The issue I want to address is the so-called Ontological Argument for the existence of God as first proposed by St. Anselm almost a thousand yeasrs go and further developed and promoted by Muslim and Christian philosophers, including relatively recent versions by Alvin Plantinga, Kurt Gödel and others.
I was asked to write about this some time ago by a fellow commenter on Massimo Pigliucci's (now no longer active) blog 'Rationally Speaking', and I said I would. However I have been slow to do so for a couple of reasons (in addition to the usual procrastination!). The first is that the argument is so obviously nutty that it seems to be scarcely worth the time to address it. The second is that it is actually quite difficult to point out precisely what is wrong with it!
I will do my best to reproduce the argument as well as I can. It goes something like the following, although my version is somewhat simplified.
God is defined as a maximally great being.
It is greater to exist than not to exist.
Therefore any maximally great being must exist.
Therefore, by definition, God must exist.
This is often expanded to talk about existing in all possible worlds. So not only does God exist, he must exist in all possible worlds. A world without God is therefore logically incoherent.
My brain rejects this argument instinctively. It simply cannot be right. But why, exactly?
My first reaction is that a similar argument could be used to prove the existence of just about anything. I can define 'foo' as a bar of gold on my desk which exists in all possible worlds. Using similar arguments to those proposed by St Anselm, it seems that foo must exist, by definition, and yet, astoundingly, I fail to find it. From this, I conclude that existence in all possible worlds is generally an incoherent idea. Perhaps the only things that must exist in all possible worlds are the worlds themselves.
It think one answer that proponents of the ontological argument might have for me is that I'm missing something by failing to deal with the concept of maximal greatness in my analogy. I do not think this is the case: we can conceive of a maximally great beer that must exist in all possible refrigerators and see that dealing with maximal greatness directly does not make the situation much better.
Another way of looking at the problem is that we have two concepts which are mutually inconsistent: a God that exists in all possible worlds, and a Godless possible world. One of these concepts must be incoherent. Proponents of the ontological argument simply prefer the former, while opponents prefer the latter. Nothing is yet proven either way, so the ontological argument fails.
However, I find it hard to see what grounds there are to think that a Godless possible world is an incoherent concept. It seems on the face of it to be a perfectly reasonable proposition. The only argument I have seen against it is the ontological argument, but to use that would be circular.
I'm a software developer by trade, and in my view one very good way to find out if some idea is incoherent is to try to model it with code. As it happens, we run computer simulations of possible worlds all the time, often with no concept of God. When playing computer games or running scientific simulations of physical processes, I have heard of programs crashing because of attempts to divide by zero, but never have I seen an error log mentioning a GodNullException on line 42.
If I define a unicorn as a magical horselike creature with a horn on its head, I don't need to append "which exists" to this definition. No purpose is served by this meaningless elaboration. I first define "unicorn" and only then assert that unicorns exist or not. Unless a concept is logically necessary, existence is a contingent predicate, not a baked-in assumption.
I think on the whole it is better not to make the existence of a concept part of the definition of that concept. Breaking this rule can lead to the kind of logical mistakes evident in the ontological argument.
A unicorn is defined a a maximally awesome horse.
ReplyDeleteIt is more awesome to be real than not to be real.
Therefore, by definition, unicorns must be real.
Elvis is defined as a maximally perfect singer.
It is more perfect to be alive than dead.
Therefore Elvis must be alive.
Yup!
DeleteI figured out a couple of years ago that arguments for God are largely designed to give the faithful comfort for a belief they hold for emotional reasons. To work, they don't have to be logically rigorous, only sound plausible enough for people who don't want to look too closely. It's not even clear to me that the ontological argument succeeds even on that ground.
ReplyDeleteCrossing threads somewhat, wouldn't the Mathematical Universe Hypothesis and the related Level IV multiverse imply that something like a god or gods existed in some of those universes (regardless of whether he/they exists in ours)? Of course, this wouldn't be a god with master over all of reality, unless he was himself is a conscious mathematical structure authoring all the others.
Hi SAP,
DeleteWhat you say about apologetics may be true, but then it's hard to be sure that counter-apologetics are any different. Perhaps I am emotionally committed to atheism as part of my identity and seek to rationalise away any killer arguments for God.
On the MUH, there must indeed be beings that bear some resemblance to God. But they cannot be God in the sense of being omniscient or of being present in all possible worlds, as both concepts are incoherent. Where such beings are omnipotent, it can only be so within restricted domains of influence, i.e. their particular universe.
Such beings are essentially cases where the laws of physics of a particular universe happen to implement a conscious algorithm. I expect such universes to be much rarer than those which do not, as algorithms which are themselves conscious are probably much rarer than those which merely allow consciousness to evolve.
The idea of one conscious mathematical structure authoring all other conscious mathematical structures is incoherent, as mathematical structures have no authors on Platonism, only discoverers.
That's an insightful observation about counter-apologetics. We're not good at recognizing our own cognitive biases. One way to flush them out is to debate those we disagree with, which I did in my aggressive atheist stage. None of the debates ever made me seriously question my non-belief, but it did make me realize how facile some of the common atheist talking points are.
Delete"as mathematical structures have no authors on Platonism, only discoverers."
This seems like an assumption, but I can see the argument that it's inseparable from the MUH.
Playing devil's advocate for a moment, can you be sure that the mathematical universe hypothesis is not the ontological argument in disguise?
ReplyDeleteI am emotionally committed to say, yes, I am quite sure.
DeleteBut I'd be interested to hear your thoughts if you cared to elaborate!
I don't have the brain power to work it out. It just struck me that there were similarities. Both are arguments that some abstract thing must exist.
DeleteI see what you mean.
DeleteHowever I doubt that theists would agree that God is an abstract thing. They think God is more than a concept. He is a real, if not physical then spiritual entity that can interact with the physical world in some way.
Mathematical Platonism is not really an argument that any particular abstract thing must exist but rather the view that the concept of abstract existence is legitimate.
The Mathematical Universe Hypothesis is not so much an argument that some abstract thing exists either but that Mathematical Platonism is correct and that the universe (which manifestly exists) is just another abstract object.
Hey DM
ReplyDeleteThe problem is you're just giving one version of an ontological argument that looks similar to Alvin Plantinga's modal version.
I'd argue something like this
Definitions:
(D1) x is a necessary being = df x exists in every possible world
(D2) x is a contingent being = df x exists in some but not every possible world
(D3) x is a concrete being - df x exists in space and time, or at least in time.
(D4) x is an abstract being = df x does not exist in space or time.
Argument:
(P1) God is, by definition, a necessary concrete being
P2) Some necessary abstract beings exist
(P3) All abstract beings are dependent beings.
(P4) All dependent beings depend for their exists on independent beings
(P5) No contingent being can explain the existence of a necessary being
(P6) The existence of any dependent being needs to be explained
(P7) Dependent beings of any kind cannot explain their own existence
(P8) The existence of dependent beings can only be explained by beings on which they depend on their existence
From (P3) and (P4) along with (D3) and (D4) we get (C1)
(C1) All abstract beings depend for their existence on concrete beings
From (P2), (P3), and (P6) we may conclude:
(C7) The existence of necessary abstract beings needs to be explained
From (C1), (P3), (P7), and (P8) we can conclude:
(C8) The existence of necessary abstract beings can only be explained by concrete beings.
