous presents affect the Kalam. Craig offers two philosophical arguments that the universe must have a beginning. The first argument argues against the metaphysical possibility of an actual infinite using thought experiments like Hilbert’s Hotel. The second argument grants the possibility of an actual infinite, but denies that an actual infinite can be formed by successive addition. (This second argument is dialectically stronger.) It is this second argument that seems to lead to problems for instantaneous presents. If Craig is right on his view of Zeno’s paradoxes, then not only can’t an infinite be formed by successive addition, but a finite can’t be formed either.

Atomic present
Alternatively, one might think of the present as having some minimal duration in time, called chronons. “One disturbing feature of such a model of temporal becoming, however, is that temporal becoming seems to be “jerky” rather than smooth (Craig 2000, p.242).”(Zeno’s stadium paradox is relevant here, but I’ll skip the details.)

The problem of jerkiness is enough for Craig to favor the next view.

Non-metrical present

We can maintain that the extent of the present depends upon the extent of the entity described as present. To quote again Andros Loizou: “… no event or state of affairs is ever present simpliciter—it is present by implicit or explicit reference to a kind of events or states of affairs, as when we speak of the present eclipse, or by reference to a time scale, as when we speak of the present hour or day, and so on.” … There is no such thing as “the present” simpliciter: it is always “the present ____,” where the blank is usually filled by a reference to some thing or event. The duration of the present will be as long or as short as the event or thing under discussion (italics mine). (Craig 2000, p.245)

Craig is saying that it makes no sense to speak of the present moment (the now), unless context is added. But surely our deciding to speak of the present hour in one context and the present day in another context does not affect the metaphysics of time: we don’t control what exists by deciding what to think. I think Craig would agree, but I don’t see how this odd view is not entailed by his non-metric view.

Craig brings up a worry about his non-metric view going back to Augustine.

The nerve of Augustine’s argument against some interval of positive duration’s being present is the assumption that in order to be present, the interval in question must be incapable of analysis into past, present, and future phases. But if what we have said so far is correct, this assumption is not incumbent upon the A-theorist. He may instead hold that an interval is present if any phase of it is present. (Craig 2000, p.247)

I share Augustine’s worry. The non-metric view entails that any interval can be present. Presentism is the view that only the present exists, but if the future and past can be in the present interval, then Craig’s view seems to be a quasi B-theory. On B-theory there is no privileged now, and all moments of time have equal ontological status, all moments are equally real. On the non-metric view, it seems the future and past can be said to exist in virtue of being contextually included in the present interval. Again, this seems to raise the same problem as before, where we can think things into existence.

What about the lower and upper limits on the “present ____?” As for lower limits:

… there need be no such minimum length or temporal duration because both space and time are potentially infinitely divisible. The duration stipulated to be present will be an arbitrary, finite duration centered on a conceptually specified instant (Craig 2000, p.246-7).

Here Craig is using the Aristotelian view applied to his non-metric view. Since, on the Aristotelian view, the whole is prior to the parts, and any parts are merely a result of our conceptualization, there won’t be a lower limit because we can always think of something smaller. Craig does not mention if there can be an upper limit on the duration of the present ____, and I don’t see how he could have a non-arbitrary upper limit. If this is right, nothing stops us from speaking about the present 13.7 billion years or the present actual infinity! So it seems one can adopt Craig’s own non-metric view and hold to actual infinities.

Stephen Puryear on Craig
Finally, Stephen Puryear (2014) has pointed out that Craig’s Aristotelian view can be equally used by the infinitist who believes in an actual infinite past, thus undermining the Kalam. The infinitist can say that the whole past infinite is prior to its parts, and since we can only conceptually divide a potential infinity there isn’t an actual infinity of events to traverse (even if there is an actual infinity in duration).

In addition, there seems to be a tension between the Aristotelian view and Craig’s argument for the impossibility of the formation of an actual infinite by successive addition—the stronger argument I was referring to earlier.

2.21 A collection formed by successive addition cannot be actually infinite.
2.22 The temporal series of past events is a collection formed by successive addition.
2.23 Therefore, the temporal series of past events cannot be actually infinite.

This argument does not seem relevant on the Aristotelian view. Given that the whole is prior to the parts, the duration of events does not consist of successive additions but conceptual divisions; successive additions presuppose that the parts are prior to the whole, contrary to the Aristotelian view.

This is not to say that there isn’t some mystery as to how an actual infinite duration can be traversed; rather, it’s that the non-metric view does not seem plausible, and that the Aristotelian view does not seem compatible with Craig’s view that the temporal series of past events is a collection formed by successive addition.

The other two options for presentism—the instantaneous and atomic presentist—seem more plausible to me, but I’ll leave that for another time.

