## Thursday, June 09, 2022

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Thank you for your response. The crux of your argument seems to be this:

(1) If x's existence is identical to x's essence (in the wide sense), then x exists in virtue of x's essence.
(2) If x exists in virtue of x's essence, then x is a necessary being.
(3) Therefore, if x's existence is identical to x's essence, x is a necessary being.
(4) x is not a necessary being.
(5) Therefore, x's existence is not identical to x's essence.

Here's the problem: Either x's existence is contingent existence or necessary existence. If x's existence is contingent existence, then (1) is false, since a contingent being exists in virtue of something external to it (i.e. not its essence). If x's existence is necessary existence, then (4) is false.

M.L.

What you are missing is that my argument is a reductio ad absurdum. What I aim to reduce to absurdity (where an absurdity is a logical contradiction) is the thesis that there is no real distinction in a contingent being between it and its existence. I begin with the putative datum or Moorean fact that there are contingent beings. (You could of course ask how I know that there are, but let's leave that for later.) I'll use my writing table as an example. Call it T. T is contingent because, although it exists, it might not have existed: it actually exists but is possibly nonexistent. The argument then goes like this:

1. There is no real difference in T between T and T's existence: T = existing T. (assumption for reductio)
2. If there is no real difference in T between T and existing T, then T's existence = T's essence.
3. If T's existence = T's essence, then T exists in virtue of T's (wide) essence, i.e. in virtue of T's whatness, quiddity, nature in the broad sense.
4. If T exists in virtue of T's essence, then T is a necessary being. But:
5. T is a contingent being.
6. It is logically impossible that any being be both necessary and contingent. Therefore:
7. (1) is false which implies that it negation is true, which is to say: there is a real distinction in T between T's (wide) essence and T's existence.

It seems the argument still falls on the horns of the dilemma above: Either T's existence is contingent or necessary. If the former, then your (3) is false since in this case, a contingent being's existence is in virtue of something external to T. If the latter, then your (5) is false.

M.L.

M.L.,
if you have the book at hand you'll see another interesting quote right on that page:

"To put it another way, if in a essence and existence are identical, then a's essence entails a's existence. But that is to say that a is a necessary being. Traditionally, there was only one being of whom this could be said, namely, God. But the 'no difference' theory in its identitarian version implies that every individual is a necessary being, which is absurd."

The issue isn't with the view in regards to necessary beings, in fact, details aside, it's the view Bill himself broadly holds to. The argument is a reductio against the No-Difference theory of contingent beings. Thus premise 5 is a given in the argument. And this is exactly what the argument is supposed to show: the assumption of contingency is impossible given the identity of T's essence and it's existence, since it would be in T's nature to exist, even giving it aseity. And this of course runs contrary to it being contingent.

And this is exactly what the argument is supposed to show: by deriving the consequences of premise 1, showing that it's inconsistent with premise 5 (T's contingency) we arrive at the negation of 1; there must be a difference between T's essence and its existence

Dominik,

You made the right response to M.L. >>The argument is a reductio against the No-Difference theory of contingent beings. Thus premise 5 is a given in the argument. And this is exactly what the argument is supposed to show: the assumption of contingency is impossible given the identity of T's essence and it's existence, since it would be in T's nature to exist, even giving it aseity. And this of course runs contrary to it being contingent.

And this is exactly what the argument is supposed to show: by deriving the consequences of premise 1, showing that it's inconsistent with premise 5 (T's contingency) we arrive at the negation of 1; there must be a difference between T's essence and its existence<<

You have understood my argument very well. Thank you.

Dominik,

I did think hard about your e-mail from April about artifacts, organisms, and modes of being. I wrote a post on it, but did not finish it. I'll try to finish it and upload it.

Dominik and BV,

If premise 5 is a given, then T has contingent existence, and so premise 3 is simply false--a contingent being exists in virtue of not of its essence, but in virtue of something external to it, i.e. its cause or ground. This is my main objection to the argument.

A second objection is that premise 3 seems metaphysically impossible. If T exists in virtue of T's essence, then since T's essence is intrinsic to T, T's essence also exists in virtue of T's essence, which is circular and so, metaphysically impossible.

A third objection is one that classical theists will raise--God is a necessary being whose essence is identical to his existence. But God does not exist in virtue of anything, much less his essence. To say God exists in virtue of something is incoherent. And so classical theists have strong reason to reject premise 3.

ML,

You need to consult a logic text and learn how reductio ad absurdum arguments work.

