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PSR Without Necessary Concreta (of Any Sort)

As I mentioned in two previous posts, it's commonly thought that a naturalist can't plausibly accept the Principle of Sufficient Reason (PSR), on the grounds that (i) she thereby commits herself to the existence of a metaphysically necessary being (more carefully, a metaphysically necessary concrete object), and that (ii) this is incompatible with any plausible version of naturalism. I critiqued (i) in the first of the two posts and (ii) in the second. Here I'd like to return to (i) and offer one more critique of it.

My previous criticism of (i) was that merely factually necessary beings are sufficient to satisfy a plausible version of PSR. Here my criticism shall be that a plausible version of PSR can be satisfied without appeal to necessary beings of any sort -- i.e., it can be satisfied merely in terms of continent, dependent beings. This sort of criticism goes back to Hume, of course, but William Lane Craig has tried to circumvent Hume's criticism in recent years. Therefore, as with the previous two posts on this topic, I'll use some of his work on the topic as my foil.

Perhaps the first thing that stands out about Craig’s version of PSR is that it’s a bit weaker than standard versions. Thus, a standard formulation of PSR can be expressed as follows:

(PSRs) There is an explanation for (a) the existence of every being, and for (b) the obtaining of every state of affairs.[1]

A standard criticism of PSRs is that clause (b) seems false, i.e., it seems that not all states of affairs can have an explanation. Craig states the standard criticism of PSRs tersely: "There cannot be an explanation of why there are any contingent states of affairs at all; for if such an explanation is contingent, then it, too, must have a further explanation, whereas if it is necessary, then the states of affairs explained by it must also be necessary."[2] In response to this criticism, Craig attempts to salvage a version of PSR by eliminating PSR(b), and just relying on PSR(a), i.e., by restricting the range of things needing an explanation to objects alone. He expresses his resultant version of PSR as:

(PSRc) Every existing thing has an explanation for its existence, either in terms of the necessity of its own nature or in terms of an external cause.[3]

Craig then deploys (PSRc) as premise (1) of his version of the Leibnizian cosmological argument to infer that a contingent universe requires an explanation in terms of a necessarily existent God.  Craig expresses his version of the argument as follows:

1. Every existing thing has an explanation of its existence, either in terms of the necessity of its own nature or in terms of an external cause.
2. If the universe has an explanation of its existence, that explanation is God.
3. The universe is an existing thing.
4. Therefore, the universe has an explanation of its existence.
5. Therefore, the explanation of the existence of the universe is God.[4]

The argument is clearly valid. Furthermore, (4) follows from (1) and (3), and (5) follows from (2) and (4). That leaves (1), (2) and (3). Why should we accept them?

For the purposes of this post, I'm granting the truth of Craig's version of PSR, viz., his (1) above. Troubles arise, however, with (2) and (3). For Craig's use of 'the universe' is ambiguous in these premises. On the one hand, it might mean 'our universe', i.e., the (roughly) 13.7 billion year old entity that began with our Big Bang. But if this is Craig's intended referent of the term, then while (3) seems true, it's less than clear that (2) is true.[5] To see this, suppose there is a beginningless series of contingent universes such that each such being is explained in terms of its predecessor, as follows:

. . .C --> B --> A

In this series, A is explained by B, B is explained by C, and so on. But if so, then each contingent being in the series (including our universe) is explained by another contingent being. And if that's right, then PSRc is satisfied in such a scenario without an appeal to a necessarily existent God, in which case premise (2) is undercut.[6]

On the other hand, by 'the universe' Craig might mean 'all physical reality'. But if this is Craig's intended referent of the term, then whatever the merits of (2), it's not at all clear that (3) is true. For it's epistemically possible that there is more (perhaps much more) to physical reality than our universe. So, for example, our scenario above involving a beginningless series of contingent universes is such a possibility.  But at least since the publication of Peter van Inwagen's Material Beings[7], it has become extremely unclear when – or even whether – two or more things compose a further thing. And if that’s right, then a fortiori it is controversial that all physical reality is a thing. Thus, whether the collection of all contingent things is itself a thing depends on which theory of material composition is correct. Universalists about material composition say that any two or more things is itself a thing. At the other end of the spectrum, nihilists about material composition say that no two things compose a thing -- there are only “simples” (or part-less beings) and their aggregates. Finally, moderates are those who fall somewhere in between universalists and nihilists, allowing that two or more things sometimes compose a thing, depending on whether they stand in a certain special relation to one another. So, for example, Peter van Inwagen’s moderate account entails that two or more things compose a new thing just in case they function together in such a way that their activities constitute a life.[8] For a moderate like van Inwagen, then, there are just two sorts of things: simples and living beings.

The problem this debate poses for Craig's argument is that each position has significant problems, in addition to their own set of strengths, and it's not clear how one should weigh each of these in determining which theory is correct.[9]  It therefore seems that an adequate defense of (3) would require a widely persuasive defense of a position in the material composition debate that entails that the universe (i.e., all physical reality) is itself a thing. Now universalism entails that the universe is itself a thing, while nihilism entails that it is not, and it's at least conceivable that a moderate position could be developed that is more plausible than universalism and nihilism, and which entails that all physical reality is itself a thing. So an adequate defense of (3) would seem to require a defense of either a universalist account of material composition or a defense of a moderate account that meets the desiderata mentioned above.[10] Unfortunately, though, Craig has yet to offer such a defense.

To sum up the criticism expressed above: the expression, 'the universe' is ambiguous in (2) and (3) of Craig's Leibnizian cosmological argument. Either (a) it means 'our universe' or (b) it means 'all physical reality'. If (a), then (3) is undercut. For it leaves open the possibility that our contingent universe is explained in terms of an infinite regress of universes (or in any case of contingent beings), where each is the cause of its successor. And if (b), then (2) is undercut. For it's extremely controversial among those who specialize in the material composition debate whether the universe (i.e., all physical reality) is a thing. And in any case, it's not at all clear that it's the sort of entity that requires an explanation.  Either way, Craig's argument appears to contain at least one dubious premise.

Craig has offered two main responses to the objections raised above.  His first response is to argue that we can tell that the universe is a thing independently of an argument on behalf of a particular account of material composition. For here we can appeal to our intuitions, which indicate that the universe is, in fact, a thing -- or at least it was a thing, during the earliest stages of its existence:  “ . . . the universe is obviously an existing thing (especially evident in its very early stages when its density was so extreme), possessing many unique properties such as a certain density, pressure, temperature, space-time curvature, and so on . . .”[11] In this way, Craig defends the standard reply that the collection of all contingent beings or things in the series is (or at least was) itself a being, in which case PSRc requires an explanation of the universe in terms of a necessary being.

His second response is to argue that the material composition debate can be sidestepped altogether, on the grounds that whether the universe is properly considered a thing or not, it is nonetheless the sort of entity that requires a cause or explanation: "I do not mean to pronounce here on ontological debates about what constitutes an object, but merely to claim that the universe is just as much a thing as are other familiar entities which we recognize to have causes, such as chairs, mountains, planets, and stars.”[12]

What to make of these responses? Now I’m inclined to agree with Craig that, at least in its earliest stages, our universe was a single existing thing, or at least the sort of entity that requires a cause or explanation in terms of one or more or other things. However, it’s not clear how this helps to answer the criticism raised above. For absent an independent argument that our universe is co-extensive with all physical reality, it’s epistemically possible that our universe is properly explained in terms of temporally prior processes involving other universes (or in any case, other natural contingent entities), and so on back ad infinitum. To answer the criticism above, therefore, it looks as though Craig will need to provide a reason for thinking that a collection of beings of the latter sort (i.e., a beginningless series of contingent universes) is itself a contingent being – or at least the sort of entity that requires a cause or explanation.

Unfortunately, the reasons we’ve looked at from his writings don’t look plausible when applied to the latter sort of case. For unlike our universe during its earliest stages, it’s just not clear that a beginningless series of contingent universes is itself a thing, or even (thing or not) an entity that requires a cause or explanation. It therefore looks as though the material composition debate cannot be sidestepped so easily after all.

In short, it looks as though Craig has more work to do in defending the Leibnizian cosmological argument against the criticisms raised here. Absent such a defense, even those who accept his version of PSR are left without a good reason for thinking there is a metaphysically or factually necessary being.
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[1] This formulation is equivalent to that stated in Rowe, William. Philosophy of Religion: An Introduction, 4th ed. (Wadsworth, 2006), pp. 23.

[2] Craig, “The Cosmological Argument”, p. 114. Cf. Rowe, William. The Cosmological Argument (Fordham University Press, 1998), pp. 103-111; Van Inwagen, Metaphysics, 2nd edition (Westview, 2002), pp. 119-122.

[3] Cf. Craig, “The Cosmological Argument”, in Copan, Paul and Paul K. Moser, eds. The Rationality of Theism (Routledge, 2003), p. 114; Reasonable Faith, 3rd edition (Crossway, 2008), p. 106. 

[4] Cf. Craig, “The Cosmological Argument”, p. 114-116, esp. p. 114; Reasonable Faith, 3rd edition (Crossway, 2008), pp. 106-111, esp. p. 106. Craig notes his indebtedness to Stephen T. Davis for his formulation of the argument. Cf. Davis, “The Cosmological Argument and the Epistemic Status of Belief in God”, Philosophia Christi 1:1 (New Series) (1999), pp. 5-15.

[5] The following criticism is based on Peter van Inwagen's. See, for example, van Inwagen, Metaphysics, 2nd ed. (Westview, 2002), pp. 126-128.

[6] Craig is of course known for his arguments against the existence and traversability of actual infinites in relation to his defense of the kalam cosmological argument. Discussion of those arguments is beyond the scope of this post. However, I've discussed virtually all of Craig's (and Moreland's) arguments on this score on other occasions (e.g., here and here). I refer the interested reader to those posts.

[7] Cornell University Press, 1995.

[8] Cf. Material Beings.

[9] For an overview of the range of positions and their strengths and weaknesses, see (e.g.) Markosian, Ned. “Restricted Composition”, in Hawthorne, John, Theodore Sider, and Dean Zimmerman (eds.), Contemporary Debates in Metaphysics (Basil Blackwell), 2007, pp. 341-364.

[10] In this regard, it's worth reiterating that van Inwagen's own moderate account does not countenance the collection of all dependent beings -- whether construed as our own universe or as all physical reality - as itself a being or thing.

[11] “The Cosmological Argument”, p. 115,

[12] Ibid., p. 130, fn. 6.

Comments

Steve Maitzen said…
Ex: Thanks for the interesting post. Two quick thoughts:

1. I think the idea that the universe (understood as all of concrete reality) never began to exist -- that there's no first being or first event -- beats the idea that it began to exist. Craig's arguments for the other side misfire. For one thing, they assume that any actual stretch of time consists of at most a countable infinity of moments (in fact, Craig concludes that it must consist of finitely many moments), whereas it seems to me better to think of any stretch of time as represented by a real-number interval: continuum-many extensionless points no two of which are adjacent to each other.