Craig, William Lane, and James Porter Moreland. The Blackwell companion to natural theology. Vol. 49. John Wiley & Sons, 2012.
Craig, William Lane. The tenseless theory of time: A critical examination. Vol. 294. Springer Science & Business Media, 2000.
Puryear, Stephen. “Finitism and the Beginning of the Universe.” Australasian Journal of Philosophy 92.4 (2014): 619-629.
Williams, Donald C. “The myth of passage.” The Journal of Philosophy 48.15 (1951): 457-472.


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Divine Conceptualism

Many theists have taken the potential existence of platonic objects to compromise God’s aseity and sovereignty. God’s aseity is the view that God does not depend on anything outside himself for his existence. God’s sovereignty is the view that everything outside of God depends on him. It’s easy to see how one might think that the existence of platonic objects would compromise God’s sovereignty, as platonic objects are generally thought to be necessary and uncreatable, thus not depending on God. It’s less easy to see how it would compromise God’s aseity. The thought is that if platonism about properties is true, then God would depend on these platonic properties for his existence, because in order to exemplify a property (e.g. omnipotence) that platonic property would have to exist. Similarly, for propositions, in order for God to have a propositional thought, platonic propositions would have to exist. In order to preserve God’s aseity and sovereignty, while maintaining realist (i.e. platonist and divine conceptualist) intuitions about abstract objects, some theists have taken towards divine conceptualism.

I take divine conceptualism to be the position that what play the role of some abstract objects are not platonic but God’s thoughts and concepts. Some candidates for abstract objects are properties, kinds, relations, propositions, numbers, sets, possible worlds, and states of affairs. I’ll limit this post to talk of two abstract objects: propositions and properties. Different issues arise for each abstract object. One may be a divine conceptualist towards propositions but a platonist towards properties. It will be open to the theist how they want to account for the rest of the candidate abstracta.

Invariably, all divine conceptualists will identify propositions with God’s thoughts. The main argument for this is what I’ll call the argument from intentionality. Paul Gould and Richard Brian Davis explain:

In short, propositions … are intentional objects; they are of or about things. And this is an essential property of propositions; for if they lacked this property, they could not possibly be claims or assertions of any kind, they could not represent anything, in which case they could not be true (/false). … For surely a proposition is true only if it represents the world as it is. And just as surely the way things stand in reality is depicted as being thus and so only if something is being claimed about the way things so stand (52-3).

Following Searle, we can distinguish between intrinsic (or original), and derived intentionality. For example, a photo of Obama is about Obama but only in virtue or our being able to think it; therefore, the photo has derived intentionality. By contrast, minds are intrinsically intentional. Divine conceptualists argue that propositions need to be about things in order for them to be true, but platonic propositions would only be derivatively intentional. The ultimate truthbearer must be intrinsically intentional; that truthbearer must be thoughts.

The next step is to show that there must be a mind capable of holding all the propositions; the mind must have an infinite capacity. In addition—since propositions are necessary beings—the mind must be necessary.  (A proposition’s truth value may be contingent—true in one world and false in another—but the existence of that proposition is necessary.) A necessary mind with infinite capacity seems much like the mind of God. So we began looking for an account for truth and end in an argument for God.

I will consider issues for divine conceptualism first for propositions, then for properties.

Issues for Propositions
Unholy thoughts
Graham Oppy notes:

… it threatens to lead to the attribution to God of inappropriate thoughts: bawdy thoughts, banal thoughts, malicious thoughts, silly thoughts, and so forth (105).

God must be constantly thinking these unholy propositions.  In addition, God must think of trivial propositions such as “For each real number r … there is the proposition that r is distinct from the Taj Mahal” (Plantinga 1998, 91). Some may think that this detracts from the greatness of God.

Nonuniform account of thoughts
On divine conceptualism, propositions are identical to God’s thoughts. For humans, it seems propositions are the contents of our thoughts. If God’s thoughts don’t have contents—since they are the contents—then, does it make sense to say that God has thoughts?

Multiply instantiating thoughts
It would be weird if the same apple were in two different places at once; we’d think they were two different apples. Similarly, nominalists tend to think it is strange that the same property of redness can be in two places at the same time.  Realists deny this weirdness; they say that properties are multiply-instantiable. This applies not only to properties, but to propositions. Realists say that if propositions were not intersubjectively available, if you and I did not have the same proposition in mind, then communication would not be possible.

But multiple-instantiation seems doubly weird for thoughts. How can someone else’s thought be multiply-instantiated in my mind (and others) as contents?

One of the main motivations behind realism is to account for resemblance, not only for properties but for thoughts. If the Trinity has three numerically distinct minds, then what accounts for the resemblance between their three thoughts when they think the same thought? It can’t be a fourth mind because that would raise the same question for four minds. It can’t be a platonic proposition without giving up divine conceptualism. If no extra ontology needs to account for it, then they seem to have one foot in the nominalist door. (Interestingly, Peter van Inwagen, who is a platonist, denies that platonism accounts for resemblance.)

