Eternity’s relation to time

A few months ago, reader Ante asked this question on my What I Believe page:

I am very much struggling how to combine a presentist account of time (like the A-theory for example) and the view that God is outside of time, in a Thomistic sense.

I would be very thankful for your help, since it seems to me that I am hitting a wall regarding this issue, since I cannot accept a B-theory of time, but at the same time the view of St. Thomas regarding God’s eternity is much more plausible than the other philosophical alternatives (especially open theism!).

For those unfamiliar with the relevant terms, we begin by briefly explaining what the A-theory and B-theory are, how they relate to presentism, and what this has to do with God’s eternity.

The distinction between A- and B-theory of time was introduced to analytic philosophy by McTaggart in his paper The Unreality of Time. Briefly, the A-theory of time holds that there is some objectively privileged moment of time we call the present, relative to which other moments of time can be categorized into past and future (called the A-series). By saying it is objectively privileged we mean that the fact of which moment is present is not a matter of perspective, but is rather a feature of reality prior to any considerations from us. The B-theory, by contrast, denies that there is such an objectively privileged moment of time, and holds that the only relations between moments are those of earlier than and later than (called the B-series). We can still speak of the present, but it must always be understood from the perspective of a particular moment under consideration. The most we can say, for instance, is that from the perspective of the 3rd of March 2018, the 2nd of March is in the past and the 4th is in the future.

Each of these theories has a number of models, which are concrete proposals for the nature of time that satisfy the requirements of the theory. Confusingly, these models are also sometimes called “theories.” A-theoretic models include presentism, which holds that only the present moment of time is real, while the past moments were once real and the future moments have not yet become real; the spotlight theory, which holds that all moments of time are equally real but only one ever has the property of “presentness”, which leads to us visualizing time as a spotlight gradually moving over a fixed timeline; and the growing block theory, which holds that once a moment is real is stays real, resulting in all past moments being equally real and forming a “block” of time, with the present being on the edge of this ever-growing block. B-theoretic models include four-dimensionalism, which treats time like a sort of spatial dimension, holding that objects have temporal parts spread across the fourth dimension of time just like they have spatial parts spread across the first three dimensions of space; and eternalism, which we will here take to be the model that all moments of time are equally real without any having the status of being objectively present, but not necessarily construed as temporal parts of objects either.

As for God’s eternity, the Thomistic view is that eternity and time represent fundamentally different modes of being. Eternity is not merely about existing without beginning or end, since this would be consistent with existing in time as long as we stipulate that (1) either time itself has no beginning or end or (2) God entered time upon creation.1 The Thomistic view can be seen as a consequence of Boethius’ definition of eternity, which says that it is “the complete possession, all at once, of illimitable life.” Such an existence is incompatible with being in time, since temporal existence requires that we have our life bit by bit rather than having all of it at once. Accordingly, God’s eternity means that he must be outside of time, and the problem of eternity has to do with the relationship between an eternal God and his temporal creation.

Thomistic and analytic approaches to time

Now, for us Thomists who are familiar with the analytic distinction between A- and B-theory, it is natural to wonder how it applies to God’s eternity and his relation to time. What is not always realized, however, is that there is an important difference between the Thomistic and analytic approaches to questions of time. The Thomistic approach is Aristotelian, and therefore starts with an analysis of change. Aristotle starts by asking questions like whether change is possible and what it consists in, and considers examples like that of a person becoming educated and an object moving location. By contrast, the analytic approach — by which I mean the approach of those in the analytic tradition broadly following McTaggart — starts with the ontology of the passage of time. The main point at issue in the debate over A- and B-theory is whether the passage of time “flows” from past to future. On the A-theory it flows as the present moves from moment to moment, while on the B-theory it is in some sense static.

We saw the analytic approach in action during our discussion on McTaggart’s paper, wherein he switches between questions about changes to reality (which is change in the everyday sense of the word) and questions about changes to the time series, as if these were interchangeable. On the Thomistic approach, time is just the measure of change,2 and it makes little sense to speak of the time series itself changing, as if this could be decoupled from the change to reality which it measures. Indeed, from a Thomistic perspective the analytic approach can seem to treat time as a sort of quasi-substance, which is certainly the impression one gets from McTaggart’s talk of moments of time merging into one another or changing properties.

We can illustrate the difference between the two approaches by considering how they would attempt to answer the question of whether temporal becoming is an objective feature of reality.

For the Thomist, temporal becoming is the feature of things when they change, as when an uneducated person becomes educated or a physical object moves from one place to another. Every change involves a coming-to-be of what was not before, and in this case the becoming is of things and in time. Given this sense of temporal becoming, we can determine whether it is an objective by determining whether change is real. And since change is evident to our experience, all we need is an account of it that shows its possibility, and therefore that our experience of it need not be an illusion.

On the analytic approach, things are less clear, because temporal becoming sometimes takes on a different sense and because the two senses are not always clearly distinguished. It’s difficult to avoid talking about changes to everyday things like people and physical objects, but with a primary concern for the ontology of time this talk gets mixed up with talk about changes to the passage of time itself.3 We are no longer simply interested in whether someone who is uneducated can become educated in the future, but also whether that future moment itself is something that can become present. This is not simply a becoming in time, but a becoming of time itself. The result is the conflation of temporal becoming with the A-theory, since only the A-theory involves the passage of time being in flux. Given this sense of temporal becoming, in order to determine whether it is objective we need to determine whether the A-theory is true, and that our experience of the passage of time itself (which is much less evident than our experience of change) is not an illusion.

So these two approaches give us two senses of the notion of temporal becoming, namely becoming in time and becoming of time. The former arises from considerations of change in the Aristotelian sense, as when an uneducated person becomes educated, and a physical object changes place. The latter arises from considerations of how the moments of time itself might change, as when a future moment takes on “presentness.”

The compatibility of (Aristotelian) change with B-theory, and its irrelevance

The upshot of all of this is that the analytic debate over theories of time is irrelevant to Aristotelian and Thomistic concerns. Both A-theorists and B-theorists recognize the reality of time with its peculiar feature of being ordered according to before and after, which is all the Aristotelian needs. As Aquinas said, “time is nothing else than the reckoning of before and after in movement” (ST I Q53 A3 corp).

Failure to recognize the different senses of temporal becoming has led some to conflate views they shouldn’t.4 The B-theory, for instance, is sometimes labeled “Parmenidean,” as if these two views are even remotely similar. Parmenides denied the existence of any distinctions in reality whatsoever, which leads to the denial of change and therefore the denial of any meaningful distinction between before and after. But the B-theory presupposes a distinction between before and after, since this is built into the relations earlier-than and later-than.

Another claim is that the B-theory excludes the possibility of change, and is therefore at odds with the Aristotelian commitment to its reality. Why does the B-theory preclude change? Well, the argument goes, if all moments of time are equally real, then the earlier moments when someone is uneducated are equally as real as the later moments when they are educated, and so they never become educated. But this clearly equivocates the two sense of becoming we’ve been discussing. The Aristotelian concern is whether someone who is uneducated at some time t1 can become educated by some later time t2, not whether t1 and t2 can somehow change their properties of “presentness.” All the Aristotelian needs is that a person can persist through time while varying in their educatedness, which the B-theory happily provides. What the B-theory does not provide — but which is irrelevant to the Aristotelian — is that this happens together with a change to the moments of time themselves. Again, the Aristotelian is concerned with becoming in time, not becoming of time.

Once we recognize the difference between Aristotelian temporal becoming and analytic temporal becoming, we can see that Thomists can happily hold to either the A- or B-theory. The analytic debate just isn’t something we have a stake in. But here’s the kicker: this doesn’t help us in any way with the problem of eternity! It is tempting to think that the B-theory would give us an automatic explanation of the relationship between the eternal God and his temporal creation, but it doesn’t. Why? Because at the end of the day, the B-theory is still a theory about time.

Let me explain.

We’ve said that time is the reckoning of before and after in the process of change, but what we haven’t mentioned is that before and after can be reckoned to something on account of a change to something else. This is an instance of what’s been called “Cambridge change,” which Feser describes as follows:

Here, building on a distinction famously made by Peter Geach, we need to differentiate between real properties and mere “Cambridge properties.” For example, for Socrates to grow hair is a real change in him, the acquisition by him of a real property. But for Socrates to become shorter than Plato, not because Socrates’ height has changed but only because Plato has grown taller, is not a real change in Socrates but what Geach called a mere “Cambridge change,” and therefore involves the acquisition of a mere “Cambridge property.”

There’s a certain ambiguity in this that we’ll discuss later, but for now consider the example he gives. Socrates remains the same height while Plato grows, and on account of this we can reckon before and after for Socrates: before he was taller than Plato and afterwards he was shorter than Plato. Thus, there’s a sense in which the change of other things can bring us along with them through time. Since this results from our being able to reckon before and after through changes to things in time, and since both the A- and the B-theory give us this, this will apply on both theories.

