More on the actual / potential infinite

0. Introduction

One of the premises of the Kalam Cosmological Argument (KCA) is that the universe began to exist. There are two types of defence for this premise; scientific and philosophical. In the latter category, there is one argument in particular that I want to focus on, which Craig calls the ‘argument from the impossibility of an actual infinite’.

The argument runs like this:

  1. An actual infinite cannot exist
  2. An infinite temporal regress of events is an actual infinite
  3. Therefore, an infinite temporal regress of events cannot exist

Craig holds that the past had a beginning, but also that the future has no end (presumably due to his beliefs about the afterlife). This invites the following objection, which has been made in the literature by Wes Morriston (here). We seem to be able to formulate a symmetrical argument which should conclude that the future has an end point:

  1. An actual infinite cannot exist
  2. An infinite temporal progress of events is an actual infinite
  3. Therefore, an infinite temporal progress of events cannot exist

(The term ‘progress’ is artificial used in this context, but it is clearly intended as the temporal mirror of the term ‘regress’)

The first argument says that the past must have a beginning, otherwise it would constitute an actual infinity. The second argument, the counter-argument, says the future must have an end, otherwise it would constitute an actual infinity.

Morriston has a thought experiment to illustrate his point. He asks us to imagine two angels, Gabriel and Uriel, who take turns saying praises to God forever. He makes the following remarks:

“It’s true, of course, that Gabriel and Uriel will never complete the series of praises. They will never arrive at a time at which they have said all of them. Indeed, they will never arrive at a time at which they have said infinitely many praises. At every stage in the future series of events as I am imagining it, they will have said only finitely many. But that makes not a particle of difference to the point I am about to make. If you ask, “How many distinct praises will be said?” the only sensible answer is, infinitely many.” (Morriston, Beginningless Past, Endless Future, and the Actual Infinite, p. 446)

To counter this, Craig argues that the endless future is best considered a merely potential infinity, (in contrast to the beginningless past, which is best considered as an actual infinity). As Craig says in his reply to Morriston, Taking Tense Seriously:

“So with respect to Morriston’s illustration of two angels who begin to praise God forever, an A-theorist will concur whole-heartedly with his statement, “If you ask, ‘How many praises will be said?’ the only sensible answer is, infinitely many”— that is to say, potentially infinitely many. If this answer is allowed the A-theorist, then Morriston’s allegedly parallel arguments collapse.”

Effectively, Craig is denying the second premise of our counter-argument. He is saying that an infinite temporal progress of events is not an actual infinity – it is merely a potential infinity.

In what follows I want to look at three types of response to this. This post will constitute the first part, and in subsequent posts I will address the second and third points.

Firstly, I will spell out an intuition that many people have, according to which if there is a potential infinity there must be a corresponding actual infinity. We will call this ‘Cantor’s Intuition’ for reasons we will get into below. If Cantor’s Intuition was correct, then Craig’s response would be defused. For then we could “concur whole-heartedly with his statement” that the future is potentially infinite, and insist that it is also actually infinite. According to this line of thinking, the potential and actual infinite are not mutually exclusive.

Secondly, I want to look at a different strategy. Perhaps the future is not actually infinite, and the second premise of the counter-argument is false. But the thought is that maybe this leaves open the door to denying the second premise of the original argument. That is, if the infinite progress of events is a merely potential infinity, maybe the infinite regress of events is a merely potential infinity as well. Craig is very dismissive of this view, but I think it is worth exploring.

Lastly, I want to look at why Craig thinks there is an asymmetry here at all. Here it seems that considerations about the philosophy of mathematics are completely irrelevant, and all that is doing the heavy lifting is considerations about the philosophy of time. Of course, all but the most fanatical would concede that time is in some sense asymmetric. Yet, this can be cashed out in lots of different ways. Do any of those ways of understanding the asymmetry do the work that Craig needs?

  1. Potential infinite implies actual infinite

The mathematical study of the infinite was revolutionised in the 19th century by the work of various mathematicians, but the primary figure is clearly Georg Cantor. He was the first to work out the mathematics of the infinite, and in particular gave a formal treatment of the actual infinite. He changed his mind quite a lot, but at one time in particular he held a view that I want to bring up here. In 1886, he wrote a letter to the mathematician Richard Dedekind, in which he made the following comments:

“… since there can be no doubt that we cannot do without the variable magnitudes in the sense of the potential infinite, then the necessity of the actual infinite can be proved as follows: In order for such variable magnitudes to be capable of evaluation in a mathematical investigation, their “range” of evaluation must be precisely known by means of a prior definition. But this “range” cannot itself be in turn something variable, for otherwise every fixed support for the investigation would give way; hence this “range” is a definite actually infinite set of values. Thus, every potential infinite, if it is to be employable in mathematics, presupposes an actual infinity.” (Quoted in ‘The Potential Infinite‘, by W D Hart, 1979)

Cantor’s Intuition seems to be that the following inference is valid:

If x is a potential infinite, then x is an actual infinite.

If Cantor’s Intuition is right, and the above inference is valid, then Craig’s argument does not work. The reason is that Craig is using the terms potential infinity and actual infinity as if they were mutually exclusive; that something can be one or other but not both. Yet, if Cantor is right here, then if something is potentially infinite, it is also actually infinite, and thus they are not mutually exclusive after all.

But is Cantor right?

2. A potential infinite that is not an actual infinite

Well, in some sense it seems that he was wrong. Not every potentially infinity presupposes an actual infinity. Consider the hierarchy of sets. So, start with the empty set (the set with zero elements):

Then there is the set with one element; namely, it has the empty set as it’s sole element:

{∅}

Then there is the set that contains two elements: the empty set, and the the set which contains the empty set:

{∅, {∅}}

Clearly, we can go on elaborating this hierarchy forever, just constructing more sets in this way. But does this constitute a completed totality – an actual infinity? There are good reasons for thinking not. Such a proposal seems to require that there is a ‘set of all sets’, and that seems incoherent. The reasoning is as follows. Suppose there was a set, V, which was the set of all sets. Well, why can’t we make another set, which has all the sets which are elements of V, as well as V, as it’s elements? Such a thing seems to be a set, and seems to employ just the process we have used at the lower levels. Yet it contains V, which we just postulated was the set of all sets. And that would mean that V is not the totality of all sets after all, but merely one more level of the hierarchy.

Such considerations seem to suggest that there cannot be a set of all sets, conceived of in this way. And if that is right, then the hierarchy of sets is potentially infinite, in that each set is finite but part of a never-ending hierarchy, where the notion of the completed totality is incoherent. Thus, along this way of thinking, we have an example of a potential infinite which is not an actual infinite. Such is the view of many people, including set theorists such as Ernst Zermelo, Kurt Gödel, and philosophers of mathematics such as Hilary Putnam, Charles Parsons, Geoffrey Hellman, and Oystein Linnebo.

And if this way of thinking is right, then Cantor was wrong here. Not every potential infinity implies an actual infinity.

3. A potential infinity that is also an actual infinity

Yet, things are not quite so straightforward. Although not every instance of a potential infinity presupposes an actual infinity; still, some might do. The hierarchy of sets is a particularly striking example where the idea of the completed infinity seems incoherent (for the reasons given above). However, the same sorts of considerations are not present in other cases.

For example, take the natural numbers. One can easily, and quite without contradiction, talk about the set of ‘all natural numbers’. This notion does not fall prey to the same worries as the set of all sets. Part of the achievement of Cantor was to elaborate the mathematical treatment of totalities such as the natural numbers. It is true that one could imagine counting forever, and such a process would increase without limit, always remaining finite and never being completed. Thus, it would be a potential infinity.

However, we can say things like “You will never have counted all the natural numbers” and when we use the phrase ‘all the natural numbers’ so we refer to a coherent concept. Even if we cannot reach the totality by counting, the concept of the totality itself does not seem incoherent in the same way as it does for the hierarchy of sets.

So in the case of the natural numbers, we have a potential infinity (instantiated by you trying to count them all), but we also have a completed infinity, which is the totality of numbers you are counting. And this is Cantor’s point. You can have a ‘variable magnitude’, which is the number you have counted (which is increasing over time), and there is the ‘range’ of numbers you are counting off, which does not increase and is an actual infinity. Thus, it seems like a potential infinity which presupposes an actual infinity.

Some people do disagree with this, of course. But such people are not merely saying that the concept of the actual infinity cannot be applied in the ‘real world’, as opposed to the mathematical world. Rather, such opposition requires disagreeing with Cantor that the actual infinity is a legitimate concept even in the mathematical realm. Carl Friedrich Gauss, for instance, strongly objected to the actual infinite even in mathematics. Such a position is called ‘finitism‘.

Craig, on the other hand, seems to have no principled objection to Cantorian treatments of the actual infinite in mathematics; he does not seem to be a finitist. If so, he should accept that sometimes there are potential infinities that are also actual infinities, such as the natural numbers.

4. Conclusion

Where does this leave us? I think we can say two things. Firstly, the following inference is invalid:

If x is a potential infinity, then x is an actual infinity.

It is invalid because the hierarchy of sets seems to be a plausible counterexample. However, unless one wants to take a very stern Gaussian position and banish the actual infinite even from mathematics, one must also concede that the following inference is also invalid:

If x is a potential infinity, then x is not an actual infinity

This seems invalid because the coherence of the totality of the natural numbers seems to be a counterexample.

This means that one cannot say that the angels prayers constitute an actual infinity merely because they constitute a potential infinity; but also one cannot say that they do not constitute an actual infinity merely because they constitute a potential infinity. Both sides can agree that they constitute a potential infinity, and this leaves open the question about whether they also constitute an actual infinity. In effect, the observation that they constitute a potential infinity is besides the point. The salient issue is about whether they constitute an actual infinity, and that is logically independent (assuming both of the above inferences are indeed invalid).

I think the lesson from this is that some potential infinities are also actual infinities, and some are not. The question becomes: which type is the future? The case we saw where something was potentially infinite but not actually infinite involved an incoherence involved in the notion of the totality. Is such a consideration present when it comes to the notion of the future?

One thing that seems plausibly problematic is the notion of the last time. One might think that the very notion of ‘a time’ implies that it has a past and a future. Such seemed to be Aristotle’s view:

“Now since time cannot exist and is unthinkable apart from the moment, and the moment a kind of middle-point, uniting as it does in itself both a beginning and an end, a beginning of future time and an end of past time, it follows that there must always be time: for the extremity of the last period of time that we take must be found in some moment, since time contains no point of contact for us except the moment. Therefore, since the moment is both a beginning and an end, there must always be time on both sides of it.” (Physics, book 6, part 1)

But such considerations shouldn’t sway us here. After all, the notion of number is similar in this respect. Just as we might think that for each moment of time there must be both past and future on either side of it, so too for each number there must be both higher and lower numbers on either side of it. The point is that we can conceive of the totality of natural numbers without thinking of there being a highest natural number. So, by analogy, even if there is no final time, this does itself stop us from conceiving of the totality of all future time.

We would be able to say that the future is potential and not actually infinite if there were some incoherence involved in thinking of the totality of future time, like there was with the totality of the hierarchy of sets. Yet, the cases seem dissimilar here. After all, what was causing the problem with the case of the sets was that the totality was itself a set. This meant that it could be fed into the iterative process that generated each preceding level in the hierarchy, generating a new level above it.

But such a move is not applicable to the notion of time. After all, the totality of time is not itself a time. Therefore, we need not suppose that the totality of time is itself followed by another time. If we did, then the case would be analogous to the set example. But it seems clearly to be distinct.

This does not establish that the case of time definitely is one that is both potentially infinite and actually infinite, but it does seem to show that if there is a reason it is not directly analogous to the hierarchy of sets example. Maybe there is an argument, but what is it?

My thought is that the time example is more like the natural numbers than the sets. Talk of the totality seems coherent. Thus, it seems entirely possible, at least conceptually, that the future is both a potential infinity and an actual infinity. And if that is right, then Craig’s reply is kind of impotent. Yes, potentially infinitely many praises will be said. But also, there is an actual infinity of praises yet to be said. The former point does not itself rule out, or in, the latter. Clearly, more needs to be said (though, hopefully not infinitely more).

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Rasmussen’s New Argument for a Necessary Being

0. Introduction

Josh Rasmussen is a philosopher at Azuza Pacific University. He recently sent me a copy of a paper entitled ‘A New Argument for a Necessary Being‘ in which he lays out an ingenious cosmological argument. I have a response to it, which I will outline here.