>>To say God exists in virtue of something is incoherent.<<

Not so. God exists in virtue of the identity in him of essence and existence.

M. L.,

last try before we give Bill any more reasons for a closed combox.

If premise 5 is a given, then T has contingent existence, and so premise 3 is simply false--a contingent being exists in virtue of not of its essence, but in virtue of something external to it, i.e. its cause or ground. This is my main objection to the argument.

You're SO close to understanding it. Notice that premise 3 is just a consequence of 2, which is a consequence of 1. If there's no difference in T's nature and its existence, then T exists by its own nature, which just means it possesses aseity and thus exists of necessity. Premise 1 is the assumption at hand, we're investigating its consistency with T's contingency. We see that 1 has consequences (3), which are inconsistent with 5. Therefore:

1 and 5 are inconsistent
5 is true (T is contingent)
Therefore
1 is false

=>there must be a difference between T and its existence.

I don't think there's any way to make this any clearer. This is the point of any reductio ad absurdum: Disprove the initial premise under investigation.

A second objection is that premise 3 seems metaphysically impossible. If T exists in virtue of T's essence, then since T's essence is intrinsic to T, T's essence also exists in virtue of T's essence, which is circular and so, metaphysically impossible.

The No-Difference theory just proposes that there's no additional entity called "T's existence" which is in any way distinct from T's nature. Bill made this clear in his formulation of premise 3, which is open enough to accommodate ideas like existence being either an essential property or in any other way intrinsic to the nature of T. Thus saying that "T's essence exists in virtue of T's essence" is just stating that it's in T's nature to exist, it's self-existent. For such a nature, a necessary being, we don't need any reference to something beyond it, since existence is already part of its concept.

Bill already answered your third objection, so I won't chime in on that too deeply. But note that the objection

But God does not exist in virtue of anything, much less his essence. To say God exists in virtue of something is incoherent.

is doubly confused. For one the classical theist will cheerfully agree that God exists in virtue of his essence/nature. It's just that his nature is identical to existence. He exists in virtue of him being Existence. Your second mistake is to assume that to affirm the identity of essence and existence is somehow a denial of essence. Not so! Existence has a certain nature, something disclosed from us since it's infinite and we're finite. And this nature of existence, identified by e.g. Thomas Aquinas with traditional theistic attributes, is what God is.

And this will be the last from me on this topic.

Well done, Dominik.

What city do you live in?

Dominik,

You write that:

saying that "T's essence exists in virtue of T's essence" is just stating that it's in T's nature to exist, it's self-existent.

This is very helpful, it shows me that we mean different things by "in virtue of", which might be causing difficulty in our discussion.

By my lights, the in-virtue-of relation is a dependence relation. Since dependence relations are irreflexive, it is impossible for T to depend on T's essence which is part of T (my 2nd objection), and it is impossible for God to depend on his essence (my 3rd objection).

You seem to understand the in-virtue-of differently. That's fine, as long as we are clear with how we use our terms. But going by how you're using "in virtue of", I think premise 4 (If T exists in virtue of T's (wide) essence, then T is a necessary being) is false.

This is because T can be X in virtue of T's (wide) essence, i.e. it can be in T's nature to be X, without T being necessarily X (i.e. being X in all possible worlds). The fact that T is X in virtue of T's (wide) essence only shows that T is X in all possible worlds where T exists. Further argument is needed to show that T exists in all possible worlds. Put another way, the following premise is false:

(A) If it is in T's nature to be X, then T is X in every possible world.

Here's a counterexample to this premise: It is in my nature to be a rational animal, but it doesn't follow that I'm a rational animal in all possible worlds.

You might say (A) is false in general, but true if X refers to existence, so that:

(A*) If it is in T's nature to exist, then T exists in every possible world.

But why accept (A*)? The best argument for (A*) I can think of is this:

(A*1) If it is in T's nature to exist, then nothing external to T can explain T's existence.
(A*2) If nothing external to T can explain T's existence, then T is self-existent.
(A*3) If T is self-existent, then T necessarily exists.
(A*4) If T necessarily exists, then T exists in every possible world. Therefore:
(A*) If it is in T's nature to exist, then T exists in every possible world.

The problem is that we can make a parody argument:

(B*1) If it is in T's nature to be rational, then nothing external to T can explain T's rationality.
(B*2) If nothing external to T can explain T's rationality, then T is self-rational.
(B*3) If T is self-rational, then T necessarily rational.
(B*4) If T necessarily rational, then T is rational in every possible world. Therefore:
(B*) If it is in T's nature to be rational, then T is rational in every possible world.