From (C7), (C8), and (P5) we may conclude:
(C9) The existence of necessary abstract beings is explained by one or more necessary concrete beings.
And from (C9) we can conclude:
(C10) A necessary concrete being exists>
QED
^which premises do you have a problem with?
Hi Cornell,
DeleteGlad you were able to comment.
Yes, I am aware there are many different versions of the argument. As I said, one reason I was so slow to comment was because I wasn't sure which version of the argument to address. The one I outlined seems to me to be quite similar to the original 'canonical' argument proposed by Anselm. The argument you present here is quite different, I think.
Firstly, I have a problem with P1, because I think that the idea of a necessary concrete being is incoherent, for reasons outlined in my post. For every concrete entity, I think there is always a possible world where that entity does not exist.
I think there is a conflict between your definition of abstract and your definition of necessary which it would be nice to clarify. Abstract entities do not exist in space or time, but necessary entities are said to exist in all possible worlds, where I take a world to be a domain of space and time. As such, the concept of necessity as stated seems to apply only to concrete objects unless the definition is amended. I think what is needed is to clarify in particular what you take abstract existence to mean.
My major problem is with P3. I would say no abstract things are dependent beings. If we take abstract objects to exist at all, then they exist independently. If we take the concept of necessity to apply to abstract objects, then I would say all abstract objects exist necessarily, and indeed that they are the only kind of objects that exist necessarily.
This is simply standard mathematical Platonism. The usual contradicting viewpoint is some sort of nominalism or physicalism which would deny that abstract objects exist at all. Views which hold that abstract objects exist but dependently are perhaps in the minority, although it might qualify as something like Aristotelian realism.
However, if we adopt Aristotelian realism, P2 would have to be false. On Aristotelian realism, abstract things exist because of how they are reflected in the physical world. However, if this is so, then abstract objects are not necessary at all, because there is always some possible world that does not reflect them.
Finally, if the ultimate conclusion is only that some necessary being exists, then why could there not be an arbitrary number of such beings, and why should any of them be anything like the concept of God? The necessary concrete being could simply be the universe or multiverse.
From my perspective, the argument has a great many problems and so it doesn't work for me at all. Could you explain to me how you would justify P2 & P3 in particular?
.
DM
DeleteGlad you were able to comment.
“Yes, I am aware there are many different versions of the argument. As I said, one reason I was so slow to comment was because I wasn't sure which version of the argument to address. The one I outlined seems to me to be quite similar to the original 'canonical' argument proposed by Anselm. The argument you present here is quite different, I think.”
^ Yes, and this is because Anselm didn’t use modal logic. This argument I’m using is by the late E.J Lowe
“Firstly, I have a problem with P1, because I think that the idea of a necessary concrete being is incoherent, for reasons outlined in my post. For every concrete entity, I think there is always a possible world where that entity does not exist.”
^ I don’t think it’s incoherent for many reasons. One reason is the fact that nothing seems to be impossible, and with that being said I can’t see why something didn’t always exist.
Secondly, the reason why I take God, if he exists, to be a concrete being in this sense is because it’s difficult to see how abstract beings could have any causal powers, including the power of creating contingent concrete beings, which God is supposed to have. To say that God exists in time is not to imply that he must change over time: he may still be eternal and immutable.
Lastly I’m not arguing for every concrete entity, I’m arguing for a NECESSARY concrete entity. With that being said we have examples of necessary abstract beings such as the natural numbers 1, 2, 3 and so on. Why should we suppose that these numbers exist? Simply because there are mathematical truths concerning them – such as the truth that 2+3= 5 – and these truths are NECESSARY truths, that is, true in every possible world. The natural numbers are truthmakers of such truths – the entities in virtue of whose existence those truths obtain – and hence those numbers must exist in every possible world, in order to make those truths obtain in every possible world.
Therefore I don’t find your criticism again P1 to be very convincing
“I think there is a conflict between your definition of abstract and your definition of necessary which it would be nice to clarify. Abstract entities do not exist in space or time, but necessary entities are said to exist in all possible worlds, where I take a world to be a domain of space and time. As such, the concept of necessity as stated seems to apply only to concrete objects unless the definition is amended. I think what is needed is to clarify in particular what you take abstract existence to mean”
^ Well all beings are either concrete or abstract, at least on the plausible assumption that a being cannot exist in space without also existing in time: the abstract/concrete distinction is exhaustive. Consequently, a being is concrete if and only if it is not abstract.
DM
Delete“My major problem is with P3. I would say no abstract things are dependent beings. If we take abstract objects to exist at all, then they exist independently. If we take the concept of necessity to apply to abstract objects, then I would say all abstract objects exist necessarily, and indeed that they are the only kind of objects that exist necessarily.”
^ I disagree, by dependent being in this context, Lowe means a being that depends for its existence on some other being or beings. This kind of dependence can be called existential dependence and may be defined (at least to a first approximation) as follows.
(D5) x depends for its existence on y = df necessarily, x exists only if y exists
(D5), however only defines the existential dependence of ONE particular entity on another. We need also to speak of the existential dependence of one kind of entity on another, which we may define (again to a first approximation) as follows, where Fs and Gs are entities of different kinds (for instance, abstract beings and concrete beings):
(D6) Fs depend for their existence on Gs = df necessarily, Fs exist only if Gs exist.
Now, if (P3) is true, it seems plausible to draw the following conclusion
(C1) All abstract beings depend for their existence on concrete beings
^QED
“This is simply standard mathematical Platonism. The usual contradicting viewpoint is some sort of nominalism or physicalism which would deny that abstract objects exist at all. Views which hold that abstract objects exist but dependently are perhaps in the minority, although it might qualify as something like Aristotelian realism.”
^ Are you a nominalist or physicalist? I can easily argue why nominalism and physicalism ultimately fail in this regard?
“However, if we adopt Aristotelian realism, P2 would have to be false. On Aristotelian realism, abstract things exist because of how they are reflected in the physical world. However, if this is so, then abstract objects are not necessary at all, because there is always some possible world that does not reflect them.”
^ No I don’t think P2 would be false simply because they would EXIST within God, as they are dependent upon God.
“Finally, if the ultimate conclusion is only that some necessary being exists, then why could there not be an arbitrary number of such beings, and why should any of them be anything like the concept of God? The necessary concrete being could simply be the universe or multiverse.”
^ because of the way abstract necessary beings relate to the necessary concrete being, this shows a rational mind as being the ultimate logician. So if the main argument is correct, then in the case of necessary abstract beings like these, the being upon which they depend for their existence and which explains their existence must be a necessary concrete being. Putting these two thoughts together – (1) that necessary abstract beings, insofar as they are objects of reason, are “mind-independent” beings, and (2) that they are dependent for their existence on a necessary concrete being – we are led to the conclusion that the being in question must be a rational being with a mind and, indeed, with a mind so powerful that it can comprehend all of mathematics and logic.
“From my perspective, the argument has a great many problems and so it doesn't work for me at all. Could you explain to me how you would justify P2 & P3 in particular?”