2. You wrote, "[I]t's just not clear that a beginningless series of contingent universes is itself a thing, or even (thing or not) an entity that requires a cause or explanation." Agreed. I can think of two things that "a beginningless series of contingent universes" could plausibly denote: (a) a set of such universes; (b) a beginningless event whose "parts" are connected temporal segments. If (a), then explaining the members ipso facto explains the set, given the identity conditions for sets (and granting that sets exist). If (b), then the only way we have of explaining events -- i.e., in terms of prior events -- isn't available even in principle.
exapologist said…
Steve,

Good thoughts.

Re: 1: I agree. I think the fact that our best scientific models of spacetime represent it as a continuous manifold provides at least burden-shifting abductive evidence that actual infinites both exist and can be traversed. I also think Craig's a priori arguments against the existence and traversability of actual infinites are all subject to undercutting defeaters.

Re: 2: Nice. A question about your criticism of your (b): I'd be interested in hearing your rejoinder to the reply that such an entity could have an explanation in terms of a sustaining cause even if it doesn't have an explanation in terms of a temporally prior originating cause.

Best,
EA
Steve Maitzen said…
Ex,

Thanks.

1. Confession: my reason for preferring continuous over discrete spacetime is philosophical rather than scientific. Even if it should turn out to be physically necessary that some particle travels discontinuously from point A to distinct point B, I find it inconceivable that the space between A and B doesn't exist, even if physics might tell me it doesn't. By contrast, I find the density of the real-number line merely weird, not inconceivable.

2. In (b), as I understand it, the state of reality at any time is causally sufficient for the state of reality at any later time. One might worry that Special Relativity forbids us from talking about "the state of reality at a time" (although a student of mine who knows his physics says, "Don't worry about that"), in which case we'd need to tweak this description. Anyway, given that causal sufficiency, I don't know what a "sustaining" cause of the series could be. Each instantaneous time-slice is causally sufficient for each later one. We may choose to designate a particular (part of a) slice as "the cause" of some later (part of a) slice, but that's our pragmatic decision; it doesn't reflect an ontological distinction. Given the causal sufficiency, what work is left for a sustaining cause to do? What needs to be sustained that isn't already sustained?
Tyrel said…
You say: "suppose there is a beginningless series of contingent universes such that each such being is explained in terms of its predecessor, as follows:

. . .C --> B --> A"

However, what do you make of Pruss' objection to this Humean out? He says, in his Leibnizian cosmological argument, that this infinite regress is actually logically equivalent to vicious circularity. See section 4.1.1.4 objection 3, here: https://bearspace.baylor.edu/Alexander_Pruss/www/papers/LCA.html

I think he's right - I think there is actually a logical problem with suggesting an infinite regress. This can be seen clearly when one considers the analogous case in epistemology against foundationalism, where instead of saying that some belief P is justified just in case it is entailed by R (where R is a basic, and justified belief), one has to say that P is justified by A, which in turn is justified by B, and so on ad infinitum, with no basic justified beliefs. The cases are exactly analogous, and to claim that an infinite regress of contingent things serves as an explanation is simply to miss the modal point of thinkers like Aquinas and Leibniz. In any case, I don't think it works.

Moreover, I'm not sure what distinction you have in mind when you say that there is a metaphysically necessary being on the one hand, and a factually necessary being on the other. Perhaps factually necessary is just a semantic confusion of terms?

Interesting paper though.
exapologist said…
Hi, Steve:

In (b), as I understand it, the state of reality at any time is causally sufficient for the state of reality at any later time . . .Anyway, given that causal sufficiency, I don't know what a "sustaining" cause of the series could be. Each instantaneous time-slice is causally sufficient for each later one. We may choose to designate a particular (part of a) slice as "the cause" of some later (part of a) slice, but that's our pragmatic decision; it doesn't reflect an ontological distinction. Given the causal sufficiency, what work is left for a sustaining cause to do? What needs to be sustained that isn't already sustained?

My sympathies are with you on this, but let me employ a thought experiment on behalf of the theist:

Consider two possible worlds, W1 and W2. At both worlds there is matter, and at both worlds, the law of conservation holds. However, the explanation as to why it holds is different in each world. In W1, the law of conservation holds because matter enjoys a sort of "existential inertia". By contrast, in W2, it holds because an external source (say, God, or some other sort of metaphysically necessary being) continually supplies being to the essence of matter.

Now perhaps there is a concern with the intelligibility of the Thomistic metaphysics (or something like it) implied by the scenario, but let's waive that and assume W1 and W2 are both epistemically possible. In both worlds, a given state of reality Sn at a given time tn is causally sufficient for the state of reality Sn' at tn+1. However, in W2, Sn involves a metaphysically necessary being, while in W1 it does not. Can physics currently tell us which of the two worlds is the actual world?

Perhaps one will argue that the hypothesis that we're in W1 trumps the hypothesis that we're in (something like) W2 in terms of simplicity, scope, conservatism, etc.? If so, then that's pretty much my view, too.

Best,
EA
exapologist said…
Hi Tyrel,

Pruss is there defending a stronger version of PSR -- one that requires explanations of contingent facts. Craig's version restricts things needing explanation to objects.

I'm also not seeing the relevance of the regress argument for foundationalism. The problem of infinite epistemic regresses there is that one can't comprehend an infinite series of reasons.

My notion of factually necessary beings is sketched in the post linked to at the beginning of this post (here).

Best,
EA
Steve Maitzen said…
Ex: You wrote, "In both worlds, a given state of reality Sn at a given time tn is causally sufficient for the state of reality Sn' at tn+1." I don't see that, assuming I understand the Thomistic metaphysics going on in W2. In W2, Sn doesn't give rise to Sn' unless something external to the universe causes Sn to do that (or at least contributes to its doing that). In that case, I wouldn't describe Sn as causally sufficient for Sn': something "external" (your word) is needed in order for Sn' to arise.
Rayndeon said…
@Tyrel: That stronger version of the PSR Pruss invokes is subject to its own set of independent problems. One particularly appealing argument to me is van Inwagen's argument, although similar strands of this can be found in William Rowe's and James Ross' work as well:

Suppose that there is conjunction of all contingent facts (and hence is itself contingent). Now, suppose there exists an explanation of this fact. Now, either this explanation is contingent or necessary. If it's contingent, then the conjunction of all contingent facts is self-explanatory, which Pruss rejects as a live possibility and which is a reasonable position to hold. The alternative is to hold that the explanation is necessary. However, wherever that explanation exists, that particular conjunction of contingent facts is actual. But, since the explanation is necessary, and the conjunction is of ALL contingent facts, then the conjunction of contingent facts must also obtain in all worlds; that is, it is both contingent and necessary, which is absurd.

So either one believes that (a) the only possible world is the actual world or (b) this version of the PSR is false. The first horn is a pretty big bullet to swallow, since it essentially eliminates modal discussion altogether. The only possible world is the actual world.

Pruss seeks an out by invoking libertarian free will. I am unconvinced by this. Ignoring the myriad problems LFW has independent of this argument, the mere existence of a divine agent is insufficient to explain why that particular conjunction obtained. Instead, the explanation must be rooted in the agent's particular act, which of course necessitates the conjunction, leading back to problem.

Pruss has then later utilized a number of other PSRs and there have been other similar modal cosmological arguments, which I also find unconvincing for various other reasons. But I think the PSR Pruss invokes in that particular paper can be shown to be decisively unacceptable.
exapologist said…
Hi, Steve.

Perhaps I wasn't clear. As I stated it, "In both worlds, a given state of reality Sn at a given time tn is causally sufficient for the state of reality Sn' at tn+1. However, in W2, Sn involves a metaphysically necessary being, while in W1 it does not" (emphasis added). By that I meant that Sn includes a metaphysically necessary being. As such, while such a being is "external" to the material world, it isn't external to Sn, in which case Sn at tn is sufficient for Sn' at tn+1, no?
Steve Maitzen said…
Hi, Ex. Sorry, I misread your proposal. If I have it right, the choices are (1) matter (really, total mass-energy) is conserved inherently; (2) total mass-energy is extrinsically and intentionally conserved by a causally efficacious necessary being. In my view, (1) wins on grounds of parsimony, and it doesn't invite the awkward question "Why is this necessary being concerned to conserve only total mass-energy but not any of the particular material objects that inhabit its creation?"
exapologist said…
Hi, Steve.

In my view, (1) wins on grounds of parsimony, and it doesn't invite the awkward question "Why is this necessary being concerned to conserve only total mass-energy but not any of the particular material objects that inhabit its creation?"

i agree completely.

Best,
EA
Rayndeon said…
Hi exapologist and Steve,

Both of you appear to be defending at least the metaphysically possibility of there being an infinite number of causes/explanations for the universe (as in everything that exists). I know that exapologist has defended against most of Craig's arguments against both the metaphysically possibility of an actual infinite and an infinite past, but what do you make of more recent arguments involving Grim Reaper paradoxes, or the like?
exapologist said…
Hi Rayndeon,

For my part, I'm not sure what to make of (for example) Robert Koons' Grim Reaper argument. I still need time to think about it.

Best,
EA
Angra Mainyu said…
On the issue of Robert Koons' Grim Reaper argument, he claims that the GR's powers and dispositions are intrinsic, but that results in problems:

For example, let G be a being such that G has the power to block the production of any particle by any other being. Surely, a theist cannot object to the possibility of such a being without denying the possibility of God.

Yet, let W be a world at which G exists and one of Koons' Grim Reapers also exists.
Then, at that world, the Grim Reaper does not have the power and disposition to produce the particle in question. So, it seems that the GR's power and dispositions aren't all intrinsic after all.
So, we can posit the following dilemma:

H1) If a being with the power to block the production of any particle by any other being is impossible, then God does not exist.

H2) If a being with the power to block the production of any particle by any other being is possible, then it seems the powers of each Grim Reaper are not intrinsic.

A theist might present some objections to the dilemma, but there seems to be no good way around it; at least, the main options appear to all fail.
For instance:

1) A theist might say that even if a more powerful being is possible, the reapers' powers are indeed intrinsic, but no such Grim Reaper exists in a world in which a being with the capability for blocking his powers exists.
However, if no such Grim Reaper exists in a world in which a being with the capability for blocking its powers exists, the beliefs of a theist committed to the necessary existence of God – such as Koons', and most theists – entail that such reapers are impossible. Yet, Koons' claims that reapers are possible.

2) A theist might say that since God is necessary, no such Grim Reaper is possible, so theists should not accept the 'Grim Reaper' argument against temporal density, but non-theists do not have that option.