  1. The argument

 Here is the argument:

  1. Normally, for any intrinsic property p that (i) can begin to be exemplified and (ii) can be exemplified by something that has a cause, there can be a cause of p’s beginning to be exemplified.
  2. The property c of being a contingent concrete particular is an intrinsic property.
  3. Property c can begin to be exemplified.
  4. Property c can be exemplified by something that has a cause.
  5. Therefore, there can be a cause of c’s beginning to be exemplified (1–4).
  6. If 5, then there is a necessary being.
  7. Therefore, there is a necessary being.

Part of the cleverness of this argument is how weak the premises are. This means that they are easier to motivate and harder to object to. Premise 1, for example, is a defeasible rule of thumb. It isn’t ruling out there being objects that don’t satisfy it; as Rasmussen explicitly says, his argument

“…allows for the possibility of uncaused natural objects” (p. 4)

The modesty of its presuppositions is a strength.

In some respects, this argument is similar to the modal ontological argument. That too has very modest premises. One supposedly only has to grant that it is possible that God exists to get that he necessarily exists, to the conclusion that he actually exists.

However, I have an objection. My objection is similar to the objection to the modal ontological argument, whereby one says that it is possible that God does not exist, from which it follows that he necessarily does not exist, and so actually does not exist.

I will essentially present a new version of premise 4, from which we get a new version of premise 5, from which we get the conclusion that there is no necessary being. I will argue that my new version of premise 4 is explicitly allowed because of the weakness of Rasmussen’s premises, and that the only way to avoid it would require tightening it up, which loses the distinctive appeal and novelty of his approach. In addition, my new version of premise 4 is a core doctrine of Christianity, and as such Christians cannot simply deny it in favour of Rasmussen’s premie (in fact, they must find a way to block one of the premises of my argument or deny its validity, else it would rule out Christianity from being true).

Before we come to that, we need to understand Rasmussen’s argument in more detail. He provides a useful summary of premise 1 as follows:

 “…any beginning of an exemplification of an intrinsic property can have a cause…” (p. 2)

As a defeasible rule of thumb, this is quite plausible. Rasmussen provides an a priori type of justification and an abductive justification. The a priori justification is as follows:

“…imagine an arbitrary, unexemplified intrinsic property i . Suddenly, something changes. Snap! Property ibecomes exemplified. At this point, you may wonder why isuddenly became exemplified. Your mind might thus be inclined to think that i ’s exemplification canhave a causal explanation (especially if ican have caused instances). I suspect that some philosophers who come to the table as sceptics of a necessary being will have this intuition.” (p. 2 – 3)

The abductive justification runs as follows:

“…when a scientist creates a new piece of technology, a new type of thing begins to exist, and the scientist thereby causes one or more intrinsic properties to begin to be exemplified. As another example, we can imagine hydrogen and oxygen atoms coming together to form the first water molecule, thereby causing the property of being waterto become exemplified. In general, when we consider a new type of object, we can coherently imagine a cause of the exemplification of the new intrinsic properties instantiated by that object. Thus, we might infer (1) as a plausible explanation of these cases of apparent causability.” (p. 3)

Thus, we can see the sorts of things that Rasmussen has in mind as being examples of what premise 1 is about. We can grant this for the purposes of my argument. It is not supposed to be a universal principle, and might have exceptional cases which are counterexamples to it, but:

If someone has reason to doubt (1) based upon certain exceptional cases, she could still accept (1) as a general rule of thumb. (p. 3)

I have no need to dispute this here.

Premise 2 just says that the property of being a contingent concrete particular is an example of an intrinsic property. The notion of being an intrinsic, as opposed to extrinsic property roughly means that the property is held of an object without relation to any other objects. It is an intrinsic property of me that I am 5’10”, but it is an extrinsic property of me that I am taller than my friend Joe, etc. It is tricky to spell this distinction out perfectly, and Rasmussen offers a simple sufficient (but not necessary) condition for being intrinsic, namely:

“p is intrinsic if one who grasps p does not thereby grasp any external”

We can grant this for the purposes of my response. We can also grant that being a contingent concrete particular is an intrinsic property.

Premise 3 says that the property of being a contingent concrete particular, i.e. c, can begin to be exemplified. The premise doesn’t say that it actually did begin to be exemplified, only that it is possible for it to be so. Rasmussen says as an example:

“…we can imagine a beginning to the existence of contingent bits of matter as they explode out of an initial singularity.” (p. 4)

Thus, in a broad sense, it is possible for contingent concrete things to have an origin point. We can grant this for now as well.

Premise 4, according to Rasmussen, says:

there can be a contingent concrete particular that has a cause. (p. 4)

In defence of this, Rasmussen says:

“Take me, for example: I am a contingent concrete particular and my existence was caused some time ago.”

That seems very reasonable. I won’t directly challenge this premise, but it is at this point that my argument will kick in (more on that in a moment). Before we get to that, let’s just see how Rasmussen ties these considerations together into a whole.

Premises 2, 3 and 4 establish that c is intrinsic, can begin to be exemplified, and can have caused instances. This means that it is the sort of property that premise 1 applies to; it is the sort of property according to which

“there can be a cause of [c]’s beginning to be exemplified” (p. 1)

But because c is the property of being a contingent concrete particular, this means that:

“…there can be a cause of a beginning of contingency” (p. 5)

This is premise 5, and it follows from premises 1 – 4.

The move to premise 6 is my favourite bit of the argument, and I think the most ingenious. So far, all we have established is that it is possible that there is a cause for the beginning of contingency. We have not established that there is a beginning of contingency, or that there is a cause; just that such a cause of a beginning is possible.

From this, Rasmussen says, it follows that a necessary being exists. Here is how he gets there.

First, suppose that no necessary being exists. If that is the case, then, Rasmussen says, there couldn’t be a necessary being. This is the familiar inference used in the modal ontological argument; necessary beings exist at all possible worlds, so if there is even one at which they don’t exist, they exist at none at all. But if it is not possible for a necessary being to exist, it is not possible for a necessary being to be to cause the beginning of contingency either. So if there is no necessary being, then it must be possible for a contingent thing to cause the beginning of contingency (for it to remain possible at all, as premise 5 states). But this is incoherent, and thus impossible. Rasmussen explains:

This is because c —the property of being a contingent concrete particular— would already have to be exemplified if a contingent concrete particular were to cause c to begin to be exemplified in the first place. In other words, the exemplification of contingency would be ‘prior to’ the exemplification of contingency, which is impossible. (p. 5)

Rasmussen concludes this section with the following:

Thus, if there is no necessary being, then it is not possible for anything to cause a beginning of contingency, which contradicts (5). Therefore, if there is no necessary being, then (5) is not true. This result is the contrapositive of (6). Therefore, (6) is true.
From (1)–(6), it follows that there is a necessary being. (p. 5)

Now, I must say, I think this is a brilliant bit of reasoning. It is ingenious and original. I really like it.

But I still think I have a problem for it.

2. Counter-argument

My response to this argument is not really to reject any of the premises or the inference to the conclusion. The type of response I am giving is a sort of stale-mate response, rather than a defeating response. I think that we have just as good a reason to think that the negation of the conclusion is true, and I have an argument which is almost exactly the same as Rasmussen’s. In this respect, it mimics a familiar response to Plantinga’s modal ontological argument. That argument can be stated as follows:

  1. It is possible that a necessary being exists
  2. Therefore, a necessary being actually exists

The response to this is to simply postulate an alternative argument, with premises that are just as plausible, but with the opposite conclusion:

  1. It is possible that no necessary being exists
  2. Therefore, no necessary being actually exists

The question then becomes which of the two premises is more plausible. Each premise is equally plausible. Without a way of deciding between the premises which does not beg the question, the argument ends in a stalemate. Plantinga seems to accept this stalemate, because he is merely interested in establishing the rationality, rather than the truth, of the conclusion:

“[modal ontological arguments] cannot, perhaps, be said to prove or establish their conclusion. But since it is rational to accept their central premise, they do show that it is rational to accept that conclusion” (Plantinga 1974, 221)

If my argument works, Rasmussen would be pushed into accepting merely this sort of less ambitious defence, or he would have to tighten up the premises and thus lose the attractiveness of them.

Here is my counter-argument:

  1. Normally, for any intrinsic property p that (i) can begin to be exemplified and (ii) can be exemplified by something that has a cause, there can be a cause of p’s beginning to be exemplified.
  2. The property c of being a contingent concrete particular is an intrinsic property.
  3. Property c can begin to be exemplified.
  4. Property c can be exemplified by something WITHOUT a cause.
  5. Therefore, there can be NO cause of c’s beginning to be exemplified (i.e. it is possible that there is no cause of c’s beginning to be exemplified).
  6. If 5, then there is NO necessary being.
  7. Therefore, there is NO necessary being.

The argument is the same up to premise 4. The new version of premise 4 mimics the form of Rasmussen’s fourth premise, but simply says that c can be exemplified by something without a cause. As we saw above, Rasmussen is explicit that his argument allows for “the possibility of uncaused natural objects”. This seems enough to buy us my new premise 4; after all we only need the possibility, not the actuality of such objects for this premise to work. We will come back to what reasons we might have to thinking that premise 4 is true, but for now, let’s see what affect this has on the argument if we were to grant it.

One way of the new premise 4 being satisfied is by there being a first contingent thing that just pops into existence uncaused. Let’s say that a teapot pops into existence uncaused, and thus exemplifies property c. Thus, property c is exemplified by something which itself has no cause. In this scenario, premise 5 is true, because the teapot is the first (and indeed only) contingent concrete particular. Thus, it is a case of c beginning to be exemplified without any prior cause. Again, we are not saying that this scenario is true; just that it is possible that it is true.

This scenario doesn’t directly rule out a necessary being, but it does indirectly. We might think that there may be a necessary being who exists necessarily, and a teapot spontaneously pops into existence, as it were, next to her; or it may be that there is no necessary being at all (and, indeed nothing at all) and then a teapot just pops into existence on its own. Either seems possible.

But, as the familiar modal ontological argument reasoning goes, if the second scenario is even possible, then the first one isn’t. So if it is possible that the teapot pops into existence on its own, then there necessarily isn’t a necessary being. And remember, the premise

“…does not assert that this is actually the case—only that it is broadly logically possible for this [scenario] to be the case”

The test of broad logical possibility that Rasmussen uses throughout the paper was just whether we can imagine it. Recall, he said in defence of premise 3:

 “…we can imagine a beginning to the existence of contingent bits of matter as they explode  out of an initial singularity.”

If that establishes the possibility that premise 3 needs, then my being able to imagine the teapot popping into being on its own establishes my new premise 4.

But what about Rasmussen’s ingenious bit at the end of his paper, where he seemed to rule out this scenario? Didn’t he establish that “it is not possible for a contingent concrete particular to cause a beginning of contingency without circularity”?

Well, we can actually grant that he did. My counter-argument doesn’t require that the teapot causes c to become exemplified. As Rasmussen said, premise 1 is a rule of thumb, and not an exceptionalness principle. The teapot coming into existence is a case of an uncaused thing beginning to exist, and of c being exemplified without cause. Thus, we do not get caught in the trap that Rasmussen lays. We are simply explaining one way that new premise 5 is satisfied, which is that c begins to be exemplified by something uncaused, and it is one of those rare cases that premise 1 does not rule out. The very modesty of Rasmussen’s argument allows for this sort of case to pop up (in the broad logical sense).

So, if it is possible that the teapot pops into existence with no cause, then there is no necessary being (via the modal ontological argument inference). As new premise 5 states, such a thing is possible; therefore there is no necessary being.

3. Justifying new premise 4

The strategy I am employing here ends up with a stalemate, or at least that is the intention. Rasmussen’s premise 4 leads to the conclusion that God (or at least a necessary being) exists, and my new premise 4 leads to the conclusion that no necessary being exists.

One response would be to suggest that Rasmussen’s premise 4 is more plausible than my premise 4. If so, that might tip the balance in favour of his conclusion. In the case of the modal ontological argument, the thought was that no non-question-begging reasons could be brought forward that favoured one argument over the other. But perhaps there are decent reasons for thinking that the original premise is more plausible than the new one. We have already seen Rasmussen’s reason for thinking that his premise is true, which are pretty straightforward, and don’t seem remotely question-begging. His own existence as a contingent concrete particular was all that seemed to be needed.