^ I did up above, and I think those problems have been properly dealt with, though I will continue to argue my case if needs be.
Hi Cornell,
DeleteI'm not sure what to make of your response, as it seems to me you explained a lot of stuff I understand and agree with while failing to deal with my points.
"One reason is the fact that nothing seems to be impossible"
Exactly. So if a godless universe is not impossible, then it is incoherent to say that God is in every universe. You may counter that the ontological argument shows that it is the godless universe that is incoherent, but I disagree, and now we're simply throwing assertions at each other so the argument has not achieved anything.
"I can’t see why something didn’t always exist."
I don't see what this has to do with anything. The question of eternal existence didn't come up. This would seem to have more to do with cosmological arguments.
"Secondly, the reason why I take God, if he exists, to be a concrete being in this sense"
I didn't question this. I am happy to adopt the premise that God is a concrete being. I am not happy to accept that there can be such a thing as a necessary concrete being because empty worlds are possible.
"I’m not arguing for every concrete entity"
I never thought you were.
"Why should we suppose that these numbers exist?"
As a mathematical Platonist I am more than happy to agree that numbers exist, and I agree that they exist necessarily according to your definition.
"Therefore I don’t find your criticism again P1 to be very convincing"
But almost none of that had anything to do with my criticism of P1. Your only point against my criticism of P1 is that anything is possible (which I would say includes empty or Godless universes), which as I have explained would make the idea of a necessary concrete being incoherent
For my criticism of P3, all you do is define dependence and then reassert P3 and reconclude C1.
I accept your definition of dependence but I deny that any abstract entities are dependent. In my view (mathematical Platonism) all abstract entities are necessary and independent.
On what do you think they depend, and why? If they are necessary, that means it is incoherent to suppose they might not have existed. Doesn't this mean that they need no explanation, that they are the very essence of independent?
"Are you a nominalist or physicalist?"
DeleteNeither. I am a mathematical Platonism. My statement "this is simply standard mathematical Platonism" referred to my objection to your argument, not to your argument. Mathematical Platonism holds abstract objects to be independent. I went on to discuss how your argument doesn't hold given other viewpoints such as nominalism or Aristotelian realism.
"because of the way abstract necessary beings relate to the necessary concrete being"
And what way is this? This is never explained as far as I can see. I am completely mystified as to how you see this relationship or how you can justify regarding abstract entities as dependent.
If you were claiming that abstract entities are dependent on conscious minds because they only exist if conscious minds are pondering them, I would reply that I still don't see why you need God. Abstract entities can exist when humans think about them and not exist when humans are not thinking about them. If you argue that this doesn't work because mathematical relations hold even without humans to think about them, then I agree, but I would say they also hold even if God isn't thinking about them or even existing at all.
But this seems not to be your view, because you later claim (and I agree) that abstract entities are mind-independent. But if this is the case, then why must there be an ultimate logician? You again reassert that abstract entities are dependent for their existence on a concrete independent being, but I see no justification of this view whatsoever.
DM
Delete"Are you a nominalist or physicalist?"
“Neither. I am a mathematical Platonism. My statement "this is simply standard mathematical Platonism" referred to my objection to your argument, not to your argument. Mathematical Platonism holds abstract objects to be independent. I went on to discuss how your argument doesn't hold given other viewpoints such as nominalism or Aristotelian realism.”
^ Good, great minds definitely think alike! Anyways, I don’t think mathematical Platonism causes a problem for me e, in fact I’m a mathematical Platonist myself. In the 2014 book ‘Beyond the Control of God?: Six Views on The Problem of God and Abstract Objects’ there are philosophers who would argue like I do, the fact that a God who is independent of abstract objects, would fall to the ultimacy problem. Consider one kind of abstract, property. If properties exist independently of God, and God has properties essentially, then God’s nature is explained by some other entity, and God is not ultimate. As Brian Leftow would argue, for a Theist like myself I would definitely want all explanations to come back trace back to God, rather than through God to some more ultimate context.
“And what way is this? This is never explained as far as I can see. I am completely mystified as to how you see this relationship or how you can justify regarding abstract entities as dependent.”
What was wrong with C1? Well let me go more into this on my next comment
“If you were claiming that abstract entities are dependent on conscious minds because they only exist if conscious minds are pondering them, I would reply that I still don't see why you need God. Abstract entities can exist when humans think about them and not exist when humans are not thinking about them. If you argue that this doesn't work because mathematical relations hold even without humans to think about them, then I agree, but I would say they also hold even if God isn't thinking about them or even existing at all.”
^ I don’t think even SOME abstract objects can exist independently as abstract beings and hereis why. Lowe argues that according to one position in the philosophy of mathematics, numbers are to be understood as being set-theoretical entities. For instance, it may be proposed that the number 0 is identical with the so-called empty set, ∅, that the number 1 is identical with the unit set of the unit set of the empty set, {{∅}}, and so on ad infinitum. Now,in this view, it seems clear that each number except for the number 0 depends for its existence on all of the preceding numbers in the series of natural numbers, simply because any set depends for its existence on its members. But it may be contended that the number 0, here taken to be the empty set, does not depend for its existence on anything else at all. However, I think we ought to be skeptical about the very existence of the so-called empty set: I believe that it s a mere mathematical fiction. After all, how could there really be any such thing as a set with no members, when what a set is, according to our common understanding, is something that ‘collects together” certain other things, these things being its members. How could something “collect together” nothing?
“But this seems not to be your view, because you later claim (and I agree) that abstract entities are mind-independent. But if this is the case, then why must there be an ultimate logician? You again reassert that abstract entities are dependent for their existence on a concrete independent being, but I see no justification of this view whatsoever.”
^ Abstract entities are mind-independent to humans who are contingent concrete beings, but like I said the existence of abstract necessary beings is dependent upon an ultimate mind itself, because humans are CONTINGENT beings, whilst God is not. This is where we go back to the ultimacy point about God.
“Hi Cornell,
DeleteI'm not sure what to make of your response, as it seems to me you explained a lot of stuff I understand and agree with while failing to deal with my points.”
^ We seem to disagree on the ultimacy point.
“Exactly. So if a godless universe is not impossible, then it is incoherent to say that God is in every universe. You may counter that the ontological argument shows that it is the godless universe that is incoherent, but I disagree, and now we're simply throwing assertions at each other so the argument has not achieved anything.”
^ Possible world semantics doesn’t speak in the sense of ‘possible universes’ in the way you are describing them, as you aren’t considering ‘local’ and ‘global’ modalities here.
Pace Alex Pruss, it is (metaphysically) possible that p providing there is a world w at which p is true. It is (metaphysically) necessary that p providing p is true at every world. This yields the standard duality between possibility and necessity: p is possible if and only if ~p is not necessary. Possible worlds now let us consider ‘local’ and ‘global’ modalities in a uniform way.
When one says ‘Hitler might not have existed’ in an ordinary way, and not by way of stating a merely metaphysical possibility, I am saying that the proposition, that Hitler does not exist is true at some world that matches our in various relevant respects.
“I don't see what this has to do with anything. The question of eternal existence didn't come up. This would seem to have more to do with cosmological arguments.”