But actually, a non-theist may simply say that, perhaps, one Grim Reaper is possible, or perhaps not. Maybe spacetime is such that those entities do not exist. Maybe one is possible, but infinitely many of them aren't. Who knows?
But leaving that aside, the non-theist has other replies, such as the following:
Let's consider the case of binary patchwork.
Let's suppose that one of the Grim Reapers exists at some region R(2) of world W(2), and an entity G exists in a region R(1) of W(1) with the following power: G can block any future production of particles in that world. Then, it seems that a copy of R(1) can't be followed by a copy of R(2) in any world, so even binary patchwork seems to fail if R(1) happens earlier. But without binary patchwork, Koons' argument is blocked.
There are plenty of alternative replies available to the non-theist; the point is that the theist is nowhere near establishing the result he's looking for.

3) A theist might say that Grim Reapers are possible, but their intrinsic power is the power to produce a certain particle under certain conditions, and in absence of anything that prevents them from using such a power.

But again, in that case, the theist has no case against the existence of a possible world in which all of those reapers exist, but their powers are blocked, and so none of them acts.
A non-theist might say that, perhaps, in a world with infinitely many reapers, precisely the existence of such reapers blocks their exercise of powers. Perhaps it's something else that blocks them. Who knows?
The burden remains on the theist, it seems to me.
Angra Mainyu said…
@Rayndeon,

On the issue of a conjunction of all contingently true propositions, Pruss rejects an objection by Davey and Clifton's, based on a 'principle of innocence'.

However, even if we assume a 'principle of innocence', it seems to me that a modification of Davey and Clifton's construction gets the Big Contingent Conjunctive Fact (BCCF) in trouble.

The only extra assumption that is required is what we could call the "Subconjunctions Principle" (SP"), which seems very plausible to me:

SP: If a conjunction C makes sense, and P is a property, then the conjunction C(P) of all of the conjuncts of C which have property P makes sense as well.

If the BCCF makes sense, since the BCCF is the conjunction of all contingently true propositions, let the BCCF(P) the conjunction of all the conjuncts of the BCCF that do not contain themselves as proper subformulas (following Davey and Clifton).

So, the BCCF(P) is just the conjunction of all contingently true propositions that do not contain themselves as proper subformulas, since a proposition R is a conjunct of the BCCF if and only if R is a contingently true proposition.

Let Q be the proposition "that BCCF(P) is true".

Since the BCCF(P) is contingently true because every single one of its conjuncts is, then Q is a contingently true proposition as well, and hence Q is a conjunct of the BCCF.
Does Q contain itself as a proper subformula?
Mirroring Pruss' explanation of Davey and Clifton's argument, we can see that either way, a contradiction follows:
If the answer is "no", then Q is a contingently true proposition that does not contain itself as a proper subformula. Hence, Q is one of the conjuncts of the BCCF(P), and thus a proper subformula of itself, which contradicts the assumption that the answer is 'no'. Hence, the answer is 'yes'.

So, Q contains itself as a proper subformula, and so it's a subformula of the BCCF(P). But since Q is not a conjunction, it must be one of the conjuncts of the BCCF(P), and thus, it's not a proper subformula of itself.
The conclusion is that the BCCF makes no sense.

Perhaps, someone could object that the "logical redundancies removed" stipulation blocks the argument. But then, that would have to be argued for. It's not clear how the removal procedure works, though. How does one remove something from something that makes no sense?
Rayndeon said…
@Angra Mainyu,

On the topic of Koons' reapers: I think your reply to Koons arguments towards the "intrinsic nature" of the GRs is quite good. It seems plainly clear to me that if such Reapers actually existed, none of them would act in the proposed Grim Reaper scenario, since there would be no first reaper to actually kill John. They would all be paralyzed into inaction. I've enjoyed our protracted dialogue here as well, in case other readers are interested: http://www.freeratio.org/showthread.php?t=315560

On the topic of the cosmological argument:

I'll have to mull over that argument. It seems to me that there might be a problem with the idea of constructing the BCCF, but wouldn't rejecting the BCCF block van Inwagen's objection in that case?

On other causal principles: Judging from your blog, you are obviously interested in cosmological arguments. What do you make Josh Ramussen's recent cosmological argument i.e. "From States of Affairs to a Necessary Being?" http://www.nd.edu/~jrasmus1/research.html
Angra Mainyu said…
@Rayndeon,

Thanks, I enjoyed the discussion as well.

On the topic of Pruss' cosmological argument, Pruss claims Van Inwagen's objection would be blocked so if not only the BCCF but all variants that could be used in such arguments are blocked as well (https://bearspace.baylor.edu/Alexander_Pruss/www/papers/LCA.html).

But if all such variants are blocked, at least all those kinds of cosmological arguments are blocked, as Pruss recognizes, though it's true that Van Inwagen's challenge to the strong version of the PSR is blocked.

I do not know whether a variant of Van Inwagen's challenge works on variants like the BCCF*, but
regardless of whether all such variants are blocked, it seems that even the strong PSR wouldn't help these cosmological arguments if Van Inwagen is correct about two key premises, and if he's not, his objection fails regardless of any considerations involving the BCCF.

The two key premises are:

1) No contingent proposition is explained by a necessary proposition.
2) No contingent proposition is self-explanatory.

Pruss contends (same paper) that we should not accept 1).
If Pruss is right about that, then Van Inwagen's objection fails.
If Pruss is wrong about that, then we get the following:

Let P(1) be any contingent proposition.
Then, there is an explanation P(2), which is a different contingent proposition.
Now, there is an explanation P(3), which explains P(2) (or, if one prefers, P(3) can be picked to explain the conjunction of P(1) and P(2), and hence in particular P(2)).
Proceeding as before, we get an infinite regress of explanations.

But what about the whole series?
Given that the denumerable conjunction S(1) of the {P(n)} makes sense and is contingently true, then we have (by PSR) an explanation of S(1), say P(1,1). But then, there is an explanation P(1,2) of that one, and so on, until we get another infinite regress on an infinite regress, and so on.

While that does not affect the strong version of the PSR, it's of no help for the cosmological argument in question.

All it leads us to is infinite regresses of explanations, and that, as a side effect, is a problem for other theistic arguments that rely on the impossibility of such regresses.

On the other hand, it's true that someone might then try to use the strong version of the PSR to run a different cosmological argument, and Van Inwagen's objection is blocked if the BCCF is impossible, or at least of all variants that are meant to play a similar role in cosmological arguments are impossible.

On the issue of Rasmussen's argument, you're quite right I'm interested in cosmological arguments, thanks for asking, but I think I'm getting too many arguments on my plate at the moment, so I'm afraid I'll have to leave it for later.
Angra Mainyu said…
ex-apologist,

I've been thinking about your reply to Craig's argument, and I find it quite persuasive: I agree Craig has more work to do.

Also, I have the impression that in case he means our universe, he may have even more work to do: as you explain, he's not shown that the a beginningless series of contingent universes is a contingent thing, or something that requires a cause or an explanation.

But what if he managed to show that (unlikely IMHO, but for the sake of the argument) if we have U(1) caused by U(2), etc., then the whole series of universes {U(n)} is a thing and requires a cause?

Even then, it seems to me that for all we know it might still be the case that the cause of the series {U(n)} is yet another universe of sorts (or multiverse, or whatever one calls it), say, U(2,1). Then, U(2,1) might be caused by U(2,2), and so on, getting another such series, and then another one, and so on, and so forth.

So, I'm thinking maybe in any case Craig would have to show that all physical reality is a thing or in any way requires a cause or explanation, or at least argue against the aforementioned variant on other grounds.

What do you think?
Angra Mainyu said…
@Rayndeon,

Regarding Rasmussen's argument (which can be found in his website, http://www.nd.edu/~jrasmus1/research.html), in my view it has a number of difficulties that would require a more detailed analysis, but I can offer a quick counter point, granting a number of points for the sake of the argument (though I'm quite skeptical about them).

In his first road to a necessary being, Rasmussen claims that there are plausibly maximal contingent states of affairs (as defined in his paper).

In particular, Rasmussen claims that even if a maximally incompatible being is not possible, Big Blob is plausibly possible (Big Blob would be a contingent being that necessarily takes up all of space).
Then, he claims that the only possible causes of Big Blob would be an object that occupies no space or shares space with Big Blob.

Let's say that that's true. Moreover, let's grant that it's possible (just possible) for a being not to occupy any space at all.

After that, Rasmussen makes the following move: He claims that a contingent state of existence composed of Big Blob plus all possible objects compatible with it would be maximal.

However, he does not argue at all for the claim that such a maximal state is possible, and it's not clear to me that it is. In fact, the assumption that such maximal state is possible does not appear to me more plausible that the hypothesis that such maximal state is impossible, for the following reasons:

Let S be a contingent state of existence consisting of Big Blob (henceforth, BB) and perhaps some other beings. By definition of 'contingent state of existence' (in his paper), S consists of BB, plus perhaps some other contingent beings that occupy space OS, plus perhaps some other contingent beings none of which occupies space NOS (OS and NOS denote the part of the state consisting of all the beings in question; their number, if any, is not important to my point).

Then, it seems plausible to me that one might add yet another being that does not occupy space to that state, getting S', so S is not maximal.

That appears quite plausible to me, even because of something Rasmussen said, namely that we don't have to worry about fitting objects into a region of space, since one can have as many angels or overlapping ectoplasm beings dancing on a pinhead as one wants to.

Well, if we can put as many angels in there as we want, who's to say that there is a maximal angel-containing state consisting in a certain arrangement of angels, such that no more angels are possible, unless perhaps something else is destroyed?

Frankly, assuming the possibility of angels or other entities that do not occupy space, that appears intuitively very implausible to me. But Rasmussen does not even attempt to back up the claim, as far as I can tell.

As for the possibility of a contingent being that is incompatible with all other contingent beings, that's not established in my view, either.

So, in my assessment, Rasmussen's first avenue to a necessary being (at least) has not been adequately supported.

Incidentally, the claim about the BB maximal state seems to have a really weird consequence for theism, which is the following: assuming theism, if Rasmussen is right, there is a possible world W at which God creates some big object plus so many angels that he cannot create any more angels no matter how hard he tries, unless he destroys at least one of those angels first, or destroys some space-occupying object.
Angra Mainyu said…
@ex-apologist and Rayndeon,

I've been considering Koons' reapers and the issue of intrinsic power again, and now it seems to me that given the way in which he defines 'intrinsic proposition', my previous objection may not succeed.

However, and because of that definition, the argument fails for the following reason:

In each world W(n), there is a region R(n) of duration d/(2^n) containing a GR, say GR(n).
The region is a semiopen temporal interval, say (t(n)-2^(-n), t(n)]; it's semiopen as a means of avoiding overlapping regions.