Why think that the new premise 4 is correct though? We already saw that nothing in Rasmussen’s argument ruled it out. The modesty of the premises, which is one of its great strengths, also means there is more room for premises like mine though. The mere possibility of uncaused contingent concrete particulars is all I need, and they seem compatible with his argument. To rule them out, he would have to tighten up the premises, which would be to surrender some of the distinctiveness of his approach, and would mean that his premises would be harder to justify. But that could be done in principle. He could also take Plantinga’s route, and fall back on his argument merely establishing the rationality of belief in a necessary being rather than establishing the truth of the claim. Something has to give though, it seems to me.

However, I have one further problems related to this, specifically relating to Christianity.

Christian theism seems particularly invested in the scenario I used to satisfy premise 4 not being merely possible, but being the actual world. On Christian theism, it isn’t just that a contingent concrete particular can be exemplified by something without cause; it is the central doctrine of the religion this happened. Jesus came to earth and took on a human form. As part of the trinity, Jesus is an uncaused necessary being; what happened when he took on human form was that he exemplified a contingent concrete particular. Thus, Christianity seems invariably committed to the truth of my new premise 4.

So, while it is true that someone could tighten up the argument to avoid my counterexample, it doesn’t seem possible for a Christian.

Richard Carrier not getting an ought from an is

0. Introduction

In the book The End of Christianity, Richard Carrier has a chapter called Moral Facts Naturally Exist, in which he claims to be able to “dispense” with the is-ought problem. I don’t think he does this. I’m not going to look at the whole piece here, because it is quite long, but I intend to come back to it later. I’m just going to look at a few remarks he makes about the ‘is-ought’ problem.

  1. The argument

Characteristically, he is quite ambitious:

It’s often declared a priori that “you can’t get an ‘ought’ from an ‘is’,” and that therefore science can’t possibly discover moral facts. This is sometimes called a “naturalistic fallacy.” But calling this a fallacy is itself a fallacy. Indeed, it’s not merely illogical, it’s demonstrably false. We get an “ought” from an “is” all the time.

Given this primer, I am expecting to see the demonstration of how to get an’ ought’ from an ‘is’. That is, I am expecting to see a valid argument, with true premises that are purely descriptive that has a conclusion which contains the word ‘ought’.

Yet, this is not what we get. Here is what we get:

For example, “If you want your car to run well, then you ought to change its oil with sufficient regularity.” This entails an imperative statement (“you ought to change your car’s oil with sufficient regularity”), which is factually true independent of human opinion or belief. That is, regardless of what I think or feel or believe, if I want my car to run well, I still have to change its oil with sufficient regularity

Now hold on a minute. Let’s break this down into the relevant bits. Firstly we have a conditional statement:

  1. If you want your car to run well, then you ought to change its oil with sufficient regularity.

We also have an expression of the consequent of this conditional:

2.  You ought to change your car’s oil with sufficient regularity

Yet, contrary to Carrier’s claim, 1 does not entail 2 (if you disagree, please tell me the inference rule used). To make it entail 2, we would have to add in a premise, 1a, about what you want:

1. If you want your car to run well, then you ought to change its oil with sufficient regularity
1a. You want your car to run well
2. Therefore, you ought to change its oil with sufficient regularity (1, 2, modus ponens)

Together, 1 and 1a jointly entail 2 (via MP), but on its own 1 does not entail 2.

Carrier says that 2 is “factually true independent of human opinion or belief”, but it doesn’t follow from 1 unless we have the premise, 1a, which explicitly references what people want. We can, of course, assert that 2 is true independently of human opinion or belief if we like, but we have not shown that it is derived from 1. Asserting that 2 is true surely cannot be held to be an example of deriving an ‘ought’ from an ‘is’; it would be just an assertion of an ‘ought’.

Indeed, Carrier changes scope in the very next sentence, from 2 being what is independent of human opinion of belief, to 1 being independent of human belief:

“That is, regardless of what I think or feel or believe, if I want my car to run well, I still have to change its oil with sufficient regularity”

Clearly, he is now saying that the conditional statement is what is true independently of what people feel or believe. In the previous sentence, he is making a different claim, namely that the consequent is what is independent of what people feel or believe.

But even if the conditional (i.e. 1) is true independently of what people feel or believe, this does not mean that the consequent of the conditional (i.e. 2) is true independently of what people feel or believe. You can’t derive ‘q’ merely from ‘if p, then q’. And you can’t derive ‘q is independent of what people feel or believe’ from ‘(if p then q) is independent of what people feel or believe’.

But perhaps his claim is just that we can derive 2 from 1 and 1a. If so, he is right. And I also think that 1 and 1a are both true. I’m not disputing the logical form of that argument, or either premise. So that argument is both valid and has true premises. Great!

So, what’s the problem? Well, premise 1 has an ‘ought’ in it. So this is not an example of an argument which has an ‘ought’ in the conclusion, but no ‘ought’ in the premises. We are not getting an ‘ought’ from an ‘is’. We are getting an ‘ought’ from an ‘ought’ and an ‘is’. That is not what was advertised.

2. Diagnosis

What is going on here is that we often express the relationship between A and B, where A is something we want and B is the ‘optimal’ way of getting A, by saying that we ‘ought’ to do B. For example, most will happily nod along to the following:

If you want to go to university, and if studying hard for your exams is the optimal way to ensure going to university, then you ought to study hard for your exams. 

But, if you stop to think about it, the relationship between the antecedent and the consequent is not one of logical entailment. That is, the following is logically invalid:

  1. You want to go to university, and studying hard for your exams is the optimal way to ensure going to university
  2. Therefore, you ought to study hard for your exams.

I admit that this argument sounds valid. It sounds valid, and it has a descriptive premise with a normative conclusion. Contrary to what I’m claiming, many people will think that this is a way to derive an ‘ought’ from an ‘is’.

Regardless of how it seems, strictly speaking it isn’t valid. In reality it is an enthymeme, or an argument in which one premise is implicit. For example, if I say “x is a horse, therefore x is an animal”, we will hear this as valid, but only because the premise “if x is a horse, then x is an animal” is implicit. In formal logic though, we need to state all our assumptions. In the ‘is/ought’ problem, this is also true.

What is implicit in our case is the following premise:

1a. If you want A, and B is the optimal way of realising A, then you ought to do B.

We might have this in our background knowledge, as an implicit assumption, but if we are talking about logical validity (as indeed we are here), then we need to make these explicit. Once we add this new premise in, we can substitute terms from 1 to 1a to get:

1b. If you want to go to university, and if studying hard for your exams is the optimal way to ensure going to university, then you ought to study hard for your exams.

Now, 2 follows from 1 and 1b via modus ponens. That is, the following is valid:

1. You want to go to university, and studying hard for your exams is the optimal way to ensure going to university
1a. If you want A, and B is the optimal way of realising A, then you ought to do B.
1b. Therefore, if you want to go to university, and if studying hard for your exams is the optimal way to ensure going to university, then you ought to study hard for your exams (1, 1a, substitution)
2. Therefore, you ought to study hard for your exams. (1b, 1, modus ponens)

This argument is now formally valid, and the premises are true. But again, we have needed to insert a premise, 1a, which is not purely descriptive – it contains an ‘ought’ in it. Once again, we are not deriving an ‘ought’ from an ‘is’, but are deriving an ‘ought’ from an ‘ought’ and an ‘is’. In addition, 1a does not seem to be something that is empirically discoverable. It looks like a kind of conceptual truth. It doesn’t look like something that science discovered though. Yet it is needed to get to the conclusion.

Carrier says that:

There are countless true imperative facts like this that science can discover and verify, and that science often has discovered and verified, from “If you want to save the life of a patient on whom you are performing surgery, you ought to sterilize your instruments” to “If you want to build an enduring bridge, you ought not to employ brittle concrete.”

I think that what science discovers is something purely descriptive, such as that sterilising your instruments is (part of) the optimal way of performing surgery on patients without them dying. What we discovered is that people much more frequently die if we perform surgery on them with unsterilised instruments. Presumably, we want to ensure that people don’t die when we perform surgery on them. That means we have the thing desired, and (let’s say) an empirically discovered fact about the optimal way to realise that desire. But as we saw above, unless we insert a premise which links what we desire, the optimal way of realising it, and what we ‘ought’ to do, we cannot derive anything about what we ought to do. And that generalised principle, even if it is true, isn’t something science discovered.

His examples only get the varnish of looking valid by smuggling in the premise which mentions ‘ought’. Thus, all of his examples seem to fall foul of the same problem, and none of them are examples of getting an ‘ought’ from an ‘is’.

3. A deeper problem

But, let’s say that we agree that there are basic hypothetical normative facts about the world of the form “if you want to do x, then you ought to do y”. As I mentioned in a previous post, some of these are clearly not moral. Perhaps it is true that if you want to torture someone, you ‘ought’ to kidnap them and tie them up in your basement. Perhaps that is the optimal way of realising your desire to torture someone. A central moral intuition is that, regardless of this empirically discoverable fact about how best to realise your desire, you ought not do that. Some things are wrong, and some things are good, regardless of what we desire. Some things, like torturing innocent people, are wrong even if you are a sadist with a desire to do it; and some things, like helping old ladies across the road (or whatever) are good even if you are selfish and don’t want to do it. Someone who believes that all morality is reducible to hypothetical norms has a very hard time explaining these sorts of situations, where bad things are in line with our desires and good things in conflict with our desires.

I suspect that Carrier wants to say that people with such sadistic (etc) views are irrational somehow, but this seems like an article of faith. Why can’t there be an internally coherent belief set in which someone desires to torture innocent people? Maybe he has a response to this, but I haven’t read enough of his work to know.

Even if there are true hypothetical norms, I think these cannot be the whole story about morality. What we need in addition to these are categorical norms. Carrier’s attempt to say everything we need to about morality purely in terms of hypothetical norms seems to me to be wide of the mark, because it cannot make room in principle for immoral desires, or for moral things that go against our desires.

4. Conclusion

I intend to come back to this essay of Carrier’s, because it has many other seemingly interesting things going on in it. To sum this up, I think he fails to show how to derive an ‘ought’ from an ‘is’, and even if we give him the hypothetical norms he wants, these can never be enough to capture all moral truths.

Molinism and the Grounding Objection, Part 2

0. Introduction

In part 1, I outlined an objection to Craig’s suggestion that Molinist counterfactuals are easily known, which I called the ‘epistemic objection’. Here I will respond to a different claim that Craig makes in his paper.

Craig argues that the truth-maker principle is dubious, and states various counter-examples to it. He also suggests that even if we grant the truth-maker principle, Molinist counterfactuals can be given certain types of truth-makers anyway.

I think this is wrong. ‘Counterfactuals of creaturely freedom’ are just an instance of a type of counterfactual, which in turn fits into a wider family of counterfactuals. The overall analysis of this family of concepts shows us a different reason for rejecting Molinist counterfactuals being true.

  1. Truth-making

The dialectic works as follows.  Molinism is the position that some ‘counterfactuals of creaturely freedom’ are true, and as such are known by God. The ‘grounding objection’ is that Molinist counterfactualshave no truth-makers, and that this means that they must be regarded as being either truth-valueless or uniformly false. If so, then there are no such truths for God to know.

Part of the response to the grounding objection is to point out that it presupposes the more general principle of truth-making, according to which all true propositions are made true by something. Typical candidates for truth-makers are such things as ‘facts’ or ‘obtaining states of affairs’, etc. While such a view might initially seem plausible, it is a matter of serious dispute amongst philosophers.

For instance, Craig offers several examples of sentences which are difficult to fit in to various naive sorts of truth-maker theory, such as the theory that all true propositions are made true by some obtaining states of affairs. Consider the following proposition:

“Dinosaurs are extinct today.”

What truth-maker makes this proposition true? The relevant state of affairs, of ‘dinosaurs existing’, is absent. So, one might argue, the proposition is not made true by a state of affairs obtaining, but rather it is made true by a state of affairs not obtaining. If so, then it is an exception to the truth-maker principle, which is that all true propositions are made true by states of affairs obtaining. The proposition would be true, but without a truth-maker. And as Craig goes on to say:

“If there can be true statements without any truth–makers of those statements, how do we know that counterfactual statements cannot be true without truth–makers?”

