Thursday, February 7, 2013

Contingency

Tyler has brought up the cosmological argument from contingency and linked to a Philosophy of Religion (POR) article and a paper by Alexander Pruss. The latter is a long article and will take me a while to read and digest. So I'm just going to post some comments on the first article by way of starting (I hope) a discussion.

The argument runs like this:
(1) Everything that exists contingently has a reason for its existence.
(2) The universe exists contingently.
Therefore:
(3) The universe has a reason for its existence.
(4) If the universe has a reason for its existence then that reason is God.
Therefore:
(5) God exists.

I have two immediate objections to the argument, which I'll call the Nature of Necessity objection and the Quantum Mechanics objection. I've already discussed QM and reasons in my debate with Prof. Feser (see here and here), so in this post I'll just address the Nature of Necessity objection.

Cosmological arguments always begin by implicitly carving out a "God exception."
  • - "Nothing can be beginningless - except God."
  • - "Nothing can exist without a cause - except God."
  • - "Nothing can be undesigned - except God."
Here we have "Nothing can exist necessarily - except God."

Properly speaking, "necessity" and "contingency" are terms that apply to propositions. Necessary truths are those that cannot fail to be true: the usual examples are mathematical and logical truths. Contingent truths could fail to be true. "It is raining right now" might be true, but it could have been the case that it didn't rain today.

The argument from contingency rips these terms out of their proper context and attempts to apply them to things. It asserts that there are contingent things - those that could possibly have not existed - and necessary things - those that could not have not existed. The problem is, no one ever seems to be able to point to something that exists necessarily - except God.

"Exists necessarily" is supposed to mean "exists in all possible worlds." But what is a possible world? Philosophers distinguish different types of possibility. Physical possibility means that which, according to the laws of nature, could happen. Logical possibility means anything that is not logically incoherent. (There are other types of possibility, but these are enough for discussion.) In making a modal argument - one based on what might happen in other "possible worlds" - it makes a big difference whether we are talking about physically possible worlds or logically possible worlds. So, it might be logically possible for the universe not to have existed, while at the same time it is physically impossible for the universe not to have existed. (That would be the case if the laws of physics somehow guaranteed that a universe spring into existence. I'm not claiming that they do guarantee this - only saying that some set of laws might do so.)

The POR article considers logically possible worlds and suggests that it seems logically possible that the universe not exist. This is, of course, true. Among the logically possible worlds is the empty world, in which nothing exists. So, no universe.

But also, no God. Because when necessary existence is construed according to logical possibility, it is an empty concept. Nothing exists in the empty world. So there is nothing that exists in all possible worlds. So there is nothing that exists necessarily.

The Nature of Necessity objection was articulated by Bertrand Russell a long time ago, so I'm sure someone has thought up a response to it. If you know of one, let me know!

26 comments:

  1. I'm not convinced this is really a problem for the theist. He can articulate "contingent existence" in terms of propositions about possible worlds, as you did. And he certainly maintains that God exists in all possible worlds. So he may be mistaken, but he's not confused about the nature of Necessity in this sense.

    I think rather the theist's problem is more about the Nature of Contingency. I think the theists are conflating two meanings of "contingent" here. There is Contingent in the sense of "it could have been otherwise", which is opposed to Necessary in the sense of "true in all possible worlds" that you discuss. There is also, however, Contingent in the sense of "x is contingent on y", as in "The existence of life on earth is contingent on its distance from our sun" and in opposition to "the electron simply appeared; it's existence is contingent on nothing".

    The first premise (or the "chaining rule") of the cosmological argument actually invokes the second kind of contingency, contingency as dependency. The second premise (the "existence claim") invokes the first type of contingency, contingency as not-necessity. Indeed, contingency as dependency is a concept that cannot be applied to the universe (taken to mean the entire multiverse, if such exists) without begging the question (against naturalism, at least, if not for theism). The entire argument is hence a fallacy of equivocation.

