The Modal Third Way

[punkforchrist]

Robert Maydole has recently developed a modal cosmological argument, known as the “Modal Third Way.” You can read his paper here: bu.edu/wcp/Papers/Reli/ReliMayd.htm

I’ve been asking others for their opinion of the argument on some other forums, and I’m finding it more and more convincing. The nice thing about this argument is its use of very minimalistic premises.

If we’re using modal logic, the proof can be expressed as follows:

Where x = a thing; C = temporally contingent; t = time; P = past time; y = explicandum; and Eyx = x explains y.

1. (x) (Cx □ → ◊ (t) ~xt).
2. (x) ◊ (□t) ~xt □ → ◊ (□t) (x) ~Pxt.
3. ~(x) (◊x □ → ◊ (x ^ Eyx)).
4. ~(□x) ◊ (□y) Eyx □ → ~(□t) (x) ~Pxt].
5. ~Pxt → ~C(x).
6. :. ~C(x).

Here’s the English version.

1. Every temporally contingent thing possibly fails to exist at some time.
2. If all things possibly fail to exist at some time, then it is possible that all things collectively fail to exist at some past time.
3. It is necessarily the case that possible truths are explicable.
4. It is necessarily the case that something is explicable if and only if there was not a time when nothing existed.
5. If there could never have been a time when nothing existed, then something temporally necessary exists.
6. Therefore, something temporally necessary exists.

It’s important for us to understand the meaning of each of the terms used. In this case, “explicable” does not mean that something necessarily has an explanation; rather, it makes the highly unambitious claim that something is explicable so long as it is explained in at least one possible world.

So, the key premise is (4). What makes this proposition more likely true than its negation is that its negation would result in some existing time in which literally nothing exists, which is a contradiction. Hence, something temporally necessary exists.

Any thoughts?

 

[Touchstone]

Robert Maydole has recently developed a modal cosmological argument, known as the “Modal Third Way.” You can read his paper here: bu.edu/wcp/Papers/Reli/ReliMayd.htm

I’ve been asking others for their opinion of the argument on some other forums, and I’m finding it more and more convincing. The nice thing about this argument is its use of very minimalistic premises.

If we’re using modal logic, the proof can be expressed as follows:

Where x = a thing; C = temporally contingent; t = time; P = past time; y = explicandum; and Eyx = x explains y.

1. (x) (Cx □ → ◊ (t) ~xt).
2. (x) ◊ (□t) ~xt □ → ◊ (□t) (x) ~Pxt.
3. ~(x) (◊x □ → ◊ (x ^ Eyx)).
4. ~(□x) ◊ (□y) Eyx □ → ~(□t) (x) ~Pxt].
5. ~Pxt → ~C(x).
6. :. ~C(x).

Here’s the English version.

1. Every temporally contingent thing possibly fails to exist at some time.
2. If all things possibly fail to exist at some time, then it is possible that all things collectively fail to exist at some past time.
3. It is necessarily the case that possible truths are explicable.
4. It is necessarily the case that something is explicable if and only if there was not a time when nothing existed.
5. If there could never have been a time when nothing existed, then something temporally necessary exists.
6. Therefore, something temporally necessary exists.

It’s important for us to understand the meaning of each of the terms used. In this case, “explicable” does not mean that something necessarily has an explanation; rather, it makes the highly unambitious claim that something is explicable so long as it is explained in at least one possible world.

So, the key premise is (4). What makes this proposition more likely true than its negation is that its negation would result in some existing time in which literally nothing exists, which is a contradiction. Hence, something temporally necessary exists.

Any thoughts?

Too late for more than a quick, obvious observation. Unless you (or Maydole) are deploying “explication” in some highly informal sense (in which case, the argument is significantly diminshed, anyway), three is provably wrong. Per Gödel, it’s necessarily the case that if you have a formal system of explication, there exists truths that are not explicable via that system (Incompleteness Theorem).

-TS

 

[punkforchrist]

Hi Touchstone,

Thanks for your thoughts. Godel’s Incompleteness Theorem is actually inapplicable to the question at hand. We’re not talking about abstract mathematical theorems when we refer to temporally contingent things. The latter refer specifically to things that stand in causal relations.

 

[Touchstone]

Hi Touchstone,

Thanks for your thoughts. Godel’s Incompleteness Theorem is actually inapplicable to the question at hand. We’re not talking about abstract mathematical theorems when we refer to temporally contingent things. The latter refer specifically to things that stand in causal relations.