However, the problem is that:

a) GR(n), which exists in the interval (t(n)-2^(-n), t(n)], would not have the intrinsic power to check what happens at any point in any interval (a, (t(n)-2^(-n))], including the endpoint t(n)-2^(-n), since GR(n)'s powers and dispositions are intrinsic to the interval (t(n)-2^(-n), t(n)].

b) The particle placed by GR(n) - if he places one – he could exist only in (t(n)-2^(-n), t(n)], and not at any time at which G(n-1) exists; the same for the other n.

Koons realizes that what's required is the persistence of signals of a certain kind. But the problem is that his infinitary patchwork principle is limited to intrinsic propositions, and fails to guarantee the persistence of signals.

Koons insists that each GR has the intrinsic active power to send a signal to a successor GR, and a passive power to receiving a signal from a predecessor.

However, by Koons' definition of 'intrinsic', the power to send signals beyond (t(n)-2^(-n), t(n)] cannot be an intrinsic power of G(n); else, G(n) would not be limited to (t(n)-2^(-n), t(n)], and infinitary patchwork would not be applicable.
Angra Mainyu,

Those are very good comments on my paper, I appreciate them!
At the time, I was thinking that perhaps there could simply
be all possible beings compatible with Big Blob--precisely because there's no problem with "fitting" them
into a single world. I've thought about the "odd consequence" you point out, and I agree that it's odd. :) Anyway, thanks again for the comment.

EA, beautiful post (as usual).
Angra Mainyu said…
Joshua Rasmussen,

Thanks for your reply.

I'm not sure I understand a point.
Are you saying that the maximal state you were thinking about would be that of Big Blob plus all possible beings compatible with Big Blob?
If that's not what you're saying, please clarify.
If that is what you're saying, and the reason you find that plausibly possible is that there is no problem fitting more objects, it seems to me that that rationale (assuming disembodied minds are possible) leads to the conclusion that a maximal state of disembodied minds is possible, in the sense that there is a world W in which there are disembodied minds, and no more disembodied minds fit (regardless of whether there are other beings); but that seems to be counterintuitive, regardless of whether one assumes theism, and for that reason precisely (i.e., it looks intuitive to me that it's always possible to fit more such minds).

Anyway, on a different note, with regard to the alternative paths, you say that it might seem ad-hoc to say that (Causal5) applies to every category except for the most general one.

However, unless there is a necessary concrete object, it seems to me that there is more than one category to which (Causal5) would not apply, and others to which it looks at least implausible (to me, anyway) that it would apply.

For instance, if there is no necessary concrete object, at least categories like "Contingent Concrete Object that is not an electron", "Contingent Concrete Object that is not a hydrogen atom", "Contingent Concrete Object that is not a lion", "Contingent Concrete Object that is not a hydrogen atom, an electron or a lion", and so on, would seem to be categories to which (Causal5) does not apply, either, and others can be defined similarly.

Alternatively, one can consider (for instance) the following categories:

Let CPB be the category 'Contingent Personal Beings', and CCPB the category 'Contingent Beings that are possibly one of the causes (immediate or remote) of there being at least one member of CPB'.

Then, if there is no necessary concrete object, it seems counterintuitive to me that (Causal5) would apply to CCPB, because that would require that at some world W, some contingent concrete objects C(i) (no matter how many, if there is a number) causally explain the existence of at least one contingent being that is possibly one of the causes (immediate or remote) of there being at least one member of CPB (say, B1), and yet none of the C(i) would possibly be a cause (immediate or remote) of the existence of at least one member of CPB, not even remotely by means of causing B1 and starting a causal chain or net.
Angra,

I appreciate those questions.

Q1. Let me try this. Define 'C' as the class of all possible things (or essences) that are compatible with Big Blog. Now for any proper subset S of C whose members can all jointly exists, it seems that there could be more contingent things that includes the members of S. I take it that this principle is very close (if not equivalent) to capturing the intuition you were expressing. But now consider that if the above principle is true, then it follows that all of the members of C itself can jointly exist (because let S = C minus one element...maybe I need the axiom of choice for that), and any situation in which that happens is by definition maximal. I think the way to use the same basic intuition against this conclusion is to suppose that it applies to C itself, but that would entail a contradiction (that there can be more things than what's possible). A different reply (definitely worth exploring) would be to take issue with defining a class that's too big to be a set (or with referring to merely possible things or their essences).

Note: I don't mean to just assume that disembodied minds are possible. Rather, I mean to use the causal principle to infer that if Big Blob is possible, then either co-located or non-spatial things are possible.

Q2.
I think you make a very astute (even clever) observation about what other exceptions there would be to Causal5 without a necessary being. And I agree that I may need to say more than what I had said about why it can seem ad hoc to deny Causal 5. When I think of it now, it strikes me as ad hoc (to some extent) that in the series of specific to more general, we should stop before the most general type. That isn't say that ad hocery cannot be outweighed by other considerations, which is why I say rational disagreement here is possible.
Very, very thoughtful replies, Angra.

First, it's happened again: I was wrong! I was wrong to think that the principle stated implies that the members of C can jointly exist (and for the very reason you gave). Not sure what I was thinking (and Zorn's lemma won't help me). But, thanks for graciously pointing that out.

I suppose for me it comes down to two conflicting intuitions: intuition A says that the joint existence of the members of any given subset of C shouldn't be incompatible with the joint existence of any other subset of C. (This was the intuition most prevalent in me when I wrote that section of the paper.) Intuition B says that no matter what contingent things exist, there could always be more. In my case, I started with intuition A, and intuition B appeared with less force... but I can very much appreciate going in the other direction; and intuition A might not even arise in you. All of this deserves further thought on my part. What you say about caution here seems exactly right!

As for your comments on Q2, I think they are right on the mark. I've thought a bit about generalizing, and I have a theory about how to make progress using baysean probability (where relative prior probabilities get assigned based upon relative simplicity). But I'm not up for getting into all that.

As for the point about pitting Causal5 against theism, maybe that actually could help the proponent of a necessary being dialectically--because she can then distance that conclusion from theism, which for some, might be a background reason to resist certain pathways to a necessary being. (On behalf of the theist, on the other hand, one might motivate the simpler principle that any type has [or can have] an explanation for its instantiation [as opposed to explanations that always have to be causal] and then suggest that an adequate explanation for the fact that there are people is that there must be people--because there is a metaphysically necessary person. That seems plausible to me.)

I need to say again that I am very impressed by the depth of your insights. Thanks for exchanging them with me.
Angra Mainyu said…
Joshua,

Thanks for your kind words, and likewise, thanks for sharing your insightful ideas with me as well.

Regarding intuition A vs. intuition B, I can see your point, and your suggestion is spot on: I started and continued with intuition B, and intuition A does not seem to arise in me. But as I mentioned before, I try to be cautious on issues like this one.

On the issue of the explanation for the existence of people, this might be a case of different intuitions as well. Not to get into a debate ;), but briefly, my intuitions on that are as follows:

If it were strictly logically necessary that there is at least one person (i.e., denying so were a contradiction), then perhaps that would be an adequate enough explanation for why there is at least one person, but we also ask for explanations of mathematical truths and the like, so I would probably be inclined to ask for a proof. Still, given the proof, that may be adequate.

However, that does not appear to be the case to me. In other words, no contradiction seems to follow from stipulating that there are no personal beings, or for that matter no concrete particulars.

If the above is correct (i.e., no contradiction is entailed), then given that and my intuitions, while the hypothesis that some specific entity B exists at possible world W without an explanation as to why B exists at W is not particularly puzzling to me, the hypothesis that some entity G exists at every possible world without an explanation as to why G exists at every possible world is quite puzzling, and in addition goes against my intuition that there appear to be possible worlds without such entity (whatever G is, and using conceivability as a guide to possibility), so I would be inclined to ask for an explanation as to why G exists at every possible world.
Angra,

I understand what you are saying. On the matter of strict necessity, I find it completely arbitrary to restrict our base of necessary truths to certain "standard" logical ones. (Even the necessity of the law of non-contradiction itself is not deducible from anything in first-order logic.) So, it makes sense to me to say that a scenario (or statement) is possible if it doesn't contradict anything that's necessary--even if the base of necessary truths is not restricted to some stipulated "standard rules".

I suspect you see why this matters here. If conceivability is a guide to possibility, then to whatever extent you can conceive of there being no concrete things (and no persons), you can surely equally conceive of there being a thing (or conscious center) that must, by nature, exist (at least it seems that I can). But these can't both be possibilities (broad logical possibilities), if whatever can be impossible actually is impossible (or equivalently, if whatever is possible is necessarily possible). Since it is evident to me that possibilities (statements that don't contradict anything that's absolutely necessary) are necessarily possible, I regard the epistemic pull of the two conceivabilities as cancelling each other out (though, actually, I have doubts about whether anyone can conceive of no concrete things, since in my own attempts, I only manage to conceive of no shaped or point-sized things).

To break the stalemate we need an extra reason to favor the one possibility over the other. And it seems to me that the ad hocery of restricting a general principle of explanation that has no known counter-examples provides one such reason, though it is defeasible.

For other reasons, you may find this website of interest (still in "debug" stage): www.necessarybeing.net
It's hard to resist, but here's a further thought about intuitions A and B. I was thinking about it again (because more than a desire to be rational or right, I want to do my best to come to see what's actually true). Start with pairs of objects that don't overlap mereologically. It seems that if some pair is incompatible, then there will be something about those objects or their environment that makes them incompatible (explains why they cannot both exist). And what is so of pairs seems to me equally so of arbitrary classes of possible objects: if there's an incompatibility between two classes, then there's something about the members or the environment that makes them incompatible. I could very well be wrong (again), but it strikes me that there's nothing about particular things that makes any group of things incompatible with any other group. So, it comes down to environment. But if "fitting" isn't a problem, then I don't see what other problem there could be (though not seeing is admittedly not the same as seeing not). All of this leads me to suspect that the members of C could jointly exist: for what would make that impossible??? I think it's thoughts like these that inspire intuition A to arise within me. (On the other hand, I more recently have technical questions about whether there can be propositions about essences of things that never existed, but that's another issue...)

Now intuition B seems clear for finite sets; when it comes to certain infinite classes, though, things are less clear for me. And here's why. The motivation for B strikes me as arising from the same sort of question that motivates A, namely, what makes it impossible? In the case of A, I want to understand what might make it impossible for all the members of C to exist. It doesn't seem that there's anything about the members or about environments that would answer that. In the case of B, by contrast, I can tell you what makes it impossible to add one more thing if everything in C were to exist. It's simply the fact that doing so entails a contradiction. This leads me to wonder if intuition B is really more aptly applied to finite sets... but all of this is admittedly murky.