    Even more importantly, however, is the manner in which contingent and reason-giving relations are understood in this argument. From the Humean understanding of the laws of nature as descriptions of the regularities in nature, something is "contingent" (in the could-have-been-otherwise) if the laws are indeterministic. The first premise is therefore totally mistaken - there is actually no sufficient reason for why the electron was detected with spin up (say). Contingency is about physical possibility, not logical possibility. The first premise is essentially the denial of "true" contingency (i.e. contingency as could-have-been otherwise), and the affirmation of a Principle of Sufficient Reason, a principle which I hold to be an irrational metaphysical dogma. The argument also fails to realize that the type of reason given is patterns within existence, so that the second premise is meaningless as by definition no external pattern exists outside existence so that it could explain existence. This I consider to be the argument's most critical failure - it doesn't understand the nature of explanation.

    Ultimately, the argument attempts to take a perfectly fine descriptive term, and apply it prescriptively to establish how reality must be like. That just doesn't work; we can use concepts to describe reality, but we're not in a position to dictate to reality how it should be. You have no basis to stretch a descriptive concept to beyond the patterns that it describes. This is a recurring problem in cosmological arguments, e.g. the First Cause argument tries to go from the descriptive "fact" of physics that every change has a cause to a metaphysical principle that transcends physical patterns and hence can reach non-physical entities like God.

    Well, that's my 2c.

    Yair

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    1. That's very well put, Yair, thanks. I was trying to say something similar in my debate with Feser: that the whole notion of causation only comes about through observation of regularities of the universe - "patterns" in the universe as you put it. And to try to apply these concepts outside the universe, in order to explain the universe, is therefore a major mistake.

      Maybe you should have been debating him instead....

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  2. First, what a joy to have listened to the 1948 Copleston-Russell debate on the BBC audio at the link you provided.

    Does any see anything going on in Nature where the first 1948 C-R debate has now been followed by the second 2013 C-R debate at Purdue?? While the names got changed, the theist - atheist relationship to the alphabet stayed the same. (C is to R, namely Craig is to Rosenberg, as Theist is to Atheist, namely Copleston is to Russell). Is that a contingent or necessary relationship?.

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  3. Second, since there are physicists here, let me restate my question from yesterday's post here and from Feser's thread a couple if days ago: Is it not true that both theists and atheist-scientists AGREE that there is an Initial Uncaused Immaterial Natural Unifying Force of the whole world?

    Feel free to adjust the particular terms there, provided you leave out, for now, notions of Being or Intelligent Being from this beginning formulation. Wouldn't both Copleston AND Russell agree to that formulation?

    If not, what am I missing?

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  4. Btw,
    isn't " Everything that exists contingently has a reason for its existence" simply a tautology? That is, doesn't contingent denote reason?

    And isn't "(4) If the universe has a reason for its existence then that reason is God" simply an axiomatic (underived) premise? If so, what is the argument? I'm being a little tongue in cheek here, because I understand the sequence of the argument - but my point is that the point of the argument should be whether reason must = God (assuming arguendo there IS a God for reason to be equal to). So how is the argument from contingency an argument for God, when the argument already assumes there is a God? This may be an argument for what an attribute of God might be, but (IMO) it is not an argument for God.

    What am I missing?

    And thanks, Yair, for your well reasoned post. I totally get your point as to the equivocation as to the meaning of contingency.

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  5. I meant to say, doesn't 'contingent' denote 'reason for' ... and the (1) got dropped, referring to the OP.

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  6. > The first premise is essentially the denial of "true" contingency (i.e. contingency as could-have-been otherwise)

    I need to ask, what do you mean here by "true"? Why not "alternate meaning of contingency" instead of "true"?

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  7. @c emerson: "since there are physicists here, let me restate my question from yesterday's post here and from Feser's thread a couple if days ago: Is it not true that both theists and atheist-scientists AGREE that there is an Initial Uncaused Immaterial Natural Unifying Force of the whole world?"

    Speaking as a physicist - I have no idea what an "Initial Uncaused Immaterial Natural Unifying Force" is.