It seems that the onus is on the anti-Molinist to defend the thesis of ‘truth-maker maximalism’, that there are no exceptions at all to the truth-maker principle, if that is to include Molinist counterfactuals. For if there are exceptions to the truth-maker principle, such as the one above, then maybe Molinist counterfactuals are exceptions as well.

We can think of the argument like this, where M is ‘Molinism is true’, G is ‘the grounding objection is successful’, T is ‘the truth-maker theory is true’.

  1. If G, then ~M
  2. G
  3. Therefore, ~M     (1, 2, modus ponens)

However, Craig’s reply is:

  1. If G, then T
  2. ~T
  3. Therefore, ~G       (via 1, 2, modus tollens)

So, Craig’s argument is designed to block the second premise of the first premise. Craig’s argument here does not prove that Molinism is true, but if successful would remove one of the reasons people have for thinking that Molinism is false.

2. Truth-making on the cheap

But Craig plays a stronger hand than this. He suggests that there are plausible truth-makers for Molinist counterfactuals, although these are not the types that anti-Molinists typically demand.

Anti-Molinists typically want counterfactual truth-makers to be things that actually exist. Yet, if we think of the counterfactual involving Louis and the bike (see my previous post), it seems that the real, actually existing, version of Louis lacks any properties that entail whether he would have freely stolen it rather than not stolen it. Modally speaking, he was just free to do either. No investigation into any of Louis’ actual properties will ever reveal which one it would have been though. Therefore, the facts about the actual Louis underdetermine whether he would have freely chosen to steal the bike or not.

In response to this though, Craig proposes a different theory. According to this theory, Molinist counterfactuals do have truth-makers, but they are not categorical (or descriptive) properties of actually existing objects. Rather, they are a different type of property, namely modal properties. The distinction between modal properties and categorical properties is fairly easy to draw, and is done so quite nicely in the first two pages of this book by Joe Melia. Categorical properties include things like the size, shape, position, and velocity of every object that there is (insofar as modern physics allows for such properties, I guess). So, a categorical fact would be that Louis is 5’10”, and is currently in his living room watching his TV. Suppose we could specify as precisely as we liked, and include exactly which colour each pixel is on his screen, and exactly which cells in his brain are currently generating his experience, etc. The thought would be that we could extend this description of Louis out from his living room and include the properties of everything else that exists, starting with his house, the street he lives on, his city, the country, the planet, the galaxy and including the whole universe.

It would be tempting to think that such a description covered everything. Yet there is reason to think that an important class of truths would have been left out of such a description. Sure, Louis is currently sitting down. But, he could have been standing up. This is a modal fact, and describes not just how things are, but introduces how things could be; it is not just categorical, but modal.

If there are modal facts, in addition to categorical facts, then Craig could use them as the truth-makers for his counterfactuals.

In order to motivate this option, Craig favourably endorses a strategy employed in the philosophy of time, concerning tense.

There are theories of propositions according to which they have tense. We call such theories A-theories. Something very similar to the grounding objection could be pressed to A-theories, and Craig is impressed with one way that A-theorists can respond to the objection.

Take the view that there are tensed propositions, such as ‘There was snow yesterday’. A truth-maker theorist might want to say that this proposition is made true by some presently obtaining state of affairs, i.e. present-tensed fact (such as the presence of snow on the ground right now, etc). The problem is that there are various future- or past-tensed propositions for which no such presently obtaining truth-maker exists (i.e. for which no corresponding present-tensed fact exists). Take the tensed proposition ‘There was snow exactly 100 years ago today’. It is doubtful that anything about the current state of affairs determines whether there was snow exactly 100 years ago today or not. Either option is possible, for all the present facts about today determine. Thus, not all future- or past-tensed facts have presently obtaining truth-makers.

The idea here is that future-tensed propositions, like “It will be that p”, are made true by future-tensed facts. If we allow that there currently are facts of the form ‘p will be made true’, then these could be the truth-makers for future-tensed propositions. Craig quotes Freddoso:

“…there are now adequate metaphysical grounds for the truth of a future–tense proposition Fp just in case there will be at some future time adequate metaphysical grounds for the truth of its present–tense counterpart p”

Freddoso is pointing out that there may be no present-tensed obtaining states of affairs that could ground the future-tensed truth, but if we allow for future tensed states of affairs (or future-tensed facts), such as “there will be at some future time adequate metaphysical grounds for the truth of its present–tense counterpart p“, then we do have a presently obtaining state of affairs to play the role of truth-maker. The idea is that future-tensed truths require future-tensed truth makers. And it is this sort of idea that Craig is going to endorse when we come to the case of counterfactuals.

So, on Craig’s proposal, a counterfactual is not made true by any categorical states of affairs, but by modal states of affairs. This is explained by Flint, according to which:

“It would be the case (if c were true) that z” is now grounded iff “z is grounded” would be the case (if c were true).

We can ground the truth of “Louis would have stolen the bike had he been tempted” with the modal fact, that ‘Louis would have stolen the bike had he been tempted’. As Craig puts it himself:

“For my part, I should say that if true counterfactuals of creaturely freedom have truth–makers, then the most obvious and plausible candidates are the facts or states of affairs disclosed by the disquotation principle. Thus, what makes it true that “If I were rich, I would buy a Mercedes,” is the fact that if I were rich I would buy a Mercedes. Just as there are tensed facts about the past or future which now exist, even though the objects and events they are about do not, so there are counterfactuals which actually exist, even though the objects and events they are about do not.”

So, in summary, Craig is adopting a strategy commonly appealed to in the philosophy of time. A certain type of truth-maker (namely present-tensed facts, or purely categorical facts) is not suitable for grounding a certain type of proposition (namely future tensed propositions, or counterfactuals of creaturely freedom), and in each case a different type of truth-maker is proposed (future-tensed facts, or modal facts).

3. Objection

It has taken a while to explain Craig’s move, and it will take just as long to explain the objection. I suggest that the anti-Molinist need not posit truth-maker maximalism; nor need they posit that all truths have merely categorical truth-makers. Maybe there are truths that are not grounded in anything, such as ‘This sentence is true’. Maybe that is true but not grounded in anything. Who knows? Maybe there are tensed facts, such as that Matt Damon will be the first man on Mars. Who knows? I don’t need to rule either of those out.

Why not? Well, because I can phrase the objection in a more specific way. Consider a fair coin, with heads on one side and tails on the other, and also a rigged coin, with heads on both sides. It seems true to say of the fair coin that it could land heads, and that it could land tails. Also, it seems false to say of the fair coin that it would (necessarily) land heads, or that it would (necessarily) land tails. Things are obviously different for the rigged coin. It is true to say that it will necessarily land heads, and false to say that it even could land tails. As such, the two coins have a different set of modal properties. The modal facts about the coins is different. But ask yourself why that is. The obvious candidate answer is that they have different categorical properties. The fair coin has different things on each side, and the rigged coin has the same thing on each side. Clearly, the categorical facts explain the modal facts; and as such the categorical facts explain the modal facts. This all seems very straightforward.

But what this means is that there are various counterfactuals which, even if they are made true by modal facts, are ultimately explained by categorical facts. Here is one:

A) ‘Had I flipped the rigged coin, it necessarily-would have landed heads’.

A) is true, and let us suppose (for the sake of the argument) that what makes it true is the modal fact had I flipped the rigged coin, it necessarily-would have landed heads (to make it in line with what Craig proposes).

My conjecture, which seems pretty obvious, is that the modal fact that makes A) true is explained by (and hence grounded in) the categorical facts about the coin, and in particular about it having heads on both sides.

Consider the following pair:

B) ‘Had I flipped the fair coin, it might have landed heads’

C) ‘Had I flipped the fair coin, it might have landed tails’

Clearly, B) and C) are. Even if this is because they are made true by modal facts, it is still the case that these modal facts themselves are going to be explained (among other things) by the categorical fact that the fair coin has heads on one side and tails on the other.

I say “among other things” because no doubt there will be some modality involved in the description of the situation. The coins need to be flipped in the right circumstances, for example. If flipped in the vacuum of space, the will just spin off forever and not land at all, etc. So we would have to say something like “in normal circumstances”, and this would involve a specification of the laws of physics acting on the coins. Laws themselves have irreducibly modal aspects to them, one might think, and if so then our description is not purely categorical.

That might be true, but it doesn’t matter even if it is. All I need is that, at least in part, the modal facts are explained via reference to categorical properties (such as the actual properties of the coins). This is my conjecture, and I think it is correct.

What does it mean to deny it though? Well, remember that the coins have associated with them different counterfactuals. We can think of this as the ‘modal profile’ for the coins. The fair coin has both B) and C) in its profile, but the rigged coin only has B), for example. The question is what explains this difference in profile. My conjecture is essentially that part of the explanation involves reference to categorical facts, and cannot be purely modal. The cost of denying my conjecture is that the explanation of why the rigged coin has a different modal profile to the fair coin becomes inexplicable. The rigged coin just has different modal facts associated with it; end of explanation. Yet, we all clearly see that there is a deeper explanation which involves the categorical facts about the coin and what is on its faces. So the cost of denying my conjecture is that you end up making something clearly explicable into a mystery. This is clearly a theoretical cost, and needless.

Yet, a Molinist has to make such a move. This is because if we introduce Molinist counterfactuals into the picture, then we have to suppose that our fair coin has in its modal profile a counterfactual proposition of the following form:

D) ‘Had I flipped the fair coin, it just would have landed tails’

This proposition doesn’t express either that the coin had to land heads, nor that it merely could have done; rather it expresses the idea that God knows which way it would have contingently landed if you had flipped it.

When it comes to these counterfactuals, Craig supposes that we can have a purely modal truth-maker for it. The proposition ‘Had I flipped the fair coin, it just would have landed tails’ can be made true merely by the modal fact that had I flipped the fair coin, it just would have landed tails.

But now consider the two things side by side. On the one hand, we have strong ‘would’ and mere ‘might’ counterfactuals, and these seem to require reference to categorical facts, even if they have modal truth-makers. On the other hand, we have Molinist counterfactuals, which Craig supposes can have purely modal truth-makers. Given that they are clearly in the same family of expressions, it is puzzling as to why they have such different types of semantics. Why does one have to have categorical aspects to it’s grounding while the other does not?

We might try to align them to avoid this weird asymmetry. We could either try to introduce some categorical facts into the explanation of the Molinist truth-maker, or we could try to remove the categorical facts from the explanation of the other counterfactual’s truth maker. Well, as I argued above, if we remove reference to the categorical facts about the coin from the explanation of the truth-makers for the first type of counterfactuals, then we made an explanation into a mystery. As such the latter option is a non-starter. As such, to align the analysis of counterfactuals, we need to introduce something categorical into the explanation of the Molinist counterfactuals. But what could this be? There is clearly nothing categorical, nothing purely descriptive, about the fair coin which determines that it would land heads rather than tails on any given flip. This is really the heart of the grounding objection. Up to the point of being flipped, the world where the fair coin lands heads is utterly identical to the world where it lands tails. As such there cannot be any purely categorical fact that tells between heads and tails.

But this leaves us with a weird asymmetry. The analysis of would and might counterfactuals takes one form, but the analysis of Molinist counterfactuals has to take another. Why is the analysis symmetric? Is there anything that accounts for it? I think there isn’t. There is no principled reason why Molinist counterfactuals have such a different type of semantics from all the other types of counterfactual. But the fact that they appear on their own, untethered from the satisfying and explanatory semantics that their cousins enjoy, makes Molinist counterfactuals look suspect. They look like gerrymadered creations. It is not just that they have to have modal facts, but they also have to have a different type of analysis of their own.

Let me make the point sharply before stopping.

Here is the analysis of a might counterfactual:

Propositions B) and C) are both true of the fair coin. Why is that the case? Well, let’s say that they have modal truth-makers which make those propositions true, i.e. which give them their modal profile. What accounts for the difference in modal profile between the rigged and fair coin? Well, this is accounted for by a deeper description, at least partially involving categorical facts about the actually existing coins themselves.

Here is an analysis of a Molinist counterfactual:

Proposition D) is true of the fair coin (at some particular time). Why is that the case? Well, let’s say that it has a modal truth-maker which makes that proposition true. What explains why D) is true right now of this fair coin, but that two minutes later, if flipped again, it would have happened to have landed tails? Well, all Craig can say is that it has a different modal truth-maker two minutes late. But why is this the case? There is no reason; the analysis ends here. Nothing categorical can be wheeled in to explain it, and all we have is a sort of brute fact.