Well, what precisely do you mean by ‘explication’ here, then? I do understand from your first post that you’ve qualified it in such a way that it only needs reification in one possible world, but I think that does not address the nature of explication itself. That’s important, as it strikes me as a case of equivocation, given your response.

Notationally, I understand this:

1. ~(x) (◊x □ → ◊ (x ^ Eyx)).

To produce semantics like this:

*For any given truth, or any possible truth, in any possible world, there exists an explication, in principle.

*Having read this again carefully, just to make sure I’m not making some hasty mistake, I am now more convinced that 3) requires that every possible truth must have an explication. If you think about it, I think you must agree, because this interepretation is the only way it helps 4) and 5). It’s a nonsequitur, otherwise.
Godel’s incompleteness theorem is just the formalized, mathematical manifestation of a more general idea, the idea that is basically the negation of 3), and thus 4) to the extent 3) is a predicate. We do not have warrant for supposing that any possible truth necessarily has an explication, even in principle. For example, I might have pointed at features of physics in our world, where QM is problematic for the idea of necessary explications, even in principle.

Even taking your objections to Godel at face value, mathematical truths are a proper subset of “all possible truths”, no? If so, doesn’t that invalidate 3) just by virtue of being an exception to a general assertion (an unqualified universal, as you have it)?

Also, having thought about this a bit more, there seems to be Thomist causational assumptions implicit here. Premise 4 seems to treat time as existentially separate from “the world”. If so, I think that’s a problematic as an antiquated bit of medieval intuition, at odds with modern physics (time-space are inextricable, a unity).

More later.

-TS

*ETA: Just thought of a simple way to focus on a key feature of 3). If I say “X is a brute fact (universe pops into existence, maybe), and thus has no explication”, how would you respond? 3) fairly denies the logical possibility of brute facts, doesn’t it? *

 

[punkforchrist]

Well, what precisely do you mean by ‘explication’ here, then? I do understand from your first post that you’ve qualified it in such a way that it only needs reification in one possible world, but I think that does not address the nature of explication itself.

I don’t see why it wouldn’t. Something is explicable just if it is capable of being explained, not if it actually has an explanation.

Notationally, I understand this:

1. ~(x) (◊x □ → ◊ (x ^ Eyx)).

To produce semantics like this:

For any given truth, or any possible truth, in any possible world, there exists an explication, in principle.

To be more precise, (3) states that for any possible truth, there necessarily exists an explanation for that truth in at least one possible world.

Having read this again carefully, just to make sure I’m not making some hasty mistake, I am now more convinced that 3) requires that every possible truth must have an explication. If you think about it, I think you must agree, because this interepretation is the only way it helps 4) and 5).

I don’t think that’s the case. (4) doesn’t rest on the assumption that every possible truth must have an explanation; instead, it relies on modus tollens in demonstrating the absurdity of an existing time in which nothing exists. Just think about that phrase: an existing time in which nothing exists.

Godel’s incompleteness theorem is just the formalized, mathematical manifestation of a more general idea, the idea that is basically the negation of 3), and thus 4) to the extent 3) is a predicate. We do not have warrant for supposing that any possible truth necessarily has an explication, even in principle. For example, I might have pointed at features of physics in our world, where QM is problematic for the idea of necessary explications, even in principle.

I’m willing to think of quantum fluctuations as causally undetermined (re: random, unpredictable), but that doesn’t mean there’s no possible world in which a given fluctuation has some explanation. In fact, I don’t know how one would go about demonstrating such a strong-modal universal negative.

Even taking your objections to Godel at face value, mathematical truths are a proper subset of “all possible truths”, no? If so, doesn’t that invalidate 3) just by virtue of being an exception to a general assertion (an unqualified universal, as you have it)?

Mathematical truths would indeed be a proper subset of all possible truths. In fact, mathematical truths I think have a necessity about them. However, they don’t stand in causal relations, so speaking of them as explicable/inexplicable commits a category mistake.

Also, having thought about this a bit more, there seems to be Thomist causational assumptions implicit here. Premise 4 seems to treat time as existentially separate from “the world”. If so, I think that’s a problematic as an antiquated bit of medieval intuition, at odds with modern physics (time-space are inextricable, a unity).

We might have to flesh out your definition of the “world” a bit more. In any case, if you prefer, you can replace “time” with “state of affairs,” and I think you’ll reach the same result in the Modal Third Way.