    "my point is that the point of the argument should be whether reason must = God (assuming arguendo there IS a God for reason to be equal to). So how is the argument from contingency an argument for God, when the argument already assumes there is a God? "

    All cosmological arguments contain the "gap problem", namely that the structure of the argument is such that it establishes at best some particular thing, not God, and you then need further arguments to bridge this gap and show that this thing really is God. The main part of the argument - establishing the first cause/ necessary being/ whatever - is generally bad enough so that the gap problem and the arguments to bridge it can be left untreated. When we speak of "the cosmological argument", we're really speaking about that first, main part, leaving the arguments to bridge the gap vague. Which is why in the abbreviated version above they were not even mentioned, premise 4 was simply postulated to formally get on with the argument so that we could move on to dissecting the first part.

    "I need to ask, what do you mean here by "true"? Why not "alternate meaning of contingency" instead of "true"?"

    The word 'true' there was in ironic double-quotes, to signify that this is what the Humean-Regulatorian sees as the "One True" meaning of the word. The sentence is in the context of the paragraph, which describes this perspective and criticizes the argument from it. On re-reading them, both that paragraph and that sentence could benefit from a rewrite. :)

    Cheers,
    Yair

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  8. Yair, thanks for your thorough reply.

    I should have realized you meant scare quotes related to "true" -- but Internet debating, due to limited space and time (no pun intended), leaves the issue of citation somewhat up in the air.

    Thanks also for your God of the Gaps explanation ... It is exactly that dividing line, between the causation part of the argument and, as a Theist in my exchange on Feser's blog referred to it, the definitional part of the argument, that I am trying to get at.

    Theists seem to be committed (perhaps only due to an historical, not metaphysical, necessity) to a particular description or definition of causation. This description has run up against the modern physicists' description of uncaused physical events (QM for one). But now, if I may, the language gets partly in our way. Both sides to the causation part of the argument seem to ultimately agree that something Uncaused does, in fact, exist: scientists call this something Force or Field or the like. Theists call this Uncaused Cause or Prime Mover or Principle of Motion or the like.

    I understand the two sides are not necessarily talking about the same 'thing' (scare quotes signifying a thing might exist but the meaning of the word equivocates).

    But this is why I chose to concoct a fresh expression, Initial Uncaused Immaterial Natural Unifying Force (IUINUF). Sometimes reformulating an expression like Unified Force and Uncaused Cause requires us to rethink those separate connotations.

    That's where your explanation of the God of the Gaps concept comes in ... or, as the theist responder on Feser's blog called it, the definitional issue. That issue, whatever it's called, is captured in the last phrase of the argument (as usually stated) ... "and this everyone understands to be God." [quoted from Aquinas by Feser, p.66].

    Again, a theist might object that I'm conflating notions of natural physical forces with the Aristotelian notion of Prime Mover or Uncaused Cause. If so, then be assured I am doing so intentionally. I'm doing so because this now moves the argument to the issue of WHAT that thing is (conflated or not) ... OR to WHAT, if 'anything', might account for, cause or sustain that other thing. [I apologize for the all caps].

    I hope it's obvious that I'm not trying to answer that question. What I am interested in is the structure of the argumentation used by theists and atheists, because they often don't have time or space (again no pun intended) to clarify their terms or defend their theory of argument. See, for example Wikipedia, Argumentation Theory, Sec.5.

    What I am also, perhaps, trying to show, is that it's not the causal side of the argument that is particularly relevant any more, it's the 'what is this' side that's relevant (IMO). I've said earlier on this blog: "I simply cannot imagine Aristotle having any problems with Newton or the quantum physics that came later. By that I mean I suspect he would have incorporated every scientific advance into his metaphysics, revising any of his metaphysical notions, as needed, as he went. Somebody explain to me if I'm wrong about this." To which Scott, who is very capable of explicating A-T, essentially agreed (and then clarified some of Feser's points for me).

    Thanks again, Yair, for your clarifications. [And kudos for an excellent discussion you had with Scott on Feser's blog somewhere on pantheism no less]. And not to get sappy, but kudos for Prof Oerter as well for promoting serious debate. Helps me enormously. [Note: I will have restricted time for blogging starting in a couple of hours, so if I fail to respond further, my apologies]. Yes, cheers.