Thanks for getting me to think about this again; I will continue to do so (especially if you have further considerations you'd like to add, which I suspect you will).
Angra Mainyu said…
Joshua,

Okay, it seems this discussion may get a little long after all. ;)

Sorry if I wasn't clear, but I wasn't trying to restrict the base of necessary truths to strictly logical ones (e.g., I have no problem with 'water is H2O').

While I was using a classification of necessities (I'll address that in a moment), that wasn't required for what I was saying about my stance on necessary beings and whether an explanation would be called for (though the specific of explanation might depend on the kind of necessity). So, I have no objection to setting the classification aside, if you object to it.

In that case, I would still say that the hypothesis that a being G exists at every possible is intuitively no less in need of an explanation than the hypothesis that G exists at the actual world.
Further, in the case of the former hypothesis (i.e., than G must exist), intuitively more needs to be explained (i.e., not only why G exists at the actual world needs explaining, but why G exists at every single possible one of them does). A potential explanation (if available) would be a proof that assuming non-existence of G would entail a contradiction, but I do not see any good reason to think that said proof exists (and further, I see good reasons to think otherwise, but I'll try to address that in more detail in the next post).

Regarding the classification of necessities, it seems to me that one may posit a non-contradictory scenario in which 'water is H2O' is not true (e.g., it's logically possible that scientists got it wrong), but not one in which 'either water is H2O or it's not the case that water is H2O' is not true.
The latter truth is of the kind I was calling 'strictly' logically necessary. If I were to suggest a hypothesis as to what the basis of the distinction is, I would say that it seems to me some necessities depend on how things actually are, due to the meaning of certain words (which fixes the referents), whereas others do not. For instance, by the meaning of the word 'water', water is whatever it is at the actual world (which turned out to be H2O), but that either water is H2O or it's not the case that water is H2O does not seem to depend on how things turn out to be at the actual world.

But as I mentioned, my position on the explanatory power (or lack thereof) of a hypothesis of a necessary being does not depend on whether we make such classification, or even whether it's for some reason or another problematic.

I have to go now, but will try to address your interesting points on conceivability and other issues later.
Angra Mainyu said…
Regarding conceivability, I do not think I can conceive of there being a conscious thing (or any concrete thing) that exists at every possible world, to the extent to which I can conceive of there being no concrete things.

In fact, using the conceivability criterion in what imo is the usual way one uses conceivability as a guide to possibility, it seems to me the result is against such necessary beings.

Basically, when we use conceivability as a guide to possibility, it seems to me what we usually do is posit a certain scenario and try to find out any problems (after considering the referents of words that are fixed at the actual world).

If a scenario appears to pass the test*, that is at least prima facie plausible that there is a possible world at which it obtains (of course, we may have different degrees of confidence, depending on how much we think about it, etc.).

So, as I see it, it's the conceivability of specific scenarios that is used as a guide, or at least as the primary guide.

For instance, let's consider the case of unicorns (defined as horse-like animals with one horn and large wings). Unicorns so defined appear conceivable, since I can think of a scenario in which they exist, and it seems no contradiction arises.

So, prima facie, it seems to me that unicorns are possible.

Someone might suggest that (for instance) one is just as well capable of conceiving of a necessarily existent, necessarily omnipotent being (say, NU) who is necessarily committed to preventing the formation of unicorns, and so the intuitions cancel each other out, which blocks our path from apparent conceivability to (plausible) possibility of unicorns.

It seems to me that the objection in question would not be successful, though. That is not how we usually use conceivability as a guide to possibility. Rather, it seems to me that in order to use conceivability to assess the NU claim, we would have to begin considering hypothetical scenarios, and try to see whether all apparently conceivable ones contain NU.
Since, scenarios without NU appear perfectly conceivable, prima facie, there are intuitive grounds for accepting the possibility of unicorns, and against the necessary existence of NU.

So, generally, as I see it, using conceivability as a guide to assessing a claim that there is a being G that exists at every possible world, would seem to require that we try to conceive of different scenarios and check whether G exists in every one of the scenarios that appear conceivable. If one can find scenarios in which G does not exist, and which appear conceivable (even after considering the meaning of words whose referent is fixed by what it actually is, etc.), that speaks against such G, as far as I know.

That may not be definitive, but it seems to me that it provides, intuitively, good reasons to think that there is no such G, since the scenario 'no concrete particulars exist' appears to pass the test.
Also, more specifically, it seems to me I can conceive of an omnipotent being O2 that is not morally good, suggesting that O2 exists at some world W2, which speaks against the necessary existence of a being who is necessarily (omnipotent and morally perfect).

So, I do not find a stalemate on intuitive conceivability grounds.


* Side note: In the case of a scenario in which water isn't H2O, we can tell that whether it passes depends on whether water is H2O at the actual world; since it is, the scenario does not pass the test. If we did not know whether water is H2O, we wouldn't be able to tell whether it passes the test (though we might be able to make probabilistic assessments, based on the information available to us).
Thanks. Real quick. I would say that for some G's, their non-existence strictly contradicts the fact that they necessarily exist. (This is why I brought up widening the base of necessary truths.) An example: the law of non-contradiction. I think it necessarily exists by virtue of being necessarily true (since nothing can be anything, let alone true, without existing, it seems to me). Now as you are no doubt aware, it's important here to distinguish between what makes something necessary and how we know it is necessary. Regarding many necessary truths, I would say either that nothing makes them necessary or that they are necessary because it is necessary that they are necessary (ad infinitum). From from an epistemological point of view, however, we want more: we want some justification for thinking it's necessary, which is where the arguments come in. It seems that in our case, we have an argument on the table for a particular sort of G being necessary, and that argument depends upon a certain principle of explanation (generalized, perhaps, from known cases of explanation). I think what you are saying is that the principle in question seems to have exceptions (in its most general form, at least) because the principle implies that certain statements are necessarily true and explainable even though they aren't deducible from the base of necessary truths. What I'm suggesting is that we can only make that argument if we've already settled on the base of necessary truths. But if that base is open (wider than the base of strictly necessary truths), then I presently see no non-question begging grounds in this vicinity for inferring a counterexample to the principle. And without an evident counter-example, it seems to me that the we have prima facie reason to accept the general principle--or at least to think it more likely than not applies in any given case (just as one may think it more likely than not that the emerald in my hand is green, prior to seeing it, based upon seen emeralds).

Okay, I'll rest from this for a bit, and I look forward to your further comments.
Angra Mainyu said…
Joshua,

I just took a look at the website; it's an interesting test, but (as you may have suspected already ;)), I do not agree with its conclusion that my position entails that there is a necessary being.

Personally, I do not consider existence, non-existence, possible non-existence, necessary existence etc., to be properties of beings. So, I responded 'it seems not' to the question of whether the property being a powerful necessary being was limiting, etc., but my actual reply would have been that that's not a property of beings (being powerful is).

Also, the test goes from 'powerful' to 'omnipotent' in the middle of an argument, but that's a minor glitch.

However, and leaving all of the above aside, in my view the argument from my position to a necessary being does not work.

If it did, let's suppose the person taking the test responds that being a powerful necessary being is itself limiting. Then, a reasoning similar to that of the test would be as follows:

1. Suppose (for the sake of argument) that a Necessary Being is not possible.
2. Then it is not possible for there to be a powerful Necessary Being.
3. Therefore, necessarily, if something is a powerful Necessary Being, then it is not the case that that something has a limiting property.
This is because the first clause -- that something is a powerful Necessary Being -- is necessarily false, which renders the "if-then" claim trivially true.
4. Therefore, being a powerful Necessary Being is not itself limiting. (by definition of 'limiting' & 3)
5. But that contradicts your report that being a powerful Necessary Being is limiting.
6. Therefore, 1 is not true. (since no true statement implies a contradiction)
7. Therefore, a Necessary Being is possible.

So, unless I'm missing something (if so, please clarify), then it seems to me that whatever they reply, the conclusion is the same, namely that a necessary being is possible.
I suppose that might not be strong enough as an objection, so I will try another one:
Is being an evil, necessary being a limiting property?
If the answer is 'yes' (if it's 'no', a similar argument can be made), then we may mirror the test's reasoning as follows:

1. Suppose (for the sake of argument) that an Evil Necessary Being is not possible.
2. Then it is not possible for there to be an Evil Necessary Being.
3. Therefore, necessarily, if something is an Evil Necessary Being, then it is not the case that that something has a limiting property.
This is because the first clause -- that something is an Evil Necessary Being -- is necessarily false, which renders the "if-then" claim trivially true.
4. Therefore, being an Evil Necessary Being is not itself limiting. (by definition of 'limiting' & 3)
5. But that contradicts your report that being an Evil Necessary Being is limiting.
6. Therefore, 1 is not true. (since no true statement implies a contradiction)
7. Therefore, an Evil Necessary Being is possible.

Clearly, if the person reported that being an Evil, Necessary Being is not limiting, a similar argument could be made, and the conclusion would still be that an Evil Necessary Being is possible.

From that, one can go to the conclusion that an Evil Necessary Being is necessary, using the same reasoning used in the website (I'm implicitly assuming that the being in question is necessarily evil, but we may also explicitly stipulate that).
Of course, similarly one can go to the conclusion that a necessarily omnipotent, evil necessary being is necessary, and also that a necessarily omnipotent, good necessary being is necessary, which entails two omnipotent beings with conflicting agendas exist, which is impossible as far as I can tell.
In my view, we may also skip the question about the limiting property, with a little more work.
If I missed something, please let me know.
Angra Mainyu said…
Joshua,

I just took a look at the website you linked to; it's an interesting test, but (as you may have suspected already ;)), I do not agree with its conclusion that my position entails that there is a necessary being.

Personally, I do not consider existence, non-existence, possible non-existence, necessary existence etc., to be properties of beings. So, I responded 'it seems not' to the question of whether the property being a powerful necessary being was limiting, etc., but my actual reply would have been that that's not a property of beings (being powerful is).

Also, the test goes from 'powerful' to 'omnipotent' in the middle of an argument, but that's a minor glitch.

However, and leaving all of the above aside, in my view the argument from my position to a necessary being does not work.

If it did, let's suppose the person taking the test responds that being a powerful necessary being is itself limiting. Then, a reasoning similar to that of the test would be as follows:

1. Suppose (for the sake of argument) that a Necessary Being is not possible.
2. Then it is not possible for there to be a powerful Necessary Being.
3. Therefore, necessarily, if something is a powerful Necessary Being, then it is not the case that that something has a limiting property.
This is because the first clause -- that something is a powerful Necessary Being -- is necessarily false, which renders the "if-then" claim trivially true.
4. Therefore, being a powerful Necessary Being is not itself limiting. (by definition of 'limiting' & 3)
5. But that contradicts your report that being a powerful Necessary Being is limiting.
6. Therefore, 1 is not true. (since no true statement implies a contradiction)
7. Therefore, a Necessary Being is possible.

