This is so illogical I don’t know where to start. In the case where you agreed that god could have made the world better and deliberately didn’t, that somehow doesn’t conflict with omnibenevolence until the better world “exists”? And if the better world existed - meaning, that we’d be living in it - then that wouldn’t allow omnibenevolence?
Your thinking here is literally backwards. You’re getting worse the longer you go!
Not really - if you accidentally prove ~G as part of your arguments, then you have just guaranteed your failure to find a flaw in the POE. It’s identical to the case of gods that can do the logically impossible in this regard.
We may not be discussing the “problem of evil or relativity”, but we’re also not discussing your incorrect model of relativity. Take your objections to world-states (which happen to be identical in function to how possible worlds are commonly understood on valuations of modal logic) and stuff them in the garbage where they belong - because I dismiss all such nonsense as incoherent and incapable of refuting anything I say.
Bullshit - anything that’s physically possible is logically possible, necessarily. I’m so sorry that logical impossiblity follows rules and makes logical sense, but unfortunately for your argument, it does.
He uses f’ing magic. He’s God. He’s omnipotent, which despite your efforts to pretend otherwise is a word that actually has a meaning.
You do realize that you can’t break the POE by pointing at styrofoam cups or other nonmipotent gods, right?
I seriously doubt I accepted it; I probably just missed it - and it’s not like “a couple of posts ago” is exactly a roadmap to finding it.
Regardless, if you’re talking about your absurd “god can’t make square circles, so that means he can’t make round circles either” argument, then I reject it on account of it being terminally stupid. Your “it’s possible that he can’t” stuff is utterly illogical and completely unsupportable by any valid or sound reasoning.
The logically possible is logically possible. The fact that some other things are not logically possible doesn’t in any way, shape, or form reduce the logical possibility of logically possible things. And this remains true no matter how many times you repeat nonsense to the contrary - even if I miss one or two of the times you do so.
Regardless, I shall lay down the law (again): any god that cannot do the things I listed is a pansy-ass weakling, is certainly not omnipotent (by definition), and is thus is not and cannot be used as any part of a disproof of the POE. You can’t disprove ~G by showing examples of ~Gs.
I didn’t find that incredibly impressive either, but even if it had been, it doesn’t make any stupid and incorrect things you say later any less stupid and incorrect.
There is no form of logic in the universe where you can leave the part of the argument you’re trying to prove or disprove “implicit”. Well, aside from bullshit fallacious rhetorical logic, but that’s not a universally recognized system.
I left nothing implicit when I said that you need to show E to disprove the POE. Obviously. And that you claim I did shows that you either are bullshitting me, or that you have no idea of how the logic works - and that you have no idea what you yourself are talking about. You have spent the entire thread arguing that “[]E” is true. Remember all this nonsense you’ve been saying about your nonmimax god being unable to make a better possible world? About how -in complete defiance of the facts- you are claiming that our actualized world is the only logically possible world? Why do you suppose you’re doing that? Can you remember?
This is blatantly false. The definition of “omnimax” is logically incompatible with unnecessary evil in any specific world. There may exist possible worlds with a god and no evil, or with evil and no god, or with neither a god nor evil, but at no point have I allowed for the possibility that the set of worlds with both a god and evil is non-empty. Becuase such worlds are impossible. By definition.
If you think I’ve stated that there might be a possible world where an omnibenevolent god chooses evil, then you’ve simply misunderstood what I said. Which wouldn’t surprise me at all at this point.
Underlining added - Gee, I wonder if I was trying to say that <>R isn’t true. It’s unfortunate that I didn’t make that clear, forcing you to have to guess and put together a blatant strawman to pretend that I don’t understand something that I obviously, obviously do.
However, I’m not sure you understand modal logic; you keep writing about it being possible that in our specific world there’s evil, when of course in actuality <>X is not a claim about any specific world; it’s a claim about the set of all possible worlds.
And incidentally, pointing out this confusion your part was the whole point of the red ball example. Would you care to answer the following question I asked in the prior post? I would find your answer instructive…and so might you:
Come back when you know how modal logic works. For starters, learn that (<>A and <>B) does not imply <>(A and B).
For a starter on that, consider the case where B is ~A: that is, ask yourself whether (<>A and <>~A) implies <>(A and ~A). As long as you think the answer is “yes”, goto 10.
Oh, I understand the argument just fine. I simply also understand that (<>G and <>E) doesn’t imply <>(G and E).
Right. However if one uses modal logic correctly, they find that it doesn’t change the results of the argument that lacks it. That’s the thing about logic; 1+1 keeps equalling 2 even if you do the same calculation in a different way.
Do yourself a favor and try to write your argument in actual formal logic, not this fallacious rhetorical crap. If you actually did that, and stuck to legal rules of logic, I think you’d find your errors rather quickly.
I’m not really sure where the problem is. If god could have put us in a better world, but didn’t (i.e. if you prove that there is a logically possible world in which there is less evil), well then obviously that’s it for omnibenevolence. But Leibniz’ argument works despite that – it still is possible for an omnimax god and a world in which evil exists to coexist; that just isn’t the case in actuality. God could have been omnibenevolent, logically; however, he isn’t in actuality. Like my car could have been white, but actually is black – doesn’t mean it’s not true that it could have been white.
Well, if relativity disproves god, then you should get the word out, seems like the Vatican didn’t get that memo.
The thing is that while I know the world states are relativistically incoherent, I don’t know that there isn’t a way for god to exist ‘outside time’ or something like that; I don’t consider it very likely, but I also can’t dismiss the possibility.
I’d like to see an argument for this incorrectness.
Nah, modal logic typically doesn’t cripple itself like that; and if you intend on insisting that it does, I’d like to see a cite.
You do indeed, problem is you lack any reasonable grounds to do so.
