Joshua says the GAE is still integral to the Mission

[Faizal_Ali]

@Tim

I think part of the problem is that this argument is intermingling definitions and assertions/propositions.

The Eiffel Tower is a tower built by the company of Gustave Eiffel in Paris in the late 19th century.

… would appear to be a valid definition of what we mean by “Eiffel Tower”.

The Eiffel Tower is a tower built by the company of Gustave Eiffel in Paris in the late 19th century. It exists.

… would appear to be problematical, as if the Eiffel Tower were destroyed tomorrow, it would still be what we meant by the Eiffel Tower.

I don’t think that analogy quite works. We are not saying “God is a maximally great being. He exists.” Rather, we are saying “God is a maximally great being” which entails necessary existence.

If we defined the Eiffel Tower as something that included necessary existence as one of its attributes, then the statement “The Eiffel Tower is a tower built by the company of Gustave Eiffel in Paris in the late 19th century” would be logically incoherent. Something that existed necessarily could not begin to exist in the late 19th century. There is no such obvious logical contradiction in the statement “God exists.”

[Puck_Mendelssohn]

I have found this discussion really interesting, in particular @Gisteron’s remarks in relation to the problems surrounding treating “existence” as a property of things.

The argument has always bothered me in a way I couldn’t quite put my finger on. The idea that one demonstrates the existence of something through word-shuffling alone, of course, is so absurd that it makes it obvious the argument lacks merit. But my understanding of just why that is was rather vague. What I have said to people before is that treating things like existence, “necessity” and possibility as though they are attributes of objects, when they really are descriptors of the logical relation of the objects to other objects, is rather like treating logical operators as properties of objects – as though, in a more ordinary setting, one declared that “God is, by definition, equal to.” One might then try to reason onward from that, but everything that follows is probably wrong (and certainly not logical). But it seems to me that @Gisteron clears up precisely what was muddy in my own mind about this.

[Gisteron]

This is one way around the issue, but in my opinion it doesn’t solve the problem, and might well introduce new ones instead:

In general, a thing, surely, is not the same as the concept of that thing, even if the thing does not exist in reality, but only conceptually. So we are still stuck unable to make statements about fictional or otherwise nonexistant things, if we go this route, because any time we try that now, we just end up saying something about the concept of the thing instead of the thing itself.

Also consider, that when we say that the late Daniel Dennett had a white beard, we (typically) do not mean that the concept of Daniel Dennett was one that included the property of having a white beard. We mean Dan Dennett himself had one, or at best we mean both. So now we need to actually investigate the existence of objects we refer to in statements before we can begin interpreting them enough to begin doing logic to them. That sounds like a plenty high cost. What’s the benefit, though?

[Paul_King]

I’m not seeing any real problems. Of course the concept is not the same as the thing itself, if we wrongly assume that Santa is real we might claim that he really has a white beard. Or if we wrongly thought that Daniel Dennett was fictional we might be talking about our concept of Daniel Dennett, instead of the actual person. So what? Those aren’t new problems created by the recognition that things that don’t exist don’t have properties. They’re true anyway. The idea that things that don’t exist do have actual properties seems far worse. If unicorns really have horns on their heads then surely those horns must exist. Isn’t that a problem?

[Gisteron]

Not if “to exist” is not a predicate, no. “Unicorns have horns” can translate to “The set of things called ‘unicorns’ is a subset of the set of all horned things”. If it turns out that unicorns do not exist, that just means that the set of things called ‘unicorns’ is empty, and the statement is trivially true. The statement could only be false if the set were non-empty, and if one or more of its elements happened to not be an element of the set of all horned things.

Admittedly, this interpretation of formal logic is vulnerable to the criticism that it… is overly formal, to the point where it becomes very difficult to derive theorems about the real world. As someone whose understanding of formal logic was chiefly shaped by some superficial study of pure mathematics, I happen to personally be comfortable making logic a framework that is purely analytic, barred entirely from making any claims about nature without first interrogating it and treating what it finds hence as a given. But I appreciate that many thinkers rather prefer logic to be at least in part about nature, rather than just a language with no strict obligations to match human experience nor to satisfy intuitions.