^ The ontological argument has similarities with Leibnizian Cosmological arguments.
Necessary existence is an essential part of God’s nature, here are two reasons why:
First, whatever is contingent must have some explanation for its existence, so if God were contingent he'd be dependent on another and thus is not worthy of even the ‘definition’ of God, because for all we know there could be a being in which this said ‘God’ is contingent upon for its very own existence.
Second God must be omnipotent bc obviously this is a perfection; hence God must be able to actualize any sufficiently good state of affairs...but if he existed only in some worlds and not others he would not be able to actualize the good states of affairs in those other worlds since he doesn't exist in them.
“I didn't question this. I am happy to adopt the premise that God is a concrete being. I am not happy to accept that there can be such a thing as a necessary concrete being because empty worlds are possible.”
^ But those empty worlds would eventually have a God that resides in them as well, as God is not a contingent being.
DM (part 3)
Delete“I never thought you were.”
^ Ok
“As a mathematical Platonist I am more than happy to agree that numbers exist, and I agree that they exist necessarily according to your definition.”
^ Good position, let me know when you want to argue against nominalists and materialists, If I was an atheist, I'd probably hold to your views on the nature of reality,
“But almost none of that had anything to do with my criticism of P1. Your only point against my criticism of P1 is that anything is possible (which I would say includes empty or Godless universes), which as I have explained would make the idea of a necessary concrete being incoherent”
^ I never said anything is possible, for instance I don’t think square circles are possible, so I don’t know where you got that from.
“For my criticism of P3, all you do is define dependence and then reassert P3 and reconclude C1.
I accept your definition of dependence but I deny that any abstract entities are dependent. In my view (mathematical Platonism) all abstract entities are necessary and independent.”
^ Again, I’m not talking about the relation between abstract beings (either necessary or contingent) and contingent concrete beings. Humans, which are contingent concrete beings don’t ground existence itself, so they obviously don’t ground necessary abstract beings.
“On what do you think they depend, and why? If they are necessary, that means it is incoherent to suppose they might not have existed. Doesn't this mean that they need no explanation, that they are the very essence of independent?”
^ I’d argue that they definitely need an explanation, in fact that’s what (C7) suggests,
(C7) The existence of necessary abstract beings needs to be explained.
This is supported by the fact that an entity x depends for its existence on an entity y does not imply that y explains the existence of x. Similarly, the fact that Fs depend for their existence on Gs does not imply that Gs explain the existence of Fs. That is to say, Existence-explanation is not simply the inverse of existential dependence. If x depends for its existence on y, this only means that x cannot exist without y existing. This is not at all the same as saying that x exists because y exists, or that x exists in virtue of the fact that y exists. So the mere fact that, by (C5), necessary abstract beings cannot exist without concrete beings existing doesn’t imply that concrete beings of just any kind, necessary or contingent, can explain the existence of necessary abstract beings. This is why we have (P7), (P8), and (P3), together with (C1) concludes into (C8) The existence of necessary abstract beings can only be explained by concrete beings.
"In my view (mathematical Platonism) all abstract entities are necessary and independent"
DeleteI don't think I addressed this enough,
An example of a contingent abstract being would be a set all of whose members are contingent beings, such as the set of all existing horses.
Hi Cornell,
Delete"What was wrong with C1? Well let me go more into this on my next comment"
Nothing really. P3 is the problem. But even granting C1, I don't know what kind of dependence you are talking about. Explain to me how the dependence works, how the concrete being brings the abstract beings into existence.
"How could something “collect together” nothing?"
Why are you using it as a verb? Nobody needs to collect together a set. A set just exists. The set of my ex-wives, which has cardinality zero, does not need to be actively collected. That is not mysterious to me.
Besides, sets are not really collections of things. Yes, that is how they are usually explained, and for all intents and purposes it is usually reasonable to hold them to be collections of things. However, mathematical sets are actually abstract entities defined by precise definitions. This definition happens to map pretty closely to the intuitive notion of a collection of things, but there may be cases where differences can be found, as you have pointed out.
All abstract entities which are well defined exist and the empty set is no different. I think you can forget the semantics of what abstract objects are about and regard them simply as symbolic definitions without semantics and rules with which to manipulate them. The empty set obeys all the rules of set theory. The empty set intersected with a set U gives the empty set. The empty set union a set U gives the set U. The cardinality of the empty set is 0. Its behaviour can be well understood and there is nothing incoherent about it.
It seems to me you are saying that you don't think the empty set is really a true set in the intuitive interpretation of the word because you think sets ought to have elements. That's OK, I have no problem with that. But just because it's not really an intuitive set doesn't mean that it isn't a legitimate, existing mathematical object. Mathematical objects are not slaves to our intuitions. They are entities with rigid unambiguous definitions, and anything so defined exists abstractly, including the empty set.
I don't think the other numbers depend on zero any more than zero depends on them. I think the system of numbers and of sets exists as a whole. The concept of zero would make no sense without the concept of one.
More later...
"but like I said the existence of abstract necessary beings is dependent upon an ultimate mind itself,"
DeleteI don't think you have really explained why this must be. You have explained why you think the empty set is fictional, but that doesn't explain to me how an ultimate mind makes sets real.
For the record, I'm perfectly happy to accept that all mathematical objects are fictional. Fictional existence and abstract existence are pretty much the same thing in my book. I just think that fictional existence is a legitimate kind of existence.
I don't understand why you think the ultimacy point should be of relevance to me, as an atheist. As you have articulated it, the ultimacy point is simply that you will not be happy with any account of God that does not hold him as the ultimate explanation for everything. As an atheist, I have no such commitment, so the ultimacy point cannot be used to persuade me of anything. If God must by definition be the ultimate, that's fine by me but since I don't believe that God exists I am free to believe in the existence of things independently of God.
"Possible world semantics doesn’t speak in the sense of ‘possible universes’ in the way you are describing them"
I disagree. I think I understand them correctly. Again, you explain at length something I already understand and agree with by outlining Alex Pruss's account of possible worlds. If you think I understand these concepts incorrectly, please show specifically where I have erred.
If by local and global modalities you think I don't understand the difference between possible and necessary, I think you're wrong. You are asserting that it seems to be coherent to suggest that there is a necessary concrete being. This is the same as the claim that there is no possible world which does not include this necessary concrete being. I don't buy that. It is not hard to conceive of worlds which are completely empty, and I don't see why they should not be possible.
As with the ultimacy argument, I'm not particularly interested in debating the theology of God's nature where it doesn't directly pertain to the ontological argument. Since there is no compelling reason to believe that God exists, in my view, I'll leave the discussions on what his nature must be to after you have convinced me of the validity of the ontological argument, if you don't mind. I'm willing to take whatever you say about God at face value until then. I am happy to assume for the sake of discussion that God, if He exists, is eternal, necessary, ultimate, etc. I just don't think he exists.
"But those empty worlds would eventually have a God that resides in them as well, as God is not a contingent being."
But now you're just assuming that God is not contingent because you have defined him as necessary. You can't define concrete things into existence. If I define an eternally godless world, that world will remain godless by definition. One of our concepts has to go. Why should I prefer yours?
