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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Why is There Anything?

Why is there something rather than nothing?  A common answer is that something is necessary.  In a recent paper, Joshua Rasmussen & Christopher Weaver argue for a thesis they call necessary foundation: “there is a necessarily existing concrete thing or things capable of causing or grounding everything else.”  In addition, they propose some arguments from necessary foundation to theism. They follow in the spirit of recent causal-based arguments for a necessary being.

The argument is as follows (quoting):

  • (P1) It is possible that there is a purely contingent totality event that has a cause.
  • (P2) It is impossible that a cause of a purely contingent totality event is purely contingent.
  • (P3) If, (a) it is possible that there is a purely contingent totality event that has a cause and (b) it is impossible that a cause of a purely contingent totality event is purely contingent, then (c) it is possible that there is a cause that isn’t purely contingent.
  • ∴ Therefore, (c) it is possible that there is a cause that isn’t purely contingent.
  • (P4) If (c) it is possible that there is a cause that isn’t purely contingent, then (d) there is a necessary thing that can be a cause.
  • ∴ Therefore, (d) there is a necessary thing that can be a cause.

The crucial and controversial premise is P1; the other premises seem sound.  The ‘can’ in the conclusion I take to be synonymous with possible. The argument concludes that there is a possible world where the necessary thing is a cause, from which it follows that a necessary thing exists.  This doesn’t entail that the necessary thing is a cause in every possible world.

They offer three lines of reasoning in support of the causal principle in P1: from inductive generalization, from causal relevance, and from conceivability.

Concerning the inductive generalization argument, they argue that the causal principle in P1 “fits with a wide range of data, including (i) our experience with contingent things (states, events, etc.) having a cause, and (ii) our lack of experience with uncaused contingent things.”  William Lane Craig’s arguments supporting the first premise of the Kalam Cosmological Argument are similar in spirit, and can act as additional support.

Concerning the causal relevance argument, they ask:

Does a totality of purely contingent events differ from other purely contingent events in a way that is causally relevant? We’ll give one reason to think not. To begin, consider the following states of affairs:

  • s1: there being exactly 1 purely contingent event
  • s2: there being exactly 2 purely contingent events
  • s3: there being exactly 3 purely contingent events

Notice that these states differ by a mere quantity of events. You might think mere quantitative differences aren’t normally relevant to causal possibility. That is, if there could be a cause of s3, then there could be a cause of s2, and if there could be a cause of s2, then there could be a cause of the smaller state, s1. This inference is supported by what Rasmussen (2014) calls “modal continuity.” … We don’t expect it to be controversial that there could be a cause of s3 … . For example, there could be two purely contingent events that give rise to a third. In this situation the two events jointly cause s3 to obtain. So, by causal uniformity, we have some reason to expect that it is possible that there is a cause of s1.

Their idea is that it is uncontroversial to say that s3 could be caused; and since the only difference between s3, s2, and s1 is mere quantity, it seems (from modal continuity) that s1 could be caused.  But what kind of thing could cause s1? The only thing that could cause s1 would have to be a necessary thing, since if a contingent event caused there to be exactly 1 contingent event, it would have to cause itself—an impossibility.

In reply, what reason is there to think there could be a cause to s2 and s3 but not s1 if the difference is mere quantity?  The immediate answer for those coming into the argument skeptical of necessary concrete things is that there is a prior belief that all of concrete reality is exhausted by contingent things.  The causally relevant feature for why s1 can’t be caused is that you can’t have a cause to the totality of concrete things without something causing itself, which is impossible.  This response will push the debate to why we have those prior beliefs, but, for the moment, the causal relevance argument is defused.  The same reasoning defuses the inductive generalization argument.

Thirdly, there is the conceivability argument.  Here we make use of a principle famous from Chalmers’ zombie argument in philosophy of mind.  The principle states that if you can conceive of a certain statement then that is a guide to its metaphysical possibility.

Since Chalmers’ methodology plays perhaps the central role in modal reasoning, a primer will be helpful.  Chalmers distinguishes between negative and positive conceivability for some statement S.

The central sort of negative conceivability holds that S is negatively conceivable when S is not ruled out a priori, or when there is no (apparent) contradiction in S.