And Last Thursdayism is physically possible? Not by any physical theory I know.
So now you want me to grant you magic as logically possible, based entirely on your assertion?
Yes, and that meaning is not ‘can do everything that’s necessary for your argument’.
That is rather a misrepresentation.
The reasoning in the argument I provided in this post is perfectly valid by anyone’s standards. It’s elementary – for your convenience: There is something that is an x that is P; hence, it is possible for something that is an x to be P; y is an x; hence, it is possible for y to be P. I don’t really see any room for argument there.
I’ve never asserted the contrary. Perhaps it’s easier if we leave the ‘logically possible’ aside for a moment and concentrate on ‘things that can’t be done’. Those two categories are equivalent, for all we know, but the latter is perhaps less of an intuition pump; while one generally thinks that everything one can imagine is logically possible, that’s perhaps not so for the latter.
So we know that there are some things that can’t be done, right? Hence, one is never justified to a priori assume that any given thing is a thing that can be done. That’s really the core of the argument. Of course, one is similarly unjustified in assuming that any given thing is a thing that can be done, and you keep claiming that this is what I am arguing for; however, it isn’t – I merely argue for the (to my mind, absolutely uncontroversial) assertion that it’s possible for everything to be a thing that can’t be done. It’s likewise possible for everything to be a thing that can be done, and I’m perfectly fine with it – however, I trust you see the asymmetry in our positions by now: for everything you assert to be something that can be done, you carry the burden of proof; I merely state the default, born out exemplary, that for every thing, it may be the case that it can’t be done.
Your task then, to prove that something can be done, seems impossible in principle – it’s Hume’s problem of induction once more: seeing x being done gives you no grounds to conclude that y can be done; indeed, strictly speaking, seeing x being done yesterday gives you no grounds to conclude that x can be done tomorrow – having seen the sun rise yesterday does not mean that the sun will rise tomorrow.
Well, that’s a bit of an easy way out, if you just get to define yourself to be right, don’t you think?
I’m not trying to prove or disprove the existence of god; the existence of god is an assumption in the POE, that is brought to an alleged contradiction (if you didn’t assume god, there would be nothing to reconcile with the existence of evil – i.e. if G is false, G -> ~E is always trivially true.) This assumption is left untouched, so I can indeed leave it implicit – the reason for that being that both G -> ~E and its negation, G & <>E, yield true statements precisely iff their second half is true, provided G is true.
OK, this is something you really finally need to get straight. I have never in this thread argued that E is true, nor will I ever do that. It would be an unnecessarily strong argument to do so.
Possibly unable. I mean, really, after all this time? Do you just still not get what has to be established to show the POE wrong, or are you just trying to strawman me?
Just out of interest, what ‘facts’ would be contradicted by that? I mean, obviously, we only experience one world, so all our experience is trivially consistent with there only being one possible world.
Yes, that is indeed what the POE says; it’s just not what your POE says.
Of which ours is one. And perhaps the only one, at that.
In W2, <>R is true. In W2, R is false. There is no tension between these statements.
Well that’s… nice I guess, but irrelevant. Your POE yields ~G upon the assertion ~~E. It thus fails at disproving the existence of god; it merely disproves the necessity of his existence, which never was under debate. Sure, it might be that things shake out such that there is no world in which G and E are both true, but that isn’t established by your argument (and is an a priori possibility without making any argument at all) – or only if you assume that G and E are in contradiction with each other, which would be begging the question.
Well, as has been noted in this thread, Alvin Plantinga thinks differently, and a majority of contemporary philosophers agree.
Half Man Half Wit, a large percentage of your prior post can be answered with a single statement, one which I have been repeating over and over again for most of the thread: you are brutalizing the ambiguous meaning of the word “possible”.
The word “possible” has two separate and distinct meanings, which must not be confused:
Logical meaning: that in the set of all possible worlds, there is at least one world in which the statement in question is true.
English meaning: in a given world, it is not yet known that the statement in question is not true.
For an illustration of this difference, consider the case where you are sitting inside your house, and are suddenly struck with curiousity over whether it’s raining outside, since you don’t happen to know. Specifically, you ask yourself, “Is it possible that it’s raining?”
In the english sense of the word, the answer is “yes”. This is because the questioner hasn’t ruled out the possibility that it’s raining in their possible world yet, due to lack of information about their specific possible world. If you got up and went and looked out your window, though, you would add a few more axioms to your knowledge base/premise set, including either “it’s raining” or “~(it’s raining)”, depending on which it happens to be. If it’s not raining, then , the answer to “Is it possible that it’s raining?” changes to ‘no’; and if it is raining, then the answer stays ‘yes’…but most people wouldn’t put it that way, since we don’t tend to think of known facts as ‘mere’ possibilities, in english. Regardless, in either case the question depends only on the state of things in the single specific world under consideration.
Now, the logical sense of the word: the answer to the question is…well, it kind of depends on what’s happening in the complete set of logical worlds, now doesn’t it? If you happen to know that it’s logically possible for it to be raining, which is to say that you know it’s raining in some logically possible world, then you can confidently assert “yes”. If you don’t know that, then you can’t assert either <>(it’s raining) or <>~(it’s raining), because you just don’t know either way. And when you look out the window, only one of those questions is answered, and the other isn’t! If it happens to be raining, then you then know <>(it’s raining) is true, since you’ve verified that in one possible world it is. But if it’s not raining, then you don’t know if <>(it’s raining) is true or not; you can only assert that <>~(it’s raining) is true, because the only possible world you’ve verified only gives an example of ~(it’s raining) and not (it’s raining).