So, unless I'm missing something (if so, please let me know), then it seems to me that whatever they reply, the conclusion is the same, namely that a necessary being is possible.
I suppose that might not be strong enough as an objection, so I will try another one:
Is being an evil, necessary being a limiting property?
If the answer is 'yes' (if it's 'no', a similar argument can be made), then we may mirror the test's reasoning as follows:

1. Suppose (for the sake of argument) that an Evil Necessary Being is not possible.
2. Then it is not possible for there to be an Evil Necessary Being.
3. Therefore, necessarily, if something is an Evil Necessary Being, then it is not the case that that something has a limiting property.
This is because the first clause -- that something is an Evil Necessary Being -- is necessarily false, which renders the "if-then" claim trivially true.
4. Therefore, being an Evil Necessary Being is not itself limiting. (by definition of 'limiting' & 3)
5. But that contradicts your report that being an Evil Necessary Being is limiting.
6. Therefore, 1 is not true. (since no true statement implies a contradiction)
7. Therefore, an Evil Necessary Being is possible.

Clearly, if the person reported that being an Evil, Necessary Being is not limiting, a similar argument could be made, and the conclusion would still be that an Evil Necessary Being is possible.

From that, one can go to the conclusion that an Evil Necessary Being is necessary, using the same reasoning used in the website (I'm implicitly assuming that the being in question is necessarily evil, but we may also explicitly stipulate that).
Of course, similarly one can go to the conclusion that a necessarily omnipotent, evil necessary being is necessary, and also that a necessarily omnipotent, good necessary being is necessary, which entails two omnipotent beings with conflicting agendas exist, which is impossible as far as I can tell.
In my view, we may also skip the question about the limiting property, with a little more work.
If I missed something, please let me know.
I'll try to address the issue of intuitions A and B later.
Nice comments. You are awesome, Angra.

Regarding the parallel arguments (which you could also run with 'necessary square circle') the problem is with the inference from 3 to 4 (because the impossibility entails that both not X and X). The corresponding inference of the original argument follows from classical logic, I believe.
Angra Mainyu said…
Joshua,

Thanks for your thoughtful posts and the compliments. Likewise. :)

Regarding the parallel arguments, what I was trying to get at is that the problem appears to be the same in the original argument. I just mirrored the original argument to reach that conclusion. As I mentioned, there might be something I missed, so if that is the case, please let me know.

With regard to intuitions A and B, I get your point about extending the latter to finite to infinite cases. It's a valid concern, though my impression is that if there is a problem in extending intuition B, it would be from sets to arbitrary categories, rather than from finite to infinite cases.

Still, in the case of intuition A, and while I realize theists would reject this, it seems to me that an object O might be compatible with, say, an omnipotent object O1, and also another omnipotent object O2, which are both possible but cannot jointly exist, so there might be mutually incompatible contingent objects, regardless of whether they occupy some space (granted, theists usually deny that).

But leaving that aside, if we assume that no two contingent disembodied beings (I'll call them angels to simplify) are mutually incompatible, I'm still not sure intuition A alone entails the possibility of a maximal contingent state of existence, either, for the following reason: Intuition A holds that the joint existence of the members of any given subset of C shouldn't be incompatible with the joint existence of any other subset of C.

But from that we seem to be able to join two sets, or a finite number of sets. But that would only give us a set, not a state of existence bigger than any cardinality. Even if we extend this principle from the finite case to the infinite case for any cardinality X (i.e., joining X sets), we still only have a state of existence of a certain cardinality.

Yet, let's suppose there is a state of existence R of cardinality X, so the cardinality of the set of angels in that state is, say, Y. Then, under the assumption that no two angels are mutually incompatible, and unless (perhaps), the whole category of possible angels has cardinality Y, it seems to me it's possible that one more angel exist jointly with the rest.
Yet, that the category of possible angels has a fixed cardinality is not clear at all, at least not to me. For all I know, it might be that for every cardinal number X, there is a possible angel A(X) who knows X truths, or something like that.

Granted, you might start with intuition A applied directly to arbitrarily big classes (not just sets); I'm not sure how intuitive you find that.

Essentially, it seems to me that what you need is a principle like the following:

Maximality: For every possible contingent disembodied B, there is a possible maximal contingent state of existence C(B) containing B.

I can see where you're coming from, but personally I do not find that principle intuitive.
Angra Mainyu said…
Joshua,

A quick clarification regarding an angel who know X truths: I'm considering the possibility of angels who necessarily know X truths (if she exists, of course).

That aside, I just checked the argument on the website again, and I still do not see why it would work.
I may be missing something, but as far as I can tell, that argument fails precisely for the reason the parallels I posted fail (i.e., the reason you explained).
Angra,

I'm enjoying this exchange, and I love your truth-pursuing+promoting heart.

Here are just a few confessions about how things strike me (in case that could be of interest to you):

1. Perhaps certain (causal) principles that entail a necessary being could, if true, be among the base of necessary truths (if the base is wider than the strictly necessary truths). And if any such principle were true, it seems we could explain the necessity of a G by your criteria.

2. In reply to the above point, there are conceivability-based considerations that suggest that 'no concrete things' is possible (since then the antecedent in 1 is called into question). I think this may be the smartest and most promising sort of reply--and it seems to be a key part of the reply you've given.

3. The term 'conceive' is tricky. Using the term broadly, I confess that I can conceive of there being no concrete things, but then in that very same sense, I find myself having no problem conceiving of there being a necessary unicorn preventer. There is a more narrow (and more helpful) sense of 'conceive'. But in that narrow sense, I find myself unable to conceive of there being no concrete things, in part because I don't know how to narrowly conceive of there being no non-spatial things. These are subtle matters, and I have very good friends who come up with different results; so I respect that. Indeed, I think conceivability considerations can constitute a perfectly rational reason to deny the existence of a necessary being (even if they don't have to).

4. For me, what gets "intuition A" going is the feeling that nothing would make certain collections (sets or classes, doesn't matter) incompatible with certain others. It's an open question for me: what explains the incompatibility? But what you say is very good and well-taken.

5. The crucial difference, I think, between the parallel arguments and the original is the word 'not': the definition of 'limiting property' is still satisfied even if the relevant consequence is not true, as long as it also is true (which is the case with an impossible antecedent). So in a sense, it's "easier" to satisfy the definition than to not satisfy it. (Of course, I might be missing something; I'm often wrong about things! Such is the price of seeking to follow reason wherever it might lead me.)

And thanks again for writing all that out; I know it can take time to work through the ideas, and I appreciate learning from you.
Angra Mainyu said…
Joshua,

I'm enjoying this exchange as well; thanks for the compliment, and likewise (you also strike me as truth-seeking+promoting).
Also, I too appreciate learning from your ideas, so thank you as well for taking the time to address my points.

As to (some of) your latest points:

1. Yes, I agree that if one start with some necessary true principles, and from there one concludes that a necessary being exists, that would indeed explain the existence of a necessary being, as long as the principles themselves are either similarly explained, or it's intuitively obvious that they're necessarily true.
Personally, while I think that there are statements that seem to be obvious necessary truths (e.g., (P v¬P)), I have not found any causal principle like that leading to a necessary being.
Also, while most of our intuitions about how things behave, etc., seem to work fine in daily events/things, Quantum Mechanics, General Relativity, etc., show that a number of our pretheoretical intuitions fail if we try to apply them to the entire observable universe, which makes an extension of causal principles from ordinary cases not just to the observable universe but to the actual world, or to all possible worlds, a matter that requires at least a lot of caution.
Still, I think one may use some principles (causal or otherwise) + some argument as providing good reasons for or against belief in a necessary beings, even if the reasons are not conclusive. That's part of what I try to do using the conceivability criterion, as you point out (if I understand correctly).

2. I would say it's key to part of my reply, namely in terms of good reasons for believing that there (probably) is no necessary being, though I do not consider that conclusive.
I think there are other good considerations regarding the arguments for the existence of necessary beings, though (i.e., some direct objections to some of those arguments, rather than a counterargument based on the conceivability criterion).

3. I agree that the term is tricky, but still, it appears to me that we use that criterion as a guide to possibility.
Also, and with regard to the unicorns (as I defined them, etc.), it seems the conceivability criterion does support their possibility, and thus the lack of the necessary unicorn preventer NU.
If you agree with that assessment (please let me know if you don't), I suppose that you consider the unicorns case a case of narrow vs. non-narrow conceivability? (i.e., unicorns would be narrowly conceivable?).

I have a different hypothesis as to where the distinction lies (I already explained a little I think; more on that in the next post), but your point that these are subtle matters is well taken.
Angra Mainyu said…
Regarding the conceivability criterion, it seems to that when we use that criterion to assess the possibility of a being with certain properties P1, P2, etc., we normally does not consider existence or necessary existence among said properties (I do not believe that existence, necessary existence, necessary non-existence, etc., are or can be properties of beings, but that aside).

So, for instance, if we're assessing the possibility of an omnipotent, morally good being (or morally perfect, etc.), we posit such being, and try to see if we can find a contradiction (even if considering fixed referents, etc.). If we can't, then the conceivability criterion supports possibility (By the way, I've not been able to find a contradiction, so I would say that an omnipotent, morally good being is probably possible).
On the other hand, if we are to assess a claim that an omnipotent, morally good being exists necessarily, the properties under consideration in each scenario are the same (namely, omnipotence and moral goodness), but now we have to assess not only whether such an entity is possible, but also whether it's possible that it does not exist.
A way to do that, I think, is to consider scenarios that appear conceivable, and see whether such entity exists in all of them, or more simply, try to conceive of scenarios in which such entity does not exist, and see whether we run into problems, and then one possibility is the simple stipulation that no concrete being exists.

However, you object to that (if I read your reply correctly) based on the narrow vs. non-narrow sense of conceivability, considering only (or mostly; I'm not sure what your stance on that is) the former as a guide to possibility.

I recognize it's a difficult matter; I will try to address the question adding the narrow-non-narrow criterion.

If I understand that perspective correctly (at least, to a sufficient extent), then the use of the conceivability criterion in support of the possibility of an omnipotent, morally good being as assessed above satisfies narrow conceivability (prima facie, as usual), and so it supports possibility by that criterion.

But we can also prima facie conceive of an omnipotent being who is not morally good (for instance). That would not, on its own, support the non-existence of necessary beings, but it seems to support the possibility of an omnipotent being who is not morally good, and thus a rejection of a claim that an omnipotent, morally good being exists necessarily, and even the rejection of the claim that an omnipotent being exists necessarily (I'm talking about beings who are necessarily morally good, not good, etc., so that if they exist, they're like that).