Delete"I never said anything is possible, for instance I don’t think square circles are possible, so I don’t know where you got that from. "
Let me refresh your memory:
"One reason is the fact that nothing seems to be impossible"
I took you to mean that no incoherent concepts are impossible. Please read me as charitably.
" I’d argue that they definitely need an explanation, in fact that’s what (C7) suggests,"
That doesn't help, since C7 and the premises from which it is derived ware what I dispute.
I understand the difference between dependence and explanation. However, I hold that necessity is its own explanation. Whatever is necessarily true needs no further explanation and is not dependent on anything else.
"An example of a contingent abstract being would be a set all of whose members are contingent beings, such as the set of all existing horses."
The most interesting point you've made in my view. My answer is that such a set is not really a set of horses. It is a set of abstract elements which correspond to horses. Such a set would exist even without any horses at all, though in such a world the set referred to by the phrase "all existing horses" would be a different set, namely the empty set. Mathematical objects which are isomorphic to each other (sharing the same structure so that they can be mapped freely onto each other) are really the same structure, so the set of 5 apples is the same as the set of 5 oranges as long as that is the fullest extent of the mathematical system we are considering. If we are considering a system containing both the set of 5 oranges and the set of 5 apples, they are no longer the same set, as they cannot be swapped without changing the state of the system.
The correspondence is getting rather long.
DeleteLet me just underscore the crucial point I am missing in your account of the ontological argument. I understand that you have tried to answer the question before, but for the reasons I have provided I do not find your answers to be compelling or relevant to my problem.
The question is this:
Why should I, as an agnostic, believe that abstract entities, which we agree are necessary, are dependent on any concrete entity?
DM
Delete“Nothing really. P3 is the problem. But even granting C1, I don't know what kind of dependence you are talking about. Explain to me how the dependence works, how the concrete being brings the abstract beings into existence.”
^If we grant C1 then there should be no problem with P3 because we get C1 from P3 and P4 with definitions D3 and D4. All I’m aiming for is the fact that all of the premises are individually considerably less controversial than its conclusion, and I shoot for mutual consistency.
“Why are you using it as a verb? Nobody needs to collect together a set. A set just exists. The set of my ex-wives, which has cardinality zero, does not need to be actively collected. That is not mysterious to me.”
^ I’m using it as a verb because I’m skeptical of the existence of an empty set.
because there are some who contend my argument and argue that the number 0, here is taken to be the empty set, that does not depend for its existence on anything else at all.
“Besides, sets are not really collections of things. Yes, that is how they are usually explained, and for all intents and purposes it is usually reasonable to hold them to be collections of things. However, mathematical sets are actually abstract entities defined by precise definitions. This definition happens to map pretty closely to the intuitive notion of a collection of things, but there may be cases where differences can be found, as you have pointed out.”
^ Ok so what exactly is wrong with P3 then? I still don’t see how an empty set negates it, as I’ve argued in P3 (all abstract beings are dependent beings) and by a dependent being, in this context, I mean a being that depends for its existence on some other being or beings.
“All abstract entities which are well defined exist and the empty set is no different. I think you can forget the semantics of what abstract objects are about and regard them simply as symbolic definitions without semantics and rules with which to manipulate them. The empty set obeys all the rules of set theory. The empty set intersected with a set U gives the empty set. The empty set union a set U gives the set U. The cardinality of the empty set is 0. Its behaviour can be well understood and there is nothing incoherent about it.”
^So, are you saying that at least some or possibly all abstract entities depend only on other abstract beings for their existence?
It seems to me you are saying that you don't think the empty set is really a true set in the intuitive interpretation of the word because you think sets ought to have elements. That's OK, I have no problem with that. But just because it's not really an intuitive set doesn't mean that it isn't a legitimate, existing mathematical object. Mathematical objects are not slaves to our intuitions. They are entities with rigid unambiguous definitions, and anything so defined exists abstractly, including the empty set.”
^ But don’t you think that these definitions still reflect how reality, really is? And yeah I wouldn’t think most metaphysicians would agree with Lowe and I with respect to P3 as qualifying as a relatively safe assumption, though I guess I could Lowe’s ‘The Possibility of Metaphysics’ and see how he defends this deeper, as this was in the footnote.
“I don't think the other numbers depend on zero any more than zero depends on them. I think the system of numbers and of sets exists as a whole. The concept of zero would make no sense without the concept of one.”
^ Well I don’t know if that’s a problem for me, because I can allow the fact that a dependent being may depend for its existence on other dependent being, provided that, via some finite chain of dependence, it ultimately depends for its existence on one more independent beings. We need to bear in mind here that the relation of existential dependence is a transitive relation: if x depends for its existence on y and y depends for its existence on x, then x depends for its existence on z.
“I don't think you have really explained why this must be. You have explained why you think the empty set is fictional, but that doesn't explain to me how an ultimate mind makes sets real.”
Delete^well with respect to an ultimate mind making sets real I’d argue that an abstract being, it would seem, is one which, by its very nature, is in some sense abstracted from – literally, “drawn out, or away from” – something else. To that extent, then, any such being may reasonably be supposed to depend for its existence on that from which it is ‘abstracted’.
“For the record, I'm perfectly happy to accept that all mathematical objects are fictional. Fictional existence and abstract existence are pretty much the same thing in my book. I just think that fictional existence is a legitimate kind of existence.”
^ How is fictional existence a legitimate kind of existence?
“I don't understand why you think the ultimacy point should be of relevance to me, as an atheist. As you have articulated it, the ultimacy point is simply that you will not be happy with any account of God that does not hold him as the ultimate explanation for everything. As an atheist, I have no such commitment, so the ultimacy point cannot be used to persuade me of anything. If God must by definition be the ultimate, that's fine by me but since I don't believe that God exists I am free to believe in the existence of things independently of God.”
^ Right, but God’s existence doesn’t depend on whether or not you believe in him. I think that every Theist needs to argue for the coherency of Theism before making a case for Theism being true in itself, and that is exactly what I’m doing here. So maybe you’re an atheist now who thinks Theism is incoherent, and false, well if I can get you to coherency and false then perhaps I’ve made progress. If you think Theism is coherent and false right now, then at least I’m giving you another way to think about how Theism could be true. So either way I still think this is relevant to the discussion.
“I disagree. I think I understand them correctly. Again, you explain at length something I already understand and agree with by outlining Alex Pruss's account of possible worlds. If you think I understand these concepts incorrectly, please show specifically where I have erred.
If by local and global modalities you think I don't understand the difference between possible and necessary, I think you're wrong. You are asserting that it seems to be coherent to suggest that there is a necessary concrete being. This is the same as the claim that there is no possible world which does not include this necessary concrete being. I don't buy that. It is not hard to conceive of worlds which are completely empty, and I don't see why they should not be possible.”
^ But that’s where you objection doesn’t work, look at (C5)
(C5) In every possible world there exists concrete beings
What (C5) means is that there is no ‘empty world’ – a world devoid of anything existing in space and time. However, there are two different reasons for which (C5) could be true.