So in short, given how you're using "in virtue of", premise 4 is false.

M. L.,

T just is T's essence connected to T's existence. The "in virtue of" would be a dependence in a contingent being where T is dependent on the actual connection of both parts. In a necessary being (I reserve necessity exclusively for entities that exist by their own nature, that possess aseity) however the dependence vanishes since there wouldn't actually be two parts of the being in question, since the essence and existence are identical.

T (contingent) = T's essence+T's existence
T (necessary) = T's essence = T's existence

The reason why the objection that God can't depend on his essence doesn't apply is simply that there's nothing that distinguishes God from his essence. And I think you would agree with me that the objection would be absurd if you want to say that God can't depend on himself.

Your constructed argument would be sound if it were any other property but existence. Being human, red or material all aren't properties that make the difference between a being actually being instead of nothing, they presuppose it. The No-Difference theory about which this post is about is that between the nature of T and the existence of T there is no difference. So you're right that I accept (A*). I'd even say it's a logical given.

A*1 is acceptable.
A*2 is not. For one, T could be a brute fact. But we both presumably don't accept that there are any and nobody should. What's crucial isn't the lack of an external explanation, but the reality of an internal one. And that explanation just is the identity of a certain nature with existence.
A*3 and A*4 are true.

The mistake in A*2 is why the parody fails. We have to be clear what we're talking about: existence is the absolute fundamental that makes the difference between something and nothing. It's important that this is kept in mind and never equivocated about. T, say a red ball, has a certain color, diameter and material it's made from. The No-Difference thesis holds that there is nothing additional to that object, the properties, or rather their specific conjunction, is identified with existence, which entails that, if existence is real, it's nature just is that red ball. Nothing is more fundamental than it, nothing can cause it, and it just being existence is what explains why it's necessary.

Dominik,

Thank you for the further response.

You say you accept (A*), but you think (A*2) is false, so presumably your reason for accepting (A*) isn't the argument with premises A*1 to A*4 above. If so, then what is your argument for accepting (A*)? Or do you accept (A*) only because it seems intuitive to you? As for me, my intuition is that (A*) is false, so an argument for (A*) would be helpful here.

To be clear, I agree that if T's essence is identical to T's existence, then T has no cause and has an internal explanation in any world where T exists. But I don't see how you get from this claim to the conclusion that T exists in all possible worlds (i.e. that T is a necessary being). At most, your comment only shows that T is what Rowe and Hick call *factually necessary*, as opposed metaphysically necessary (existing in all possible worlds).

In other words, what needs to be shown is how T's being factually necessary entails T's being metaphysically necessary.

Additional thoughts: The parody could be somewhat saved, in the sense that your mistake in A*2/B*2 doesn't affect it. For one, I don't have any problem with a being that has an internal explanation for its rationality, I firmly affirm that humans are such creatures.

Your big blunder is that it's simply invalid.
The steps from either B*3 to B*4 or B*4 to B*5 (dependent on what you're trying to say in ) are one big logical mess. From T being necessarily rational, you could only conclude that it's necessarily rational, IF it exists at all. So your B*4 would have to be:

(B*4) If T necessarily rational, then T is rational in every possible world in which it exists.

That qualification is necessary and could also be made in premise 5 instead. Both premises say the same thing superficially, but I fear that with premise 5 you intended to go from "Essentially X in every possible world", to " Actual X in every possible world." The necessity of a particular property in order to be a certain nature doesn't entail its actual existence, otherwise every being with essential properties would necessarily exist.

1. It's in the nature of water to be H2O
2. There's nothing external that explains water being H2O but the nature of water itself. (Internal explanation)
3. Water is necessarily H2O
4. If water is necessarily H2O, then it's H2O in every possible world
5. Therefore, in every possible world, water is H2O

And now we'd come to the crucial premise: So far your parody would be valid, but uninteresting. We would have merely stated that identical natures share essential properties across possible worlds. That I agree with. In order for your parody to be an actual parody though you need to go from "necessarily H2O" to "necessarily exists".

In summary: Your parody is invalid. To make it valid you have to remove the parallels with the initial argument you intended to parody. In either case, it fails.

Dominik,

Did you see my previous my comment? I think the heart of our disagreement is that, while I agree that if T's essence is identical to T's existence, then T has no cause and has an internal explanation in any world where T exists, I don't see how this entails that T exists in all possible worlds. You need additional premises to get to that conclusion.