The real problem of God’s eternity, then, isn’t about whether the nature of time is such that all moments are equally real, but about how our movement through time doesn’t bring God along with us. And since this happens for both A- and B-theories of time, neither of them is capable of solving the problem.

Starting over with relations

Rather than a theory of time, what we need is a theory of relations. The reason Plato brings Socrates along with him through time is that Socrates is really related to Plato in some respect. In the above example it is that they are really related in regards to their height, but it could equally have been their relative location, color, age, or whatever. Conversely, if Socrates were not really related to Plato with respect to some feature of Plato that changes, then there would be no way of reckoning before and after for Socrates in terms of a change in Plato.

Aquinas worked out a detailed theory of relations, and we will summarize the relevant parts here. First, relations are divided into real relations, which obtain in reality prior to any consideration by an intellect, and logical relations, which result from such consideration. Socrates being taller than Plato is a real relation, but Socrates being to the left of Plato is logical since it is dependent upon how one considers their relative positions. When something has a real relation to another thing we say that it is “really related” to it. In English, the word “really” is often used to mean “truly” — as when we say something “really happened” — but in our present case “really” just indicates the nature of the relation. Socrates being to the left of Plato is not a real relation, but it is nevertheless true that Socrates is to the left of Plato.

Now, a relation between two things is not some separate reality floating outside of those things, but is instead grounded in them. When we have some relation R between A and B, it is therefore technically more precise to speak of R as a pair of relations, R1 from A to B and R2 from B to A. Socrates is taller than Plato (R1) and Plato is shorter than Socrates (R2). Each relation has a foundation in the thing it relates from, and this foundation grounds how that thing relates to others. For instance, Socrates has a certain height H, by virtue of which he will be shorter than things with heights taller than H and taller than things with heights shorter than H. This generic relational fact comes to be “resolved” to one of the alternatives when considered with respect to a particular individual: Plato has a height shorter than H, and so Socrates is taller than Plato. Notice that since the relation from Socrates to Plato will depend on both their heights it can change without Socrates ever changing, as when Plato changes his height while Socrates remains the same. It is this change in the relation from Socrates to Plato that brings Socrates through time when Plato changes.

We can also talk about the type of relation, which is derived from the type of its foundation: the taller-than relation is based on height while the brighter-than relation is based on color. In addition to the foundation in A, a real relation from A to B requires something in B of the relevant type, which we might call the relation’s co-foundation. It makes little sense, for instance, to say that Socrates is taller or shorter than an immaterial angel, since a relation of height from Socrates to another thing requires that that thing have a height as well. There is no co-foundation of the relevant type in the angel.

We say that the co-foundation must be of a “relevant” type rather than the “same” type because sameness is not always required. The height relation is an example that requires the co-foundation to be the same type, but consider what happens when I come to know a material object. In this case I take on its form in my mind, which serves as the foundation for a real relation from me to it and which has the object’s own form in itself as the co-foundation. But these two forms have different types: the form in my mind is intentional while the form in the object is entitative; the form in my mind does not turn my mind into that object whereas the form in the object’s matter does.

Knowledge is also an example of what is called a non-mutual relation. We have said that my real relation to the object has its foundation in the intentional form in my mind and its co-foundation in the entitative form in the object. This works because of the intentional form by its very nature refers to the object of the intention. But the entitative form is about constitution rather than reference, and so does not refer back to the intentional form in my mind. It can serve as the foundation of relations to other things by comparison to their entitative forms, but that’s about it. This means that there is no corresponding real relation from the object to me that has its entitative form as foundation and the intentional form in my mind as co-foundation. This asymmetry in foundation and co-foundation is what makes the relation non-mutual. When a real relation from A to B is can be turned into a real relation from B to A simply by flipping the foundation and co-foundation, then that relation is mutual.

If this were not complicated enough, consider what happens with active and passive powers. Here we have an agent with an active power (ability to influence others) and a patient with a passive power (capacity to be influenced by others), and when the agent actually does influence the patient then we have action and passion. The active power of an agent is grounded in some actuality (actual feature) of the agent, like motion, size, intentions, and so on. Any relation that arises from the active power, then, will have this ground as its foundation, which will determine which co-foundations are relevant. The passive power of a patient is slightly different in that it is grounded in the potential of the patient to be influenced in a particular way. This potential will be the foundation of the relations that arise from the passive power, and the co-foundations will be any actuality that can actualize it.

There is an important asymmetry here, in that the conditions for an agent to really relate to the patient are different from the conditions of the patient to really relate to the agent. For a patient, all that is needed is something capable of actualizing it, but for the agent, the conditions will depend on the ground of the active power. It could happen, then, that a patient is really related to an agent by a non-mutual relation. Consider, for instance, a saw cutting through wood. We might say that the active power of the saw is grounded in the sharpness of its serrated blade, while the passive power of the wood has to do with its potentiality for being split. Certainly there is a real relation from the wood to the saw because of this passive power, but as for the active power the wood is not really comparable in terms of sharpness or serratedness. The wood is really related to the saw, then, with a non-mutual relation. Of course there are other real relations between the two that have to do with active and passive powers and which are mutual. The saw might be used to push the piece of wood, for instance, in which case the ground of the active power (the motion of the saw) has a relevant co-foundation in the wood (the motion of the wood).

The problem of eternity

With this we can state the Thomistic answer to the problem of eternity: God is not really related to creation, and is therefore not brought through time by our changes.

This arises from applying what we’ve said about relations to the nature of God. For Thomists, God is a being of pure actuality, with no potentiality in him whatsoever. This makes him radically unlike anything else in reality, all other things being made up of a combination of potentiality and actuality. Furthermore, since potentiality is what allows for the diversity of actuality within a thing, it follows that God’s purely actual substance is the only possible foundation for real relations from him to others. But since pure actuality is so different to anything else in existence, it follows that there can be no relevant co-foundation to this purely actual foundation, and that therefore God cannot be really related to anything else.

Creation is still really related to God, mind you, but this relation is non-mutual. We are really related to God by virtue of our dependence on him for our being, and by virtue of being ordered toward him as the ultimate final end (cf. ST I Q44). Both of these arise from us being patients of God’s activity, and it is because of the potentialities in us that we can be really related to him — although pure actuality might be very different from us, it is nevertheless capable of actualizing all the potentials in us. Conversely, since God has no potentiality in himself there can be no chance of him really relating to us by virtue of us acting on him in some way.

Not only does God’s pure actuality exclude real relations from him to us or our acting on him, but it also excludes the possibility of change within him. All change involves the actualization of a potential, after all, and so without a potential there is no possibility of change. This notwithstanding, he is the source of all actualizations of potentials, including all instances of change. Thus God is called the Unmoved Mover, or Unchanged Changer, or more generally the Unactualized Actualizer. It might sound a bit strange to say that something could cause change without itself changing, since in our experience these tend to coincide. But it is a consequence of the fact that action and passion arise by an actuality of an agent actualizing a potential of a patient.5 This does not require that the agent’s actuality itself be the actualization of a potential, even if that happens with all the material agents we experience in the world.

Now, we might wonder why God would not be really related to us by virtue of knowing us. God is omniscient, after all, and earlier we mentioned that a knower is really related to the object of their knowledge. Here we must again appreciate the difference between God and ourselves. We come to know things outside ourselves through inquiry and exploration, by means of which we acquire the intentional version of its form in our mind. The entitative form in the object stands as a measure to our conception of it, and it is to the extent that our conception fulfills this measure that it is said to be true or accurate. With God, things look very different. His act of knowing reality is the same act whereby he creates and sustains everything in reality, and so he has no need of inquiry or exploration. He does not discover anything and has no need to acquire new knowledge by means of taking on the intentional forms of things. Since it is by his activity that all things continue to have their being, and since his act of knowing is the same as this activity, it also follows that God’s knowledge is measure of things rather than the other way around. All of this means that God’s knowledge does not make him really related to us like our knowledge makes us really related to the objects of our knowledge.

So, God does not change and is not really related to things that change. This means that there is no way of reckoning before and after for him and that therefore he is not in time. This notwithstanding, he is still the creator and sustainer of everything, and by virtue of this we are really related to him. Just as God is an unchanged changer, so too is he the non-temporal cause of things in time. We must remember, of course, that being really related to something is not the same as being truly related to it. Despite not being really related to us, God is still truly related to us as Lord, Creator, Knower, and so on; it’s just that these true relations are based on logical relations from him to us rather than mutual real relations between him and us.