When put like this, the two analyses seem very different, and the onus is on the Molinist to either realign their analyses or to find some non ad hoc way of accounting for the difference. I think it is obvious that they cannot be realigned (as we went through the options above), and given the closeness of the propositions grammatically, any explanation of why their analysis is so different is bound to be ad hoc. Maybe God wants them to have different analyses, for example, is not going to cut it.

4. Conclusion

The conclusion is that counterfactuals, even if they have modal truth-makers at some level, are tethered to categorical facts about how things actually are. It is because Molinist counterfactuals cannot be tethered to reality in this way, and can only be supported by purely modal facts, that we can see that they are just a philosopher’s fantasy. This is the real grounding objection, in my opinion. I’m not proving that they are a philosopher’s fantasy, but I am bringing out how much strain they put on the analysis, and what a big semantic problem they have. Craig makes it seem like it is an effortless move to make, but by making the move he breaks from the clear and obvious way we analyse all other counterfacuals. The complaint is that the difference in analysis can only be justified by special pleading. Counterfactuals are analysed like this, says me. That’s true of the others, but not when it comes to these ones, says Craig. But why are they treated differently? That is the question I need to hear an answer to, and I don’t think there is one, apart from ‘because if they are then my theory works’, which is the definition of ad hoc.

Sam Harris not getting an ought from an is

Sam Harris recently made a series of Tweets which, he claimed, showed how to get an ‘ought’ from an ‘is’. Here they are:

  1. Let’s assume that there are no ought’s or should’s in this universe. There is only what *is*—the totality of actual (and possible) facts.
  2. Among the myriad things that exist are conscious minds, susceptible to a vast range of actual (and possible) experiences
  3. Unfortunately, many experiences suck. And they don’t just suck as a matter of cultural convention or personal bias—they really and truly suck. (If you doubt this, place your hand on a hot stove and report back.)
  4. Conscious minds are natural phenomena. Consequently, if we were to learn everything there is to know about physics, chemistry, biology, psychology, economics, etc., we would know everything there is to know about making our corner of the universe suck less.
  5. If we *should* to do anything in this life, we should avoid what really and truly sucks. (If you consider this question-begging, consult your stove, as above.)
  6. Of course, we can be confused or mistaken about experience. Something can suck for a while, only to reveal new experiences which don’t suck at all. On these occasions we say, “At first that sucked, but it was worth it!”
  7. We can also be selfish and shortsighted. Many solutions to our problems are zero-sum (my gain will be your loss). But *better* solutions aren’t. (By what measure of “better”? Fewer things suck.)
  8. So what is morality? What *ought* sentient beings like ourselves do? Understand how the world works (facts), so that we can avoid what sucks (values).

The whole thing boils down to premise 5. He says that we ought avoid things that ‘suck’. By ‘suck’ he basically means things that are painful (as his example of the stove indicates). So premise 5 basically just says: we ought to avoid pain. That is assuming an ought coming from an is: we ought not do things that cause pain (that ‘suck’).

The only thing he says to justify this is “If you consider this question-begging, consult your stove, as above”. But all ‘consulting the stove’ would do is remind us how painful the experience was. It wouldn’t, on its own, show us that we ‘ought’ not do it.

What Harris is relying on is the fact that we don’t want to have the experience of pain that touching the stove provides. The idea is that there is a hypothetical norm of the following form:

If you don’t want to feel pain, you ought not put your hand on the stove.

Harris is relying on the fact that we all don’t like feeling pain, and so the antecedent condition applies universally. But still, it is a hypothetical norm, not an unconditional (or ‘categorical’) norm.

What difference does that make?

Well, it isn’t really an example of getting an ought from an is; at least, not in any morally significant sense anyway. That’s because hypothetical norms are just the best ways of realising your desires. If you desire x, you *ought* to do y, when y is the optimal way of realising x. They can be morally significant things, like if you want to make the world a better place, you ought to give to charity, etc. But they can also be morally neutral: if you want to get your car fixed, you ought to take it to a mechanic; if you want to loose weight, you ought to take more exercise. They can also be immoral: if you want to murder your neighbour, you ought hit him over the head with this rock.

Morality, on the other hand, is usually thought of as being unconditional, or ‘categorical’. Take my last example. Sure, hitting your neighbour is an efficient way of murdering him. But we generally think that we simply ought not murder people at all. Even if I want to, I ought not do it. The ‘is-ought’ issue is about how to derive these sorts of ‘oughts’ from mere ‘is’s.

So the mismatch is that he is asserting a categorical normative statement (“we should avoid what really and truly sucks”), and he is offering only a hypothetical norm as it’s justification (which is that if you don’t want to experience things that suck, you ought not do things that will produce experiences that suck).

Hypothetical norms can’t justify categorical norms though, because the former require you to have a particular desire, whereas categorical norms are independent of what you desire; hypothetical norms only apply to you if you have a certain desire, but categorical norms apply to you regardless of whether you do.

Its a bit like saying ‘Everything is A’, but justifying that with the statement ‘Everything which is B is A’. Even if we agree with the latter, that cannot justify believing the former.

 

CosmicSceptic and objective morality

0. Introduction

CosmicSceptic is an atheist YouTuber, called Alex, from England. Despite those similarities, we see things a bit differently. He recently made a video, called Morality Can’t be Objective, Even if God Exists. In it, CosmicSceptic (henceforth CS) makes a few pretty sloppy arguments, and I’m going to explain where I think he went wrong here.

  1. The main claim – morality is subjective

At the start of the video, CS explains that he has had something of a change in his view recently. Apparently, he used to think that atheists had to be subjectivists about morality, but that theists could be objectivist about morality. In contrast to that, he now believes that:

“…even they, the religious … can’t provide an objective basis for morality either” (1:17).

So what CS is going to argue is that nobody can provide an ‘objective basis’ for morality; all morality is subjective, whether atheistic or theistic in nature.

1.1 Subjective and Objective

An immediate issue is that CS doesn’t tell us exactly what he means by ‘objective’ or ‘subjective’. It’s not a particularly controversial topic, and this Carneades video does a good job explaining it. Basically:

  • x is objective if and only if (iff) x does not depend on what we think or feel about x.
  • x is subjective iff x does depend on what we think or feel about x.

On the other hand, I think CS sometimes means something slightly different by the term ‘objective’. Sometimes, it sounds like he means the following:

  • x is objective iff it can be shown (or demonstrated, or proven) to be the case

These are two ideas are distinct, because (at least in principle) something can be objective in either sense without being objective in the other.

For example, unproven (or or even unprovable) mathematical formulas are still true or false independently of what anyone thinks about them (although some philosophers disagree, most don’t). So, there can be things that are true independently of what we think, but not demonstrable.

Conversely, something can be demonstrated to be the case, yet not be true independently from what we think about it. For example, we can demonstrate the value of the dollar vs the pound (by pointing to the latest exchange rate), but all monetary value is a product of collective human agreement, and would not exist if minds did not exist.

So being mind-independent and being demonstrable are logically distinct notions, and should not be conflated. Unfortunately, there is a sort of ambiguity present whenever CS says ‘objective’. For instance, when CS makes his central claim, it seems to me to be infected with the above ambiguity. He says (1:45):

“I am now of the view that all morality, even religious morality, is ultimately subjective”.

Is he saying that: all morality depends on our mental states or that: morality cannot be shown to be true? These are quite different. His central claim is not clear. Maybe he has explained this in other videos, but haven’t seen him ever explain this. This will become important towards the end.

Anyway, CS explains that he will outline the following:

  1. How he defines morality
  2. Why he thinks religious morality is subjective.

So let’s take these in turn.

2. Defining morality

CS defines morality as (5:43):

“The intuition that we ought to do that which is good and ought not do that which is bad.”

He puts this as text on the screen so we are sure to note it. There are several big problems with this though.

Firstly, it completely begs the question against the moral realist. Usually, moral realism is the view that moral claims, such as “x is good” or “one ought to do x”, state truths, and these are true independently of what people think or feel about them (i.e. they are objectively true). Yet, CS defines morality explicitly in terms of intuitions, which are mental states. If there were no minds to have intuitions, then there would be no morality according to CS’s definition. That rules out moral truths as being ‘objectively’ true from the outset.

Before he gives his definition, he talks about something that Tracy Harris said on an episode of the Atheist Experience. CS disagrees with Harris because he thinks that when talking about what makes someone moral or not, she left out the idea of having moral intuitions. CS imagines a robot that is programmed to act fairly, but this wouldn’t make the robot moral, according to CS. To be so, the robot needs moral intuitions, says CS.

Perhaps a moral agent requires intuitions of what is right and wrong (although I’m not sure I buy that either), but that definitely doesn’t mean that morality itself should be defined as being an intuition about what is right and wrong. Morality, surely, is what our moral agent has intuitions about; that is what we need to be defining. So I think I can see how CS got to his definition, but he should drop the word ‘intuition’ from it (and indeed he later does).

Secondly, and this is more important, there are clear counterexamples to the central aspect of his proposal. He is basically offering two conditionals, which relate the moral properties of ‘good’ and ‘bad’ with the moral duties, or obligations, which are what you ‘ought’ and ‘ought not’ to do. His conditionals are as follows:

  1. If something is good, then we ought to do it
  2. If something is bad, then we ought not to do it

CS seems to think these are mere platitudes. Yet, there are seemingly obvious counterexamples to this.

In general, being obligatory is a stronger requirement than being good; there are things which are morally good to do, but which you are under no obligation to do. For example, friendship is morally good, but it is not morally obligatory to have friends. The concept of what is morally good is larger than what is morally obligatory; it contains what is obligatory, but also contains things that are not obligatory (like friendship).

Similarly, there are things that are morally bad, which are not impermissible. Exactly what the examples of this category are is debatable of course, but gambling or eating meat are examples of things that are plausibly morally bad but not impermissible. In that way, bad contains the impermissible as a proper subset, and also things that are not impermissible.

We can place actions on a moral scale, as follows:

  1. Both good and obligatory (like saving a person who is drowning in front of you)
  2. Good but not obligatory (like friendship)
  3. Neutral (like having toast for breakfast)
  4. Bad but not impermissible (like eating meat, or gambling)
  5. Both bad and impermissible (like murder or rape)

The fact that we have categories 2 and 4 stops CS’s idea, that we ought to do what is good and ought not to do what is bad, from looking plausible.

2.1 Argument

(The causal reader can skip this bit if they like.)

We can even make an argument which shows what is at stake by adopting CS’s idea, as follows. Consider the principle that ought implies can:

  1. If x is obligatory, then x is possible.

This principle seems very intuitive. Yet, if CS’s view were correct, we would have to abandon it. The reason is that there is no ‘good implies can’ principle, and this makes the pair asymmetric. Here is an illustration:

Imagine you have just one $5 note in your pocket, and are faced with two charity collection buckets; one for a dog charity and one for a cat charity. Giving to the dog charity is morally good, and giving to the cat charity is morally good. Giving to both is morally good. Yet, if we ought to do what is good, then we ought to give the $5 bill in both the dog and cat bucket. But it is impossible to do that; the same bill cannot go in each bucket. Tearing the bill in half will result in giving nothing of any value to either, which is bad. So we have something which is good to do (give to both), and is therefore something that we ought to do (by CS’s principle), but which is also something that we cannot do (because we can only give to one and not the other). Thus there is something we ought to do that we cannot do, which clashes with the ought implies can principle. We can avoid this difficulty by recognising that although both are good, neither is obligatory, which is to throw out CS’s principle.

Here is a slightly more formalised version of the argument, for people who like that sort of thing. If you don’t, you can definitely skip this bit. It’s a reductio ad absurdum:

  1. ~(◊(Dog & Cat))                                   (Assumption)
  2. G(Dog) & G(Cat)                                  (Assumption)
  3. O(x) -> ◊(x)                                          (Ought implies can)
  4. G(x) -> O(x)                                          (CS’s principle)
  5. ∴ G(Dog & Cat)                                    (2, distribution)
  6. ∴ O(Dog & Cat)                                    (4, 5, modus ponens)
  7. ∴ ◊(Dog & Cat)                                    (3, 6, modus ponens)
  8. ∴ ◊(Dog & Cat) & ~(◊(Dog & Cat))    (1, 7, conj. intro.)