ETA: Just thought of a simple way to focus on a key feature of 3). If I say “X is a brute fact (universe pops into existence, maybe), and thus has no explication”, how would you respond? 3) fairly denies the logical possibility of brute facts, doesn’t it?

Broadly-speaking, it is logically possible for the universe to exist as a brute fact, e.g., without any explanation. However, it doesn’t follow from this that the universe is inexplicable. Even if the universe, or some part of the universe, is unexplained in this world, it may have an explanation in another possible world.

 

[Touchstone]

I don’t see why it wouldn’t. Something is explicable just if it is capable of being explained, not if it actually has an explanation.

Unless you are supposing that in some given world W, that a truth T has to have some actualized explainer E, in order to satisfy the qualificaction “has an explanation”, I think that’s a distinction without a difference.

That is, if *T *is capable of being explained, in principle, I understand *T *to “have an explanation”. It seems odd to require that explainer E must be present to satisfy “has an explanation”.

If that sounds like a nitpick, it’s not. “Capable of being explained” is problematic with respect to 3) and 4). It may be the case that some truth *T1 *exists in any given world and is not capable of being explained (implicit being made explicit, in other words). This all turns on the specific semantics and constraints embedded in “capable of being explained”.

To be more precise, (3) states that for any possible truth, there necessarily exists an explanation for that truth in at least one possible world.

Well, let’s run with that. Here’s what you have for 3):

3. It is necessarily the case that possible truths are explicable.

For me, this gets justified like this (or, here’s what I take to be implicit in that statement):

1. An “explicable truth” is a proposition which can be explained.
   1a) A proposition which “can be explained” necessarily means that explanation is possible.
2. For some truth *T, *if there is a possible world in which T has an explanation, T is an “explicable truth”.
3. By necessity, then, for any explicable truth X, there exists a possible world supporting an explanation for *X.
   *4) It is necessarily the case that [any given] possible truths are explicable.

Sounds good, right? Well, it’s absurd, actually. Try it this way:

1. A “liftable object” is an object which can be lifted.
   5a) An object which “can be lifted” necessarily means that lifting it is possible.
2. For some object O, if there is a possible world in which *O *is liftable, then O is a “liftable object”.
3. By necessity, then, for any liftable object *O, *there exists a possible world where *O *can be lifted.
4. It is necessarily the case that [any given] possible objects are liftable.

8 is absurd, and the problem is shown clearly in 5) and 6), particularly 6). It construes “liftability” to be a metaphysically normalized property, and makes the mistake that “liftability” is a trans-world property, logically speaking. I chose “lifting”, because it’s patently obvious that “liftability” does not, need not translate across possible worlds. The implied “necessity” there is show to be illicit.

1-4 (your version, as I understand it) is the very same argument, and we’ve no basis for thinking it is any more sound than 5-8. It only passes the “absurdity detector” because *explicability *is vague, and ill-defined. No one using the term has a rigorous set of semantics that go with it, so it’s more difficulty to see the absurdity in construing it as a trans-world property.

The only rebuttal I can think of from you on this is that in connection to Maydole’s 3) and 4), analytic truths are somehow special in being temporally required. That brings up the specter of Thomist/Aristotelian metaphysics, if so, and for me, explains the root of the problem, here.

If I’m right in thinking this through, and the foundation of this is some kind of special pleading for analytical truths as prior necessities by virtue of some Thomist intution, then we should get that out one the table, and save ourselves a big waste of time going further. If that’s the grounding here, you and Maydole should just skip all the Rube Goldberg stuff in this argument and tell me you just think Aristotle’s intution and your own are correct, and that’s that.

If I’m wrong, please correct me, and let me know how you rescue 1-4 from the absurdity shown in 5-8 without some kind of presupposition of metaphysical realism.

-Touchstone

 

[Touchstone]

I don’t think that’s the case. (4) doesn’t rest on the assumption that every possible truth must have an explanation; instead, it relies on modus tollens in demonstrating the absurdity of an existing time in which nothing exists. Just think about that phrase: an existing time in which nothing exists.

This is to confuse language difficulties with conceptual absurdities. If we think about the “end of time”, the “Big Crunch” of our universe, we have a conceptual “border” after which no time exists. It’s just very clumsy and unwieldy to be precise because of the “time prejudice” built into our language, so we would say that “there is no time after the Big Crunch”, even though we are aware that “after” is a problematic term, implying that time extends beyond the Big Crunch, even though it physically does not.