Positive notions of conceivability require that one can form some sort of positive conception of a situation in which S is the case. One can place the varieties of positive conceivability under the broad rubric of imagination: to positively conceive of a situation is to in some sense imagine a specific configuration of objects and properties. It is common to imagine situations in considerable detail, and this imagination is often accompanied by interpretation and reasoning. … Different notions of conceivability correspond to different notions of imagination. One such notion is tied to perceptual imagination. … For example, one can perceptually imagine that a pig flies by forming a visual image of a flying pig, where this can be understood as an image that relevantly resembles a visual experience as of a flying pig. … There is a sense in which we can imagine situations that do not seem to be potential contents of perceptual experiences. One can imagine situations beyond the scale of perception: e.g. molecules of H2O, or Germany winning the Second World War. One can imagine situations that are unperceivable in principle: e.g. the existence of an invisible being that leaves no trace on perception.

Since positive conceivability—i.e. the ability to imagine—is a richer type of conceivability it is considered to be preferable over negative conceivability.  Chalmers notes two types of positive conceivability: one is perceptual, and the other, I’ll call, conceptual.

Following Chalmers’ test, Rasmussen and Weaver say:

With Chalmers conceivability tests in hand, let us now return to our causal principle, [P1], which says that possibly, there is a cause of a purely contingent totality event. Does conceivability justify [P1]? According to Chalmers, it does to the extent that we can imagine a situation in which a totality event has a cause. So consider the following scenario. There is a supremely powerful entity E (whose nature we leave unspecified), which is capable of causing any and every purely contingent event, including a totality event. We may imagine, for example, that whatever event can occur could be caused by E. Or if that is too much to imagine, then imagine merely that E causes whatever purely contingent events happen to occur. Or if even that is too much, then imagine a particularly big contingent event, which is known to be causable, like a galaxy forming, and then imagine that E causes that event. Now add to your imagination empty space around the caused event so that there are no other purely contingent events. The imagined galaxy is now a totality of purely contingent events, and no incoherence is revealed by supposing that it still has a cause. These imaginations are … coherent, and thus, by Chalmers’ lights, they provide … evidence for the metaphysical possibility of the imagined situation. We have thus identified a third line of potential support for our causal principle.

They offer three scenarios for us to imagine.  If we can imagine any of those situations, then we have support for its metaphysical possibility, from which a necessary being follows.  The first scenario seems to be a conceptual imagining, and the second and third scenarios seem to be a perceptual imagining.  I will consider the 2nd and 3rd perceptual case for two reasons: (1) if we are considering the argument and have the option to use perceptual imagining, it seems like a plus and not a minus since adding more detail doesn’t seem bad, and (2) the use of perceptual imagination is where I think the argument runs into counterintuitive results.

Consider the third scenario: “imagine a particularly big contingent event, which is known to be causable, like a galaxy forming, and then imagine that E causes that event.”  It seems easy to perceptually imagine that the cause is a gas cloud.  Then I can imagine the cause of that stretching back to a singularity.  If you followed the original argument, it should be clear that, since the galaxy formation is the totality of purely contingent events, the singularity has to be a necessary concrete being—an unintuitive result.  We can construct similar scenarios to open up a Pandora’s box of necessary concrete beings.

One possible move is to say that the singularity should have been included in the totality of purely contingent events in the first place.  I think to do that would be to give up on this causal part (where we imagine the possibility of cause) of the argument and go back to whatever method we were using in the first place.  Essentially, the causal part of the argument is vetoed by whatever our primary method (e.g. Chalmers’ test) is for figuring out whether concrete things are necessary or contingent. At best, the causal part can offer suggestions, but it’s not the final arbiter.

The next phase of their argument provides a path to theism.  They propose that the necessary being must have omnipotence, which is plausibly a great-making property.  Their reasoning follows the spirit behind modal continuity.  (I will only offer a short paraphrase.)  The idea is that it seems arbitrary for there to be some cutoff to what this necessary being can cause.  For example, why think the necessary being can cause a galaxy forming but not a tree forming?  Presumably, if you think the galaxy forming can possibly be the totality of purely contingent events and possibly have a cause, you also think the tree forming can possibly be the totality of purely contingent events and possibly have a cause.  So, to avoid arbitrariness, it seems that the totality of necessary concrete beings must be able to cause all possible totalities of purely contingent events, and, therefore, be omnipotent; otherwise, there seems to be an arbitrary break in modal continuity.  It is here that the causal part of the argument does play some role.

They further argue that N, the totality of necessary concrete beings, must not have a geometry.