Now, the astute person will notice that I just said, if you haven’t looked out your window yet, that rain would be possible in the english sense and might not be possible in the logical sense. And yes, you read that right. This is because the english sense of the word has nothing to do with logical possibility at all. What it’s about, is ignorance. If you are ignorant of whether something is true or not, then you can say “it’s possible”. It you know either way, then you generally don’t use the term. Of course if you happen to know something is logically impossible then you’re not ignorant anymore and it’s no longer possible in the english sense either. But that doesn’t mean that the english sense is the same as the logical sense; not at all. It simply isn’t; the closest logical analogue to the english sense of the world is not <>A, but instead (A or ~A).
As the terms mean completely different things, you need to be very very careful about knowing which one you are using, and being clear about which one you are using. In my opinion the best way to go about this is to very deliberately never use the english sense at all. To do otherwise risks fallaciously swapping one with the other. As you do constantly.
The point of the red ball scenario was to call to your attention that you are doing these fallacious swaps. Essentially I’m going back to modal logic basics in the attempt to get you back on the correct page. If that seems like I’m insulting your intelligence in doing that, well, what else am I supposed to do?
Now, on to your post itself. I won’t necessarily respond to everything, just things that I think need further elaboration beyond the above explanation.
Leibniz’ argument is that there is not a logically possible world with less evil in it than our world. He is arguing that all the evil in our world, every speck of it, is logically necessary. If he convinced us that he was correct about this, then that would be an effective counter to most variants of the POE - the main exception being that it is susceptible to the accusation that he’s making the god so non-omnipotent that it doesn’t count as omnimax. (That accusation may sound familiar to you too.)
So, Leibniz’ argument does not work ‘despite’ a (english) possibility that there’s a better world than ours; he must disprove that (english) possibility to be able to continue. Or at least, talk his listeners into dismissing it as a (english) possibility - which is probably pretty easy for thiests like himself who have a vested interest in accepting his argument and don’t mind cognitive dissonance. Mysterious Ways are very popular among those types as a way of saying “God can’t do this - yet He’s still omnipotent somehow!”
As for the rest, you are confusing the multiple definitions of “possible”. All of your white car stuff is explicitly based on those errors.
There are an assload of memos the Vatican hasn’t gotten. I think we can agree that that’s not proof of anything.
God existing outside of time wouldn’t help. If relativity was as you describe it his omniscience and omnipotence would be abrogated if any part of anything anywhere had relativity, because then that would be some part of God’s domain that he could not know/control.
You’re specifically arguing that the universe cannot be ended at any point in time, or started at any point in time. That is, you are arguing that it’s impossible for this universe and its timeline to have ever begun. That is, you are arguing that this universe does not and cannot exist.
Any loophole you find that allows time to have started via big bang or other method is a tunnel large enough to drive momentary world-states through.
Perhaps you’re unaware of what modal logic is. It divides the logical sphere into discrete ‘slices’ in which all the logical statements under consideration have a single difinitive True or False value. Like, for example, “Socrates is dead” has a true or false value. Of course, the state of the world changes as time passes; the truth values of statements change. So, when you have statements like “Socrates is dead” (or “God exists”), then you must consider the world under consideration to refer to a specific moment in time; what I am calling a “world state”. The possibility of world-states is built directly into modal logic; and very arguably (as I’ve said) in most cases the possible worlds you’re talking about are actually possible world-states.
B-b-b-but that’s not right!, you’ll protest. That statement was supposed to be 'Socrates was dead on 10/6/2010" instead! The truth statments have to have time stamps!
That is, of course one way of defining your statements and modal worlds. But it’s definitely not the only way. And there’s no hint of that being the way it’s defined in the POE, either; I don’t see any timestamp on “God exists”.
So yeah - the definition of modal logic is my cite, and the reason I dismiss your denial of possible world-states.
The funny/ironic/sad thing is, that’s how you are defining it. For the sake of your argument you are defining God to be absolutely impotent regarding our universe - literally! You are saying he is unable to break natural law, unable to do miracles, unable to change anything at all in any possible way. And then you have the audacity to claim that that doesn’t stop him from being omnipotent.
I say, hell no. I declare that any omnipotent god has at least as much control over our universe as the writer of a book has over its contents. They can reach in and twiddle, change things, rewrite whole sections, make things happen for no reason, make things appear and disappear, deus ex machina things left and right - and, start the book with whatever setting they choose. Including the following setting: modern earth, last thursday.
If you don’t like that, then will all due respect, too fucking bad. Go whine to somebody who cares. The POE isn’t interested in disproving styrofoam cups and it’s not interested in disproving your nonmipotent gods. It’s interested in disproving the gods that people actually call omnipotent, or all-powerful, or capable of miracles, or able to part seas, or able to turn water into wine. Author gods. Gods with power. Gods who can do with the universe as they will.
As long as you restrict yourself to talking about powerless little pansies, the POE in unfazed by your efforts; you are rather literally shooting in a different direction from where your proposed target is standing.
This does not work if you use “possible” correctly. Specifically, this says nothing at all about about whether y is a P in our possible world. Which is the issue under discussion.
You are grossly misusing “possible”. And you cannot handwave your claim that virtually nothing is physically (and thus, logically) possible. This is not seriously disputable; the laws of physics have variables in them and everything, allowing variance in the way things can physically be. Wide variance.
Plus, of course, you don’t get to redefine “omnipotence” to the degree necessary for you to handwave evil into logical impossiblity. Both the physics of reality and the definitions in question disagree with you; are you going to try and reject both simultaneously?
You don’t get unstated assumptions in logic. Period.
That kind of shit is only done in rhetorical ‘argument’ - since it’s a breeding ground for fallacy. I do not do that, I am not going to do that, and I am not going to let you do that. If you try to do that, I will call what you write the fallacious gibberish it is.
And you apparently also don’t understand how proofs by contradiction work, either. The existence of god is very explicitly what in the POE is attempting to prove/disprove, regardless of how the formulation you’re looking at happens to be laid out. (Not all of them are written as proofs by contradiction, either.)