It’s a “cheat” for reasons of communications expedience. But conceptually it’s not a problem. That means that your basis for modus tollens here with respect to 4) (denying the consequent) is mistaken. Conceptually, a “point after which there is no time” is not problematic. What is problematic is the language tools we have available for discussing this. Your literalist interpretation of “an existing time in which nothing exists” should give way to the understanding that “existing time” is an expedient proxy for “the concept of absence of existence, temporal or spatial”.

This, I think, is also at the root of foundational problems in Aristotelian metaphysics. The confusion about where the difficulty lies had Aristotle thinking non-existence was a logical problem rather than a linguistic problem.

I’m willing to think of quantum fluctuations as causally undetermined (re: random, unpredictable), but that doesn’t mean there’s no possible world in which a given fluctuation has some explanation. In fact, I don’t know how one would go about demonstrating such a strong-modal universal negative.

I don’t either, and would say the prospects for that are vanishing at best. But back to my previous post, this objection rests on the assumption that “explicability” is transitive across worlds. Why would you say that it is, any more than “liftability” is a trans-world modal? I understand one possible response, of course, being familiar with Aristotelian/Thomist metaphysics. Is that it?

In any case, you are quite right that QM does not rule out any possible world where such indeterminacies become determined. But it should suggest to you the weakness of Thomist/Aristotelian (and Platonic, come to think of it) intuitions about causality and determinacy. Here in our own world we have features of reality, features that could not be even contemplated as empirical observations in Aristotle’s or Aquinas’ day, that work right against the universality of the causation principle.

I wasn’t offer the QM example as a proof precluding explication, but rather just as a real-world point of instruction that should undermine “causal intuitions”.

Mathematical truths would indeed be a proper subset of all possible truths. In fact, mathematical truths I think have a necessity about them. However, they don’t stand in causal relations, so speaking of them as explicable/inexplicable commits a category mistake.

OK, so the constraint here would be to restrict “explicable truths” to causal explananda.

We might have to flesh out your definition of the “world” a bit more. In any case, if you prefer, you can replace “time” with “state of affairs,” and I think you’ll reach the same result in the Modal Third Way.

I suppose we might say that “state of affairs” has the same problem as “time” – a dependency on a time-context, but if we just decide to construe it in some atemporal way (!), we get this rephrasing of your objection:

an state of affairs in which nothing exists

See above for my explanation of why “a time where nothing exists” is non-problematic; this is even more straightforward. Keep in mind that by “state of affairs” you/we are NOT referring to the existential situation, but rather to you conception of that existential situation. So it may help to take it one step further and transform it thus:

**a conceptualization of perfect non-existence.

**As stated, that’s not a problem, any more than using “zero” is a problem. What is actual is the electro-chemical patterns in your brain that correspond to your conception of ‘non-existence’. The non-existence itself non-exists. There is no actualized referent, and thus no contradiction.

Broadly-speaking, it is logically possible for the universe to exist as a brute fact, e.g., without any explanation. However, it doesn’t follow from this that the universe is inexplicable. Even if the universe, or some part of the universe, is unexplained in this world, it may have an explanation in another possible world.

Yes, it may, and may is a qualification that sinks Maydole’s argument. I can agree with what you say here as a possibility. No resistance there. But that’s a much different proposition from saying that is the case, or – goodness! – that must be the case, which, is, having now gone to read up on this a bit with Google, ostensibly what Maydole is aiming at here.

There may well be explanations for as-now-possibly-forever unexplained actualities in this world that obtain in other possible worlds. But that does not establish necessity. We do not (as I see it) have any warrant for suppose that such a possible explanation in another possible world is “transitive” to this world, any more than I have warrant to believe that what is “liftable” in some possible world is necessarily “liftable” in this world, or any other.

-Touchstone

 

[TheWhim]

Dear punkforChrist,

I do not quite understand Maydole’s critique of the argument Aquinas laid out. Perhaps you feel like having enough leisure time to spare to explain to me what is so wrong with it as to require an improvement with sophisticated modal logic.

Let’s examine this statement:
3. But it is impossible for these always to exist, for that which can not-be at some time is not.