In other words, we have reason to think that if N has a geometry, it could have had a different one.

This result is especially significant if N’s contingent states can be caused. For then N can be an ultimate cause of geometric reality. Moreover, to avoid causal circularity, N can lack a geometry altogether—prior to its causing there to be a geometric reality. There is more. Suppose one thinks that whatever has a geometry must have a geometry. Then one may infer that N is essentially geometric-less and thus immaterial.

I don’t find this plausible, since by parallel reasoning we could imagine N not being geometric-less.  Additionally, one might think that geometric reality exhausts all of concrete reality, which entails that there can’t be a cause to geometric reality.

They “leave open whether the N picks out a single thing, sum of things, or a plural of things.” It is likely they have further arguments (outside of this paper) that the totality of the necessary causal foundation can’t be a plurality of things, but, for the moment, their argument seems to support a Pandora’s box of necessary concrete beings (which would satisfy the omnipotence requirement.)

Chalmers, David. “Does conceivability entail possibility?” Conceivability and possibility (2002): 145-200.
Rasmussen, Joshua & Weaver, Christopher. “Why is There Anything?” Two Dozen (or so) Arguments for God: The Plantinga Project (forthcoming).

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William Lane Craig says he does not know how they would respond to his three points against Atheistic Moral Platonism

In this video Craig offers three criticisms to what he calls atheistic moral Platonism.

(I suspect Christian Platonists about morality, like Terence Cuneo, would object to this term. And, I have never seen any metaethicist ever use this term. It should simply be called Moral Platonism or a robust non-naturalism à la Enoch, as opposed to Parfit’s Quietism.)

When asked by a questioner, Craig says that he does not know how the atheist moral Platonist would reply to his three criticisms. Really? I don’t expect Craig to accept their reply, but I find it odd that he wouldn’t even know how they would reply. I’ll quote Craig’s criticisms in full then offer standard replies.

Criticism 1: The view seems unintelligible. What does it mean to say, for example, that the moral value justice, just exists? It’s hard to make sense of this. It’s easy to understand what it means to say that some person is just, but it’s bewildering when somebody says that, in the absence of any people, justice itself just exists. It becomes even more bewildering when you reflect on the fact that justice itself is not just anymore than loyalty is loyal or intemperateness is intemperate. So, if there were no people around who are just, then how could justice exist? It seems like there wouldn’t be any justice, this abstract object is not just, there aren’t any just people, so justice wouldn’t seem to exist, which contradicts the view that justice just exists on its own as an idea. Moral values seems to be properties of persons, and so it’s hard to understand how moral values like justice can exist as an abstraction.

Reply: This first criticism doesn’t seem to be specifically about atheism or morality, but about Platonism from someone with Aristotelian leanings.  (Briefly, on Platonism, there are external abstract properties that are exemplified by particulars, and there are such things and unexemplified properties.  On the Aristotelian view, all properties are immanent in the particular, and there are no unexemplified properties.)  We can equally imagine Craig saying: It’s easy to understand what it means to say that some concrete object is red, but it’s bewildering when somebody says that, in the absence of any concrete objects, redness itself just exists. Since one of Craig’s philosophical specialties has to do with abstract objects, I’m sure he’s heard of the third man argument; so he should know the reply. The idea is that it seems to the Aristotelian that the form of red must itself be red, but, then it seems we need another form to account for the redness of the form of red and we’re off to an infinite regress, in which case Platonism never solves the original problem of accounting for the redness of a particular, say, an apple. One reply, given here and here, is to say:

Plato’s theory of forms proposes that for any irreducible simple element F exhibited by particulars, the primary function of the form F is to explain (give being or existence to) the F-ness of those particulars that partake of F.   Specifically excluded from Plato’s description is any attempt to explain the F-ness of F.   Plato does not open the possibility of an infinite regress of forms of F-ness, each of which explaining the F-ness of the forms of F-ness below it in the hierarchy.   The form of F can explain the F-ness of the original plurality of F particular things.   But it cannot explain the F-ness of F.   That requires no explanation because he maintains that F-ness is equivalent / identical to F.   Hence, the move in the Third Man Argument to demand a “higher level”Form in order to explain the F-ness of the larger set of things that includes the Form of F is specifically invalid.