Then you don’t know what the hell you’re talking about. To disprove the POE with a Leibniz-like argument, you must convince your audience to accept the premise E - or more accurately, that all evil we see on earth is necessary, and thus that there is no unnecessary evil in our world.
Just proving <>E gives you nothing at all. As should be obvious, because glancing around at our world proves <>E to be obviously true, and that didn’t ever slow anybody making the POE down any.
Your belief that you don’t have to prove E to make a Leibniz-like argument is based on your errors with the word “possible”. You’re wrong.
I know exactly what I’m saying, thanks very much. If you disagree with me about what I’m saying, that’s your error.
Actually I’m not sure that “In W2, <>R is true” makes sense. That is, I think it’s explicitly gibberish, of the “yellow addition” variety. The way I was taught <> only has meaning when referring to a set of possible worlds. I mean, what do you imagine “In W2, <>R” means?
I don’t know what you imagine the POE says, but this isn’t it. And my comment was directly relevent to the blatant error you were making, Try reading it with the text it was responding to in mind and perhaps it will make more sense to you.
And as I responded to that note in this thread, the Plantinga argument is about libertarian free will and is readily countered based on the fact there’s no such thing. And argumentum ad populum and appeals to authority are fallacies, incendentally.
Ah, I think I see what you mean now. What you call the English meaning, I would call the epistemic meaning of possibility; your logical meaning I know as the metaphysical meaning.
However, both are valid logical meanings of ‘possibility’, epistemic (modal) logic being just as much of a logic as alethic modal logics; also, note that I can use possible in English for both meanings, as well: ‘it is possible that black swans exist’ can mean either ‘for all I know, there are black swans’ (epistemic meaning) or ‘whether or not there are any, black swans are possible (in the sense of not necessarily nonexistent)’ (metaphysical meaning).
You accuse me of confusing epistemic and metaphysical possibility. I don’t think I do, but let’s work through this.
You’re right in noting that in your example, there is a difference whether we interpret the modalities epistemically or metaphysically. In an epistemic interpretation, <>r (r for it’s raining) and <>~r are true a priori, since before I look, I don’t know whether it rains or not. After I’ve looked, it is no longer epistemically possible that I don’t know whether or not it rains; if it rains, I know that it rains, hence, r.
That’s not the case metaphysically. After I look out of the window, the knowledge I gain is that r is true (if it rains, that is). I also gain the knowledge that ~r is false. You claim that I gain the knowledge that <>r when I look out of the window; that’s not entirely true, however, since it also may be that r (this of course entails <>r, but it’s stronger, since it also entails ~<>~r, which is not decided by seeing it rain outside). It is precisely true if (and only if) it was true before I looked out of the window.
This is rather intuitive if you think about it – looking out of the window, i.e. gaining epistemic knowledge, can’t change which set of worlds we actually are in, it can only change our knowledge of which sets we may possibly be in.
So, a priori, we are in one of three world-sets:
A) in which it rains in all worlds
B) in which it rains in some worlds (and consequently, doesn’t rain in others)
C) in which it rains in no world.
Epistemically, I can thus assert a priori that <>r, or that <>~r; both are consistent with my knowledge. Metaphysically, it may be the case that either is wrong, if either r or ~r. You’re right in noticing the need to distinguish between both possibilities.
Now, if I look out of the window, I gain epistemic knowledge, and am able to exclude one set of worlds from the three, either that in which r, or that in which ~r. I am not, however, able to decide which set of worlds I am in precisely. This is, I think, where you’re mistaken.
Let’s look at the white car once more. You going to check its actual colour tells you (epistemically) that we’re in one of two world sets: that in which cars must be its actual colour, or that in which cars may be its actual colour; and it excludes the (epistemic) possibility that we are in a set of worlds in which the car can’t be its actual colour, since, well, it is its actual colour.
Metaphysically, we can (‘actually’) be in either of these two world sets, which means that epistemically, it is possible that we are in the set of worlds in which cars can be a colour different from the one my car does actually have. This is the possibility my argument is intended to establish.
You are thus right in saying that my argument mixes epistemic and metaphysical modalities, however, it doesn’t do so fallaciously. The metaphysical part is in establishing that there exists a world set such that it is possible for both omnimax god to exist, and for there to be evil; and the epistemic part consists of noting that it is possible (epistemically – we don’t know that we don’t) for us to exist in this set of worlds.
As I noted, in epistemic logic, the general reading of what you called the ‘English sense’ of possibility is ‘for all x knows, it may be true that’.
Leibniz’ argument establishes the metaphysical possibility of god and evil coexisting; if you prove the existence of a better world, you disprove the epistemic possibility of us living in a world set in which this metaphysical possibility is actual. Doesn’t mean that such a world set is no longer metaphysically possible any more than the observation that it’s raining means that it is metaphysically impossible that it doesn’t rain; it is only epistemically impossible.
Even this can be gotten around by the hypothesis that relativity is logically necessary, which is a (epistemic) possibility.
Well, yes, that’s how current cosmology works – the universe wasn’t created in time, but with time.
That, of course, doesn’t follow.
They’d still be inconsistent with relativity, though.
That’s the problem! In a world state, such as, for example, my spatial hypersurface of simultaneity, there is no Socrates – that word is a non-denoting name, as much as ‘the present king of France’. So there is no definite truth value to the statement ‘Socrates is dead’, other than on those world slices in which it is wrong. And yet, typically, every possible world should be able to assign a truth value to this statement.
The problem relativity introduces is then that my world state, my hypersurface of simultaneity, possibly includes an Andromedan to whom Socrates is alive in his plane of simultaneity (even though he has no way of knowing that).
Well, you always have to include context in any proposition that is dependent on context, of course. Consider one of your world states, and the statement ‘gravity is about g/6’. On its own, it’s meaningless – it needs a ‘space stamp’, like, for instance, ‘gravity is g/6 on the moon’. Only then can one assign a truth value to this statement.