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  9. BTW, I elaborated a bit on my poker probability based argument vis a vis Oerter's Fine Tuning Argument for Naturalism over on Tyler's blog where he and Oerter have been discussing FTAN, if interested.

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  10. Very briefly I want to say a few words about Professor Oerter's objections to the cosmological argument from contingency:

    you say "Properly speaking, "necessity" and "contingency" are terms that apply to propositions. Necessary truths are those that cannot fail to be true: the usual examples are mathematical and logical truths. Contingent truths could fail to be true. "It is raining right now" might be true, but it could have been the case that it didn't rain today."
    I for one do not see why not. If it is because you think that existence cannot be a first-order predicate I would point out that there is no good reason to think that is a necessary truth about modal syntax or grammar (notice all Kant does is give weakly inductive arguments to demonstrate it, and not even Frege has done better). In fact, Krypke's quantified modal logic does use existence as a first-order predicate. Perhaps that would leave Krypke with other problems for running a successful modal ontological argument, but it at least does show that it is logically possible to develop a modal logic wherein existence is a first order predicate. Moreover, as Peter Van Inwagen has argued, even if existence is not a first-order predicate, that is no reason at all to think that 'necessary existence' is not a first order predicate. It is logically possible that some metaphysical being be necessary in the sense of existing a se, and in all logically possible worlds. Necessity is a term which can apply to propositions and can apply to beings. By the way, Russell's theory of descriptions, which he was using as his main line of 'defense' in conversation with Copleston, is considered today to be an abject failure because of the work of philosophers like Krypke and others - nobody holds to it any longer, to the best of my knowledge (for further reading, also check out http://analyticscholastic.blogspot.ca/2012/12/one-more-reason-why-russellian.html).
    I could say more on this point, but I'll digress (have to bunker down and continue studying for my midterms).

    "The problem is, no one ever seems to be able to point to something that exists necessarily - except God."

    Frankly, I don't see why that should be a problem. It would be a problem only if we couldn't point to any being, but of course it isn't absurd to think only one being could be necessary (it is absurd to think that no being is necessary if the argument is successful). Of course, if you think it would help perhaps you could talk about platonic forms being necessary beings (though I think you would wind up with some other problems, but again I don't see why it is a problem that God is the only necessary being which possibly grounds the sufficient reason for why all contingent beings exist).

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  11. You also say that your second objection is from Quantum Mechanics. This it seems to me is a little too trivial an objection at best, but what surprised me is that it seems that you haven't fleshed it out at all. It's hard to know how to respond to it therefore. But, I think we can say the following in response to it. First, the Copenhagen interpretation of Quantum Mechanics is not the only one, and there are a number of others, with equal empirical adequacy (in the van fraassen sense) which are deterministic such that they don't come close to challenging the PSR. However, even if the Copenhagen interpretation of QM were the preferred scientific model, it would not follow that these events are without metaphysical cause. As Pruss suggests in his book 'the principle of sufficient reason' it could be God who causes this or that quantum particle to appear, or indeed it could be monads (he says this surely isn't correct, but I'm actually inclined to think something like the monadology is true, and so something like that suggestion is plausible). However, Pruss' work represents the most serious and seminal treatment of the Principle of Sufficient Reason in easily the last hundred years; I don't think one can even license the claim to know what they are talking about when talking about the PSR unless and until they have taken his work into account. I also think he decisively demonstrates that no objection from quantum mechanics can justify casting doubt on the PSR. If you had another objection from QM in mind, then I don't know what it is.

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  12. You say: "The POR article considers logically possible worlds and suggests that it seems logically possible that the universe not exist. This is, of course, true. Among the logically possible worlds is the empty world, in which nothing exists. So, no universe."