I think in the Third Way Aquinas presupposes an uncaused infinite universe – otherwise his argument wouldn’t be explainable. And it is only quite natural that he should argue from the starting point of the conception of such an universe because if he would start to argue with an universe which already is presupposed to have been caused by an external agent, God would already have been knocking at the door, Aquinas would not have been in any trouble to elaborate the Third Way and could have dropped it altogether. – Instead, obviously, he tries to convince sceptics and infidels. Well, in an (uncaused)infinite universe something that exists infinitely will never fail to exist – that is, it cannot be contingent. But contingent entities must, for some reason or other, fail to exist because their always existing would make them surpass their state of mere contingency.

If contingent entities can some time or other possibly fail to exist, then in an infinite universe they will some time or other fail to exist(otherwise they would exist infinitely and couldn’t be called contingent entities anymore). An infinite universe presupposed, the present moment has been preceded by an infinite past. There is no reason to suppose that there will always remain a contingent entity even if all the others have passed out of existence – in other words, their is no necessity underlying the claim that there will always remain at least one contingent entity in time. But if there is no necessity to this, it is possible that all contingent beings will fail to exist at the same moment some time or other. Given an infinite past, they all failed to exist some time or other(because only a necessity preventing this could make them survive an infinitude of time, which knows no limit to act out all the possibilities). – But if this were so, there was a time when there was nothing: which is absurd etc.

Honestly, I do not comprehend at which step in the argument Aquinas has gone wrong.

 

[punkforchrist]

Unless you are supposing that in some given world W, that a truth T has to have some actualized explainer E, in order to satisfy the qualificaction “has an explanation”, I think that’s a distinction without a difference.

I don’t think it’s a distinction without a difference at all. If T does not have any explanation E, then T may still be explained by E in some possible world.

That is, if *T *is capable of being explained, in principle, I understand *T *to “have an explanation”. It seems odd to require that explainer E must be present to satisfy “has an explanation”.

That’s not how truth-makers are thought of by theorists of possible worlds semantics. “Explicable” is much broader than “actually explained.”

If that sounds like a nitpick, it’s not. “Capable of being explained” is problematic with respect to 3) and 4). It may be the case that some truth *T1 *exists in any given world and is not capable of being explained (implicit being made explicit, in other words). This all turns on the specific semantics and constraints embedded in “capable of being explained”.

But, as I mentioned, the demonstration of such a strong-modal universal negative is next to impossible, if not literally impossible. How would one go about knowing that T1 is not capable of being explained?

Well, let’s run with that. Here’s what you have for 3):

3. It is necessarily the case that possible truths are explicable.

For me, this gets justified like this (or, here’s what I take to be implicit in that statement):

1. An “explicable truth” is a proposition which can be explained.
   1a) A proposition which “can be explained” necessarily means that explanation is possible.
2. For some truth *T, *if there is a possible world in which T has an explanation, T is an “explicable truth”.
3. By necessity, then, for any explicable truth X, there exists a possible world supporting an explanation for *X.
   *4) It is necessarily the case that [any given] possible truths are explicable.

Sounds good, right? Well, it’s absurd, actually. Try it this way:

1. A “liftable object” is an object which can be lifted.
   5a) An object which “can be lifted” necessarily means that lifting it is possible.
2. For some object O, if there is a possible world in which *O *is liftable, then O is a “liftable object”.
3. By necessity, then, for any liftable object *O, *there exists a possible world where *O *can be lifted.
4. It is necessarily the case that [any given] possible objects are liftable.

(8) should entail liftable objects are lifted in some possible world, which isn’t an absurdity. In fact, it does appear to be necessarily true.

 

[punkforchrist]

This is to confuse language difficulties with conceptual absurdities. If we think about the “end of time”, the “Big Crunch” of our universe, we have a conceptual “border” after which no time exists. It’s just very clumsy and unwieldy to be precise because of the “time prejudice” built into our language, so we would say that “there is no time after the Big Crunch”, even though we are aware that “after” is a problematic term, implying that time extends beyond the Big Crunch, even though it physically does not.

Even under such a scenario, something would still be temporally necessary. “Temporal necessity” simply entails that something exists at each moment of time; it doesn’t assume that time is infinite in both the past and the future.

In any case, you are quite right that QM does not rule out any possible world where such indeterminacies become determined. But it should suggest to you the weakness of Thomist/Aristotelian (and Platonic, come to think of it) intuitions about causality and determinacy. Here in our own world we have features of reality, features that could not be even contemplated as empirical observations in Aristotle’s or Aquinas’ day, that work right against the universality of the causation principle.