7 contradicts 1. One has to deny either 3, or 4, or show that some step is invalid. Is it invalid to infer from two things being good that their conjunction is good (premise 5)? Premise 3 is very intuitive, premise 4 is CS’s principle. Given the above reasons for doubting CS’s principle, it seems obvious that we should just avoid it and block the inference to the conclusion.

2.2 Moore

Despite saying that he is a big fan of moral philosophy, frustratingly, CS only mentions one actual moral philosopher, G E Moore. CS says (6:55) emphatically that:

“…the reason that morality can’t be objective is precisely because ‘good’, ‘bad’ and ‘ought’ can’t be defined. I subscribe to G E Moore’s notion that Good is like the colour yellow. It has no synonyms. It can’t be described to someone who has never experienced it. Nonetheless, you know what I mean by yellow, and you know what I mean by good”

So, not everyone holds to this view, that moral notions can’t be defined. If you think that good actions are those that maximise happiness (or wellbeing, or whatever), then you do think you can say something about what ‘good’ means. Also, if you think that good actions are ones that God commands, then you think you can say something about what good means. Moore disagreed with both of these types of approaches to meta-ethics, and argued that no definition could be given. So, when CS says that he subscribes to G E Moore’s notion that “good is like the colour yellow. It has no synonyms,” it seems like he is saying that he is a moral non-naturalist, like Moore.

But it is strange to see CS endorsing Moore, because Moore was a famous moral realist, who thought there were mind-indepenedent truths about morality. For example, in the opening section on Moore’s moral philosophy in the Stanford article, we find the following point:

“Moore’s non-naturalism comprised two main theses. One was the realist thesis that moral and more generally normative judgements … are objectively true or false. The other was the autonomy-of-ethics thesis that moral judgements are sui generis, neither reducible to nor derivable from non-moral, that is, scientific or metaphysical judgements.”

Clearly then, Moore held that moral notions were both objective and indefinable. In contrast, CS says that moral notions can’t be objective because they are indefinable (“the reason that morality can’t be objective is precisely because ‘good’, ‘bad’ and ‘ought’ can’t be defined”). This is really quite different from Moore.

In fact, Moore is at pains to stress that cases of moral disagreement are like cases of mathematical disagreement (which is paradigmatically objective). We do not simply say that each party has their own subjective view of what is at stake in mathematics; rather, we explain it by supposing that (at least) one party is making a mistake somewhere. As Moore famously says about finding someone doing mathematics seemingly incorrectly:

“If we find a gross and palpable error in the calculations, we are not surprised or troubled that the person who made this mistake has reached a different result from ours. We think that he will admit that his result is wrong, if his mistake is pointed out to him. For instance, if a man has to add up 5 + 7 + 9, we should not wonder that he has made the result to be 34, if he started by making 5 + 7 = 25. And so in Ethics, if we find, as we did, that ‘desirable’ is confused with ‘desired’, or that ‘end’ is confused with ‘means’, we need not be disconcerted that those who have committed these mistakes do not agree with us. The only difference is that in Ethics, owing to the intricacy of its subject-matter, it is far more difficult to persuade anyone either that he has made a mistake or that that mistake affects his result” (Moore, Principia Ethica, §87).

Moore clearly thinks that ethical disputes are as objective as mathematical disputes, and only look different (i.e. look potentially subjective) because ethics is harder than mathematics.

Thus, CS has only a passing connection to Moore’s philosophy here. If this was the first time you had encountered Moore’s moral philosophy, you might come away thinking that his view is similar to CS’s, when they are extremely different

Confusingly, CS seems to change his own tune. Firstly, he starts off saying that moral terms can’t be defined (and cites Moore), but later on he seems to be advocating a pragmatic strategy, which is that by simply not defining them, isn’t taking a stand on moral philosophy at all. He says (7:45):

“The moment we attempt to define good, as in to give it a synonym, we necessarily have to presume a particular moral philosophy. I might define ‘good’ as ‘what God commands’, or as ‘what procures wellbeing’. But to do so I would automatically be agreeing with a certain philosophy. And this is why I haven’t defined ‘good’, ‘bad’ or ‘ought’ in my definition.”

So there are two different reasons given for why CS doesn’t define moral terms:

  • “…the reason that morality can’t be objective is precisely because ‘good’, ‘bad’ and ‘ought’ can’t be defined”
  • “…to [define moral terms] I would automatically be agreeing with a certain philosophy. And this is why I haven’t defined ‘good’, ‘bad’ or ‘ought’ in my definition.”

Moore’s claim was that moral terms are indefinable. He has arguments for that claim (such as the open question argument, and the naturalistic fallacy). That is itself a type of moral philosophy, called non-naturalism. Advocating the position that moral terms are indefinable is already to take a stand on moral philosophy, and to disagree with people who define moral terms in relation to God’s commands or maximising wellbeing. Moore didn’t just refrain from giving a definition because otherwise he would “automatically be agreeing with a certain philosophy”. He wasn’t avoiding advocating a moral philosophy. He had a very distinct, and influential, moral philosophy of his own.

CS seems to think in this section that by not defining the terms he is not taking a stand deciding between moral philosophies. That’s not only false (because he would be endorsing a version of non-naturalism, which is itself a species of realism), but it is also different from what he said above. Either CS doesn’t define moral terms because he thinks, like Moore, that they can’t be defined; or he merely holds off from defining them in order to make a statement that other people can get on board with. These are not the same, but CS doesn’t seem to recognise that.

We are left feeling that his grasp of what Moore’s moral philosophy is, is shaky at best.

3. Religious morality – Craig’s argument

CS examines some quotations from William Lane Craig. CS sets up the challenge as follows (10:55):

“So why does Dr Craig feel that atheism can’t provide a basis for objective morality?”

The quote from Craig goes as follows:

“Well, because if morality is just based in feelings, and relationships with other people, and the way we were raised by our parents and society, then it’s all relative – someone who has different feelings or was raised in a different society might have a vastly different set of values and moral duties – and therefore it’s not objective; its purely subjective”

CS comes back immediately after playing the clip by saying:

“Ok, so that’s crucial. Note the use of the word “therefore”. Dr Craig says that atheistic morality can vary upon a person’s upbringing, their geographical and social background, their environment, which ‘therefore’ shows that it is subjective, because it wouldn’t be variable if it were objective.”

I take it that this is CS summarising what he takes to be Craig’s argument here. We can put it like this:

  1. Atheistic morality can vary due to geography, etc.
  2. Therefore, atheistic morality is subjective.

CS thinks that this argument can be turned against religious morality though:

“It seems by that logic that if I can show that religious morality can vary in the same way, it too is therefore subjective. And of course a moment’s reflection allows us to realise that religious views too, obviously, vary in exactly the same way. A person’s religious view is more often than not determined by their social and geographical background, just as atheistic morality is.”

CS is making the following argument:

  1. Religious morality can vary due to geography, etc
  2. Therefore, religious morality is subjective.

Let’s try to be clear about what is going on. I’m going to make two distinct points about this. Firstly, he seems to be strawmanning Craig’s assertion. Secondly, CS is using the term ‘atheistic morality’, but he doesn’t explain what he takes that phrase to mean, and this causes problems with how he takes the argument even if we think he didn’t strawman Craig.

3.1 Treating Craig Fairly?

I think that there is reason to seriously doubt that CS’s idea of Craig’s argument is what Craig was really saying. CS seems to ignore entirely the first part of Craig’s sentence. Consider it again:

“… if morality is just based in feelings, and relationships with other people, and the way we were raised by our parents and society, then it’s all relative.”

It is a conditional, and the first bit of the antecedent is “morality is just based in feelings”. The conclusion, following on from the word ‘therefore’ that CS told us was crucial, was “it’s not objective – its purely subjective”. Let’s recall that the standard definition of subjective just means that it is dependent on our thoughts and feelings. On one reading then, what is going on here is that Craig is really just spelling out that:

If “morality is just based in feelings” then “it’s not objective; its purely subjective”

That is a simple definitional consequence. That’s just what it means to be subjective.

The words that follow the ‘therefore’ (i.e. “it’s not objective; its purely subjective”) isn’t primarily supported by the idea that morality varies from place to place. That is merely an illustration of the wider antecedent assumption, which is that “morality is just based in feelings”. This seems to be the most straightforward way to hear what Craig is saying here.

Looking at it the way CS does though, Craig is making a really poor argument. He might be doing so, but given that there is another easy way of reading him, why think that he is? Why not consider the better argument? Either CS didn’t ever realise that Craig could be read like that, or he simply misunderstands Craig (due to not being clear on what ‘objective’ means), or he is strawmanning Craig. I don’t know which one it is.

3.2. Atheistic morality

CS uses the term ‘atheistic morality’ when summarising Craig’s argument. But it is not clear what this means. Obviously, it indicates that God isn’t required as part of the theory, which makes divine command theory definitely not a candidate. But we don’t know anything else about it. And it matters for what CS wants to say in a minute. So just to be clear, let’s distinguish two possible ‘atheistic moralities’:

  • Moral subjectivism – there are moral truths, but they depend on human minds for their existence
  • Moorean non-naturalism – there are moral truths, and they are objective non-natural truths.

CS gives us no reason to think that one of these is what ‘atheistic morality’ means rather than the other. Both seem like options available to an atheist (Moore’s theory requires no reference to a God). So, again, we have an ambiguity over what CS is talking about. And this matters here, because it will infect his argument.

So, to recap, CS characterised Craig’s argument as saying that because ‘atheistic morality’ varies from place to place, that means it is subjective. CS then said that he can turn this logic on religious morality, because that varies from place to place too. At this point, CS says that there is an obvious rebuttal to this turning back of Craig’s argument (12:10):

“Ok, I can already hear the sounds of religious objection. Of course religious views vary, but that’s not because my religion is only subjectively correct. It still has an objectively true morality. It’s just that other people have gotten it wrong, and follow a false morality, because they feel that their religion is objectively true when it really isn’t. My morality is still objective even if other people have gotten it wrong.”

So the response CS imagines hearing is someone basically saying that variation in opinions does not mean that the topic is subjective. This response is exactly what Moore said about moral disagreement. For a moral realist, whether religious or not, the fact that people have different views about morality is just like when they have different views about mathematics. It doesn’t show that it is all subjective; it shows that at least one person is incorrect.

CS thinks that there are two problems with this as a response:

“Firstly, the exact same could be said of atheistic claims to objective morality. Of course atheistic claims of morality vary by social and geographical backgrounds. But that doesn’t mean it’s not objective, just that other people have gotten it wrong. It’s the same thing”

But now the failure to distinguish between the two potential versions of ‘atheistic morality’ starts to make trouble.

If ‘atheistic morality’ is a version of subjectivism, then this rebuttal is not available to the atheist. On subjectivism, if you think X is wrong, and I think X is right, we cannot explain that as a case of one of us being mistaken. Each of us is just reporting our own individual opinion, like saying “I like X” and “I do not like X”. That doesn’t count as a case of disagreement, and cannot be explained by one of us making a mistake. It is deeply disanalogous to mathematics.

On the other hand, if ‘atheistic morality’ is a version of realism, like Moore’s theory, then the rebuttal is available. However, CS states very explicitly that he is a subjectivist about morality, so this response is not available to him.

So he can only take this route by denying the central claim in his video.

CS has a second reason:

“Secondly and more crucially, the only reason that anybody could possibly choose one religious morality as more ethically viable than another is because they feel that it provides a better framework for moral truth. How else could a person possibly prove to themselves or to others that one religion has a superior ethical code to another? How else can a Christian possibly believe that the ethical code of Christianity is superior to that of Islam? If you want to compare the ethics of two religions you need some moral basis on which to judge them. That moral basis obviously can’t be one of the religions and so the only way you can decide which religion is morally superior is through a subjective analysis of which you feel is better. It’s ultimately a subjective decision based on your, not your religion’s, moral intuition.”

So, let’s recap a bit. The argument CS takes himself to be responding to is his version of Craig’s argument, which was that because atheistic moral opinions vary, that means it is subjective. He replied that the same could be said of religious views; they vary as well, so they should be subjective on that logic. He then painted a possible reply from religious people, who say that the difference of opinion doesn’t imply subjectivism. This is his second reply to that move. He is saying that if you were to decide between two religious moral systems, that would be “through a subjective analysis of which you feel is better”.