[Paul_King]

I don’t see that deals with the point. If unicorns don’t need to exist to have actual horns in their heads then why would it make a difference whether they exist or not?

[Gisteron]

“All unicorns have a horn” is true in the following cases:

• The set labeled ‘unicorns’ is empty.
• The set labeled ‘unicorns’ is not empty, and all elements therein contained are also elements of the set of all horned things.

“All unicorns have a horn” is false in the following case:

• The set labeled ‘unicorns’ is not empty, and one (or more) of the elements therein contained is not an element of the set of all horned things.

“There exists a unicorn that is pink” is true in the following case:

• The set labeled ‘unicorns’ is not empty, and one (or more) of the elements therein contained is also an element of the set of all pink things.

“There exists a unicorn that is pink” is false in the following cases:

• The set labeled ‘unicorns’ is empty.
• The set labeled ‘unicorns’ is not empty, but none of its elements is an element of the set of all pink things.

There is a difference between the set of unicorns being empty or not: Universally quantified propositions (for-all-statements, ones that say something about the particular properties of all elements of a set) are trivially satisfied for empty sets, but conditionally satisfied for non-empty ones. Existentially quantified propositions (for-some/there-exists-statements, ones that say something about the presence of an element with certain particular properties within the set) are trivially violated for empty sets, but conditionally satisfied for non-empty ones.

[Faizal_Ali]

@Gisteron

“All unicorns have a horn” is true in the following cases:

• The set labeled ‘unicorns’ is empty.

Hmm. It seems to me that is not correct. In that case, the set “All things that have a horn” would include no unicorns. Whereas, if it is true that “all unicorns have a horn”, then that set would have all the unicorns, rather than none.

Although, if “none” is the number of unicorns, then “no unicorns” would also be “all unicorns.”

Is that it?

[Paul_King]

So perhaps you can explain how a non-existent unicorn can have a horn that doesn’t exist?

It still makes more sense to me to say that only an existing unicorn could actually have a horn.

[Gisteron]

@Faizal_Ali

Although, if “none” is the number of unicorns, then “no unicorns” would also be “all unicorns.”

Is that it?

That is exactly it.

I admit I do not know how debated this is among philosophers, but in mathematics, such formalizations of quantification over sets is ubiquitous and non-controversial. That’s not to say that nobody ever made any attempts to formalize things differently since the advent of Zermelo’s and Fraenkel’s set theory and the subsequent reconstruction and axiomatization of mathematics. But suffice it to say that these days, pretty much all of the maths any of us learned at school, as well as all of the higher maths used in engineering and the sciences is rooted in a formal logic that defines its terms in just this way.

@Paul_King

So perhaps you can explain how a non-existent unicorn can have a horn that doesn’t exist?

A unicorn does not have horn, if no unicorns exist to say this about. But “all unicorns have a horn” is not a statement about if or how many individual unicorns exist. It is rather “For all x: If x is a unicorn, then x has a horn”. It doesn’t matter how many objects x that happen to be unicorns there are. It only matters that of all the unicorns that there are, not a single one is without horn. If there happen to not be any unicorns at all, that’s fine, too: It is even then still the case that there are zero hornless unicorns.

@Paul_King

It still makes more sense to me to say that only an existing unicorn could actually have a horn.

Let Charlie be a unicorn, and let’s suppose Charlie the unicorn exists. In that case, between the propositions “Charlie the unicorn has a horn” and “It is not the case that Charlie the unicorn has a horn”, exactly one is true, and the other is false. These propositions are a true dichotomy. Moreover, the truth-value of the proposition “Charlie the unicorn has no horn” may well depend on the truth-values of the ones above. We are naturally inclined to say that it cannot have the same truth-value as “Charlie the unicorn has a horn”.

Now suppose Charlie the unicorn does not exist, and let’s go with your suggestion of properties being only true for existing things. In that case “Charlie the unicorn has a horn” is false, for the having-a-horn attribute can only be assigned to things that exist. However, “Charlie the unicorn has no horn” is also false, because, again, having-no-horn is also an attribute, and those can only be assigned to things that exist.