Well, just to point that out, I did in the OP refer explicitly to histories in total, rather than timeslices.
It’s just that, in your modal logic, the vast majority of statements are undecidable – like ‘Socrates is dead’, for every world state in which it isn’t false.
I’m not sure why I keep trying to explain this, or why you seem to have such a hard time with it – I am not saying that he is unable to do anything at all. I’m saying that for every thing you pick out, it may be the case that he is unable to do so – a simple (epistemic) possibility gleaned from the fact that he is not able to do everything.
That would be overreaching, since I can very well write a book in which its protagonist crosses all of Königsberg’s bridges one after the other, but god can’t make a world in which that is the case.
The thing is, we know that god can’t do with the universe as he will.
No, the issue under discussion is whether it’s possible for y to be a P.
Which is commonly thought to be an artefact of us not yet having a complete theory of everything. String theory, for instance, contains as far as I know only one freely adjustable parameter, the string tension. It still yields a proliferation of physically possible worlds – last time I heard, on the order of 10[sup]500[/sup] of them, which is a lot, but far from infinity, meaning that yes, almost everything is physically impossible. If a selection principle can be found, which is currently the hope of those string theorist not wishing to succumb to anthropic reasoning, it might well be the case that only our own world emerges as physically possible.
I have stated what I assume clearly before; and besides, this whole discussion wouldn’t make sense if we weren’t operating under this assumption.
Yes, but not what I am trying to prove/disprove.
Do we have to go through this again? I have previously shown that accepting G -> ~E as the problem of evil, what has to be demonstrated to disprove it is G & <>E. Since in both cases, if G is true, the truth value does only depend on whether or not the latter half of the statement is true, I can afford not to bother with it. Putting it more succinctly, if I prove that <>E under all circumstances, <>E is true if there is a god, as well.
Hell, I’ve even given you a cite to that effect some hundred posts back!
So, you’re right, and if I disagree, I’m wrong. Got it.
It has a very precise sense in that in every world accessible from W2 (‘accessible from’ here meaning that one would hold to be logically possible in W2 – which in general reduces to a world that is logically possible, period), R may or may not be the case.
You’re exactly right, the POE doesn’t say this. However, your POE does. That’s why I don’t think it works as a POE. We agree that your POE implies G -> ~E, yes? Then, what the POE is supposed to accomplish is to yield, via modus tollens, the nonexistence of god upon the assertion of the existence of evil.
However, applying this modus tollens to your POE yields merely the non-necessary existence of god; any theist could completely agree with your argument, and yet rationally continue believing in god.
Actually, Plantinga’s argument merely needs for ‘if there is libertarian free will, then god can’t create a world with no evil’ to be true in order to work, not for there to actually be libertarian free will. He needs, as I do, to exhibit possible circumstances in which god and evil coexist to disprove the POE; he chooses to do so by example, exhibiting a concrete world in which this is so to get to his desired conclusion. There’s nothing wrong with that, and in principle, you can buy his argument even if you disbelieve in free will (and should if you can’t find a way to show that even in a world in which there is morally significant libertarian free will, it is possible for god to keep it evil-free). Basically, all that I do differently is that I contend myself with arguing that you can always find such an example; that for every given act intended to better this world, you can always construct a (usually ridiculous) example such that this act actually makes everything worse.
Recall the Franklin quote: “To show propositions are logically compatible, all that is needed is to exhibit a merely possible scenario in which they are all true.”
This is the reason I don’t have to show that all the evil in our world is necessary, or that god actually can’t do something or create some world, but merely need to show the possibility that this is so. This is also the reason Plantinga can content himself with showing that if there is morally significant free will, then god can’t create a world without evil. For Plantinga’s argument, you don’t need to grant that there is free will, you merely need to grant that if there were, there’d be evil in the world, even though god is omnimax; for my argument, you don’t need to grant that a world with less evil is logically impossible, merely that it is possible that there is no such world.
This is really the crucial point that you miss whenever you assert I have to show E, or that I have to show that god can’t create a world with less evil than this one, or anything like that. I’m sorry to put it so bluntly, but as long as you do that, you just show that you don’t get what the argument is about. I really don’t think there’s any point in continuing as long as you fail to realize this.
Every time you use the symbols <> and for “epistemic” possibility, it breaks my brain. I’ve never seen the symbols being used like that, I’ve never heard of the symbols being used like that, and of course it has nightmarish effects on the readability of the argument to overload the symbols like that.
Especially since it’s completely redundant, since epistemic possibility is already encoded into symbolic logic of every type from the simplest to the most complex. (Epistemic )p is written ‘p’. (Epistemic )~p is written ‘~p’. And (epistemic <>)p and (epistemic <>)~p are designated by the absence of either ‘p’ or ‘~p’, or alternatively the written statement ‘p or ~p’.
Since overloading <> and , and the words “possible” and “necessary”, is a horrible horrible evil nasty monstrous thing to do to a poor innocent argument and its poor innocent readers, I don’t suppose you could be troubled to eschew the evil and just stick to the old-fashioned, unambigous, ‘p’/‘p or ~p’/’~p’ way of describing epistemic possibility?