    No, the Theist's main contention is in fact that it is not logically possible that nothing exist. In other words that to say there is a logically possible world where nothing (meaning not-anything) exists is a contentless claim, and metaphysically absurd. It is literally not logically possible. This is in fact the principle premise for my articulated modal cosmological argument here: http://thirdmillennialtemplar.wordpress.com/2012/06/01/a-modal-cosmological-argument-for-the-existence-of-god/
    In other words, the Theist believes there is a logically possible world where not a single contingent being exists, but that is NOT to say that nothing exists because an incontingent being would still exist. In fact, for a logically possible world with at least one contingent being to exist logically entails that in all logically possible worlds an incontingent being exists (which is what the argument here is trying to establish, and does establish if successful).

    Well, that will have to do for now. Cheers.

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  13. Great stuff, Tyler, thanks for the responses. This gives me a lot to chew on (as well as another book to read, sigh) in addition to your comments at your own blog that I haven't responded to yet. Don't know when all that's going to happen, but I am very appreciative of your effort.

    BTW I meant to do a post on QM that's directed at the contingency argument, rather than let you try to figure out what parts of the other argument applied. So that's coming sometime too, maybe. But if I need to read Pruss first, maybe not very soon.

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  14. OK, so I've got to start with this:

    Tyler wrote, "No, the Theist's main contention is in fact that it is not logically possible that nothing exist."

    So what claim are you making here? That you can prove the empty world is a logical impossibility? I'd like to see that.

    At your link you write, "The first premise [that it is not logically possible for nothing to exist] is not very controversial among modal logicians...."

    That seems to be just straighforwardly false. For example, here's Alexander Pruss in a comment on his blog:
    "Whether an empty world is possible in some logical system L depends on the axioms and rules of inference you allow in that system. "
    And here's paper that argues the empty world can be reached via a subtraction process.

    So, if you have a proof that the empty world is logically impossible, let's have it!

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  15. >I have two immediate objections to the argument, which I'll call the Nature of Necessity objection and the Quantum Mechanics objection. I've already discussed QM and reasons in my debate with Prof. Feser (see here and here), so in this post I'll just address the Nature of Necessity objection.

    >Cosmological arguments always begin by implicitly carving out a "God exception."

    * - "Nothing can be beginningless - except God."
    * - "Nothing can exist without a cause - except God."
    * - "Nothing can be undesigned - except God."

    I reply: This is just the question begging "then who created God?" retort.

    It's like asking "What is illuminating this room?". Answer: "Light is illuminating this room" then retorting "Well then what illuminates light?". It's a silly objection not unlike the reverse "gaps argument" found in your quantum mechanic objection.

    Something contingent by nature requires something necessary(unless you wish to throw out logic) and all of the classic cosmological argument formulations use phrasing such as "which men take to be God".

    "God" here can be defined in the Classic Sense, or Theistic Personalist, The Force, or unequivocally impersonal etc but the admission of Unconditioned Reality at the bottom of our conditional reality grants the lion's share of the argument to the generic theist.

    PS. I don't know why I am posting here I am still quite a bit miffed at you Dr. Oerter.

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  16. Ben wrote,
    "I reply: This is just the question begging "then who created God?" retort. "

    Not a retort, just noticing a commonality among cosmological "proofs."

    Ben wrote,
    "Something contingent by nature requires something necessary(unless you wish to throw out logic)"

    Um, no, it doesn't. Or, if you think you can prove it does, fire away.

    Ben wrote,
    "PS. I don't know why I am posting here I am still quite a bit miffed at you Dr. Oerter."

    Welcome back, Ben. ; )

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  17. "Ben wrote,
    "Something contingent by nature requires something necessary(unless you wish to throw out logic)"

    Um, no, it doesn't. Or, if you think you can prove it does, fire away."

    Well, that brings us right back to the issue of the PSR and it's relation to modal logic(s), doesn't it? :P

    Coming to your responses to my comments; notice that Pruss' claim is compatible with mine so long as one also accepts that the axioms of classical First Order Logic are correct. I do believe that. Moreover, it isn't as pedantic a matter as whether classical FOL is objectively correct - I submit to you that you can neither imagine nor conceive of a world where not-anything exists. If you think you can then I think you're confused. I think it is this latter claim which is not very controversial among modal logicians - but of course, there may be rare exceptions. In any case, it seems incredible to me that one should seriously call it into question. Do you think you can imagine or conceive of a world in which not-anything exists? If you cannot, then that combination of words has no propositional content (it doesn't propose a model of the way the world 'could be' to you). So I think one's modal intuitions can settle the matter.