Now before we conclude, we said earlier that there is an ambiguity in the notion of Cambridge change, and we are finally in a position to see why. Sometimes Cambridge change is proposed as a solution to the problem of God’s eternity, but of itself this is insufficient. To say that God only undergoes Cambridge change is to say that he does not undergo any change within himself. This is fine so far as it goes, but it doesn’t explain why he isn’t brought through time by changes to other things — as we saw in the example of Plato and Socrates we used to introduce Cambridge change. This further step requires the approach we’ve outlined in this post. The upshot of this is that either we should say (1) that God doesn’t even undergo Cambridge change, or (2) that Cambridge change must be divided into instances that bring us along through time and instances that don’t. In this second option, the two species of Cambridge change are distinguished by whether there are the relevant real relations in place or not.

Conclusion and further reading

So, Ante, thanks for the question and sorry for taking so long to reply. As I see it, the Thomistic approach to time is largely indifferent to the analytic debate over A-theory and B-theory, and the problem of eternity is not caused or solved by embracing either of these. What we need for a solution is an account of when and why things are brought through time, and an explanation for why this does not apply to God. To this end, the Thomistic account of relations provides us with a promising start. I hope what I’ve managed to outline here helps.

On the topic of relations, Mark Henninger’s Aquinas on the Ontological Status of Relations and David Svoboda’s Aquinas on Real Relation are both excellent discussions on the account of relations laid out by Aquinas. From Aquinas himself, perhaps the most important place to start is his discussion in question 7 of the De Potentia, especially articles 9–11. His discussions on God’s knowledge through his substance and the divine relations in the Summa Theologica are also noteworthy, since they push the account of relations to its limits when applying it to God.

More broadly, Edward Feser’s Classical Theism Roundup is a great resource for thinking through issues like eternity. Moreover, while I think Thomists don’t have a stake in the analytic debate between A-theory and B-theory, that is not to say that we don’t have interesting contributions to make. A case in point is Elliot Polsky’s Thomistic Special Relativity, which provides a three-dimensionalist account of length contraction and time dilation using a Thomistic framework that is different from other A-theoretic approaches I’ve seen.


  1. This is the view of William Lane Craig. See, for instance, his God, Time and Eternity. I also discussed it in my pre-Thomist days in an earlier post.
  2. Or, more accurately, it is the numbering of change according to “before” and “after”. (ST I Q10 A1 corp.) We’ve discussed before the connection a measure must have with what it measures.
  3. I’m not the only one who sees this. According to the SEP article on Being and Becoming in Modern Physics, “What emerges from the McTaggart literature is, first of all, a tendency to identify the existence of passage or temporal becoming with the existence of the A-series (that is, to think of becoming as events changing their properties of pastness, presentness or nowness, and futurity) and hence the tendency for debates about the existence of passage to focus on the merits or incoherence of the A-series rather than examining alternative accounts of becoming.” Note that the “events” mentioned in the parenthesis should be taken to mean “event-slices,” since an event in the everyday sense is something that spans multiple moments of time, and not all slices of it will be present (or past, or future) simultaneously. Again, this is a usage that we see in McTaggart’s paper.
  4. I stumbled upon a recent example of this while writing this very post.
  5. See my earlier post Lonergan on Aquinas on Causation for a discussion of this in Aquinas, as well as the essential agreement between him and Aristotle despite a terminological difference.

Natural law vs the moral argument

Up until recently, I had thought that natural law theory was compatible with moral arguments formulated as follows:

  1. If God does not exist, then objective moral values and duties do not exist.
  2. Objective moral values and duties do exist.
  3. Therefore, God exists.

Moral arguments of this kind have been made popular by defenders such as CS Lewis and William Lane Craig, and this specific formulation comes from the latter. In a post from a few years ago I explained my position on the compatibility of this with natural law theory as follows:

I think technically we can still use [the argument] as [formulated above], but we must recognise that it is partly dependent upon something like the fifth way for its soundness. At the end of the day I think much moral debate can be had without reference to God, since it is based on what is knowable about our nature. But ultimately I think any viable ethics depends on God, including natural law. (section 4.1)

This is admittedly not giving much credit to the argument, but I have since realized that even this weak support for the moral argument is misplaced. It seems to me that once we clarify the above formulation, the first premise will be seen to be incompatible with natural law theory, or at least some increasingly popular versions of it.

To start on the more technical side of things, the first premise should be understood as a non-trivially true counterfactual with an impossible antecedent (see here for details):

1′. If God did not exist, then objective moral values and duties would not exist.

So far there is still no obvious incompatibility with natural law theory, but we can go further. Presumably, if we are running this argument, then we think that there is something special about moral values and duties that calls out for a theistic explanation. That is, we are not interested in the general fact that anything whatsoever exists, but particularly the fact that moral values and duties exist. If this were not the case, then wouldn’t really be running a moral argument at all, but would instead be running a cosmological argument.

The point of the first premise, then, is that we finite agents are not sufficient to account for objective moral standards, and so the presence of such standards would imply the existence of God. This suggests that another way of stating the first premise is as follows:

1*. If we were to exist without God, then objective moral values and duties would not exist.

(Those of us who are convinced that God is required to account for any existence should also read this as a non-trivially true counterfactual with an impossible antecedent.)

Apart from the reasoning that got us here, further confirmation that (1*) captures the intent of (1) comes from how the premise is often defended. Consider, for instance, the following quote from Craig:

If there is no God, then any ground for regarding the herd morality evolved by homo sapiens as objectively true seems to have been removed. After all, what is so special about human beings? They are just accidental by-products of nature which have evolved relatively recently on an infinitesimal speck of dust lost somewhere in a hostile and mindless universe and which are doomed to perish individually and collectively in a relatively short time. Some action, say, incest, may not be biologically or socially advantageous and so in the course of human evolution has become taboo; but there is on the atheistic view nothing really wrong about committing incest. If, as Kurtz states, “The moral principles that govern our behavior are rooted in habit and custom, feeling and fashion,” then the non-conformist who chooses to flout the herd morality is doing nothing more serious than acting unfashionably. (William Lane Craig, The Indispensability of Theological Meta-Ethical Foundations for Morality)

Notice that this line of argument envisions a world where we exist without God, and puzzles over where moral values and duties are supposed to come from in such a world.

Now, while natural law theory may not pose any obvious problem for (1) or (1′), once we recognize that these amount to (1*) the problem becomes clear. The whole burden of a natural law theory is to ground moral truths in the natures of things, and having the nature that we do is part of what it means for us to exist. In the world described by (1*), then, the fact that we still exist with natures means that we still have objective moral duties and values even though God is not in the picture — at least from the perspective of natural law.

Of course, the exact details of this will differ depending on the version of natural law theory we consider. On Platonism these natures will be unchanging Forms in some third realm, on Aristotelianism they are intrinsic teleologies in things, and the new natural lawyers focus more on the nature of practical reason than on the natures of things. And each of these has variants within it. Some versions of Platonism equate the Forms with divine ideas, so that taking God out of the picture will take out natures with him. But other versions have God completely separate, meaning that natures stay even after God is removed.

Thomistic natural law theory is of the Aristotelian variety and is the version I find most compelling. On the one hand, it agrees with Aristotle that morality is fundamentally grounded in the intrinsic teleology built into us by virtue of the natures we have. On the other hand, contrary to Aristotle, it says that this intrinsic teleology still depends on God. Mind you, not in a way that makes it distinct from our nature, as if our teleology could in any way be separated from what we are. Rather, it is by creating and sustaining us as the kinds of creatures we are that God upholds the intrinsic teleology that fundamentally grounds morality. Of course, the details of this are quite complicated, but the point is that on the Thomistic view our intrinsic teleology is not mutually exclusive with God being the cause of our nature.

This brings us back to (1*). This premise asks us to consider the world where per impossible God does not exist and yet we still do. Because in such a world we still exist, we also still have natures and the intrinsic teleology which fundamentally grounds morality. This remains true even our natures arose through blind evolutionary processes since what’s important is the nature we have, not how we got it. So, in this world where we exist without God there is still the foundational morality that arises from the natural law: it is still wrong for us to lie, to murder, to steal, etc.; we still have categorical obligations, are held accountable, and have a basis for moral authorities (see section 2.4 here); we still have objective virtues and vices; actions are still objectively good and bad. Of course, there will be no duties arising from divine commands, but on natural law theories, these are in addition to the natural law, not instead of it.

So, then, for those of us who accept the Thomistic account of natural law, the moral argument we’re considering should be rejected as unsound. And I suspect the same would be true for some other versions of natural law theory, whether they be Platonic, Aristotelian, or from the new natural lawyers. It is certainly true for Aristotle’s own version, which doesn’t even construe God as the cause of our intrinsic teleology. On the other hand, there is also a lesson for those defenders of the argument who don’t accept any of these natural law accounts: a full defense of the first premise requires a thorough critique of these different natural law theories, which is no simple task. Certainly not as simple as the quote above appears. After all, natural law theories have a long pedigree in the history of Western thought.