Actually, while I’m asking favors, I don’t suppose we could write this entire argument in predicate logic instead, using the variables as possible worlds? As best I can tell you can completely model modal logic that way, with A(for all) standing in for and E(there exists) for <>. So, the POE might be written:
G(x) = there is an omnimax god in possible world x
E(x) = there is evil in possible world x
The Leibniz response, of course, is to reject Premise 1, and instead rewrite the whole POE argument as:
G(x) = there is an omnimax god in possible world x
QE(x) = the quantity of evil in possible world x, as a comparable orderable quantity
NE = the minimal necessary quantity of evil
1: Ex.Ay.(QE(x) <= QE(y)) -from QE being orderable
2: Ay.(QE(min) <= QE(y)) -from 1, with min for x
3: Ax.(G(x) -> (QE(x) = QE(min))) -from omnimaxness
4: QE(earth) > 0 -from observation
5: QE(earth) > QE(min) -from observation
6: G(earth) -> (QE(earth) = QE(min))) -from 3
7: ~(QE(earth) = QE(min)) -from 5
8: ~G(earth) -from 6,7
…and then Leibniz rejects 5, while accepting 4 and instead asserting 9: QE(earth) = QE(min), which of course means that 10: QE(min) > 0 -from 10, 4. The counter of course is to criticize his arguments for rejecting 5 - a counter which I find compelling, because mysterious ways are bullshit.
Of course, I don’t know that it’s possible to write your arguments in formal predicate logic - but then, I don’t know that it’s possible to write them in formal modal logic either (which for the love of cheese I hope disallows conflating metaphysical and epistemic possibility). After all, you have not yet done so.
Leibniz’ argument attempts to establish the metaphysical possibility of god and evil coexisting, by baldly asserting it to be true. Or more specifically, by baldly asserting that QE(min) is nonzero, and then further baldly asserting that QE(earth) is QE(min), with an argument behind it that is pretty much only convincing to the choir.
And if one proves the mere unactualized metaphysical possiblity of a min with less evil than earth, then that disproves Leibniz and disproves God.
But disproves omniscient Gods. Adding Ax.~G(x) (or ~G, if you prefer) to the set of knowns does the theist perspective no favors.
That’s what I means, sorry for the unclarity.
It does follow, from what I meant, and if world-states are inconsistent with relativity then so is the existence of the universe. If the universe could have started with the moment of the big bang, then it could have started with the moment of last thursday, and have ended with the same moment. By “moment” here, I am definining “moment” to be whatever you think happened at the big bang. So if you get a big bang, I get world-states.
It’s pretty easy to define “Socrates” in such a way that it is a denoting name. Same with “dead”. Even with both relativity and world-states (which, as noted, must be compatible if we exist).
It’s always easy to define your terms so nothing makes sense. But in the POE, they’re defined so they do make sense. You can’t counter the POE with an argument that doesn’t address it on its own terms.
Except that as I believe we’ve agreed on, an epistemic possibility can be instantly eliminated by proof to the contrary. Which in this case means that any argument that shows that something is logically possible beats it.
Your argument here is basically of the form “Socrates is a man. Plato is a man. Therefore, there is an epistemic possibility that Socrates is Plato”. Which is true, as far as it goes - but it doesn’t actually go anywhere. It is not in any way a disproof of “Socrates is not Plato”, and in fact is swept away instantly by the entry of that fact. Succinctly, an epistemic possibility is not a counterargument to anything, by definition!
So, when I say “the definition of omnipotence says god can cure cancer”, and you say “but it’s epistemic possibility that he can’t”, that’s why your statement doesn’t make a dent. I have a definition here, and it trumps your epistemic possibility without even slowing down. If you want to counter my definition, you have to bring something has argument merit - which epistemic possibility by definition lacks.
It’s impossible to write a book in which its protagonist crosses all of Königsberg’s bridges one after the other by following the rules. If the god cheats, by teleporting him around or reducing the ‘crossing count’ of bridges or just declaring victory without going through the steps, those outcomes aren’t defined to be logically impossible by the Königsberg scenario.
I stand by my definition of omnipotence. But, I also invite you to provide your own! Please give a complete list of the kinds of things God can do, without elimitating the epistemic possibility that he is unable to improve the earth. I’ll let you know if that definition sounds like omnipotence to me.
He can get close enough to make the POE ironclad, though.
Epistemically possible? Epistemically speaking, it’s possible that I’m a talking dog. Nobody gives a shit about epistemic possibility.
Then what means “omnipotence”?
Of course you don’t have to assume the existence of god to write the POE; neither of my predicate formulations do. And I don’t give a shit about what you stated in some rhetorical way some while ago: when you write something in sybolic logic, you do not get unstated assumptions. Ever. Period. Full stop.
This horse is dead. Stop beating it. You will never convince me that you don’t have to state what the hell you’re talking about in formal logic.
Trying to prove that you can’t disprove god counts too.
This horse is also dead. If you’re not talking about whether god can be disproved or not, then you are not talking about the POE, and that is that.
Who is saying that G -> ~E is the POE? I’ve never seen a formulation where that is the case. In all the valid formulations of it I’ve seen, you never mix symbols with and without modal tags on them. Heck, I’m not even sure what the resulting sentences are supposed to mean. What does G -> ~E mean? The existence of god implies that there no evil in any possible world? The existence of God where? In one possible world? In all possible worlds? Somewhere in the middle?
Seriously - modal logic sybology is bullshit anyway; I’ve literally never seen it used except in making fallacious religious arguments. But if you’re going to use it, at least be consistent about it.
About the meaning of my on words? Yes, that’s right. When I say something and you misinterpret it, then you’re wrong. Life’s tough that way.
Ah, okay, that ‘accessibility’ garbage. Didn’t I dismiss that as irrelevent a few billion posts ago? God’s not limited to what accessible from here, and there’s literally no way that that limited set of worlds can possibly be relevent to the discussion. So there’s no need to further obfuscate the situation by introducing such things.
If you actually want to introduce something like accessible worlds, use something like predicate logic where they can be defined and tracked unambiguously. Unless, of course, obfusaction is the point.
Didn’t we already establish that you are mistaken about what I was talking about?
Look, let’s back up to before all this. Why don’t you tell me what version of the POE you want to talk about. Its precise arguments, its precise formulation. Because there are so many different variants of the thing that we’re very likely talking past one another. Heck, I provided two more of them at the top of this very post!