    Interestingly, I was reading the back and forth between Dianelos Georgoudis and Alex Pruss, and I would advance against Georgoudis that if, as he says "First order logic is a epistemological method that applies to our world. Now any epistemological method uses concepts which refer to something. In an empty world there is nothing concepts may refer to [...]" then put simply it isn't a logically possible world. A logically possible world is a model of the way the world could possibly be. There is, however, no way to understand a logically possible world in which there is nothing concepts may refer to. This seems obvious to me. If there is absolutely no conceptual content, then it cannot be referred to, even within possible world semantics.

    I am inclined to agree with Kenny Pearce's comment that "But one proposition can be impossible all by itself, for instance, there is a round square. Perhaps there is nothing at all is a proposition like that." I submit, more strongly, that it IS such a proposition - it is unintelligible.

    As for the paper you linked me to (I appreciate it very much by the way, it's an excellent paper and I've already begun to dig in), as the abstract says, the paper's argument hangs on the soundness of the subtraction argument.

    I will have to read it more carefully, but it seems to me the paper goes wrong near the beginning when it states implicitly that: "a possible world is a maximally spatiotemporally interrelated mereological sum of things" and then adds "it seems that there is no null world, no possible world consisting of absolutely no spatiotemporally located things."

    I can conceive of a logically possible world without space or time, so long as there are substances with relations (say, a world of monads which do not have petites perceptions). However, the intuition of the authors here is only in superficial concord with the typical Theist (let's say the Theist of the Leibnizian persuasion). Although they begin by arguing that the empty-world seems impossible, their conclusion is going to be that "by allowing
    for a world containing nothing but the null individual" they can establish the possibility of what they call metaphysical nihilism. However, notice that the null individual is not nothing. More significantly though, the argument doesn't even address the problem we're discussing since what it means by metaphysical nihilism is NOT a logically possible world where not-anything exists. They are speaking, it seems to me, of a qualified sense of 'metaphysical' possibility of an empty world.

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  18. As I understand it, classical first order logic rules out the empty world by axiom. That, of course, is not a proof that the empty world is logically impossible.

    It seems your only argument is that your intuition says the empty world is not a coherent concept. That's not a proof, either.

    In some formulations, a "possible world" is simply a collection of mutually consistent propositions. It seems to me that a collection of propositions about an empty world need not be contradictory. But, again, if you can prove otherwise, please enlighten me.

    But I think the empty world is really a bit of a red herring. What about a possible world whose domain is the real numbers? If God exists in that world, then God is a real number or a collection of real numbers. What about a world consisting of a single geometrical point? If God exists in that world, then God is a a single geometrical point.

    I think the usual theistic approach is to step back from logical possibility, and say God is necessary in some other sense of possibility - generally some vaguely defined "metaphysical possibility" that lets them avoid counterexamples like those above. So it's interesting to see you try to defend strict logical possibility.

    But you've got to have something better than your modal intuition to back it up, man.

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  19. [Sorry this comes so late, I wrote the whole thing and then, of course, lost it because the browser closed down... hate it when that happens].

    Ok, where did I begin last time... oh yes - whether I need more than modal intuition to back up my modal claims. Really, do I? What else would I have? I submit that I don't need anything else, and neither do you - intuition is operative on the most basic level of logical inference. However, I'm not only making the argument that I have this intuition (which would make my argument really an autobiographical account of my belief formation) but I'm suggesting that you have this same intuition as well.

    Now, whether a logically possible world is a collection of mutually consistent propositions seems obvious to me: it cannot be. Take Grim's Cantorian argument against omniscience, for example, which is not a successful argument against omniscience, but it does successfully demonstrate that there is no such thing as the set of all true propositions. You can find that argument elaborated here: http://benwallis.blogspot.ca/2011/05/philosopher-patrick-grim-since-early.html
    If logically possible worlds were maximally consistent sets of propositions then the actual world would not be a logically possible world. There are better ways of talking about logically possible worlds (for instance as maximally specific propositions from which can be derived any number of other propositions consistent with each other). More on that later perhaps.