That said, I think I'm implicitly still applying the criterion I mentioned above, in addition to the narrow vs. non-narrow one. But without the criterion in question, it seems to me that the use of conceivability as a guide to possibility of unicorns would be blocked as well (because of the unicorn preventer), but it seems to me that would block the conceivability criterion in a very broad manner (without that criterion, what is our guide to the possibility of unicorns?).
Angra Mainyu said…
5. I commend you for your pursuit of truth, and thank you again for taking the time for replying to my questions about this argument.

I've been trying to understand how the meaning of 'limiting' would play a role, but I have to concede I've not been able to see how that makes a relevant difference.
exapologist said…
Whoops -- this comment from Angra Mainyu got rejected on accident -- sorry, you two!

-EA

Joshua,

Thanks for the replies.

Regarding your point that you don't want to just assume the possibility of disembodied minds, point taken, but I'd rather assume it anyway, else that would lead also to questions about the possibility of Big Blob that I was trying to set aside.

That aside, and regarding Q1, in order to derive the conclusion that all of the members of S can jointly exist, it seems to me that you're making the assumption that all of the members of (C=S minus one element) can jointly exist.
I do not find that assumption intuitive.
On the contrary, under that assumption, intuitively I would say that one can add one more member, but that would result in the conclusion that all of the members of S can jointly exist, and so no more angels, etc., can be added...which is precisely what I find counterintuitive, which is why my intuitions would also lead me to rejecting the assumption that all of the members of S minus one can jointly exist.
Of course, my intuitions on the matter might not be right; moreover, I tend to think that when it comes to arbitrary categories of objects bigger than any cardinality (which may well be the case of S), our intuitions about possibility should be used with considerable caution.
On the other hand, that caution would at most give me some reason to doubt the conclusion that it's not the case that all of the members of S can jointly exist, but not to reach the conclusion that they can (i.e., at most that would lead me to agnosticism on the matter).

Side note: Another potential difficulty for the joint existence of all such objects is that it might be that some of the members of S are incompatible with each other, but I do not think that that would be a problem for a claim of maximality; the previous difficulty remains, though, as far as I can tell.

As for Q2, my impression is also that generalizing to arbitrary categories of objects from what we observe in daily life is generally a suspect procedure, even if defining them is not a problem.

For instance, let's consider a rationale similar to that behind Causal5: we start we a common object (say, armchair) and we conclude that a causal explanation as to why armchairs exist is possible.

However, for that matter, we might conclude from armchairs or other common objects that a causal explanation of the existence of any categories of objects is possible (dropping the 'contingent' part). Alternatively, we might go from there to a conclusion that a causal explanation in terms of contingent objects of the existence of any category of contingent object, is possible.

Of course, in those cases, we reject the generalization since it leads to a contradiction, but I'm not sure is why we should accept that kind of generalization as a general principle; i.e., why we should generally accept an extension from ordinary cases to arbitrary categories of objects, and which ones.

Incidentally, it seems to me that a case where the generalization does not lead to obvious contradictions, but in which most theists would probably reject the generalization, is the following:
We may begin not with an armchair but, say, a person (say, Obama), and wonder why that person exists, but we can go to wonder why any person exists at all. In both cases, we may wish to generalize, and conclude that there possibly is a causal explanation of the existence of any personal beings at all.
That alone might not entail that no personal being is necessary (it might be compatible with that conclusion that, say, a necessary non-personal entity necessarily causes a certain personal being to exist), but it seems to me it would be problematic enough for theism, and at least that nearly all theists would reject that, even as a prima facie principle.
Angra Mainyu said…
EA,

Thank you for taking the trouble.
It wasn't that post, but a different one. Now I think I may have entered the wrong captcha, or made some other mistake when posting.


Here is a similar post, though with some differences:

Joshua,

I'm enjoying this exchange as well; thanks for the compliment, and likewise (you also strike me as truth-seeking+promoting).

Also, I too appreciate learning from your ideas, so thank you as well for taking the time to address my points.

As to (some of) your latest points:

1. That's a good point.
I agree that if one start with some necessary true principles, and from there one concludes that a necessary being exists, that would indeed explain the existence of a necessary being, as long as the principles themselves are either similarly explained, or it's intuitively obvious that they're necessarily true.

Personally, while I think that there are statements that seem to be obvious necessary truths (e.g., (P v¬P)), I have not found any causal principle like that leading to a necessary being.

Also, while most of our intuitions about how things behave, etc., seem to work fine in daily events/things, Quantum Mechanics, General Relativity, etc., show that a number of our pretheoretical intuitions fail if we try to apply them to the entire observable universe, which makes an extension of principles from ordinary cases not just to the observable universe but to the actual world, or to all possible worlds, a matter that requires caution.
But that does not mean we can't use them at all.

2. I would say it's key to part of my reply, namely in terms of good reasons for believing that there (probably) is no necessary being, though I do not consider that conclusive.
I think there are other good considerations regarding the arguments for the existence of necessary beings, though (i.e., some direct objections to some of those arguments, rather than a counterargument based on the conceivability criterion).

3. I agree that the term is tricky; still, with regard to the unicorns (as I defined them, etc.), it seems the conceivability criterion does support their possibility, and thus the lack of the necessary unicorn preventer NU.
If you agree with that assessment (please let me know if you don't), I suppose that you consider the unicorns case a case of narrow vs. non-narrow conceivability? (i.e., unicorns would be narrowly conceivable?).
Angra Mainyu said…
Joshua,

Regarding the law of non-contradiction, I missed that earlier post of yours.

It seems to me we have very different takes on laws of logic, propositions, numbers, etc.
I would say that for any proposition and any domain of discourse, ¬(P&¬P) is true, that there are necessarily true formulas, and necessarily false formulas, in the sense that there are formulas like ¬(P&¬P) that are true in any domain no matter what P is, and others like (P&¬P) that are false in any domain no matter what P is.
But I do not understand that 'there are' as a claim that could be similar in a metaphysically relevant sense as a claim that, say, God exists, or planets exist, etc.; when we talk about formulas (or numbers, etc.), it seems to me we're considering some abstract domains (e.g., formulas, the set of natural numbers), but not making any ontological claims, or implying them, as far as I can tell.

However, hopefully that won't be a problem for assessing other matters.

I get your point about the distinction between ontology and epistemology; as for the issue of principles, I hope my replies after that post address the issues you address sufficiently, at least with regard to clarifying my views.
mpg said…
I'd just like to thank all the philosophers posting on this thread. It's been fascinating and educational, in the extreme. A pleasure.

mpg
Thanks, Angra. One further remark just for fun: if 'omnipotence' is defined as having the power to possibly bring about (weakly or strongly) any contingent state of affairs (or something like that), then an omnipotent being would arguably have to exist at the head of every possible world (else it wouldn't be able to [weakly] bring about that world, which is a contingent state of affairs). So, one might argue that if an omnipotent being is possible, then there is a necessary being. Of course, defining 'omnipotence' is no trivial matter (and you may deny the antecedent).

BTW: I thought your point about the omnipotent evil being was clever.
Angra Mainyu said…
Thank you, Joshua, and I think you make a clever point about omnipotence and the difficulty to define it.

Briefly (more or less;)), going by that definition, it seems to me that there are contingent states of affairs no being in our world can bring about, like that the Moon Landing never happened.
Using similar considerations about other worlds, one might want to qualify the definition of 'omnipotence' to exclude past states, but in that case, let's suppose (assuming this is possible) that a contingent omnipotent being exists at some world W, at time t. Then, the fact that she cannot bring about past states of W would not be incompatible with her omnipotence.

That said, even leaving past states aside, if we stick to something like that definition (with some modification to exclude the past), conceivability (in my case, at least) now would seem to work against the possibility of omnipotence, since that some contingent object O exists without any cause of its existence appears possible to me, though I know it's disputable.

I suppose it might be suggested that omnipotence entails timelessness, and so the exclusion of the past is not required, but then I do not know how to conceive of timelessness, so conceivability wouldn't suggest possibility of omnipotence in my case at least.

Regarding an evil omnipotent being, thanks. I'm thinking one may relax the hypothesis: she might not be evil, but just not morally good, or not morally perfect. She might be more or less in between good and evil, or perhaps even an entity that is not a moral agent at all.

On a different note, I've been thinking about the possibility of maximal contingent states of existence, I have to say that given the assumption of essentialism (which I've been making for the sake of the argument), I can't at this point tell one way or another. I'm thinking now that there might be ways of coming up with such a state, setting up the necessary properties of beings in some ways, but I'm not sure one way or another.

As for causal principles, in ordinary life, I would say it's intuitive that every being we find possibly has a cause (without adding the 'contingent' part to the principle), but again extending this to arbitrary categories isn't clear to me, and especially essentialism makes me doubt it; the same goes for principles like the principle that contingent states of existence possibly have a cause, etc.

I'll need to think more above some of the consequence of essentialism, given that one can set up beings that necessarily do this or that, know this or that, etc.
Angra Mainyu said…
Joshua, I'm thinking there may be a way to sidestep the issue of the definition of omnipotence, by means of introducing a power which is much more easily defined.

Definition: A being B has particle power (or PP) if she has the (infallible) power to bring about that there is a particle at any spatial location x of her choosing, or that there is no particle at x.

Let's say a being is of type B1 if she necessarily has particle power, and is necessarily morally good (if she exists, of course). Let's say a being is of type B2 if she necessarily has particle power, and is possibly not morally good (or necessarily not morally good, etc.; this part is not crucial).

Then (and as usual assuming essentialism), it seems to me narrow conceivability supports that it's possible that there is a being of type B1, and it's also possible that there is a being of type B2.

But then, it seems to me that narrow conceivability supports the hypothesis that there is no necessary being who necessarily has particle power, since it seems to me that a being of type B1 and one of type B2 cannot coexist (else, what if they make opposite choices for the same spatial location x?).
I was thinking that 'having the power to possibly' could be interpreted to imply just 'possibly (at some time)' (and so could handle the time problem), after re-reading "Maximal Power"... In the end, I think the problem is with (narrow) conceivability, as you suggest (though I don't myself think most possibly situations are narrowly conceivable, even if the reverse holds.)

BTW: I just read your extremely thoughtful critique of cosmological arguments on your website; e-mail me if you would like some comments. :)
Angra Mainyu said…
That's a good point about how to handle the time problem under that definition of 'omnipotence', thanks.

So, under that definition and under the interpretation you explained, it seems you've cleverly showed that if such a being (say, O) is possible, it would have to exist at every possible world, at least at some time.

On the other hand, it seems to me that that definition might not guarantee necessary existence, due to potential situations like the following one (which is odd, but does not look contradictory to me, assuming possibility of O):

What if, say, O destroys all other beings at W (or sets up some deterministic conditions for all other beings), and then annihilates itself at some time t?