You tell me what version of the POE you’re disproving, and how you’re disproving it, and I’ll tell you whether your argument works or not. Let’s keep it self-contained and simple, so no other variant POEs and counterarguments slip in. Okay?
Actually, Plantinga’s argument merely needs for ‘if there is libertarian free will, then god can’t create a world with no evil’ to be true in order to work, not for there to actually be libertarian free will. He needs, as I do, to exhibit possible circumstances in which god and evil coexist to disprove the POE; he chooses to do so by example, exhibiting a concrete world in which this is so to get to his desired conclusion. There’s nothing wrong with that, and in principle, you can buy his argument even if you disbelieve in free will (and should if you can’t find a way to show that even in a world in which there is morally significant libertarian free will, it is possible for god to keep it evil-free). Basically, all that I do differently is that I contend myself with arguing that you can always find such an example; that for every given act intended to better this world, you can always construct a (usually ridiculous) example such that this act actually makes everything worse.
Recall the Franklin quote: “To show propositions are logically compatible, all that is needed is to exhibit a merely possible scenario in which they are all true.”
This is the reason I don’t have to show that all the evil in our world is necessary, or that god actually can’t do something or create some world, but merely need to show the possibility that this is so. This is also the reason Plantinga can content himself with showing that if there is morally significant free will, then god can’t create a world without evil. For Plantinga’s argument, you don’t need to grant that there is free will, you merely need to grant that if there were, there’d be evil in the world, even though god is omnimax; for my argument, you don’t need to grant that a world with less evil is logically impossible, merely that it is possible that there is no such world.
This is really the crucial point that you miss whenever you assert I have to show E, or that I have to show that god can’t create a world with less evil than this one, or anything like that. I’m sorry to put it so bluntly, but as long as you do that, you just show that you don’t get what the argument is about. I really don’t think there’s any point in continuing as long as you fail to realize this.
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Epistimic possibility is argumentively worthless - to the point of not even being worth mentioning. Which is why your ‘crucial point’ is no point at all.
And no, you can’t defend Plantinga that way. “If there were an elephant on your head, then you’d be dead. There isn’t one, but it’s still possible you’re dead anyway, despite evidence to the contrary,” is not good argument.
Checking in, I’m following the thread as an edification exercise in formal logic. I thought Leibniz’s and the HMHW’s argument is an epistemological proposition, that we can’t KNOW (with certainty) that this isn’t the best possible world an omnimax god can create. As a materialist, I can grant this under the ground rules of formal logic and not care, just as I don’t care about brain-in-a-vat. (Silly me, I think induction means something.) In his latest post, HMHW asserts “Leibniz’ argument establishes the metaphysical possibility of god and evil coexisting.” Well, if true, that would be interesting, but I haven’t seen it (though, admittedly, I’m working only from secondary sources). What’s the metaphysical argument?
BTW, begbert2, since I’m posting, I’'d like to point out again that just because you think free will is dead letter doesn’t make it so. For example, the IEP article on free will summarizes the current state of the debate as follows:
Which is to say that Plantinga’s defence passes the possible test. Whether it’s true is another matter. And whether it meets the evidential POE is yet another (here, I think he fails massively, and that as someone who believes in meaningful volition).
Well, my argument against free will isn’t dependent on deterministm vs. nondeterminism per se; it’s based on a computational understanding that cognition is necessarily carried out by processes that can be distilled into the two categories “determined” and “random” with no “magical sentient atomic free will particles” left over. And observational analysis that people are mostly capable of walking in a straight line proves that what randomity there is, if any, is largely corrected for by the determined processes anyway. (I’m a computer scientist; calculative processes are my forte.) I am not under the impression that the philosophers entertaining libertarian free will are accounting for this line of argument.
Regardless, Plantinga’s argument, as best I understand it, relies on God having a different kind of free will than ours, an omnibenevolent one - which leaves one asking how he was able to omnibenevolently give us broken crappy non-omnibenevolent free will, when something that would create a better result is available. If Plantinga answered this, I guess I missed it.
Actually, Plantinga’s argument doesn’t have anything to do with God’s free will. That’s just a point that has come up in the logical POE debate and I mentioned it (many days ago) as it resembled an argument Voyager had made. Rather, the fundamental thesis of Plantinga’s defense, as quoted in the IEP article, is this:
Although framed in terms of LFW, there’s no obvious reason this is necessary. I’m pretty sure my thesis of soft or psychological compatabilism would be sufficient. As would most forms of traditional compatabilism of which I’m aware. For that matter, so would your process thesis, if you allow for moral responsibility.
As I said, I think Plantinga’s defense runs into real trouble in the context of the evidential POE, including for the reason mentioned in your next-to-last sentence. A bigger problem, IMHO, are the aspects of human nature that make so many of us such crappy people. For purposes of a logical defense, though, my understanding is that none of this matters. See § 7 of the IEP article.
Well, epistemic logic is one of the more common subspecies of modal logic – it even made the wiki page.
Epistemic statements are statements about the knowledge of an agent (or a group of agents), so it can be the case that <>p, even if ~p.
Actually, I’m not sure I could. It’s not easy to capture the whole of epistemic logic in predicate logic, and I’d probably bungle it up somewhere.
Well, you can recast any modal argument in predicate logic, in principle, using what’s called the standard translation; however, this requires talk about accessibility relations, which you don’t seem to like for some reason.
Neither is asserted; both are argued to be possible. This really is the key point.
First, you say that the universe being created with time is what you mean; then, you say this, which is wildly contradictory. There is no good notion of the ‘moment’ of the big bang, anymore than there is a good notion of the location of the big bang.