    A collection of propositions about the empty world cannot exist because in an empty world (notice that by empty world you must mean a world where not-anything exists, rather than the 'empty world' in the qualified sense spoken of in the paper to which you have linked me) there are no predicate-bearers. That is to say, the empty world has no properties at all, and thus, strictly speaking, one cannot say ‘elephants do not exist’ in a world where nothing exists – it is just linguistically confused to speak that way because there is no such logically possible world to which the predicate ‘has not elephants’ can be applied. In other words, for something to be said of a logically possible world, it has to be the case that the logically possible world is a predicate-bearing subject (for the sake of modal grammar), but, if a logically possible world consists of not-anything then there is nothing in virtue of which it can bear any predicates.


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    1. Concerning a possible world whose domain is the real numbers, or a geometrical point, it seems confused to suggest that if God exists in such worlds then he is a number of a geometrical point. Perhaps I can illustrate with a parody: in a logically possible world where only contingent beings exist, if God exists in all logically possible worlds, then God is a contingent being. See the problem? We all know that what we mean by God is not a contingent being, just as well as we know that it is not a number or a geometrical point. To say that there is a logically possible world with only real numbers or only a single geometrical point (even if those worlds might be absurd for other reasons), is simply question-begging against the Cosmological argument. One cannot say that prima facia there seems to be no problem with positing such worlds and conclude from that that any demonstration that it is problematic must be wrong. Instead one has to consider a demonstration which makes it problematic and decide in light of that whether we can really speak of such worlds. The Leibnizian cosmological argument is supposed to demonstrate that it is problematic, so whether we can speak of such worlds coherently is going to depend on whether that demonstration succeeds.

      Finally, you say that the usual theistic approach is to step back from logical possibility and say that God is necessary in some sense other than the logical sense, such as being metaphysically necessary. First, I think this is rarely done among Theists. Those Theists who do in fact make that move away from talk of logical necessity are usually considered somewhat maverick among their Theistic peers (eg. look at the thread you linked me to – which was the side on which there were more Theists?).
      In any case, I do defend strict logical necessity when I say that God is necessary. Moreover, if the cosmological argument is successful then it establishes that God (the sufficient reason for the whole 'world', understood here to be the totality or aggregate of beings, real or imagined, which do not contain in themselves the reason of their existence) is necessary in the logical sense as well as the metaphysical sense.

      I can’t recall if I made any other points last time.. I feel like I did, but I suppose I’ve said enough for now. Ok, back to my exams.

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  20. Sorry, Tyler, I think you're confused. The Leibnizian cosmological argument is not supposed to show that such worlds are logically impossible, only that they are metaphysically impossible. To show something is logically impossible you would need to show that it entails a logical contradiction. I don't think anyone claims that a 9suitably defined) world of pure mathematics entails a logical contradiction.

    Re: Grim's argument - this is essentially Russell's paradox from set theory, and it the reason we talk of "collections" of sets rather than "sets of sets". You'll notice I used the word "collection", not "set" of propositions. Your definition, "maximally specific propositions from which can be derived any number of other propositions consistent with each other," is a better way of putting what I was saying.

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    1. [Sorry for getting back so late, but school is still taking up all my time, (eg. I have five essays due tomorrow)].

      Oh, don't be sorry. Then again, though, don't be so sure either. :P

      Well, it seems to me that Leibniz intended his argument to come with the full force of deductive closure. Notice that what makes Leibniz's argument different from any of St. Thomas' is that Leibniz intends it to prove the logical impossibility of God's non-existence, not just the metaphysical impossibility (that's standardly how they're differentiated). Notice that modern defenders of the Leibnizian argument, such as Pruss, argue for a logical version, not a metaphysical version. Notice as well that people typically refer to Leibnizian cosmological arguments as modal cosmological arguments (arguments in modal logic).