That aside, it seems to me that a potential difficulty for a being that is omnipotent under that definition is random particle decay (random in the sense that given the state of a world before some time t, it's possible that the particle decays at t, or that it does not, and no cause determines that the particle decays at at).
The phenomenon seems conceivable, and if possible, it seems to me it's not possible to strongly bring about that a particle P decays at some specific time t (even P is not bringing about its own decay; rather, it happens to P).
It does not seem to be possible to weakly bring it about, either, because it seems the counterfactual 'If O were to bring about T, then particle P would randomly decay at t' is not true, for any T and O. It seems to me it would still be possible that P fails to decay at t.

Anyway, I would need to think more about that definition of 'omnipotence' and its consequences.

On the other hand, if 'omnipotence' is understood more or less like 'having power that no other being can possibly match or surpass', that would avoid some potential difficulties, though there are others (e.g., how powerful would a being like that actually be?).

On the BTW, thank you for the offer. I'll send you a PM.
BTW, I wrote that argument a while ago, and while I've added a few minor improvements ever since, there are some points I would have to change if I were to write it again.
The particle power scenario is interesting (and cool) and deserves reflection. Of course, it leaves open the possibility of a naturalistic necessary being (necessary particles, say), which is consistent with the conclusion I had in mind to argue for. (The 'infallible' part leaves me unsure; but I'll give it more thought.)
Angra Mainyu said…
Regarding the 'infallible' part, does it leave you unsure about narrow conceivability of beings with PP, or about the compatibility of beings with PP and the existence of necessary particles?
Narrow conceivability--because it carries the very modality that tends to wreck my intuitions for me. There's also the issue of greatness: if unmatchable power is possible, then it seems to me that unmatchable greatness should be too, which, I'd argue non-trivially entails necessary existence. I heard a wise person once say, "there's a difference between seeing that it's possible and failing to see that it's impossible". The distinction seems relevant here. I'll keep thinking about it.

Sorry, EA, for straying so far from your original post. :)
Angra Mainyu said…
Thanks, Joshua,

Regarding narrow conceivability, if the 'infallible' part is a problem for narrow conceivability, would you say that it is so too for the narrow conceivability of Big Blob?

An attempt to conceive of a being with PP would be as follows: suppose that A1 necessarily has PP; it seems to me we can conceive of her being able to place particles at x, or bring it about that there is no particle at x, whatever x is, and always succeeding.

A potential objection to narrow conceivability would be as follows: but what if there is a world W, at which A1 exists, and when she tries to place a particle at x, she's blocked by some other being?
How can we narrowly conceive of a A1 if there is that potential problem?

A potential reply to that objection would be that in that case that would be an entity similar to A1, but not A1, because A1 necessarily has the power to successfully place the particle at x if she tries, and so an entity without that power would not be A1, but we can still conceive of an entity who successfully goes around placing particles or removing them, even if similar, almost duplicates fail.

But perhaps, the reply fails because it carries the same modality you mention.

In that case, perhaps the following objection might be raised against narrow conceivability of Big Blob:

Let's say that at some world W1, Big Blob exists, and occupies all of space, which is 3-dimensional. But, perhaps, there is some other thing E1 at W1 that brings about a separate, 9-dimensional space thing, which is not occupied by Big Blob, or moves Big Blob outside some part of space.

An objection to that objection would be that Big Blob by definition necessarily occupies all of space if it exists, so that would not be Big Blob, but some other entity. But isn't that reply similar to the reply to the objection to A1's narrow conceivability?

If one fails, doesn't the other fail as well?

Regarding your point about unmatchable greatness, I would have to look at your argument.
Angra Mainyu said…
On a different note, I've been thinking a bit more about the 'limiting property' argument, and it seems to me that if it works, a similar argument proves a lot more than the existence of a necessary being, for the following reasons.

Let's assume that the argument in question is sound.
Then, in particular, it's valid.
Furthermore, being a powerful necessary being is a property (else, the argument would fail).
But then, being a powerful, knowledgeable, intelligent, self-aware necessary being is also a property (it seems to me that the only thing that makes that contentious is the 'necessary' part, but that would block also the original argument, which by assumption works).

So, given the above, one may argue as follows:

1: The property of being a powerful, knowledgeable, intelligent, self-aware necessary being is not limiting.
2. A powerful, knowledgeable, intelligent, self-aware necessary being is not possible.
3. Therefore, necessarily, if something is a powerful, knowledgeable, intelligent, self-aware necessary being, then that something has a limiting property.
This is because (by 2.), the antecedent of the "if-then" claim is necessarily false, which renders the "if-then" claim trivially true.
4. Therefore, being a powerful, knowledgeable, intelligent, self-aware necessary being is itself limiting (by 3.& definition of 'limiting').
5. Therefore, being a powerful, knowledgeable, intelligent, self-aware necessary being is limiting, and being a powerful, knowledgeable, intelligent, self-aware necessary being is not limiting (by 4. & 1.).

Since the conclusion 5. is contradictory, in particular it's false. Hence, the argument is unsound.
Since the argument is valid (because the original one is by assumption, and this one is relevantly similar), then at least one of the premises is false.
But premise 1 is clearly true. Hence, premise 2 is false.

Thus, a powerful, knowledgeable, intelligent, self-aware necessary being is possible.
The argument from that to the conclusion that a powerful, intelligent, self-aware necessary being is necessary follows just as in the original argument.

Also, sorry for straying EA. :)
exapologist said…
No need to apologize -- I'm enjoying the discussion!
Angra, I like your question about Big Blog. For what it's worth, it's hard for me to see how some possible space could be occupied if not all could, considering that no difference between possible regions would seem to account for a difference with respect to occupiability. Maybe there's a similar consideration in support of possible infallible power, I don't know. These are deep and difficult waters, but it's been fun exploring with you.
So to be clear: I think I would say that narrow conceivability fails in both cases, but that other considerations may support possibility in the case of BigBlob.

(Thanks for the further comments on "limiting" properties. I agree with you that parallel arguments can, in principle, constitute a reason to object to soundness.)
Angra Mainyu said…
Joshua,

With regard to Big Blob, I'm not sure I've been clear.
My suggestion is that it seems to me Big Blob would infallibly occupy all of space (if it exists), since there is no world at which it exists and fails to occupy it all, so it seems to me that the situation of an entity with the causal power to infallibly occupy all of space is not better in terms of narrow conceivability than that of an entity with the causal power to infallibly bring it about that there is a particle at any spatial location x of its choosing, or to bring it about that there is no such particle.
But now I see that you think conceivability fails in both cases, but there may be other considerations supporting possibility in the case of Big Blob. I suppose there might be, but it might be the other way around as well (i.e., there might be other considerations in the case of entities with particle power).
So far, though, I don't see any other considerations supporting possibility in one case rather than the other. But maybe you have a way to distinguish it?
Just that no difference between possible regions would seem to account for a difference with respect to occupiability (and "infallible" occupation would seem to be follow from occupying all possible space, assuming the material in question couldn't shrink on account of being maximally dense; or if it could, then the problem of "fitting" all possible things seems undercut...though here I confess to being out of my depth). Not sure there's an analogous consideration concerning particle power; not sure there isn't.
Angra Mainyu said…
Joshua,

I'm not suggesting that there is a difference in terms of occupiability. But I'm not getting why that's a difference between the scenarios. Particle power also makes no difference in terms of where the particles can be placed.

Your comment about shrinking is interesting.

Let's sat that a being E1 occupies all of space.
Why is it not conceivable that it would shrink and leave some of it, perhaps pushed by a powerful being that can move any being out of any spatial location of her choosing?
I'm not sure why maximal density would be possible. For instance, if we extrapolate indefinitely into the past using General Relativity, density grows arbitrarily.
Granted, we're not justified in making such extrapolation because we would have to factor in forces other than gravity, but that seems to be a matter of how the universe actually is; I do not see anything impossible about indefinitely growing density.

Granting that maximal density is possible, I'm still not sure why the density of a space-occupying object can't decrease first, and then increase as it shrinks, leaving some part of space unoccupied.

Granted, one may stipulate that the density of the object can't decrease by definition of its essence (not that I think that works, but I'm assuming essentialism for the sake of the argument), but in that case, I'm still not sure why that's relevantly different from stipulating by definition that an entity has the infallible power to place particles in places of her choosing, or remove them.

That said, I'm thinking there might be a way in which the definitions of the entities might be used to make a difference, if (for instance) it's stipulated that Big Blog can't shrink because if some powerful entity tried to make it shrink, the resulting object that wouldn't occupy all of space but most of it would no longer be Big Blob but a similar object, since the essence of Big Blob is such that it necessarily occupies all of space, and its density is maximal.

However, if that argument works (assuming essentialism, as usual), I think it's simpler to posit Lonely, similarly saying that any attempt to create other beings would transform Lonely in some other being that isn't Lonely.
Angra Mainyu said…
Joshua,

I'm not suggesting that there is a difference in terms of occupiability. But I'm not getting why that's a difference between the scenarios. Particle power also makes no difference in terms of where the particles can be placed.

Your comment about shrinking is interesting; perhaps it will help clarify the matter for me.

Let's sat that a being E1 occupies all of space.
Why is it not conceivable that it would shrink and leave some of it, perhaps pushed by a powerful being that can move any being out of any spatial location of her choosing?
I'm not sure why maximal density would be possible. For instance, if we extrapolate indefinitely into the past using General Relativity, density grows arbitrarily.
Granted, we're not justified in making such extrapolation because we would have to factor in forces other than gravity, but that seems to be a matter of how the universe actually is; I do not see anything impossible about indefinitely growing density.

Granting that maximal density is possible, I'm still not sure why the density of a space-occupying object can't decrease first, and then increase as it shrinks, leaving some part of space unoccupied.

Granted, one may stipulate that the density of the object can't decrease by definition of its essence (not that I think that works, but I'm assuming essentialism for the sake of the argument), but in that case, I'm still not sure why that's relevantly different from stipulating by definition that an entity has the infallible power to place particles in places of her choosing, or remove them.

That said, I'm thinking there might be a way in which the definitions of the entities might be used to make a difference, if (for instance) it's stipulated that Big Blog can't shrink because if some powerful entity tried to make it shrink, the resulting object that wouldn't occupy all of space but most of it would no longer be Big Blob but a similar object, since the essence of Big Blob is such that it necessarily occupies all of space, and its density is maximal.

However, if that argument works (assuming essentialism, as usual), I think it's simpler to just posit a contingent being that is incompatible with any other contingent beings (i.e., Lonely), similarly saying that any attempt to create other beings would transform Lonely in some other being that isn't Lonely.

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