Regardless of everything else, this still doesn’t follow. You’ll have to get here from there, and there might, for all we know, be only one way to do so. Claiming that the existence of one way for the universe to evolve to its present state implies the existence of another is like claiming that the sun rose yesterday implies the sun rises tomorrow; it’s just an inductive fallacy.
What I think happened at the big bang really doesn’t have anything to do with how one could define moment sensibly to obtain a state of the world. Really, you fail to appreciate just how soundly relativity abolishes naive Newtonian notions of time.
But not in such a way as to refer to the individual you and I mean when talking about Socrates – as that doesn’t exist in your world state.
What we learn if you show that my car is indeed black is that we live in a world-set in which it is possible for my car to be black. What we don’t learn is whether it is impossible for my car to be white; i.e. of the three possible world sets in which 1) my car is black in all worlds, 2) my car is white in some worlds and black in others (ignoring other colourings for the moment), 3) my car is white in all worlds, we can eliminate 3). Leibniz’ counter to the POE asserts that we may live in 2); the POE asserts we live in 1). So pointing out my car’s blackness doesn’t decide that question (though it does, of course, decide the question of what colour my car actually is; same as showing that it is possible for the world to contain less evil decides whether or not god actually is omnimax – he isn’t, in that case).
Well, it is a counterargument to any epistemic claim, of course. One could claim that from ‘Socrates is a man’ and ‘Plato is a man’, one could conclude that ‘Plato is not Socrates’, but using epistemic logic, it is rather easy to show that this doesn’t follow – with just these two bits of information, you can’t conclude that Socrates isn’t Plato. As you say, you have to bring in extra info to do so; however, even after you’ve done that, the first argument still remains fallacious. So, as far as the POE entails a claim about knowing which worlds are possible, it is only fair to point out that our knowledge is actually not good enough (and can’t be) to make that claim.
No. What you have is an overreaching assertion of knowledge.
They are also not shown to be logically possible by your saying so.
That’s the thing – I can’t. And neither can you. My definition of omnipotence is the ability to do anything that can be done. I just don’t know what exactly that is, and, despite your continuing assertions to the contrary, neither do you.
It’s not. I know, for example, that dogs lack the vocal apparatus as well as the cortical sophistication to produce speech. So I know there are no talking dog. So I know you are not one. See? Epistemic argument, nevertheless it established something about the real world. There’s great use to epistemic logic, and your denial of that, frankly, seems a bit odd.
I’ve stated it very clearly; and for a cite that you don’t have to carry around assumptions as long as they don’t change, here’s the wiki on modus tollens; see the formulation including the gammas. Now that’s of course not what I’ve been doing, but it shows that you do get unstated assumptions, at least in some cases.
Well, I’m not trying to do that, either. I’m just trying to show that the POE fails.
Come on, of course I can attack an argument without needing to talk about its conclusion! I can show the premises faulty, or find a formal flaw, neither of which necessitates any talk about the content of the argument.
Then you probably just haven’t seen very many modal arguments. Here’s one with quite liberal mixing; and hell, even the axioms of modal logic contain terms with and without operators! So I’m really not sure where you get this ‘non-mixing’ from, and frankly, it casts some doubts on your claimed mastery of modal logic.
Just the existence of god, nothing else. There’s really no controversy there.
Well, it is an elementary concept in the valuation of modal logic, so your dismissal doesn’t really mean terribly much.
Well, you did claim that I was, without backing it up in any way. Basically, you proposed a version of the POE in modal symbology, which I don’t think makes the cut, and made an argument to that effect, showing that it implies a situation in which god possibly exists, and there is evil in this world. You then said that that was not what you meant, and best as I can gather, you seem to just mean that you meant for your symbology to capture the actual POE; but that doesn’t change the fact that it doesn’t.
Damn, again? Oh well: The argument can be formalized as modus tollens from G -> ~E; so that, upon asserting E, ~G follows (and not, as in your version, ~G).
Disproof works by showing ~(G -> ~E) <-> G & <>E.
Basically, we may live in one of three world-sets:
in which, whenever there is a god, there is no evil;
in which there may or may not be evil when there is a god; and
in which there is always evil when there is a god.
The POE asserts that we live in 1); alternatively (but equivalently), it asserts that the premises a) god is omnipotent, b) god is omniscient, c) god is omnibenevolent, d) there exists evil are incompatible, since a contradiction can be derived from them. (From a), b), c) it follows that there is no evil, from d) it follows, trivially, that there is.)
This is a claim that is both metaphysical and epistemic: it asserts that we both live in 1), and know that we do (by deriving the contradiction from a, b, c, and d). The Leibniz argument now intends to show that (for all we know), we may live in either of the world sets.
In my version, it does so by noting that there are some things that god can’t accomplish (the logically impossible things), and that a priori, there is no way for us to know which things these are, by, for instance, noting that for each way that can be thought of to improve this world, one can think of a way in which this improvement might make matters worse, or be flat impossible. Plantinga’s version gives a concrete example of such an allegedly impossible thing, the existence of morally significant free will without the possibility of evil things happening (out of interest, do you agree that granting Plantinga free will, his argument works?).
The key thing to realise is that Leibniz’ account in no way settles the question of whether we live in 1), 2), or 3), and doesn’t aim to – it merely argues that it is possible for us to live in 2) (or even 3), and hence, for the metaphysical claim of the POE that we live in 1) to be false. Showing ‘we can’t know whether we live in 1), 2), or 3) a priori’ amounts to showing the POE false, as it asserts that we can know that we live in 1). Of course, it is easy to empirically establish that we don’t live in 1) or 3), but that doesn’t tell us anything about whether or not we live in 2); so as long as it’s (epistemically) possible for us to live in 2), the POE doesn’t go through. This epistemic possibility is established by noting the possibility of any given thing to be impossible to accomplish even for an omnipotent being.
And doesn’t have anything to do with the argument actually being made.