One possibility is that (C5) is true because there is a necessary concrete being – a concrete being that exists in every possible world. This, of course, is what I should like to prove to be the case. And, indeed, it is because (C5) is true that we have at least prima facie reason to believe that the following is true (or, at least, not to reject it out of hand as false):
(C6) a necessary concrete being is possible
But another possibility is that (C5) is true just because in every possible world there exist contingent concrete beings – different ones in different worlds. This is just where I get warmed up.
DM
Delete“As with the ultimacy argument, I'm not particularly interested in debating the theology of God's nature where it doesn't directly pertain to the ontological argument. Since there is no compelling reason to believe that God exists, in my view, I'll leave the discussions on what his nature must be to after you have convinced me of the validity of the ontological argument, if you don't mind. I'm willing to take whatever you say about God at face value until then. I am happy to assume for the sake of discussion that God, if He exists, is eternal, necessary, ultimate, etc. I just don't think he exists.”
^ There are plenty of good reasons to think a necessary concrete being like God exists
(P5) No contingent being can explain the existence of a necessary being
A necessary being is, by definition (D1), a being that exists in every possible world, whereas a contingent being is, by definition (D2), a being that exists in some but not every possible world.
Suppose, then, that N is a certain necessary being (e.g., number 8) and that C is a certain contingent being (e.g.’ Mount Everest). How could C explain N’s existence? After all, N exists in possible worlds in which C does not exist – so C evidently cannot explain N’s existence in those possible worlds. But how, then, can C explain N’s existence even in worlds in which C does exist? For what C would have to explain is why N, a necessary being, exists in those worlds, that is, a being that exists in every possible world. Therefore, it would, apparently, thereby have to explain why N exists also in worlds in which C does not exist, which we have already ruled out as impossible.
"But those empty worlds would eventually have a God that resides in them as well, as God is not a contingent being."
“But now you're just assuming that God is not contingent because you have defined him as necessary. You can't define concrete things into existence. If I define an eternally godless world, that world will remain godless by definition. One of our concepts has to go. Why should I prefer yours?”
^ This won’t work because you have a total misunderstanding of this ontological argument. The point of the OA is not to bring something into existence through a definition. Rather, the point is that the concept of God is such that it requires recognizing that He necessarily exists. The definition is supposed to make us see reality, not create it.
“The correspondence is getting rather long.
Let me just underscore the crucial point I am missing in your account of the ontological argument. I understand that you have tried to answer the question before, but for the reasons I have provided I do not find your answers to be compelling or relevant to my problem.
The question is this:
Why should I, as an agnostic, believe that abstract entities, which we agree are necessary, are dependent on any concrete entity?”
^ I went over this in the beginning of this comment 7 May 2014 03:11.
I will go more into it in my next response
Week is getting busy, so I will not be able to reply as fast as I was.
DeleteThanks for the debate though, I enjoy the sparring as you are a worthy opponent.
Dm. I was thinking more about the existence of empty sets and I think the acceptence of them makes a case for nihilism, are you a nihilist?
Deletei Cornell,
Delete"If we grant C1 then there should be no problem with P3 because we get C1 from P3"
What I mean is that I don't have a problem with C1 given P3, but I have a problem with P3 so I don't accept C1.
"Ok so what exactly is wrong with P3 then? I still don’t see how an empty set negates it,"
It doesn't, but it seemed to me you were offering the non-existence of the empty set as a defense of P3. I neither accept the non-existence of the empty set nor see its relevance to P3.
What is wrong with P3 is simply that I don't accept it. I think abstract objects are necessary and independent of any concrete entity, and I can't imagine how they could be both necessary and dependent on concrete entities.
"So, are you saying that at least some or possibly all abstract entities depend only on other abstract beings for their existence?"
I suppose so but I wouldn't think in terms of dependency. In my view, dependency is not a relevant concept for necessary things. Necessary things cannot help but exist. Whether they are independent or dependent on each other is just two ways of looking at it. Is the concept of truth dependent on the concept of falsity or vice versa or are they mutually dependent or is the system of truth and falsity a coherent independent whole? I would lean towards the latter interpretation, but I think it's all just different ways of describing the same situation and there is no fact of the matter.
"But don’t you think that these definitions still reflect how reality, really is?"
They often do, but not necessarily. There are various different kinds of space in geometry, and not all of them describe the physical space we see around us.
"I wouldn’t think most metaphysicians would agree with Lowe and I with respect to P3 as qualifying as a relatively safe assumption"
DeleteIf so, then you can appreciate why I don't find Lowe's version of the ontological argument convincing.
"We need to bear in mind here that the relation of existential dependence is a transitive relation:"
OK, but your argument was to place zero as the root of the natural numbers and then to argue that zero must be dependent on something else. I responded that zero is just as dependent on one as one is on zero, so there is no root. In this view, dependence of numbers is not only transitive but symmetrical - x depends on y and y depends on x. As such, there is no single root that needs an external entity to explain its existence. Alternatively, if dependence is defined so as to rule out such symmetry, the numbers are independent. Either way, the set of numbers as a whole exists necessarily and independently of any concrete entity.
"To that extent, then, any such being may reasonably be supposed to depend for its existence on that from which it is ‘abstracted’."
Arguments from etymology do not convince me, I'm afraid. What I mean by "abstract" is not something "drawn out" from something concrete. I simply mean something which is not concrete.
"How is fictional existence a legitimate kind of existence?"
The character of Sherlock Holmes exists fictionally. We can talk about his fictional appearance, his fictional biography, attitudes, aptitudes and failings. He may not be a physical person, but he exists as a concept. Fictional existence is the same as abstract existence.
"if I can get you to coherency"
Theism is a broad concept with many variants. Some kinds of theism are certainly coherent. Some beliefs of some theists are not. But we're not debating the coherency of theism, we're debating the coherency of the ontological argument.
"But that’s where you objection doesn’t work, look at (C5)"
DeleteBut I don't accept C5.
Incidentally, you didn't list C5. I don't know what it depends on but I suspect it depends on premises which I reject.
I also don't accept C6, by the way.
Your argument about Everest and the number 8 is, yet again, explaining to me something I understand and agree with while missing my point. I accept P5. Indeed, it is obvious that no contingent being can explain the existence of a necessary being. But this doesn't get you to what you're trying to show, which is that there "are plenty of good reasons to think that a necessary concrete being exists". This is because I don't think any concrete being explains the existence of any necessary being.
"This won’t work because you have a total misunderstanding of this ontological argument. "
I don't misunderstand it. Of course I know that you are not trying to conjure God into existence. What I mean by "you can't define concrete things into existence" is that you can't use a definition which asserts that a concrete thing exists to prove that it exists. To define God as a nesssary concrete being is simply to assert that God exists in all possible worlds. To define a godless possible world is simply to assert that it is possible that God does not exist in all possible worlds. Again, one of these definitions must be incoherent. Why should I prefer yours?
"Why should I, as an agnostic, believe that abstract entities, which we agree are necessary, are dependent on any concrete entity?”
^ I went over this in the beginning of this comment 7 May 2014 03:11. "
You mean the argument from etymology? I need more than that, I'm afraid. Could you put together some sort of syllogism?
"I was thinking more about the existence of empty sets and I think the acceptence of them makes a case for nihilism, are you a nihilist?"