While this objection doesn’t affect all moral arguments, it is noteworthy because the version it does affect is quite common. The argument might still have apologetic value insofar as it could convince someone who already rejects natural law, but such a rhetorical strategy makes me somewhat uneasy.

Essentially ordered series

The notion of a series, or chain or regress, comes up a number of times in philosophical discussions. In this post, we’re going formalize the notion in general, and then develop this into a formalization of essentially ordered series in particular.

Intuitively, a series is when we start with some member and from there we trace through the other members one at a time, possibly indefinitely. The order in which we trace or discover the members in the series can be (and often is) the inverse of their order in reality. This happens with causal chains, for instance, when we start with some effect A, which is caused by some B, which in turn is caused by some C, and so on. Here, tracing up the series — as we just did — involves tracing backward through the causes. In other words, later members in the tracing correspond to earlier causes in reality.

To give this a formal notation, we can write a series as S = (→sn) = (… → s3 → s2 → s1), where the index of each member represents the order of our tracing backward through the members, while the order of the members represents the order of reality. Thus, because s1 has the first index it is the first of in tracing, but because it is the last member it is the last in reality.

Technically we could drop the requirement that a series has a last member, allowing it to be infinitely extended in both directions. But for our purposes here this would just clutter the notation unnecessarily, so we’ll keep the requirement for the sake of clarity. Nevertheless, the central result of this post does not hinge on this requirement.

Mathematical underpinnings of our notation

Note: if you’d rather not read a bunch of maths, and are happy with our above notation, then you’re welcome to skip this section.

We can give our series notation a mathematical underpinning by analyzing it in terms of a well-known mathematical structure: a sequence. The idea is simple: start with the sequence of indices (which represent our tracing backward up the series), match them up to members in the series, and then give those indexed members the reverse order to that of the indices. More formally, a series (or chain, or regress) is a structure S = (S, I, <, σ) where:

S1.
S is a non-empty set of members and I is a non-empty set of indices,
S2.
σ:I→S is a map from indices to members,
S3.
< is a strict total order on I,
S4.
For each i∈I, if the subset of all indices greater than i is non-empty, then it has least element,
S5.
I has a least element, written 1.

In (S1) we separate S (the members) and I (the indices) because, in general, the same member might appear multiple times within the series.

In (S2) the map σ connects the two sets and captures repetition in the series when two distinct indices map to the same member.

(S3) and (S4) tell us that the indices form a sequence. (S3) guarantees that for any distinct indices i and j, either i < j or i > j, and (S4) guarantees that each index (except the last) has an index immediately after it, which we can label i+1.

(S5), which is technically optional, allows us to write this sequence starting with a first member as (in) = (1, 2, 3, 4, …).

Using the map σ, we can move from this sequence of indices to a series of indexed members, which are the true members of the series. For each i∈I, we have the indexed member si = (σ(i), i). They’re called indexed members because they’re members with an index attached. How do we order these indexed members? In order to get what we had earlier, we need the indexed members to be in the opposite order of their indices. So, if i and j are distinct indices with i < j, then their two corresponding indexed members will be si and sj respectively, with si > sj. Given that the starting order on I was a strict order, there is no problem with inverting it into a strict order on the indexed members, and so we can safely write our series with the above notation of S = (→sn) = (… → s3 → s2 → s1).

So, the members of the series S are the indexed members ordered inversely to their indices. So, s1 is the last member in the series. Notationally, we will refer to the series with either a bold-face S or the arrowed (→sn), depending on which is easier to read at the time. These two notations are interchangeable.

Some examples

I admit that all of this is quite abstract, and so before continuing, we’ll consider some examples. As mentioned before, a familiar class of examples is causal chains. These start with some final effect (s1), and trace backwards to its cause (s2,), and then to the cause of that cause (s3), and so on. For instance, consider the causal chain of me moving my arm, which in turn moves a stick, which in turn moves a stone. We would write this series as (me → arm → stick → stone). Similarly, we could we depict the series of the successive begetting of sons as (… → grandfather → father → me → son → grandson).

But causal chains are not the only kinds of series. Say we define word1 in terms of word2, word2 in terms of word3, and so on. This would give us a series of definitions (→wordn) = (… → word3 → word2 → word1). And, as we saw in a previous discussion, some good1 might be desirable as a means to some other good2, where this good2 is itself desirable as a means to some other good3, and so on. This would give us a series of desires ordered from means to ends, (→goodn) = (… → good3 → good2 → good1). Let’s say we took members from the moving chain above and ordered them as a desiring series: I desire to move my arm, as a means to moving the stick, as a means to moving the stone. This desiring series would then be written as (stone → stick → arm), which has the members in the opposite order from a causal chain.[1]

Each example so far is a series where earlier members depend on later members. Call such a series a “dependent series.” We’ll return to these below, but for now, we note that not every series is a dependent series. Imagine, for instance, we had three lights of different colors (red, blue, and green), such that only one light is on at a time, and where the light that’s on switches randomly and endlessly. The series of switched-on lights up until some time might then be something like (… → red → green → blue → blue → red).

Some notes

Two final points on notation before we proceed.

First, sometimes it will be helpful to talk about sub-series, which are taken from a series by excluding some of the later members. So, the sub-series as (→sn)n>i consists of all the indexed members of (→sn) that come before s(remember that the order of the indices is the inverse of the order of the indexed members in the series). Unsurprisingly, we write this as Sn>i = (→sn)n>i = (… → sn+3 → sn+2 → sn+1).

Second, in the interest of not cluttering everything with brackets, we say that entailments have the lowest precedence of all logical operations, so that a statement like A ∧ B ⇒ C ∨ D is the same as a statement like (A ∧ B) ⇒ (C ∨ D).

Active series

For any series or member thereof, we can talk about its activity, in the sense of whether it is active or not. What it means to be active is determined by the series we’re considering: to be moving, to be begotten, to be defined, to be desired, or to be on are what it means to be active in each of our examples above respectively. The notion of activity enables us to distinguish genuine series from merely putative ones, and compare them within the same formalism. To see what I mean, consider the moving stone example again. Let’s say the stone is moving and there are two putative series that could be causing this: me moving it with a stick, and you kicking the stone with your foot. These would be depicted as (me → arm → stick → stone) and (you → foot → stone) respectively. Both series are putative because each would account for the movement of the stone if it were active. Nevertheless, only the one which is active actually accounts for the movement of the stone.

We encode the activity of a member with a predicate α, which is true of a member if and only if that member is active. The necessary and sufficient conditions for α will depend on the kind of series we’re considering, and sometimes we will be able to give an explicit formulation of it. Nevertheless, it is safe to say that a series is itself active only if each of its members is active, so that:

AS.
α(S) ⇒ (∀siS) α(si),

As an illustrative example, consider the lights from earlier. Imagine we had three putative series for which lights went on in which order: (green → blue → red), (red → blue → red), and (blue → red). Now assume the lights went on in the order specified by the first of these. In this case, both the first and third series would be active, but the second series would be inactive because it would have an inactive member.

Dependent series

Now, we want to focus specifically on dependent series. In such series, the activity of later members depends on the activity of earlier members. More formally, si depends on sj if and only if α(sj) factors into the conditions of α(si). We’ll call the inverse of dependence acting: an earlier member acts on a later member if and only if the latter being active depends on the former being active.

Before we continue we need to make a technical note about how the series and its members are being considered. A series is always considered in terms of an order given by a particular activity (and dependence) on the members themselves. Take the example of me moving the stone with the stick with my arm. When we write this as (me → arm → stick → stone) it must be understood that we are considering me, my arm, the stick, and the stone in terms of the movement only. This series is not meant as a universal description of dependence between the members, but just dependence with respect to a particular instance of movement. So, in the present series “me → arm” just means that on account of some activity within me I am imparting movement on to my arm; it says nothing about other ways my arm may or may not depend on me.

Essentially ordered series

The particular kind of dependent series we’re interested in here is called essentially ordered. In such a series, we distinguish between two types of members. A derivative member is not active of itself, but is active only insofar as the previous member is active. Or, put another way, a derivative member continues to be active only so long as the previous member continues to act on it. A non-derivative member, by contrast, does not need another to be active but is active of itself — it has underived activity. An essentially ordered series is a dependent series because deriving activity from something is one way of depending upon it.

The moving example from earlier is an essentially ordered series: the movement originates with me as the non-derivative member, and propagates through the derivative members (my arm, the stick, and the stone), each of which moves something only insofar as it is moved by something else. Something similar can be said for the defining series and the desiring series, each of which is also essentially ordered.