Now, what CS says there is true, in a sense. But, it is true for all decision making. Decision making is something that you do in your mind; it is inherently subjective. Ultimately, you base your decisions on things that you believe to be true, and as such they depend on these beliefs. So when I’m doing a bit of mathematics, I have to ultimately decide whether I believe I have got the answer right. I could look at the text book, but even there I have to believe that I understand it properly. I could ask you if I have got it right, but I have to ultimately believe whether I trust you, or whether I understand what you are saying, etc. There is no possible way to decide anything that isn’t “through a subjective analysis of which you feel is better”, in the sense that it doesn’t depend on beliefs at some stage. It’s not clear to me what an ‘objective analysis’ even means. It sounds like saying an ‘objective belief’ or an ‘objective desire’.

But does that mean that everything is subjective? I think the answer is clearly no. All we need to do is distinguish between the belief and the content of the belief. It’s up to me whether to believe the mathematical proof in front of me, but that doesn’t make the proof itself only subjectively true. In the same way, it is up to me whether I believe in a version of moral realism, say divine command theory, but that fact doesn’t make divine command theory a subjectivist theory as a result.

The ‘big argument’ CS has here is just that all morality, including ‘religious morality’, has to be subjective because the only way to decide whether to believe in any moral system is through a decision process which is subjective in nature. This is a terrible argument.

Just in case you thought I was straw manning CS, here he is making pretty much exactly this point:

“The only thing that seems to distinguish religious morality from atheistic morality …  is that the religious believer feels like their morality is objective whereas the atheist recognises the subjectivity lying at the heart of ethical decision making.”

But this isn’t what distinguishes religious morality from atheistic morality. It is true that there is a subjective element at the heart of decision making (whether ethical or not), but this fact doesn’t make what is being decided about subjective.

If I am deciding which action to take, if I am trying to work out which is the right thing to do, my decision will necessarily have a subjective element to it. It happens in my mind. It’s informed by my beliefs. But that doesn’t mean that if I pick option A over option B, that there is no objective truth about whether A is the morally better option. In the same way, if I pick between two religions, I have to make my own mind up about which one I want to go for, but that doesn’t stop the claims of those religions being objectively true (or false). CS seems to think that this is what makes objectivist theories impossible, and he is quite wrong about that.

And it’s not like religious philosophers think that there is no subjective element to moral decision making. Everyone has to ultimately decide for themselves when they make a moral decision if their choice is the morally right one or not. That much subjectivity is present in everyone. Realists just hold that there is a mind-independent fact about whether your choice was the morally correct one.

It might be that what is going on here is that CS has the other version of ‘objective’ in his head when he is making these arguments. Maybe he is saying that you can’t demonstrate, like with a logical proof, that “one religious morality [i]s more ethically viable than another”, and that because of this all religious systems are ‘subjective’.

5. “I’ve got more…”

CS runs a little thought experiment, according to which we grant that God exists:

“Let’s say that somehow we were able to objectively demonstrate that some God, say the God of Christianity exists. We know this for a fact. You might say that if this is the case, religious morality is objective. Because if God is the author of everything, then it is he who determines what is ‘good’ and ‘bad’ – objectively. Clearly, if God exists, and has objectively defined certain things as good and bad, we can objectively determine how we ought to behave. Morality is objective. Right?”

Here I think we can see the creep of defining ‘objective’ as being ‘demonstrated’, rather than being ‘mind-independent’. There seems to be other uses of the word in this passage which make little sense even if read like that. Consider: “it is he who determines what is ‘good’ and ‘bad’ – objectively”. What does it mean to ‘determine something objectively’? I can assess something according to some mind-independent standard, like when I check my proof in the textbook, but even then I must make a subjective decision at the end, because I will still need to decide whether I believe that I am reading the text book correctly. All ‘determination’ requires some element of subjectivity, even in the most objective sounding situation of consulting a text book. So what is CS thinking of when he says this?

God is also said to have “objectively defined” morality. But what is the difference between objectively defining something and subjectively defining something? Did God mind-independently define morality? Did he define morality in a way we can demonstrate to others? What is going on here?

The best I can make out is that ‘objectively defining’ something means to define it in such a way that after you have defined it, it becomes true ‘objectively’ (i.e. mind-independently) after that. It is dubious whether there can be anything that counts as an ‘objective definition’, if that is what he means.

Anyway, he goes on:

“Here is the single question that completely changed the way that I view religious morality: why ought we do that which is good? I want you to really think about this, because it’s crucial. Why ought we do that which is good? Let’s say that ‘good’ really was defined by God. We’ve said that we’ve proven beyond a shadow of doubt that the God of Christianity really does exist, and really did write the 10 commandments, let’s say. We can therefore ‘objectively’ say that murder, adultery, bearing false witness, etc are bad ‘objectively’. That’s not enough. You still need to demonstrate, objectively, that because something is good you ought to do it, and because something is bad, we ought not do it. Now it seems stupidly obvious and instinctive that we ought to do what’s good – of course we ought to do what’s good. But can you prove it?”

Well, given my comments in sections 2 and 2.1, I don’t think you ought to do what is good. I think that if you ought to do something, then it is good. But there can be things that are good (like friendship) that you are under no moral obligation to do. CS thinks it is “stupidly obvious” that we ought to do what is good, but I think the general principle is false, because of the counterexamples.

But the confusions keep coming in this passage. Consider: “the God of Christianity really does exist, and really did write the 10 commandments, let’s say. We can therefore ‘objectively’ say that murder, adultery, bearing false witness, etc are bad ‘objectively’.” Firstly, try and tune out the meaningless repetition of the word ‘objectively’, which has no stable content at all. The ten commandments are not proclamations about certain actions being ‘good’ or ‘bad’. They are commands. God says ‘Thou shalt not…’ If anything, it is God trying to impose an obligation to his people, not assigning a moral value for them. So why does CS think that this would be enough to ‘objectively’ know that adultery, etc, is bad rather than that we should not do it? It is unclear.

Yet that is what he thinks, because he goes on to say that even if we (somehow) accepted that by saying “thou shalt not commit adultery” God had established that it was bad to commit adultery, we would still be faced with the problem of why we ‘ought not’ commit adultery.

Once again CS imagines a response from ‘the religious’:

“The religious might respond that of course we can prove that we ought to do that which is good, because God commands us to do that which is good. God defines good, and God commands us to do that which is good, and so morality is objective.”

CS says there are two problems with this. He says:

“Firstly, you’ve just pushed the issue back. I can still ask why I ought to do what God commands. And any answer you give me can be questioned in the same way.”

But the problem with this whole set up is that we granted a premise that makes no sense, and now we are being told that we cannot grant another one.

Let’s clean up the example, so that it fits with what CS wants it to say. Imagine that God said: “Giving to charity is good”. The question we can ask at this stage is: how does God saying that make it the case that giving to charity is good?

CS wants us to imagine being in a situation where God’s commandments are enough to establish moral values existing (even that his ‘objective definitions’ can make them exist), yet not enough to establish moral obligations from existing. But why not? If we had an answer to how his saying that giving to charity is good makes it good, why wouldn’t we also have an answer to why his saying that you ought to give to charity makes it the case that you really ought to do it? In each case we have God saying something, and the mystery is how him simply saying something makes it the case. There is no special mystery here about obligations which is different to moral values.

There is a legitimate question to be asked, which is ‘why ought I do what God commands?’ But that is really not different from the question: ‘why ought I value as morally good that which God says is morally good?’ Those are both interesting questions, but CS thinks one is problematic and the other isn’t. Or that if you had solved one, you would still have to solve the other. But any solution to one would be a solution to the other. If God’s saying something actually made it the case, then that would work for values or for obligations. Or, if there is some extra difficulty here, CS provides no reason for thinking so.

What CS is fumbling around for is the idea that moral principles, like values or obligations, seem to be what they are independently of what anyone says or thinks about them. God commanding this or that might reveal what he wants, or what the consequences are for doing certain things, but it doesn’t seem like it can be enough to actually make it the case that certain things really are good, or obligatory in the moral sense. But what he is getting at is the intuition that is the main motivation for realism about morality, which is the opposite to what he says he wants to defend in this video.

Anyway, we are at the end of the video now, so I’ll wrap up.

6. Conclusion.

There are various confusions in this video. The idea of ‘objective’ is thrown around, but there seems to be no stable meaning to it. There is a principle about what morality is, which ties moral values to obligations in a way that has obvious counterexamples, but CS seems to be unaware of them. There is a poor characterisation of Craig, which leads to a confusing discussion about ‘atheistic morality’ which suffers from not having a clear idea about whether it is supposed to be objective or subjective. It’s also unclear how that section contributes to showing that religious morality is subjective, as CS ends up arguing against the claim that Craig’s argument can be turned back on him. The idea that all morality is subjective because all decision making involves a subjective element is guilty of conflating belief with the content of belief. At the end, CS seems to think there is an issue for obligations that is not there for values, but he doesn’t explain why this is the case.

Loke’s Singing Angels: the Kalam and abstract entities

0. Introduction

Readers of this blog are likely well aware of the Kalam cosmological argument, and its presentation by William Lane Craig. In particular, readers will probably be well aware of the line of defence for the second premise according to which the past must be finite.  This says that the past must be finite because, if not, then there would be an ‘actual infinite’ (or a ‘completed infinite’), and such a phenomenon could not exist without ushering in various purported ‘absurdities’ (such as those illustrated by Hilbert’s Hotel).

Craig and Wes Morriston have had an interesting exchange on this issue (a useful summary of which is found here). In short, Morriston argues that if the past cannot be beginningless because it would constitute an absurdity, then the future cannot be endless, or else it would constitute a symmetrical absurdity. Morriston imagines a pair of angels who take it in turns to sing praises to God forever. Theists, such as Craig, who hold that the future is everlasting, need to show that such a scenario is possible without resulting in the sorts of absurdities that apply to Hilbert’s Hotel, or to the beginningless past. They need a symmetry breaker between past and future.

Craig’s move is to argue that a beginningless past is an ‘actual infinite’, whereas an endless future is merely a ‘potential infinite’.

“No absurdity there, for the number of praises said by the angels will always be finite, even though increasing toward infinity as a limit” (Craig, “Taking Tense Seriously in Differentiating Past and Future: A Response to Wes Morriston,” Faith and Philosophy, 27:4 (2010), 451-456, p. 452)

The debate centres around what the notions of ‘actual infinite’ and ‘potential infinite’ refer to. Craig is right that the number of praises that have been said will always be finite. Yet, Morriston argues that this misses the point:

“But I was not asking for the number of praises that have been said. Instead, I was asking for the number of praises yet-to-be-said – that is, for the number of praises, each of which will eventually be said. In the world of my thought experiment, the series of praises yet-to-be-said is not growing, is never finite, and does not satisfy Craig’s definition of “potentially infinite.”” (Morriston, “Beginningless Past, Endless Future: A reply to Craig”, Faith and Philosophy 29 (4):444-450 (2012), p. 3)

Into this debate steps Andrew Loke, with his paper “On beginningless past, endless future, God and Singing Angels: an Assessment of the Craig-Morriston Dialogue“. In particular, Loke says:

“…the distinction between abstract and concrete infinities is helpful for responding to Morriston’s counter-argument based on the number of angelic praises yet-to-be-said” (p. 58).

It is to this response to Morriston that I want to focus here.

  1. Loke’s argument (?)

Loke makes the central distinction between the number of praises that will have been said, and the number of praises that will be saidSomewhat confusingly, he refers to them as those ‘that-will-be-said’ and those ‘yet-to-be-said’, which sound like synonyms to me. However, he seems to be applying these labels in the right way, when he says:

“Craig’s response that the number of praises that-will-be-said is a potential infinite is inadequate, for Morriston is not asking about the praises that-will-be-said, but rather the praises yet-to-be-said, the series of which, Morriston argues, is not growing, is never finite, and does not satisfy Craig’s definition of potentially infinite, as noted above. Craig’s main point in reply to Morriston was about the praises that-will-be-said, not the praises yet-to-be-said, and thus he misses the thrust of Morriston’s counter-argument” (p. 63)

I agree with this much of Loke’s interpretation of the debate. Loke promises to respond in a way that does not merely fall into the same equivocation that Craig does, “In what follows, I shall (unlike Craig) focus on ‘the praises yet-to-be-said’” (p. 63).