Criticism 2: Secondly, this view provides no basis for moral duties. It tries to give a basis for moral values, but it has nothing to say by way of an explanation of our moral duties. Let’s suppose for the sake of argument that moral values like justice, loyalty, mercy, forebearance, and so on, just exist. How does that result in any moral obligations for me? Why would I have a moral duty to be, say, merciful? Who or what lay such an obligation on me? Notice that on this view moral vices such as greed, hatred, rapacity, selfishness, and sloth also exist as abstractions. So, why are we morally obligated to align our lives with one set of these abstractions rather than with some other set of these abstractions. Atheistic moral Platonism, lacking a moral law giver, has no grounds for moral obligation.

Reply: Craig says that our moral duties are constituted by divine commands, but in the 17th century, theologian Ralph Cudworth noticed that this type of divine command theory cannot account for all moral obligations.  (This criticism survives today and is talked about by metaethicists like David Baggett, C.S. Evans, and Terence Cuneo.)  It seems that Craig would agree that we’re obligated to obey God’s commands, but what accounts for that obligation? On a DCT, where all duties are constituted by God’s commands, God would have to command us to obey his commands in order for us to be obligated to obey his commands. But why are we obligated to obey that 2nd order command? God would have to command us again, and we’re off onto an infinite regress. It seems, for Craig, there has to be at least one obligation that can’t be accounted for by God’s command—namely, the obligation to obey God’s commands—in which case DCT is false. Maybe it’s just a necessary truth that we’re obligated to obey God’s commands, but that opens the door to say that it’s a necessary truth that we’re obligated to follow the golden rule (or whatever). If at least one obligation is not accounted for by a command, it wouldn’t be queer, in the Mackian sense, that a second is.

Criticism 3: And, finally, number three, it’s fantastically improbable that the blind evolutionary process should spit forth precisely those sorts of creatures who correspond to the abstractly existing realm of moral values. This seems to be an utterly incredible coincidence when you think about it. Remember that this realm of moral values as an abstract realm is utterly independent of the natural realm. It is causally unconnected with the natural realm. So how is it that exactly that kind of creature should emerge from the blind evolutionary process that corresponds to this independently existing moral realm. It’s almost as though the moral realm knew that we were coming. I think that it’s far more plausible to think that both the natural realm and the moral realm are under the authority of a God, who gave us both the natural laws and the moral law, than to think that these two independent realms of reality just happen by coincidence to mesh. So for those reasons, I think that atheistic moral Platonism is a less plausible theory of ethical values and duties than is theism.

Reply: Here, there seems to be two criticisms: (1) an epistemological problem for platonists, (2) an argument similar to Plantinga’s EAAN. As for (1), one way for the Platonist to reply, for abstract objects in general, is given by Michael Loux in his Metaphysics A Contemporary Introduction book:

And they will argue that the Aristotelian’s contention that the Platonist faces insoluble epistemological problems is overblown. They will insist that while some universals have no instances in the spatiotemporal world, many do; and they will claim that our knowledge of exemplified universals can be captured by a thoroughgoing empiricism. As they see it, we come to have cognitive access to these universals simply by experiencing the spatiotemporal particulars that exemplify them; whatever other knowledge we have of universals is grounded in our knowledge of these exemplified universals. Thus, we come to know about some unexemplified universals by extrapolation from our empirically based knowledge of instantiated properties, kinds, and relations (p. 43).

On how “moral realm knew that we were coming”, the most famous reply is David Enoch’s pre-established harmony—to borrow a phrase from Leibniz. The idea is that there is a pre-established harmony between what is evolutionarily advantageous and what is good—a happy coincidence.  For another, similar reply, see Knut Olav Skarsaune’s Darwin and Moral Realism.  Skarsaune proposes that:

if pleasure is usually good and pain usually bad, then the required relation between evolutionary pressures and the evaluative facts (realistically understood) exists [since] evolution has caused us to value reproductively beneficial things by making us such that we take pleasure in these things, and caused us to disvalue reproductively harmful things by making us such that these things cause us pain. … But now if … pleasure is usually good (for the subject), then to the extent that evolution has influenced our evaluative beliefs through the mechanism just described, that influence has been truth-conducive.

As for (2), the literature on Plantinga’s EAAN is vast—too much for me to want to repeat here.  See James Beilby’s Naturalism Defeated and Plantinga & Tooley’s Knowledge of God.

The point isn’t that these replies to Craig are good (I’m skeptical of reply 1 and 3), but that it is odd that Craig would say that he’s not aware of the responses.

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