Traditionally essentially ordered series have been contrasted with accidentally ordered series, in which later members depend on earlier members for becoming active but not for continuing to be active. The begetting series from earlier is accidentally ordered: me begetting my son does not depend on my father simultaneously begetting me.

Now, the fact that in essentially ordered series the dependence in view is derivativeness, makes it relatively straightforward to give a necessary condition for the predicate α. Let η be a predicate which is true of a member if and only if that member is active of itself, so that η(s) if and only if s is a non-derivative member. Then we can explicitly give the following necessary condition of α:

ES.
α(si) ⇒ η(si) ∨ α(Sn>i).

This formulation captures both the non-derivative and derivative cases. Non-derivative members are active of themselves and so can be active irrespective of the activity of the chain leading up to them. Derivative members, by contrast, are not active of themselves but by another, and so will only be active if the chain leading up to them is active.

From (ES), we see that the following holds for essentially ordered series:

α(S)
⇒ α(s1)
⇒ η(s1) ∨ α(s2)
⇒ η(s1) ∨ η(s2) ∨ α(s3)
⇒ …
⇒ η(s1) ∨ η(s2) ∨ η(s3) ∨ ….

Given that a disjunction is true only if one of its disjuncts is true, it follows that any active essentially ordered series must include a non-derivative member:

EN.
α(S) ⇒ (∃u∈S) η(u).

From (AS) and (EN) it follows fairly straightforwardly that in an active essentially ordered series, every derivative member is preceded by some non-derivative member:

ENP.
α(S) ⇒ (∀s∈S) (∃u∈S) η(u) ∧ u ≤ s.

Now, because non-derivative members are active regardless of the activity of the members before them, it follows that they do not depend on any members before them. And because essentially ordered series are a species of dependent series, we can say that if a member is non-derivative, then there are no members before it. We’ll call this the non-derivative independence of essentially ordered series, and formulate it as follows:

ENI.
η(u) ⇒ (∀s∈S) u ≤ s.

Together, (ENP) and (ENI) entail that any active essentially ordered series will have a first member which is non-derivative, which we call the primary member. We call this the primacy principle and formulate it as follows:

PP.
α(S) ⇒ (∃p∈S) (∀s∈S) η(p) ∧ p ≤ s.

This is the central result of this post.

Questions and objections

This property of essentially ordered series — that they must include a primary member — can and has been leveraged in a number of ways. It is perhaps most well-known for its controversial usage in first cause cosmological arguments arising from the Aristotelian tradition. We’ve seen previously how Aristotle uses it when arguing for the existence of chief goods. It is also the formal reason behind the intuition that circular definitions are vacuous. For the remainder of this post, we will address various questions and objections that might be raised, first two shorter ones and then two longer ones.

First, some will be quick to point out that what we’ve said here doesn’t prove that God exists. And this is true: the result given here is very general, and any successful argument for God’s existence would need additional premises to reach that conclusion.

Second, some might wonder if our use of infinite disjunctions is problematic. While infinitary logic can be tricky in some cases, our use of it here is fairly straightforward: all it requires is that a disjunction of falsehoods is itself false. As such, I see nothing objectionable in our use of it here.

Third, astute readers will notice that we have not shown, namely that every active essentially ordered series must be finite. This is noteworthy because it is at odds with traditional treatments of such series. For example, in his Nicomachean Ethics Aristotle argues for a chief good by denying an infinite regress of essentially ordered goods:

If, then, there is some end of the things we do, which we desire for its own sake (everything else being desired for the sake of this), and if we do not choose everything for the sake of something else (for at that rate the process would go on to infinity, so that our desire would be empty and vain), clearly this must be the good and the chief good. (NE, emphasis mine)

And in his Summa Contra Gentiles Aquinas argues for the prime mover by arguing against an infinite regress of essentially ordered movers:

In an ordinate series of movers and things moved, where namely throughout the series one is moved by the other, we must needs find that if the first mover be taken away or cease to move, none of the others will move or be moved: because the first is the cause of movement in all the others. Now if an ordinate series of movers and things moved proceed to infinity, there will be no first mover, but all will be intermediate movers as it were. Therefore it will be impossible for any of them to be moved: and thus nothing in the world will be moved. (SCG 13.14, emphasis mine)

Our result in (PP), however, is perfectly consistent with the series being infinite: all we need is for it to have a first member. This, for instance, is satisfied by the following series:

ω+n → … → ω+3 → ω+2 → ω+1 → ω → … → 3 → 2 → 1

where ω is the first ordinal infinity and n is some finite number. The question, then, is what the present result means for the validity of the traditional treatments.

On the one hand, the key property leveraged by thinkers like Aristotle and Aquinas is not that there are finitely many members, but rather that there is a primary non-derivative member. Now it’s possible that they conflated the question of finitude with the question of primacy, but it’s also possible that they merely used the language of infinite regress to pick out the case where there is no such primary member — something we might more accurately call a vicious infinite regress. Either way in the worst case they were slightly mistaken about why a primary member is needed, but they were not mistaken that it is needed.

On the other hand, in the kinds of essentially ordered series Aristotle and Aquinas were considering, it is a corollary of (PP) that there are finitely many members in the series. In general, (S4) guarantees that every member in the series (except the first) has a previous member, but it does not guarantee that every member in the series (except the last) has a next member. It’s precisely because of this that there can be series with beginning and end, but with infinitely many members in between. However, if a series is such that every member (except the last) has a next member, then given (PP) that series will also be finite.[2] Now, each series discussed by Aristotle and Aquinas have this second property. And so they are somewhat justified in talking as they do.

Finally, we might wonder why it is not sufficient to have a chain of infinitely many active derivative members, where each is made active by the one before it.[3] After all, if the chain were finite we could pinpoint one derivative member not made active by a previous member. But in an infinite chain, it can be the case that each member is made active by the previous.

Now, behind this objection lies the unfortunately common confusion between a series considered as a part and a series considered as a whole. When we consider a series as a whole we’re considering it as if it is all there is, so far as the series is concerned. For a series considered as a whole to be active, then, it must contain within itself the necessary resources to account for its members being active. By contrast, for a series considered as a part to be active, it need only be part of a series which, considered as a whole, is active. To illustrate this, imagine we see a stone moving, then realize it’s being moved by a moving stick, and stop there. In this case, we’d be considering the two-member series (stick → stone), where both members happen to be active. The series is active, but not when considered as a whole, since it needs additional members (like my arm, and me) to be able to account for the motion of its members.

Given this distinction the central question is what the conditions are for a series, considered as a whole, to be active.[4] Naturally, the answer will depend on the kind of series we’re considering, but merely pointing to a series in which all members are active is not enough to show that such a series considered as a whole can be active — as the previous example illustrates. What we need is an account of the distinctive characteristics of such a series, and a derivation from these what the conditions for activity are when such a series is considered as a whole.

Now, as we’ve seen the distinctive characteristic of essentially ordered series rests on the distinction between derivative and non-derivative members. Derivative members are only conditionally active, whereas non-derivative members are unconditionally active. Derivative members propagate the activity of earlier members, whereas non-derivative members originate the activity. The result encoded in the (PP) is that no members have their conditions actually met if all members are only conditionally active. Again, it’s that no member can propagate without some member originating. The point is not about the number of members, but about their kind. It doesn’t matter whether you have finitely or infinitely many pipes in a row, for instance, they will not propagate any water unless something originates the water. It doesn’t matter how many sticks you have, they will not move the stone unless something originates the movement.[5]

In short, then, the mistake of the objection is that it confuses the activity of an infinite series considered as a part, with the activity of an infinite series considered as a whole. The example does not contradict the present result because the objector has given us no reason for thinking the series in question is active when considered as a whole.

Updates

This page was significantly rewritten on 26 Aug 2017. The notation for series was made easier to follow, by distinguishing the sequence from the series so that the latter could follow the order of the series in reality. I also reordered the conclusions and formulated more in symbolic terms.

On 15-16 Dec 2017 I reworked the introduction and order of formalizations, so that the maths section is now optional. I also changed the Greek letters used to be closer to their English counterparts (sigma for the map into the series, and alpha for the active predicate).

Notes

  1. Well, an efficient causal chain. The chain here is, in Scholastic nomenclature, a final causal chain.
  2. We leave the proof of this as an exercise to the reader.
  3. This objection is inspired by Paul Edwards’ famous objection to first cause arguments for God’s existence.
  4. From a formalization perspective, this means that our formalism of series considered as wholes can include the answer if done correctly. Indeed, this is why we introduced the active/inactive distinction so that we can “step outside” and analyze the differences.
  5. To be sure, there is a difference between finite and infinite cases, in that a finite inactive series there will always be a first inactive member. This will sometimes happen in the infinite cases, as we saw above with our ω+n example, but not always. This difference, however, does not entail that infinite series can be active without non-derivative members.