So knowing the lack of some attributes of an entity is insufficient to conclude anything about whether it has any others. We have to also know whether the entity exists, only then can we begin doing logic to statements about it. Most troublingly, contradictory attributes (or lacks of such, as the case may be) are outright allowed for entities that happen to not exist.

Now, I’m not saying this is necessarily a bad thing. It is possible to keep this from exploding into total contradiction-spraying absurdity, if we just introduce some rules of inference that restrict what can or cannot be derived from propositions, depending on whether things referred within them exist or not. All I’m pointing out here is that there may be intuitions on this topic that find the implications of your suggestion concerning, and that a legitimate case can be made against adopting it, just as intuitively as your case in favour of it may be.

[Tim]

@Faizal_Ali

No, I have only agreed that, if they are possible, then they are necessarily true.

No, you have agreed to the definition, which states God’s necessary existence without that conditional.

If you wish to insert that conditional into your acceptance, you would have to state something along the lines of:

I accept the Classical Theism definition of God, only if God is possible.

This is a different statement from:

I accept the Classical Theism definition of God.

(Simpliciter)

@Faizal_Ali

The attempt here, as I understand it, is to demonstrate that if a necessary being possibly exists, then it does exist.

That would, to me, seem to be trivial, given the definitions and logic involved.

The real heavy lifting is demonstrating that “a necessary being possibly exists”. This would seem to involve not only demonstrating that this being is not a logical impossibility but also that all worlds without this being are a logical impossibility. This would appear to be an impractically large task.

I think part of my problem with all this is that hypothesising a necessary being would seem to negate the analytic purpose of hypothesising other possible worlds in the first place. Constraining them to all contain this necessary, omnipotent, omniscient, omnibenevolent foundation-of-all-existence would seem to make them fundamentally the same.

You are no longer talking about different possible worlds, but the same world over and over again.

So why bother? (Other than to trick unwary atheists?)

[Tim]

@Faizal_Ali

I don’t think that analogy quite works. We are not saying “God is a maximally great being. He exists.” Rather, we are saying “God is a maximally great being” which entails necessary existence.

The analogy is not perfect – it cannot be, as we neither have direct access to all possible worlds, nor have we any way, other than logical impossibility, of assessing necessity.

The are however the same in that they are both a ‘pseudodefinition’ that includes a definition and an assertion about the thing-defined’s existence (and an assertion of necessary is inherently an assertion of existence). It does not matter if that assertion is contained in the ‘top level’ of that definition, or embedded within a subsidiary definition. In both cases we are defining something into existence – which is logically invalid.

Getting back to an earlier comment of yours, existence in turn entails that the thing that exists is possible. So by agreeing to a definition that asserts God’s necessary existence, you have also already agreed to him being possible.

Once you have unconditionally agreed to this definition, it is quite simply Game Over.

[Paul_King]

@Gisteron

Now suppose Charlie the unicorn does not exist, and let’s go with your suggestion of properties being only true for existing things. In that case “Charlie the unicorn has a horn” is false, for the having-a-horn attribute can only be assigned to things that exist. However, “Charlie the unicorn has no horn” is also false, because, again, having-no-horn is also an attribute, and those can only be assigned to things that exist.

And how exactly is this a problem? It seems to be obviously correct. We can still say that if Charlie the unicorn exists, then Charlie has a horn. We can still assume for the sake of argument that Charlie the unicorn does exist and examine the consequences,

@Gisteron

So knowing the lack of some attributes of an entity is insufficient to conclude anything about whether it has any others. We have to also know whether the entity exists, only then can we begin doing logic to statements about it. Most troublingly, contradictory attributes (or lacks of such, as the case may be) are outright allowed for entities that happen to not exist.

What you seem to be saying is that we can’t assume for the sake of argument that Charlie exists. But why not? That seems to be where the absurdity is.