Actually, I don’t think Aristotelian metaphysics even requires that strong of a causal principle. Aristotle and Thomas believed that being could not arise from non-being, but they left the possibility of indeterminism open. After all, both philosophers affirmed human free will.

It seems to me that you’re conflating the Aristotelian causal principle with Leibniz’s strong version of the principle of sufficient reason (S-PSR). In any case, the Modal Third Way doesn’t depend on either.

For the record, I do agree with Aristotle.

I wasn’t offer the QM example as a proof precluding explication, but rather just as a real-world point of instruction that should undermine “causal intuitions”.

Even if QM succeeded in demonstrating this, it wouldn’t apply to broad modality.

I suppose we might say that “state of affairs” has the same problem as “time” – a dependency on a time-context, but if we just decide to construe it in some atemporal way (!), we get this rephrasing of your objection:

“Atemporal” seems a little too God-like to me.
As stated, that’s not a problem, any more than using “zero” is a problem. What is actual is the electro-chemical patterns in your brain that correspond to your conception of ‘non-existence’. The non-existence itself non-exists. There is no actualized referent, and thus no contradiction.

Under any form of metaphysical realism, it would be a contradiction, but that’s another matter.

 

[punkforchrist]

I do not quite understand Maydole’s critique of the argument Aquinas laid out. Perhaps you feel like having enough leisure time to spare to explain to me what is so wrong with it as to require an improvement with sophisticated modal logic.

I’ll do my best!

Let’s examine this statement:
3. But it is impossible for these always to exist, for that which can not-be at some time is not.

I actually agree with Thomas on this point, but it’s not something absolutely provable. For, that which can not-be may not-be at some time, but it’s logically possible for all temporally contingent things to always exist.

Well, in an (uncaused)infinite universe something that exists infinitely will never fail to exist – that is, it cannot be contingent. But contingent entities must, for some reason or other, fail to exist because their always existing would make them surpass their state of mere contingency.

The difficulty here is that Thomas is using “contingency” in two different ways. As his argument progresses, he jumps from temporal contingency to modal contingency. If the universe were to exist forever, it would still be modally contingent.

. . . But if this were so, there was a time when there was nothing: which is absurd etc.

Thomas does state that if nothing existed, then nothing would be able to come into being, which I agree with. However, there’s no broadly logical impossibility about this. The impossibility is a metaphysical one.

 

[TheWhim]

I actually agree with Thomas on this point, but it’s not something absolutely provable. For, that which can not-be may not-be at some time, but it’s logically possible for all temporally contingent things to always exist.

Well, this very idea I tried to challenge in my previous post, summarizing, so it seems to me, nothing else but the basic perceptions of Thomas’ mind. What I’ve written can be resumed thus: In an uncaused infinite universe it isn’t logically possible for all temporally contingent things always to exist(because this assured infinite existence would bespeak that they’re not contingent at all). - Where does the argument outlined in my previous post goes wrong?

And where, anyway, does Thoma make his assumed jump from metaphysical to modal contingency? I’m quite ignorant of this.

Thomas does state that if nothing existed, then nothing would be able to come into being, which I agree with. However, there’s no broadly logical impossibility about this. The impossibility is a metaphysical one.

Agreed.

I hope I don’t rely too heavily on your patience.

 

[punkforchrist]

Well, this very idea I tried to challenge in my previous post, summarizing, so it seems to me, nothing else but the basic perceptions of Thomas’ mind. What I’ve written can be resumed thus: In an uncaused infinite universe it isn’t logically possible for all temporally contingent things always to exist(because this assured infinite existence would bespeak that they’re not contingent at all). - Where does the argument outlined in my previous post goes wrong?

Causation is itself a metaphysical notion, as opposed to a purely logical one. It’s one that I agree with, though, and subsequently I agree with Thomas. If I might put it another way: I’m just lowering the bar - that is, I’m trying to assume as little as possible in trying to present an argument that will (hopefully) persuade the atheist.

And where, anyway, does Thoma make his assumed jump from metaphysical to modal contingency? I’m quite ignorant of this.

He begins with the normal metaphysical view of causation, which is quite defensible. As he continues, however, he assumes that this metaphysical axiom will translate into which states of affairs are instantiated. Possible states of affairs, in contemporary modal logic, are determined by merely what is logically possible in the broad sense, which wouldn’t necessitate the metaphysics that Thomas starts with.

Agreed.

I hope I don’t rely too heavily on your patience.

You’re good. This is basically my job, which is something I greatly enjoy!