Crutches and culture

I was thinking about silly claims like “religion is a crutch” or “people are religious because of their culture.” It seems to me that these claims are either uninteresting or false.

If taken as a claim that many religious people are religious because of perceived psychological benefits or cultural bias, it is uninteresting, at least from for the person interested in the veracity of religious claims. In many areas of life the vast majority of people hold the positions they do for non-intellectual reasons. The real question is whether there are good reasons for a position (religious or not), not the psychological factors that lead some people to hold that position. There’s also irony in that such caricatures apply equally to irreligion. We might as well say that irreligion is often due to rebellion or cultural bias. Again, who cares?

If, on the other hand, we take these as claims that there is no evidence for religious positions, and that therefore the only reason to be religious is deluded comfort or social acceptance, then the claim is blatantly false. Philosophical arguments for classical theism and historical evidence for Christianity have been around for ages. With regards to the former, see the Natural Theology section here.

Craig’s timeless moment sans creation

William Lange Craig’s model of how God relates to time can be stated succinctly: God is timeless sans creation, and temporal since creation.[1] The reason we word it like this is obvious: he can’t be timeless before creation, since before-ness is a temporal relation and creation includes time itself. Craig holds this view largely because he is a presentist,[2] believes that time is relational,[3] and that the past is finite.

Ok, now let’s talk about “states.” Let’s say that a state is constituted by a collection of things exemplifying properties, and that an event is a change from one state to another.[4] We’ll say that a state is maximal if it is not properly contained within any other state. We’ll use the word moment as synonymous with maximal state. Finally, we’ll call the moment of God existing sans creation the timeless moment.

The central problem of this post comes when we try and answer the question, “What makes a state temporal?” Or, in different words, what is a moment of time? One is tempted to say something like the following:

1. The moment S is temporal if and only if there is another moment T such that S is causally prior to T or T is causally prior to S.

There’s an interesting consequence of (1): combined with finitism (of the past), relationalism, and presentism, it entails that God began to exist. To see this, picture the scene: God exists and nothing else exists. We’re in the timeless moment, call it t1. God creates something, bringing about the first change, and therefore the first event, and therefore time itself. Let t2 be some moment later than the beginning of this first event. How are t1 and t2 related? Well, there have been a series of changes that lead from t1 to t2, so either they’re the same moment, or t2 is later than t1. They’re not the same, so t2 must be later than t1. But, given (1) it follows that t1 is a moment of time. And because God didn’t exist before t1 (since there is no “before”), it follows that God’s existence is completely contained within time. And since the past is finite, God’s existence (extended temporally backward) is finite, and thus he began to exist.[5]

Such a conclusion is certainly worrying for theists. But regardless of whether one is a theist or not, surely it’s absurd to think that the timeless moment is temporal, or that it somehow went from being timeless (sans creation) to temporal (since creation)!

So, what’s wrong? It seems to me that the entire approach to time seems to start in the wrong place. On relationalism, time is understood as a relation between events, not states.[6] Furthermore, it seems that a necessary condition for a moment being a moment of time is that there be an event occurring at that moment. After all, surely it always makes sense to ask what is happening at a given moment of time? Moments are temporal, then, only by virtue of being “part of” or “contained within” an event.[7]

Now, go back to our timeless moment. Certainly, no events are happening at this moment: things only start happening at the first moment of creation, and surely the moment sans creation is not the same as the first moment of creation. So the problem doesn’t arise once we start in the right place. However, I’d still like an account of what makes a moment temporal, in terms of just moments (like we had in (1)). This time, of course, taking into account the fact that in reality it is their relation to events that makes moments temporal. Assuming that “instants” of time are merely potential,[6] and that in reality all temporal intervals are open, the following might work:

1′. The moment S is temporal if and only if there is another moment T such that S is causally posterior to T.

That is, there is a series of changes that lead from T to S.

There’s another interesting perplexity that is solved by starting the right place is this: the timeless moment is causally prior but not temporally prior to creation. This does seem strange at first glance. I suspect it seems strange because we try to make sense of this cause as an instance of event-event causation. But, obviously, since the timeless moment is timeless, it is not contained in any events, and so we simply can’t make sense of this as an instance of event-event causation. And of course, since the effect is an event, we can’t make sense of this as an instance of state-state causation. What we need is some sort of state-event causation, and this is what leads Craig to introduce agent-causation as the solution.Actually, thinking of agent-event causation as an instance of state-event causation can be quite helpful: the state in question is the agent being impressed by various reasons for an action combined with the causal powers they possess in that state, and the event in question is the agent freely choosing to act in accordance with some of these reasons.[8]

Notes

  1. Here we are including time and all reality apart from God in the notion of “creation” and ignoring concerns about Platonic abstract objects.
  2. Presentism is the A-theoretic view that only the present exists. That is, the past no longer exists, and the future hasn’t but will exist.
  3. The relational view of time holds that events or change is explanatorily prior to the passage of time. Thus, if there were no events, there would be no progression of time.
  4. This definition allows for states to be constituted by events: the state of me waving my hand consists of the event of me waving my hand.
  5. “Having one’s existence completely contained within a time range finitely bounded in the earlier-than direction” is, for me, a defining characteristic of “beginning to exist”. A cool paper to read about defining “beginning to exist” is Adolf Grunbaum and the Beginning of the Universe by David Oderberg.
  6. Indeed, the whole idea of thinking of events as collections of instantaneous moments seems wrong, for Zeno paradox-like reasons. I’d refer the interested reader to another of David Oderberg’s papers, Instantaneous Change Without Instants, particularly section 3.
  7. I might need to be a bit more precise than this: considering that in note 4 we said that states can be constituted by events, it’s also possible for a moment to be temporal insofar as an event is part of it. This nuance is not relevant to the upcoming discussion, so I’ve left it here as a sidenote.
  8. This suggestion is highly influenced by Timothy O’Connor’s paper Agent Causation, and Alexander Pruss’ paper Divine Creative Freedom (particularly section 4).

Divine simplicity and the bootstrapping objection

Divine simplicity is the thesis that God has no parts, and that he is identical with his nature, his existence, and all his properties. Absolute creationism is the thesis that abstract objects exist and that God created each one of them [1]. Now, without divine simplicity, we can raise the bootstrapping objection against absolute creationism: logically prior to God creating anything (abstract objects included) he exemplifies the property of omnipotence, and therefore, the property of omnipotence exists externally to God prior to God creating it. Clearly, this is a contradiction.

However, if divine simplicity is coherent and true (which we assume for the sake of argument), then God himself is every one of the divine properties. Therefore, these properties do not exist logically prior to themselves, and there is no bootstrapping problem. For example, omnipotence exists, since God exists and God is omnipotence. Thus, God is free to create all the remaining abstract objects.

Notes

  1. There’s a nuance here: as far as I’m aware, it is typically understood that what makes abstract objects abstract is that they can’t stand in causal relations. However, if they’re being created by God, clearly these objects are standing in causal relations, and so perhaps calling them abstract isn’t strictly correct. I’ll just use the term to designate objects which are typically understood to be abstract (ie. propositions, properties, universals, etc.).

Divine simplicity and constituent ontologies

I’ve recently begun reading about Aristotelean-Thomistic philosophy. In A-T metaphysics, the doctrine of divine simplicity has a central place. This is the doctrine that God has no parts, be they physical or metaphysical. From this it follows that he is identical to his nature, to his existence, and to each of the divine attributes. Now this may sound really strange to some, but I recently read the SEP article on Divine Simplicity, and the distinction between constituent and non-constituent ontologies is both informative and helpful in making sense of divine simplicity. Worth a read.

What’s a negative property?

In discussing the Gödelian ontological argument recently articulated by Alexander Pruss[1] (here and here) there was a need to define what we mean by “positive property”. In the first post, we defined a positive property (in a very Anselmian way) as a property that is better or greater to have than not. In his second paper, Pruss suggests a different route: define “negative property” first, and then define “positive property” from that. That’s what we’re going to do here. If people don’t like the Anselmian intuitions behind our first definition, this should be a more acceptable route. Note what our goal is: we seek a coherent and non-gerrymandered definition of “negative” such that the axioms in the argument are true. I’m not here seeking to give an analysis of negative properties as if they’re an already established concept. Rather, I’m giving a definition.

Limitation as negativeness

We’ll try to flesh out the suggestion by Pruss[2]:

We might, however, proceed differently, by taking as our primitive the notion of a negative property, which is actually more natural than the Gödelian notion of a positive property. We can think of a negative property as one that limits a being in some way.