It depends what you mean by nihilist.
Firstly, I think that the existence of the empty set has nothing to do with nihilism. I can only imagine you may be thinking that since I believe in the empty set, I believe in nothing, which makes me a nihilist. But that is to confuse believing in the concept of nothingness with not believing in anything.
My beliefs with regard to nihilism are that there is no such thing as objective moral truth, and that there is no purpose to the universe.
However, I have a set of moral values I believe in subjectively and would fight for. In the right circumstances, I might die for them. My own purpose is simply that which guides me through my life, which is to live to the best of my ability to seek happiness while upholding my values to the best of my ability, so trying to contribute to society, developing myself, being kind to those around me, doing good work, etc.
Thanks for the discussion, Cornell. We can return to it whenever you have time.
DM
Delete“What I mean is that I don't have a problem with C1 given P3, but I have a problem with P3 so I don't accept C1.”
^ Gotcha
“It doesn't, but it seemed to me you were offering the non-existence of the empty set as a defense of P3. I neither accept the non-existence of the empty set nor see its relevance to P3.
What is wrong with P3 is simply that I don't accept it. I think abstract objects are necessary and independent of any concrete entity, and I can't imagine how they could be both necessary and dependent on concrete entities.”
^ Well I’d still argue the fact that we should be skeptical of the existence of empty sets, this was actually put forth as a summary with respect to Lowe’s book. As Lowe says, the only universals which could exist in a world with
no concrete entities would be universals whose instances are abstract particulars, i.e. sets.
But sets cannot exist if their members do not exist. Now, as a consequence of his
rejection of the empty set, Lowe admits only impure sets, whose members are non-sets.
So a world in which only abstract objects exist would be a world where the only non-sets
are universals whose particular instances are sets. But this is impossible, according to
Lowe, ‘for in such a world the sets depend for their existence upon the universals and the
universals depend for their existence upon the sets, creating a vicious circle which
deprives both universals and sets of the possibility of existence’ (1998: 254). So, Lowe
concludes, there cannot be a world which only contains universals and sets and hence
there cannot be a world in which only abstract objects exist. Thus abstract objects depend
for their existence upon that of concrete entities – for if there are abstract objects there are
concrete entities.
“I suppose so but I wouldn't think in terms of dependency. In my view, dependency is not a relevant concept for necessary things. Necessary things cannot help but exist. Whether they are independent or dependent on each other is just two ways of looking at it. Is the concept of truth dependent on the concept of falsity or vice versa or are they mutually dependent or is the system of truth and falsity a coherent independent whole? I would lean towards the latter interpretation, but I think it's all just different ways of describing the same situation and there is no fact of the matter.”
^ Well if you did then I would take this as problematic then, because it would imply that, where abstract beings are concerned, there can be either circles of existential dependence or infinite descending chains of existential dependence, with the consequence that the existence of some or all abstract entities is not property grounded. Lowe would rule this out explicitly by invoking another premise.
(P4) All dependent beings depend for their existence on independent beings. Lowe calls this the axiom of foundation, by analogy with a similar principle in set theory.
“They often do, but not necessarily. There are various different kinds of space in geometry, and not all of them describe the physical space we see around us.”
^ Right, well as long as some do then I’m fine.
DM
Delete“If so, then you can appreciate why I don't find Lowe's version of the ontological argument convincing.”
^ Sure, I think I see a few spots where you and I disagree, while I don’t think it’s gamebreaking to the actual argument, I do admit that it is a bit controversial, and I’d like for this argument to have more force, so I’d have to get his book on metaphysics to understand him a bit more with respect to empty sets. I think I could use his arguments against nihilists as well. (nihilists with respect to concrete entities)
“OK, but your argument was to place zero as the root of the natural numbers and then to argue that zero must be dependent on something else. I responded that zero is just as dependent on one as one is on zero, so there is no root. In this view, dependence of numbers is not only transitive but symmetrical - x depends on y and y depends on x. As such, there is no single root that needs an external entity to explain its existence. Alternatively, if dependence is defined so as to rule out such symmetry, the numbers are independent. Either way, the set of numbers as a whole exists necessarily and independently of any concrete entity.”
Well I’m just bringing that up, because one position in the philosophy of mathematics holds to position that numbers are to be understood as being set-theoretical entities. Anyways, when you say ‘As such, there is no single root that needs an external entity to explain its existence’ do you think I’m talking about causal considerations? When Lowe speaks of existence-explanation, he does not mean causal explanation, but only metaphysical explanation.
“Arguments from etymology do not convince me, I'm afraid. What I mean by "abstract" is not something "drawn out" from something concrete. I simply mean something which is not concrete.”
^ I don’t know if it really comes down to etymology, however that’s the whole gist of this argument, in fact I think this is where the theological implications of the argument really show its face, that is to say, Pace E.J Lowe, all of the most plausible examples of abstract beings are, interestingly enough, entities that are, in a broad sense, objects of reason – such entities as numbers, sets, and propositions. They are all objects that stand in rational relations to one another, such as mathematical and logical relations. Arguably, however, it does not make sense to think of such entities as existing and standing in such relations independent of some actual or possible mind that could contemplate and understand them. But then we have a very good candidate for the sort of being “from” which such entities may be supposed to be somehow “abstracted”: namely, a mind of some kind, upon which they would thereby depend for their existence. But if Lowe’s argument is correct, then in the case of necessary abstract beings like these, the being upon which they depend for their existence and which explains there existence must be a necessary concrete being.
“The character of Sherlock Holmes exists fictionally. We can talk about his fictional appearance, his fictional biography, attitudes, aptitudes and failings. He may not be a physical person, but he exists as a concept. Fictional existence is the same as abstract existence.”
^ Oh, I see what you’re saying, and I agree on the point that some fictional things, or maybe most fictional things can be the same as abstract existence, however I don’t think that all things are fictional, in fact, I’ll use math as an example I can’t see Einstien being as successful as he was if he did E=m3 rather than E=mc2.
“Theism is a broad concept with many variants. Some kinds of theism are certainly coherent. Some beliefs of some theists are not. But we're not debating the coherency of theism, we're debating the coherency of the ontological argument.”
Delete^ Right, but I think either way this still has theological implications on the conclusion, I went over this in this reply.
“Your argument about Everest and the number 8 is, yet again, explaining to me something I understand and agree with while missing my point. I accept P5. Indeed, it is obvious that no contingent being can explain the existence of a necessary being. But this doesn't get you to what you're trying to show, which is that there "are plenty of good reasons to think that a necessary concrete being exists". This is because I don't think any concrete being explains the existence of any necessary being.”
I think I can address this by pointed to other premises, Now, while I’d argue that while there may be no need to explain the existence of a necessary being that is an independent being that is an independent being, I think that the existence of dependent beings does always call for explanation.
And this is where I think C5, and C6 holds the most force.
Take P6,
(P6) The existence of any dependent being needs to be explained
Now if I recall your major problem was not with P2, but P3, so we I’d argue that by endorsing P2, that some necessary abstract beings – such as the numbers – exist and that, by P3, these are all dependent beings. So, with the additional help of P6, I can now infer
(C7) The existence of necessary abstract beings needs to be explained.