The main thrust of Loke’s response is outlined in the following passage:

“In response to Morriston’s counter-argument, it seems that proponents of the Kalam Cosmological Argument do not have to follow Craig’s proposal to either deny Platonism with respect to propositions or deny that there are an infinite number of propositions. Rather, they can hold the view that the argument against the possibility of the actual infinite based on paradoxical implications is directed against the existence and actualization of an actual infinite number of concrete entities or events; it is not directed against the existence of an actual infinite number of abstract entities.” (p. 63)

Clearly, Loke is going to make his response to Morriston focused on the concrete/abstract distinction. Unfortunately, there is a slide between talking about an infinite number of propositions, and an infinite number of events. Also unfortunately, we are not given a definition of either ‘abstract’ or ‘concrete’. Loke appeals several times to J P Moreland, and a paper called “A Response to a Platonistic and to a Set-Theoretic Objection to the Kalam Cosmological Argument” (Religious Studies, Vol. 39, No. 4 (Dec., 2003), pp. 373-390) (henceforth ‘Response’). In that, Moreland offers a definition of ‘abstract object’ that we can only assume is close to what Loke has in mind. Moreland says:

“An entity is abstract just in case (a) it is not a person, and (b) it exists outside space and time in that it has no spatial or temporal location or duration” (Moreland, Response, p. 376).

Loke’s explicit reference to ‘Response’ is not to this, but to a similar distinction, according to which an actual infinite is absurd like the Hilbert’s Hotel example only if:

“(1) the members of the set are finite, located, moveable entities, which opens up the possibility of adding, subtracting, or rearranging the members of the set, and (2) the members of the set are spatially extended.” (Loke, p. 63)

Moreland’s idea is that what makes an actually infinite collection absurd is that it meets these two conditions. He explains that what the hotel example is supposed to be showcasing involves spatially located guests ‘moving about’:

  • “Regarding Hilbert’s Hotel, the problem is that if we move the guests from one location to another, there just are no rooms available into which they can be moved. All of them are already filled. Moreover, there is no way to open up a new room by this procedure because there is no spatial region available into which they can be moved or new rooms can be added” (Response, Moreland, p. 379).

  • “If one adds (or subtracts) members to an actual infinite set, then one has not increased the number of members of that set, but this is false since we have before us the new member who was added” (ibid)

Moreland is careful to identify the absurdity of an actual infinite with the ability to manifest this sort of behaviour. On page 380 of the same paper, Moreland makes the following careful statement of what is ruled out by Craig’s appeals to absurdities associated with the actual infinite:

“An actual infinite number of finite, contingent entities that i) can be added to or subtracted from a set and ii) are spatially (or spatio-temporally or temporally) extended cannot exist”

Moreland’s idea can be put like this: if an actual infinite meets both i) and ii), then it cannot exist. If it can exist, then (using modus tollens), we can infer that it does not meet both i) and ii).

Indeed, Moreland draws exactly such a conclusion, arguing that a platonist can affirm the existence of an actually infinite number of abstract entities. These entities fail to fulfil either of his conditions, in that they cannot be subtracted from or added to, and they are not spatially or temporally extended.

It should be noted that to avoid the absurdities, an actual infinite only need avoid satisfying one of Moreland’s two conditions, and not necessarily both (they are individually necessary and jointly sufficient conditions). We will come back to this.

So let’s make the distinction between two types of actual infinities; there are ‘active’ and ‘passive’ actual infinities. An actual infinity is ‘active’ iff meets both of Moreland’s conditions above, and it is ‘passive’ iff it is not active.

Loke shares Moreland’s insight, which is that actual infinities that are composed entirely of abstract objects are passive. For example, take the natural numbers, construed as platonic abstract objects. These constitute an actual infinity. These entities, it seems reasonable to think, cannot be ‘moved about’ in any way. It makes no sense to rearrange them, or subtract them. Of course, one can perform ‘subtraction’ using numbers, but one cannot remove a number from the total collection of the natural numbers. They are utterly unchangeable. Thus, some actual infinities, such as the natural numbers, are passive because they are abstract objects. As Loke says:

“Since abstract entities are not finite, located, moveable entities nor spatially extended, the argument against the possibility of the actual infinite based on paradoxes such as Hilbert’s Hotel does not apply to them” (p. 63).

So far, so good.

At this point, I think it will be helpful to codify this in a principle, which I shall call Loke’s principle (or ‘LP’):

Loke’s Principle) Actually infinite collections of abstract objects are passive.

 

Loke goes on to make what seems to me to be the central argument of the paper:

“Having made the point that argument against the possibility of the actual infinite based on paradoxical implications is directed against concrete rather than abstract entities, the proponent of the Kalam argument can reply to Morriston as follows: The number of praises yet-to-be-said – that is, the number of praises, each of which will eventually be said – is actual infinite, but the number of praises yet-to-be-said do not yet exist as concrete entities or events.” (p. 64)

Let’s try to be clear about what is being said here, because the passage is hard to read clearly. When he says “argument against the possibility of the actual infinite based on paradoxical implications is directed against concrete rather than abstract entities”, Loke seems to be merely articulating what is encoded in LP. If so, it is a statement against which I have no objection.

Loke makes the claim that the not yet uttered praises “do not yet exist as concrete entities”. There is an unfortunate scope ambiguity here. It’s not clear here which of the following Loke means to convey:

a) The future praises currently exist, but are not currently concrete

b) The future praises are currently concrete, but do not currently exist

Is the idea that they do not yet exist at all, or that they do exist, but merely as abstract objects? The phrase is ambiguous.

Loke goes on, but the ambiguity persists:

“Neither would it ever be the case that all of them have been actualised as concrete entities or events, for no matter how many praises have been said, an angel could still say one more. As noted earlier, Morriston agrees that ‘the number of praises that have been said by the angels in my scenario will always be finite,’ and that ‘the collection of praises that have been said will increase without limit.’ One might think it absurd that an actual infinite number of praises will never be said even though each of the praises will eventually be said, but given that ‘the praises that will eventually be said’ do not yet exist as concrete entities or events, this is a problem that remains in the abstract and does not cause problem in the concrete world.” (p. 64, emphasis added)

The phrase “this is a problem that remains in the abstract and does not cause problem in the concrete world” is even more difficult to understand. The implication seems to be that future praises are not concrete, and this quarantines the actual infinite in the abstract realm and not “in the concrete world”. Just like the way Moreland can have an actual infinite collection, just so long as they are abstract objects, Loke seems to be implying that the the praises that will eventually be said is an actual infinite, but one that is not a problem due to being a collection of abstract objects.

The question though is whether we should consider future praises to be abstract objects, or concrete objects.

Let us refresh our memories of the clear (enough) definition offered by Moreland:

“An entity is abstract just in case (a) it is not a person, and (b) it exists outside space and time in that it has no spatial or temporal location or duration” (Moreland, Response, p. 376).

Presumably, and entity is concrete iff it is not abstract. (Is there a third category?) If they are mutually exclusive, then we can ask ourselves wether future praises fulfil both of Moreland’s criteria or not. If so, then they are abstract; if not, then they are concrete.

Clearly, future praises are not people, so they meet condition (a). But do they exist outside space and time and have no spatial or temporal location or duration? There is a small head-scratcher about whether ‘a time’ itself is temporally located or not, but a a ‘future event’ seems to be clearly temporally located. It is in the future! The praise will also have a duration; it will take some definite amount of time to say the prayer. Thus, it seems like the future praises are not abstract by this criteria. Although they meet criteria (a), they do not meet criteria (b). They are quite obviously not ‘outside time’ being events in time (in the future) and they have duration. Unless there is a third category, future praises are concrete.

If that is right, then the ambiguity in Loke’s claim can be cleaned up. The future praises are currently concrete, but not currently existing. As time passes, they do not ‘become concrete’; rather, they begin to exist. Perhaps we can put it like this; as time passes the future praises ‘become actual’. Either way round, what is happening is that the merely potential future praises, which are always concrete, become actual and/or existing present praises, before becoming past praises.

But if that is right, then what has become of the original promise made by Loke in the start of the paper? Recall, he said:

“…the distinction between abstract and concrete infinities is helpful for responding to Morriston’s counter-argument based on the number of angelic praises yet-to-be-said” (p. 58).

Yet, future praises are concrete, just like past praises, given Moreland’s distinction. How is that a symmetry breaker? It is unclear how, if at all, the distinction between the abstract and concrete is supposed to be helping.

3. What do ‘abstract’ and ‘concrete’ mean for Loke?

If Loke were using Moreland’s definition of abstract, then he could not argue that future praises are not concrete. That would mean arguing that future praises are outside of time. This is clearly not the case. Thus, Loke must have something else in mind when he uses these terms. But what could that be?

One starting point is David Lewis’ book, Plurality of Worlds, chapter 1.7: Concreteness (p. 81 – 86). Lewis says:

“A spectator might well assume that the distinction between ‘concrete’ and ‘abstract’ entities is common ground among contemporary philos- ophers, too well understood and uncontroversial to need any explaining. But if someone does try to explain it, most likely he will resort to one (or more) of four ways” (p. 82)

These are:

  1. The Way of Example: “concrete entities are things like donkeys and puddles and protons and stars, whereas abstract entities are things like numbers”, p. 82.
  2. The Way of Conflation: “the distinction between concrete and abstract entities is just the distinction between individuals and sets, or between particulars and universals, or perhaps between particular individuals and everything else”, p. 83.
  3. The Negative Way: “abstract entities have no spatiotemporal location; they do not enter into causal interaction; they are never indiscernible one from another”, p. 83.
  4. The Way of Abstraction: “abstract entities are abstractions from concrete entities”. p. 84.

Could Loke mean one of these ways of construing the distinction?

If he took the Way of Example, then he would be saying that future events are “things like numbers”. Part of the problem here is what it means to be a number. Moreland gave an example of what it means to be a number, but that required that the entity does not exist at any time, which clearly future praises do not do. Moreland also thinks that numbers are “immutable” (‘Response, p. 380). Yet going from being abstract to being concrete certainly seems like a type of change. All these give us reasons to think that future praises are not “like numbers”.

I’m tempted to think that Loke is a member of the Way of Conflation. He doesn’t conflate the concrete/abstract distinction to the individuals/sets distinction though. If I was being mean, I would say that I think he conflates the concrete/abstract distinction with the future/not-future distinction. That would be entirely question begging. We are looking for a way of breaking the symmetry between past and future praises. Loke thinks that “the distinction between abstract and concrete infinities is helpful”, but if saying that future events are abstract just means that future events are future, then we have not been given anything at all. Mere tautologies cannot break the symmetry, surely.

More charitably, he may just mean to the distinction between the actual and non-actual. Future events are not actual (yet). They are mere potentials. As such they occupy a lower rung on the ontological ladder than present or past praises. It is hard for me to understand how this succeeds, although it is probably the most promising option. The future praises are ones which will happen. It is possible that our angel will curse his fate rather than praising God. It is possible for him to do so, even though he won’t do it. This is Craig’s view, as a Molinist. He thinks there is a course of contingent future events that God divinely foreknows will actually happen. It doesn’t matter whether God’s knowledge is propositional or not. What matters is that if there is an actual future, how can it be maintained that the future is merely potentiality? To hold that view, you should endorse open theism, according to which there are no truths about the future. One way or another, the set up of the thought experiment is that there is an angel who (actually) will say praises forever. Given that, the future is not mere potentiality, but is quite determinate (at least in this respect). Thus, this escape route doesn’t seem open. Or, at any rate, if we are arguing about whether there can be any truths about the future at all, we would be having a completely different conversation altogether. It has nothing to do with the abstract / concrete distinction any longer.

The Negative Way seems also no help to Loke. If abstract objects have no temporal location, then they cannot be future. Yet, future praises are future.

The Way of Abstraction also seems to be no help. Future praises are not the result of “somehow subtracting specificity” (Lewis, p. 84) from present or past praises. This Way treats the abstract / concrete relationship to be analogous to that between the map and the terrain. One is a less detailed version of the other. But in the set up, each praise is exactly the same.

4. Conclusion

At the end of all this, I cannot see what Loke is getting at. He wants future events to be non-concrete entities. But they don’t seem to be any good reasons for considering them to be abstract objects. They are a very bad match if we are considering Moreland’s view, which is the only thing Loke references, and he gives no explanation of what he means independently of that.