So, we’ll define a property of some being to be “negative” if and only if it is limiting to that being in some way. Perhaps this is too rough. After all, properties can be limiting in some circumstances but not others. We can be more specific, then, and say that a property of a being is negative if in every circumstance, it is limiting to that being in some way. What do we mean by “limiting to a being”? It seems natural to take this to mean something along the following lines: in exemplifying the property, the being has less control or is less capable in some sense than if it wasn’t exemplifying the property. That is, the property leads to more restrictions or hindrances to the being than its negation. Note that the property is limiting to the being. Self-existence, for example, is the ultimate form of ontological independence, and as such is limiting to a being’s dependence upon other beings. However, it is certainly not limiting to the being itself. As such, it isn’t a negative property.

We’ll say a property is “positive”, then, if and only if its negation is negative.

How about some examples? Sure: not knowing that 1+1=2 is a negative property, for no matter what circumstance a being (that exemplifies this property) finds itself in, it’s cognitive abilities will always be limited by not knowing that 1+1=2. Being trapped is a negative property since it limits the being’s freedom. Moving to more of the relevant properties, omnipotence is positive, since omnipotence is plausibly just perfect freedom of will and perfect efficacy of will[3], both of which are clearly positive properties. Since not being self-existent is limiting to one’s control, freedom and self-sufficiency, it follows that it’s negative. And so self-existence, which is the ultimate property of self-sufficiency and independence, would be positive. Omniscience would also be a positive property. Perfect goodness would also be a positive property, since being evil is limiting to a being’s goodness. We might be able to push this a bit further: surely not being the paradigm of moral goodness is limiting in the sense that there is a standard above one to which one must submit? In this case, being the paradigm of moral goodness (which is stronger than being merely perfect good) would be a positive property.

Back to the ontological argument

Ok, that seems like enough examples. Let’s turn back to the ontological argument from earlier. The following two axioms follow quite naturally from how we’ve defined negative properties:

F1*. If a property P is negative, then ~P is not negative.

F2*. If a property P is negative, and a property Q entails P, then Q is negative.

Awesomely, (F1*) and (F2*) entail (F1) and (F2) from our earlier post. Furthermore, since self-existence is positive and it entails necessary existence, it follows from (F2) that necessary existence is positive, giving us (N1).[4]

We could go through the whole argument again, this time maybe even talking in terms of negative properties rather than positive ones. But that’s too much effort, so once again, I leave it as an exercise for the reader 😛

Notes

  1. He’s formulated and defended this argument in two papers: “A Gödelian Ontological Argument Improved” in Religious Studies (2009) and “A Gödelian Ontological Improved Even More” in M. Szatkowski (ed.), Ontological Proofs Today (2012).
  2. This appears in the second of the two papers mentioned in the previous note.
  3. See “Understanding omnipotence” by Kenneth Pearce and Alexander Pruss, Religious Studies 48 (2012): 403-414. Even if we don’t accept their analysis of it, any good analysis of omnipotence should be that of having unlimited power, which is sufficient for it to be a positive property.
  4. We can also get their via the property of being the paradigm of moral goodness like before.

The gap problem

In the previous two posts (here and here) we looked at a Gödelian ontological argument from Alexander Pruss, which we’ll use a bit in this post.

The gap problem

Right, so what is the gap problem? Simply put, solving the gap problem involves bridging the gap between (i) the first cause or necessary being that we arrive at in cosmological arguments and (ii) the God of classical theism. Different philosophers have approached this problem in different ways and here I hope to survey and briefly discuss some of those. I haven’t read nearly enough to give any sort of comprehensive list, but this is a start.

Now, there are two things we need to keep clear. First, there are many properties of the God classical theism, and for each of these properties we can come up with different arguments. For example, in section 5 of his Blackwell Companion article on Leibnizian Cosmological Arguments, Alexander Pruss briefly deals with agency, goodness, simplicity, and oneness. Or, in his paper “From a Necessary Being to God”, Joshua Rasmussen argues for properties such as volition, infinite power, infinite knowledge, and infinite goodness. In this blog pos, we will concern ourselves only with the personhood of the first cause/necessary being. Second, in each case the arguments we mention will depend on what being we’re talking about. For example, the first cause that we arrive at with the Kalam argument does not have to be necessary or the explanation of every contingent fact. This limits what we can deduce about it. In each of the cases, I will make clear exactly what being I’m working with. Ok, so let’s get started.

Using the ontological argument #1

Assume we’ve arrived at the existence of a necessary being. In our previous posts in this series, we pointed out that both necessity and omniscience are positive properties. Thus, using essentiality of contingency or S5, it follows that there exists a necessary being who could have been omniscient. Now, we could assume that there are two necessary beings, but there’s no reason to think that these aren’t the same being and explanatory tools like Occam’s Razor suggest we should conflate them until we have some reason to think them distinct. So, it’s plausible then, that our necessary being could have been omniscient. But only persons can know things. Thus, this necessary being is probably personal.[1]

Using the ontological argument #2

Consider another way to use the ontological argument, which ends up building a quasi-ontological argument from an explanatory principle of a cosmological argument. For this we need the EPSR or a stronger explanatory principle:

EPSR. Everything has an explanation for its existence, either in the necessity of its own nature or in an external cause.

Now, we can use this to avoid commitment to the idea that necessity is a positive property. Again, clearly omniscience is a positive property. So is being the creator of everything else (itself, strictly weaker than aseity). So, in some possible world there is a being N who is the creator of everything else and omniscient. But, by the EPSR this being must be necessary. Then, by S5 or essentiality of contingency, this being exists and is necessary and personal. If we used Brouwer, we’d get a being who exists, is personal and could have been the creator of everything. Of course, if we take “being the creator of everything” as a strongly positive property then Brouwer will also give us a personal necessary being.

Explaining the BCCF

Imagine now we’ve arrived at our necessary being via one of the following equivalent explanatory principles[2, 3]:

PSR. Every contingent fact has an explanation.

WPSR. Every contingent fact could have had an explanation.

POE. If only one putative explanation can be given of a phenomenon, then that putative explanation is correct.

Now, we call the conjunction of all contingent facts the Big Contingent Conjunctive Fact (BCCF) of a possible world. When these principles get applied to the BCCF of the actual world, we arrive at a necessary being and a necessary fact involving the causal activity of that being[ which explains the BCCF[4]. Is this being personal? Well, since we have a necessary fact explaining a contingent fact, the explanation must be non-entailing, and non-entailing explanations are either statistical or libertarian. But statistical explanations seem inherently contingent, for there doesn’t seem to be any reason why the relevant probability couldn’t have been something like 0.00000000000000000001 more or less than it actually is. Thus, the explanation in this case must be libertarian, which means that the necessary being is an agent with free will (in the libertarian sense), and therefore personal.

Principle of determination

In his various writings, William Lane Craig has defended three reasons for thinking the first cause that we arrive at from the Kalam Cosmological Argument (KCA) is personal[5]. I’ve recently come to appreciate two of them which we’ll look at now. First there’s the argument from determination which starts with a peculiarity: assuming we have a first cause which is beginningless and changeless sans the universe (which is the conclusion from the KCA) it is rather puzzling that we find ourselves in an ever-changing universe. If the conditions for the effect had been met from eternity, then why is the effect not co-eternal with the cause? That is, why is the effect not changeless too? The puzzle is really about how the first event came about; about how change was effected from a changeless state.

Now, I’m going to phrase the actual argument differently to how Craig does, but it captures the same ideas he discusses:

  1. There was a first event, caused by a changeless and beginningless being. (KCA)
  2. The first event was either the effect of state-state causation, event-event causation, or agent-event causation. (Premise)
  3. It was not the effect of state-state causation or event-event causation. (Premise)
  4. Therefore, it was the effect of agent-event causation.

From (4) the first cause is an agent, and therefore personal. (1) comes from the KCA, so we won’t concern ourselves with that here. (2) is a list of possible ways causation can happen, and it seems to me to be comprehensive. Someone might suggest something like “state-event” causation, but I don’t think any coherent interpretation of this can be given that doesn’t eventually collapse into state-state or event-event causation. We can see (3) is true by seeing why each of its conjuncts are true. First, we’re considering the first event, and so it clearly can’t be the effect of state-state causation. Second, we considering the first event, and so there just are no prior events, be it logically, causally, or temporally.