On one divine conceptualist view God’s creative activity creates propositions, and hence the possibility of truth. It seems that it would already have to be true that (a) God’s creative activity creates propositions. But this would require God to create the truth that (b) God’s creative activity creates propositions, and that would require God to create the truth that (c) God’s creative activity creates the truth that God’s creative activity creates propositions, ad infinitum.

I’m not sure how good this criticism is; (b) and (c) may collapse together. The real worry seems to be a necessary precondition that God exists in order for God to create propositions—that is, for God to think.. In other words, causally (but not necessarily temporally) prior to God’s creative activity, it has to be true that the cause (God) exists.  But if divine conceptualism is true, then there are no propositions causally prior to God’s thoughts, so it’s neither true or false that God exists.

If God’s thoughts creates truth, then God creates the truth that God exists. If God creates that truth, then does God cause his own existence? Self-causation is thought to be impossible. Paul Gould and Richard Brian Davis deny that this entails self-causation:

The principle grounding … seems to be that “x makes true y” entails “x causes y” or (more accurately and awkwardly, since y is a proposition) “x causes the object y is about.” Far from it. Socrates’ drinking the hemlock makes it true that Xantippe is a widow, but it doesn’t follow that Socrates’ drinking the hemlock causes her to become a widow … (77).

Even if this is right, it still seems odd to say God makes it true that he exists. The issue, again, seems to do with the logical priority of truth.

Issues for Properties
In this section, I will consider divine conceptualists that think properties are numerically identical to God’s thoughts. Some divine conceptualists deny this, and are only conceptualists about propositions.

Berkeleyan Idealism?
I tend to think divine conceptualism doesn’t lead to Berkelayan Idealism, but Paul Gould and Richard Brian Davis think otherwise:

“All properties and relations are God’s concepts.” It is easy to see that this principle undermines basic attempts to explain the notion of a substance. Consider, for example, the bundle theory: conjoined with PCP, it leads to a form of Berkeleyan idealism. For suppose a material thing is nothing but a bundle of compresent multiply exemplifiable properties. Then if properties are God’s concepts, and if relations are God’s thinking concepts together, every material object is a mere collection of divine concepts or ideas, in which case we shall have to say that a substance changes just when God starts or stops “thinking together” His own concepts or ideas. Not only does this eradicate the material nature of reality, it smacks of an objectionable divine determinism (59).

Similar considerations are offered for other metaphysics of substances.

How can thoughts be properties?
How can one of God’s thoughts be numerically identical to redness? It doesn’t seem like God’s thought about redness can itself be redness. Since God is thinking about redness, mustn’t redness be distinct from that thought? If that’s right, what kind of thought would be redness if it’s a thought that’s not about redness?

If properties are identical to thoughts/ideas, and thoughts are intentional, then properties are intentional. But is redness about something?

Bootstrapping, again
If all properties are created as a result of God’s thoughts (and God has properties) then God must create his own properties. But it seems God must already have the property of being able to create a property to create a property.

In answer to this worry, Paul Gould and Richard Brian Davis have a hybrid view where God creates all properties except his own. But this creates a disunified account of properties, which is inelegant, at least. Does the Trinity also create all numbers except 1, 2, and 3?

Gould, Paul, ed. Beyond the Control of God?: Six Views on the Problem of God and Abstract Objects. A&C Black, 2014.

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Platonism, a short introduction

By platonism, I will mean the contemporary view on it in analytic philosophy, and not necessarily Plato’s view.

Platonists believe that the existence abstract objects are needed to make sense of three phenomena: resemblance, subject-predicate discourse, and abstract reference.   By contrast, nominalists think that we can explain the three phenomena without the extra ontology. Some candidates for abstract objects are properties, kinds, relations, propositions, numbers, sets, possible worlds, and states of affairs.  (A platonist needn’t accept all these candidates into their ontology.)

Here is a short summary of those three phenomena.  A more detailed treatment can be seen in Michael Loux’s Metaphysics A Contemporary Introduction.

Apples and roses resemble each other in their redness.  Platonists think this resemblance is explained by the particular apples and roses both exemplifying the abstract object of redness.

Subject-predicate discourse
Consider the proposition “Socrates is wise.”  Platonists argue that in order for this proposition to be true ‘Socrates’—the linguistic object—must be correlated to a non-linguistic object—the person Socrates.  Likewise, ‘wise’ must be correlated to a non-linguistic object.  While the subject ‘Socrates’ operates as a noun—a singular term—the predicate ‘wise’ is an adjective and operates as a general term.  That is, the predicate ‘wise’ can be true of many things like Socrates and Plato.

Abstract reference
Corresponding to the adjective ‘wise’ there is the noun ‘wisdom’. Since objects are referred to by nouns, it seems like the use of a noun implies the existence of a non-linguistic object to be referred to. Nouns also play the role of the subject in a sentence. In its use as a subject in the sentence “Wisdom is a virtue”, it seems ‘wisdom’ is explicitly referring to an abstract object.

Loux, Michael J. Metaphysics: A contemporary introduction. Vol. 2002. London: Routledge, 1998.

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