[Gisteron]

@Paul_King

We can still say that if Charlie the unicorn exists, then Charlie has a horn. We can still assume for the sake of argument that Charlie the unicorn does exist and examine the consequences,

Ex falso quod libet. The proposition “If Charlie the unicorn exists, he has a horn” is true in virtue of Charlie not existing. The proposition “If Charlie the unicorn exists, he does not have a horn” is also true, again, in virtue of Charlie not existing. If we wish to formulate this in modal logical terms, there exists a possible world, where Charlie the unicorn exists and has a horn, and another possible world, where Charlie the unicorn exists and does not have a horn. Because he does not exist in the actual world, the statement that he has a horn and the statement that he doesn’t are both true in the actual world.

Again, I’m not saying this is a problem. I’m just saying that some thinkers may find this uncomfortable, and choose to interpret existence and to choose the prerequisites for logical expressions differently for reasons that are just as intuitive to them as yours are to yourself.

@Paul_King

What you seem to be saying is that we can’t assume for the sake of argument that Charlie exists. But why not? That seems to be where the absurdity is.

We can assume for the sake of argument that Charlie exists. In fact, let’s. What conclusions can we draw from it? We know perhaps that the concept of the unicorn is one that includes the attribute of having a horn. But a unicorn is not the same as the concept of a unicorn. We don’t know that every unicorn has a horn. In fact, because unicorns generally do not exist, we know that it is not the case that any of the other unicorns have a horn, and we know that it is not the case that any of the other unicorns do not have horn. The only unicorn we have assumed the existence of is Charlie. How can we logically prove or disprove that Charlie has a horn, assuming Charlie’s existence and, perhaps, the concept? If we cannot, what else can we prove under these assumptions?

[Paul_King]

@Gisteron

Ex falso quod libet. The proposition “If Charlie the unicorn exists, he has a horn” is true in virtue of Charlie not existing. The proposition “If Charlie the unicorn exists, he does not have a horn” is also true, again, in virtue of Charlie not existing.

If you’re going to assume that Charlie exists you can’t use the fact that Charlie does not exist to establish the truth of either proposition. That’s basic logic - you can’t assume a contradiction and get any meaningful results… Instead you use the definition of a unicorn to establish the truth of “if Charlie the unicorn exists, he has a horn”

@Gisteron

If we wish to formulate this in modal logical terms, there exists a possible world, where Charlie the unicorn exists and has a horn, and another possible world, where Charlie the unicorn exists and does not have a horn.

That’s obviously wrong. In a possible world where Charlie the unicorn exists it is true that Charlie the unicorn exists. So obviously you can’t rely on the falsehood of “Charlie the unicorn exists” to establish the truth of “if Charlie the unicorn exists then Charlie does not have a horn” in that possible world. (If it’s any consolation I’ve seen the same error attributed to Plantinga - but it’s still a very obvious error).

@Gisteron

Because he does not exist in the actual world, the statement that he has a horn and the statement that he doesn’t are both true in the actual world.

Surely they are both false in the actual world. But the situation in the actual world would be irrelevant to a possible world where Charlie does exist.

@Gisteron

We can assume for the sake of argument that Charlie exists. In fact, let’s. What conclusions can we draw from it? We know perhaps that the concept of the unicorn is one that includes the attribute of having a horn. But a unicorn is not the same as the concept of a unicorn

That’s also not a problem since we use the definition rather than relying on the more nebulous concept.

[Gisteron]

@Paul_King

@Gisteron

f we wish to formulate this in modal logical terms, there exists a possible world, where Charlie the unicorn exists and has a horn, and another possible world, where Charlie the unicorn exists and does not have a horn.

That’s obviously wrong. In a possible world where Charlie the unicorn exists it is true that Charlie the unicorn exists. So obviously you can’t rely on the falsehood of “Charlie the unicorn exists” to establish the truth of “if Charlie the unicorn exists then Charlie does not have a horn” in that possible world.

I do not find the wrongness of this obvious at all. I do not know a priori what attributes Charlie the unicorn has. We said (maybe) that the concept of Charlie has a horn, but that is not the same as saying that Charlie has a horn in all possible worlds. In fact, if the actual world is a possible world, and Charlie does not exist in it, and existence is a prerequisite for having attributes, then the statement “Charlie the unicorn has a horn in all possible worlds” is outright provably false.