Best candidate for explanation

The second reason Craig gives goes as follows: the first cause must be immaterial and timeless sans the universe. The only things we know that are both of these are unembodied minds and abstract objects. But abstract objects are by their very nature causally effete. Therefore, the first cause is probably a mind. This is a clear-cut case of inference to the best explanation, and for a long time I thought one could easily get around this by saying that an impersonal, [non-deterministic,] immaterial, and timeless being was the cause. But this is not an equally good explanation, because this doesn’t actually give us a candidate that does the explaining. All it does it list a bunch of properties. Now, if all we knew was that the cause was personal or impersonal and had no potential candidates for either of these, then I think such a move would be alright. But once one of the sides gives a concrete candidate that fits a set of properties, then if the other side can’t give a putative candidate, its position becomes explanatorily weaker since it gratuitously postulates unknown entities and if it can’t give any reason for not accepting the candidate from the first side, then its position also becomes ad hoc. Consider an analogous scenario: Alice and Bob find prehistoric tools, and Alice suggests that there was some sort tribe that made them. Bob, however says they weren’t made. Alice asks if Bob knows of anything that could explain the tools? Bob can’t give a candidate, but says it must’ve been some impersonal tool-forming process that occurred. Clearly Bob’s suggestion is explanatorily deficient, for he neither knows of any such process nor does he have any good reason for rejecting Alice’s explanation. Alice on the other hand, didn’t just say it was some personal tool-forming process: she gave a candidate. Now, inference to the best explanation isn’t conclusive and is usually tentative, but it lies at the foundation of scientific enquiry[6] and does contribute to a cumulative case for the personhood of the first cause. We shouldn’t let an unwelcome conclusion stand in the way our own consistency.

Moral arguments

If we don’t consider the cosmological argument in isolation, we can use the other theistic arguments to give us reason for thinking the first cause/necessary being is personal. We could, for example, launch the moral argument. This argument arrives at a personal being and it seems that the creator (ie. first cause) is a non-arbitrary candidate for this being who imparts duties to us. Not much more needs to be said about this.

Design arguments

We could also look to fine-tuning and complexity arguments. For example, in their paper “A New Cosmological Argument”, Pruss and Gale point out that “The actual world’s universe displays a wondrous complexity due to its law-like unity and simplicity, fine tuning of natural constants, and natural purpose and beauty” which suggests that the cause is intelligent and therefore personal. Now this is interesting to me, because I personally think the combination of the many-worlds hypothesis and the weak anthropic principle, while disgustingly gratuitous and usually driven by unchecked biases, is a sufficient to block the theistic conclusion of the existence a cosmic designer. But here we are not using the fine-tuning as an argument for the existence of the first cause/designer. We have already come to the conclusion that the universe has a cause, and are noting that the fine-tuning of the universe is best explained by this cause being intelligent. If the detractor is going to suggest an an infinity of universes to escape merely the move to personhood, they’re going need a good reason. Otherwise this suggestion’s ad hocness and lack of simplicity will count significantly against it, making the personal alternative a better explanation. I like how Robert Koons addressed this issue in his paper “A New Look at the Cosmological Argument” (note that he uses “cosmos” to refer to the many-worlds ensemble):

A standard non-theistic response to the data underlying the anthropic principle is to suggest that there may be an infinity of parallel universes, representing every possible permutation of possible physical laws and initial Big Bang conditions. Only an infinitesimally fraction of these permit the development of life and consciousness, but it is not surprising that we inhabit one of these vanishingly rare universes, since otherwise we would not be here to observe it….

This objection brings out the importance of considering evidence for design in the context of the cosmological argument. Without the cosmological argument, we would be forced to the conclusion John Leslie reaches, namely, that there are two equally good possible explanations of the anthropic data: a cosmic designer, and observer selection in a world of infinitely many, uncaused universes. However, once we know that the cosmos (including our universe) has a cause, the second hypothesis is excluded. It is still possible that the First Cause caused a junky cosmos, and that the evidence for intelligent design is illusory, but in the absence of positive evidence for these other universes, the reasonable inference to draw from the only universe we can observe is that the First Cause encompasses the existence of an intelligent designer.

There is another serious drawback to the junky cosmos hypothesis: if employed globally, it has the consequence that any form of induction is demonstrably unreliable. If we embrace the junky cosmos hypothesis to explain away every appearance of orderedness in the universe, then we should assume that the simplicity and regularity of natural law is also an artifact of observer selection. Universes would be posited to exist with every possible set of natural laws, however complex or inductively ill-behaved.

Now take any well-established scientific generalization. Among the universes that agree with all of our observations up to this point in time, the number that go on to break this generalization is far greater than the number that continue to respect it. The objective probability that every generalization we have observed extends no farther than our observations is infinitely close to one. Thus, relying on induction in such a universe is demonstrably futile.

In short, the junky cosmos hypothesis is both the most flagrant possible violation of Occam’s razor and a death sentence to all other uses of that principle. This hypothesis postulates an infinity of entities for which there is absolutely no positive evidence, simply in order to avoid the necessity of explaining the anthropic coincidences we have observed. This is the height of metaphysical irresponsibility, far worse than the most extravagant speculations of medieval angelology. Moreover, it undermines all subsequent appeals to simplicity or economy of explanation. If the junky cosmos hypothesis is true, it is demonstrable that the simplest hypothesis of astronomy or biology is no more likely to be true of our universe than the most complicated, Rube-Goldberg constructions. We would have absolutely no reason, for instance, to believe that the Copernican hypothesis is more likely to be true than a fantastically complex version of Ptolemy’s system, elaborated as far as necessary to save the astronomical phenomena.

Conclusions

I’ve summarised a bunch of different reasons for thinking the first cause/necessary being we get at the end of cosmological arguments is personal. Taken them by themselves, perhaps only a few are conclusive, but taken together I think they form a good cumulative case for the conclusion we want, and I see no reason for thinking the being should be impersonal. There are certainly more out there (I haven’t considered Joshua Rasmussen’s paper that I mentioned earlier, or arguments from the regularity of natural laws, and I didn’t mention epistemological arguments for a designer) but hopefully I’ve given you an idea of some ways personhood might be argued for. I’ll be sure to list new arguments as I come across them.

Notes

  1. If we get more specific and take omniscience to be a strongly positive property, then we have a necessary being who is probably omniscient too.
  2. Clearly PSR entails POE and WPSR. The other directions are argued for in Pruss’ book titled, The Principle of Sufficient Reason: A Reassessment.
  3. We could call the POE the “Sherlock Holmes principle”, for as the famous adage goes, “when you have eliminated the impossible, whatever remains, however improbable, must be the truth”.
  4. It involves the casual activity of this being because the BCCF includes positive existential facts, and these are plausibly only possibly explained causally. The being must be necessary for it cannot explain its own existence (unless, of course, its self-explanatory. But self-explanatory beings are necessary anyway, so that caveat is without relevance).
  5. See his book Reasonable Faith 3rd Edition, pp. 152-154, his essay in The Blackwell Companion to Natural Theology with James Sinclair, or even these Q&As from his website: http://www.reasonablefaith.org/is-the-cause-of-the-universe-an-uncaused-personal-creator-of-the-universe and  http://www.reasonablefaith.org/must-the-cause-of-the-universe-be-personal-redux.
  6. Modern physics and and evolutionary biology, arguably two pillars of modern science, both make extensive use of inference to the best explanation.

Fitch, Humberstone, and an omniscient being

I just read the paper “Omnificence” by John Bigelow[1]. In the preamble he recounts the following argument for an omniscient being

  1. Any fact (true proposition) is knowable by someone. (Premise)
  2. Therefore, every fact is known.
  3. Therefore, someone knows every fact.

Fitch[2] was responsible for showing that (2) follows from (1). One way to see this is a follows: for reductio assume, contrary to (2), that there is some fact p that is not known by someone. Then, p and no-one knows p is a fact, and by (1) is therefore knowable. Therefore, it is possible that someone knows p, and at the same time knows that no-one knows p, which is absurd. Thus (2) follows from (1).

The move from (2) to (3) comes from Humberstone[3]. Again, for reductio assume, contrary to (3) that for every person x, there is some fact p(x), that x doesn’t know. Now let X be the conjunction formed by taking all facts of the form p(x) and x doesn’t know p(x). Clearly this conjunction is true. By (2) it follows that there is some y who knows X. But one of the conjuncts of X will be p(y) and y doesn’t know p(y), and since y knows X, y also knows this conjunct, which is absurd. Thus (3) follows from (2).

I’m not going to argue for (1) here, although I must admit I struggle to imagine that there could be a fact that is in principle unknowable. What I found particularly interesting in Bigelow’s paper was the comment that logical positivism entails (1): take the verification principle of that movement, which said that a statement is meaningful if and only if it is verifiable. Now, only meaningful statements can take on a truth value, so it follows that every fact is verifiable, and therefore knowable.

Notes

  1. J. Bigelow, “Omnificence,” Analysis 65/3 (2005), pp. 187-196.
  2. F. Fitch, “A logical analysis of some value concepts”, Journal of Symbolic Logic 28: 135-42.
  3. I. Humberstone, “The formalities of collective omniscience”, Philosophical Studies 48: 401-23.