      So, if the Leibnizian cosmological argument works, it shows precisely that there is no logically possible world in which God does not exist, and that means that even if there is a logically possible world consisting 'only' of mathematical 'objects', God would exist in that world as something other than a mathematical object precisely because what is meant by the Theist when she says 'a world consisting of only mathematical objects' is a world in which, other than God, there exist only mathematical objects. She just properly ignores for the sake of convenience always saying 'except for God' or 'other than God'. Think it through though, and it is the obvious implication of accepting the soundness of a Leibnizian cosmological argument that there just are no logically possible worlds in which God does not exist. In fact, I think it's an implication of accepting classical theism which affirms that God's essence is existence.

      Moreover, not that I mind, but I think we need to be more careful before making an allegation of confusion. You would perhaps have discovered, with due diligence (For instance if you either read the literature available some of which I have already provided you with or simply perused other materials) that Leibnizian arguments are essentially about the logical necessity of God's existence. For example, Dr. William Lane Craig has said that the Leibnizian Cosmological argument aims precisely to demonstrate that there is no logically possible world where 'nothing exists' precisely because there is no logically possible world without at least one incontingent being. Look around and take an inventory of the arguments on offer - it should become palpably clear (perhaps comically clear) that the Leibnizian cosmological arguments ALL aim to establish that God exists by arguing that the opposite is not logically possible. If there is a possible exception, then you might think Copleston is one (and I suspect he articulated his version his way because he wanted to avoid accounting for the truth of subjunctive counterfactuals of creaturely freedom), but notice that even his version attempts to establish that it is literally incoherent to say, once one has admitted the PSR (which, you'll recall, is a modal principle, not a metaphysical one), that God does not exist.

      Finally, even if you thought I were wrong about the consensus view (which I note, again, that I'm not), you started this discussion with me in mind, and MY argument is adamantly and overtly aimed to establish in the most explicit manner that God's non-existence is not logically possible. Perhaps you thought my argument wasn't a Leibnizian argument? I don't know what you could be thinking... but in any case, I will simply reiterate the point that, in fact, A Theist who believes in the soundness of the Leibnizian Cosmological argument will never admit that there is any logically possible world wherein God does not exist.


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    2. Now, obviously one's understanding of logically possible worlds is going to here come into play. For instance, Hume thought that imagining a brick without imagining a cause was enough to license the claim that there was a logically possible world where there existed a brick without a cause (Pruss does not, and I am inclined to agree). Notice that the Leibnizian arguments articulate some version of the Principle of Sufficient Reason - precisely because they aim to establish God's existence by appealing to a logical, not metaphysical, principle (the PSR is generally articulated as concerning propositions, not beings, and is thus logical, not metaphysical). That makes at least Pruss' argument a logical, not metaphysical, one.

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  21. Well, I'm no expert on Leibniz, but this SEP article says that he was unclear about whether he intended the PSR to apply to event or to propositions:

    "So it appears that, in these texts, Leibniz is thinking of the PSR as a principle that applies to events and not truths. Perhaps Leibniz did not notice that some of his formulations of the PSR entail that it applies only to truths and that others entail that it applies only to events. Or perhaps he thought that the two formulations are equivalent because he thought the for every event there is a truth that describes it and that for every truth there is an event described by it. (It must be noted, however, that the later assumption is quiet questionable. Many truths, e.g., mathematical truths, do not appear to describe events.)"

    Craig's version of the LCA takes as its first premise:
    "1. Anything that exists has an explanation of its existence (either in the necessity of its own nature or in an external cause)."

    This, and (1.) from the POR article, both employ the existence rather than the truth version of the PSR. In other words, both arguments begin with a metaphysical premise. No?


    Also, according to this article Leibniz explicitly denied that the PSR entailed logical necessity:

    "… [he who completed the whole demonstration would then show] that it was rational and therefore definite that this would happen, but not that it is necessary in itself, or that the contrary implies a contradiction (Discourse on Metaphysics, §13)."

    Finally, yes, I realize that your argument is indeed one for the logical impossibility of God's non-existence. That's the very difference I was commenting on.

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