For all I know, maybe there exists a world where Charlie exists, has no horn, and where the concept of Charlie happens to also be one that does not include the horn-having attribute. Certainly there seems to not be a contradiction in that. After all, we have not established that concepts are somehow special. I would assume on the outset that propositions about them are subject to the same rules of predicate and modal logic as all other propositions, and none of our premises explicitly state that even just the concept of Charlie the unicorn is the same throughout all possible worlds.

So: I know Charlie does not exist in the actual world, and as such, in the actual world he neither has the attribute of having a horn nor of not having one. I also know that Charlie neither has a horn in all possible worlds, nor is lacking a horn in all possible worlds, because both options are violated by at least one world, namely the actual world. Additionally, there seems not to be any contradiction between saying that Charlie the unicorn exists and saying he has a horn, nor between saying that Charlie exists and saying he has no horn. So there exists a possible world for each scenario.

Therefore, assuming Charlie exists, i.e. reviewing the subset of all possible worlds that happen to be ones where Charlie exists, we are looking at one or more worlds where Charlie has a horn, and at one or more worlds where he does not. We can therefore not conclude that, even in the subset of worlds where Charlie exists, he always has a horn, nor that he never does. Concluding his having or not-having of a horn is impossible without more premises.

[Paul_King]

@Gisteron

I do not find the wrongness of this obvious at all.

Do you agree that in a possible world where Charlie the unicorn exists then it is true that Charlie the unicorn exists ?

Do you agree that if Charlie the unicorn does exist you cannot assume that Charlie does not exist to show that it is true that “if Charlie the unicorn exists then Charlie the unicorn does not have a horn”?

@Gisteron

In fact, if the actual world is a possible world, and Charlie does not exist in it, and existence is a prerequisite for having attributes, then the statement “Charlie the unicorn has a horn in all possible worlds” is outright provably false.

I don’t see that being able to prove that a falsehood is indeed false is much of a drawback.

@Gisteron

For all I know, maybe there exists a world where Charlie exists, has no horn, and where the concept of Charlie happens to also be one that does not include the horn-having attribute. Certainly there seems to not be a contradiction in that

Indeed, but we would not be talking about the concept of Charlie the unicorn in that world. The concept of Charlie the unicorn we would be using would be ours. Just as we would be using our notation of 2+2 = 4 in discussing the truth of that statement in a possible world, not the notation of that world (surely there is a possible world where the symbols for “4” and “5” are interchanged).

@Gisteron

Therefore, assuming Charlie exists, i.e. reviewing the subset of all possible worlds that happen to be ones where Charlie exists, we are looking at one or more worlds where Charlie has a horn, and at one or more worlds where he does not. We can therefore not conclude that, even in the subset of worlds where Charlie exists, he always has a horn, nor that he never does. Concluding his having or not-having of a horn is impossible without more premises.

Since the only stated premise you have used is “Charlie the unicorn does not exists’ is seems rather obvious that you need something more to establish that Charlie does or does not have a horn. So really you are only stating that we would have to use the same unstated premise that you have already used and we have been assuming all along.

[Faizal_Ali]

@Tim

No, you have agreed to the definition, which states God’s necessary existence without that conditional.

If you wish to insert that conditional into your acceptance, you would have to state something along the lines of:

I accept the Classical Theism definition of God, only if God is possible.

This is a different statement from:

I accept the Classical Theism definition of God.

(Simpliciter)

I disagree.

For instance, I can accept the definition of “A married bachelor” as “An unmarried man who has a spouse” without agreeing that such a thing can possibly exist.

@Tim

That would, to me, seem to be trivial, given the definitions and logic involved.

Yes, that’s kind of the point: That it is a trivial truth that, if a necessary being exists in a possible world, then it exists our world.

@Tim

The real heavy lifting is demonstrating that “a necessary being possibly exists”. This would seem to involve not only demonstrating that this being is not a logical impossibility but also that all worlds without this being are a logical impossibility. This would appear to be an impractically large task.

I agree. Maybe that is why even Plantinga admits this argument does not establish that God exists. Only that a rational person can believe God exists. It’s a pretty low bar, IMHO.