Observe, next, that the fact that an entity x depends for its existence on a an entity y does not imply that y explains the existence of x. Similarly, the fact that Fs depend for their existence on Gs does not imply that Gs explain the existence of Fs. Existence-explanation is not simply the inverse of existential dependence. I think I said this before, but if I didn’t I’ll go over it again. If x depends for its existence on y, this only means that x cannot exist without y existing. This is not at all the same as saying that x exists because y exists, or that x exists in virtue of the fact that y exists. So the mere fact that, by (C5), necessary abstract beings cannot exist without concrete beings existing doesn’t imply that concrete beings of just any kind, necessary or contingent, can explain the existence of necessary abstract beings. Indeed, I think I’ve argued good reasons to uphold P5, in fact you said that you accepted it, (that no contingent being can explain the existence of a necessary being. At the same time, it is clear that only concrete beings of some kind can explain the existence of necessary abstract beings since the latter, being one and all dependent beings, cannot explain their own existence.
(P7) Dependent beings of any kind cannot explain their own existence
So it seems clear that
(P8) The existence of dependent beings can only be explained by beings on which they depend for their existence.
From (P7), (P8), and (P3), together with (C1), I can now conclude
(C8) The existence of necessary abstract beings can only be explained by concrete beings.
And from (C7), (C8), and (P5) we may conclude
(C9) The existence of necessary abstract beings is explained by one or more necessary concrete beings
From (C9) we may finally infer my desired conclusion
(C10) A necessary concrete being exists
I see this as a pretty strong argument for the existence of God, in fact I think a good number of Ontological arguments (Godel’s, version, Maydole’s version) are also solid.
“I don't misunderstand it. Of course I know that you are not trying to conjure God into existence. What I mean by "you can't define concrete things into existence" is that you can't use a definition which asserts that a concrete thing exists to prove that it exists. To define God as a nesssary concrete being is simply to assert that God exists in all possible worlds. To define a godless possible world is simply to assert that it is possible that God does not exist in all possible worlds. Again, one of these definitions must be incoherent. Why should I prefer yours?”
DeleteBut I’m not arguing that, You’re bringing up an MGB argument that starts everything off with that premise, but even if I did argue for that you wouldn’t get anywhere as an atheist, because you’d have to hold to equipollence with respect to both conclusions. This argument I’m using swerves around that, (unlike Plantinga’s) because something exists now, and nothing is impossible. C5 also argues for every possible world having concrete beings, and I’ve already went over why it’s implausible to assert an ‘empty world’. So you should prefer mine, because something necessarily exists, and if you want to call it the universe then I’m going to need reasons on why the theological implications that I gave for how a necessary concrete being relates to abstract objects makes less sense than whatever alternative you’re proposing.
“You mean the argument from etymology? I need more than that, I'm afraid. Could you put together some sort of syllogism?”
I went over it a bit more in 8 May 2014 02:49
“It depends what you mean by nihilist.”
^ By Nihilism I shall understand the thesis that it is metaphysically possible that there
are no concrete objects.
“Firstly, I think that the existence of the empty set has nothing to do with nihilism. I can only imagine you may be thinking that since I believe in the empty set, I believe in nothing, which makes me a nihilist. But that is to confuse believing in the concept of nothingness with not believing in anything.”
I think it does, are you familiar with the subtraction argument for nihilism?
Rodriguez-Pereyra, G. 1997. There might be nothing: the subtraction argument improved.
Analysis 57: 159−66.
“My beliefs with regard to nihilism are that there is no such thing as objective moral truth, and that there is no purpose to the universe.”
^To me, that would be moral nihilism
“However, I have a set of moral values I believe in subjectively and would fight for. In the right circumstances, I might die for them. My own purpose is simply that which guides me through my life, which is to live to the best of my ability to seek happiness while upholding my values to the best of my ability, so trying to contribute to society, developing myself, being kind to those around me, doing good work, etc.”
Yeah we can argue morality some other time
“Thanks for the discussion, Cornell. We can return to it whenever you have time.”
^No problem, I’m glad to engage this as it made me very aware of nihilism.
"God is defined as a maximally great being.
ReplyDeleteIt is greater to exist than not to exist.
Therefore any maximally great being must exist.
Therefore, by definition, God must exist."
To be honest, I don't think I've ever seen anyone defend this, as even Plantinga would argue something like this
1. It is possible that a maximally great being exists.
2. If it is possible that a maximally great being exists, then a maximally great being exists in some possible world.
3. If a maximally great being exists in some possible world, then it exists in every possible world.
4. If a maximally great being exists in every possible world, then it exists in the actual world.
5. If a maximally great being exists in the actual world, then a maximally great being exists.
6. Therefore, a maximally great being exists.
Premise (1) is relatively modest, for it states only that the existence of an MGB is possible. An MGB is a being who exemplifies the greatest possible array of great-making properties, such as omniscience, omnipotence, etc... In order to falsify (1), One must show that the existence of an MGB is impossible due to its being self-contradictory -- quite a tall task. Now from (1), (2) follows, since the very idea of something to be possible means that it must exist in at least one possible world. P3 is simply a statement of axiom S5 of modal logic, which is that:
S5: If possibly necessarily P, then necessarily P.
If an MGB is possibly necessary, then it exists in at least one possible world. But it follows from this that it must also exist in all possible worlds qua maximally great, since maximal greatness entails necessary existence. Since the actual world is part of the set of possible worlds, the MGB must also exist in the actual world. Therefore, a maximally great being exists.
I think I have already argued against the points this syllogism relies on in my post. In fact, I don't think it is substantially different from my simpler summary of the ontological argument. It fails for precisely the same reasons.
DeleteI disagree that premise (1) is modest. I think it is extravagant if not incoherent if we imagine that a maximally great being is something that exists in every possible world. As argued in my post, it is not legitimate to bake into the definition of any concept that it must exist in every possible world, whether you do this directly or indirectly. This tactic could be used to 'prove' the existence of anything at all.
From my perspective it seems that it is possible that there is a world with no MGB. As I stated in my post, you are simply choosing to regard the MGB hypothesis as coherent while I prefer to regard the godless universe hypothesis as coherent. Since the whole argument rests on this debatable point, the argument doesn't really add anything.
But even aside from that it should be clear from the maximally great beer analogy that the argument doesn't work.
1. It is possible that a maximally great beer exists.
2. If it is possible that a maximally great beer exists, then a maximally great beer exists in some possible world.
3. If a maximally great beer exists in a some possible world, then it exists in every possible world.
4. If a maximally great beer exists in every possible world, then it exists in the actual world.
5. If a maximally great beer exists in the actual world, then a maximally great beer exists.
6. Therefore a maximally great beer exists.
Furthermore, it is greater to exist in every refrigerator than to exist in only some, so not only is there such a thing as a maximally great beer in this world, it must be in my refrigerator right now.
Yeah I'm going to defend this argument up above as I was just posting an argument that I thought you were going after, however I will continue to defend the Modal Ontological argument that I listed on my first comment.
Delete*Yeah I'm NOT going to defend this argument up above ( May 4th 2014 02:39)
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