@Tim

I think part of my problem with all this is that hypothesising a necessary being would seem to negate the analytic purpose of hypothesising other possible worlds in the first place. Constraining them to all contain this necessary, omnipotent, omniscient, omnibenevolent foundation-of-all-existence would seem to make them fundamentally the same.

I don’t think so. If this necessary being is also omnipotent and omniscient, there are very few limits to the sort of worlds that can exist. In fact, it is only limited to every possible world!

@Tim

So why bother? (Other than to trick unwary atheists?)

I think it can also be helpful for theists to clarify how they ought to think about God and his existence. But, I agree, it is often used as a trick by apologists, who may not even understand the argument themselves.

@Tim

Getting back to an earlier comment of yours, existence in turn entails that the thing that exists is possible.

Yes. But the question at hand is whether a being that, by definition, exists necessarily does actually exist. Its actual existence is not entailed merely by one accepting the definition.

@Gisteron

Let Charlie be a unicorn, and let’s suppose Charlie the unicorn exists.

Video evidence that he does:

Charlie the Unicorn

[Gisteron]

@Paul_King

The concept of Charlie the unicorn we would be using would be ours. Just as we would be using our notation of 2+2 = 4 in discussing the truth of that statement in a possible world, not the notation of that world (surely there is a possible world where the symbols for “4” and “5” are interchanged).

There is a distinction, in my opinion, between a concept and a notation. The notation is a linguistic representation of a thing (concept or otherwise), while the concept is the idea of a thing. When we discuss the truth and necessity (or not, as some might find ways to argue) of the proposition that the sum of two and two is identical to four, we are not discussing the necessity (or otherwise) of the symbol string “the sum of two and two is four” or “2 + 2 = 4”, but rather the actual identity itself. The notation may differ in a different world is irrelevant, but the notation isn’t the subject of the discussion.

In my opinion, then, the analogy is somewhere between somewhat flawed and severely flawed. As I said, at least on the face of it it seems no contradiction results either from assuming that the concept of Charlie the unicorn is one that includes him having a horn, nor from assuming that the concept of Charlie is one that includes him not having a horn, nor from assuming that the concept of Charlie is one that does not include either attribute explicitly. However, I’m not sure the same contradiction-free-ness can be assumed about altering the definitions of addition or identity of numbers.

I suppose one could construct a completely different arithmetic, where addition and identity are different but still somehow consistent with all the other definitions in said arithmetic. Whether such an alternate mathematics would be even remotely recognizable as a counterpart to what we have in the actual world, I’m not sure, though depending on just how many attributes we assign to Charlie the unicorn besides the matter of a horn, it may be rather easy to have concepts that are almost identical in so numerous other regards that it becomes agreeable to recognize them as each other’s counterparts in the respective possible worlds. At least intuitively, re-defining all of maths consistently, much less doing so in a way that leaves it recognizable as “something quite like maths, but just a little different”, seems like quite a lot more work than the comparatively trivial task of defining two or more near-identical concepts of Charlie the unicorn that happen to differ on at least as much as the matter of the horn.

Of course, one of the big challenges in the philosophy surrounding modal logic is precisely the issue of how and when one can recognize items from different possible worlds as each other’s counterparts, and I make no pretense of having an agreeable solution that can withstand any amount of scrutiny here.

[Paul_King]

@Gisteron

There is a distinction, in my opinion, between a concept and a notation. The notation is a linguistic representation of a thing (concept or otherwise), while the concept is the idea of a thing. When we discuss the truth and necessity (or not, as some might find ways to argue) of the proposition that the sum of two and two is identical to four, we are not discussing the necessity (or otherwise) of the symbol string “the sum of two and two is four” or “2 + 2 = 4”, but rather the actual identity itself. The notation may differ in a different world is irrelevant, but the notation isn’t the subject of the discussion.

But exactly the same thing applies to the concepts. In both cases the meaning of our statements comes from us. So when we are talking about “Charlie the Unicorn” it is what we mean by “Charlie the Unicorn” that matters just as it is what we mean by “2+2=4” that matters, and not the meaning attached to those symbols in whatever possible world we are discussing.