You write:

The necessity of a particular property in order to be a certain nature doesn't entail its actual existence

Yes, this is precisely the point I've been making all along. The mere fact that it's in T's nature to exist doesn't show that T actually exists (otherwise, I could define things into existence--for example, call a "super-unicorn" a unicorn whose nature is identical to its existence, therefore, a superunicorn exists). All that follows is that, *if T exists*, T's existence is uncaused and has an internal explanation. This doesn't show that T actually exists, and more importantly, this doesn't show that T exists in all possible worlds. (It also doesn't show T can't cease to exist, but we can leave aside that worry for now.)

There is no intuition at work here. A* is true because it is what a necessary being must be like. Remember again, I mean aseity, self-existence.

Now remove every contingent/dependent being from a possible world, so that only the beings that exist a se are left. What do they have in common? An internal explanation for why they are. Why? Because the entities in question are no brute fact and their existence therefore isn't a freak accident. And there can't be an external explanation for their existence, since there are no beings that could cause or sustain them. Therefore we're left with an internal explanation; the reason for the existence of the object will be found by analyzing its very own nature.

Frankly, there's nothing to disagree here about, thus far we're only moving in the territory of mere definitions. There are two mistake I believe you're committing:

1. The correction of A*2 wasn't a mere semantic point, but a conveying of an important metaphysical point: The internal explanation is reserved to necessary beings. We both as humans don't have an internal explanation for our existence, nothing in our nature explains why we actually are, we always need to introduce external factors. At most we can understand why we aren't impossible, meaning that there's no contradiction in our nature that would prevent us ever coming about.

So if you're saying:

while I agree that if T's essence is identical to T's existence, then T has no cause and has an internal explanation in any world where T exists, I don't see how this entails that T exists in all possible worlds.

then you're contradicting yourself. If we already have an explanation of T's existence in the otherwise empty world, due to the nature of what T is, then its non-existence is impossible. After all, existence is already in what it is and there couldn't be any existence without there being T.

Essentially,

2. I think you're actually not respecting enough what existence is supposed to be and it seems that you treat it interchangeably with every other property. However, existence isn't a property, but the having of properties. It's no question that me necessarily being a human kind of explains why I'm a human in every world in which I exist. However the question of why I should exist necessarily if existence is part of what I essentially am, borders hard on the unintelligible. Here's an argument though:

1. If existence is part of T's nature, then it's an essential property of it.
2. No essential property can be gained.
3. No essential property can be lost.
4. Therefore if existence is an essential property of T, it's always an essential property of T.
5. If existence is always an essential property of T, then T's non-existence is impossible.
6. If T's non-existence is impossible, then T exists of necessity.
7. Therefore, if existence is part of T's nature, T exists of necessity.

2 and 3 are true for the same reasons, there is no circumstance under which T already is what it is before gaining a property that makes it what it is and there's no circumstance under which T is still what it is after loosing something that is essential to it. We both can cease to exist for example, but we could never cease to be human since there is no Dominik or M.L. left after our humanity is gone. Therefore our human nature is essential to us, while existence is not. For a better explanation, reread pages 50-51 of Bill's book.

The third mistake is here:

All that follows is that, *if T exists*, T's existence is uncaused and has an internal explanation. This doesn't show that T actually exists, and more importantly, this doesn't show that T exists in all possible worlds.

If you have to add the conditional *if T exists* you can't have an internal explanation for T's existence, this is a contradiction. The factually necessary being of Rowe, Hick, but also of Swinburne is a mere brute fact, something that just happens to exist, perhaps has an explanation why it must be uncaused if it happens to exist, but lacks the resources to actually explain why it exists, although that's a question that is perfectly legitimate to ask. If we are talking about such a being, we are NOT talking about a being whose nature includes existence. However in the discussion we were and in that case its necessary existence simply follows. You're conflating two different kinds of beings here. The most immediate way to see that is that a necessary being is the conclusion of an affirmation of the PSR. Rowe however, explicitly restricted the principle to the degree that this conclusion can be avoided. Thereby his ontology lacks something whose nature is existence.

The mere fact that it's in T's nature to exist doesn't show that T actually exists (otherwise, I could define things into existence--for example, call a "super-unicorn" a unicorn whose nature is identical to its existence, therefore, a superunicorn exists).

No. Be careful not to equivocate on what existence means. Kants point against the ontological argument wasn't that it would be irrelevant whether a concept includes existence, but rather that there are no concepts who do. Same with the superunicorn. If however that object were identical with existence, then of course it would exist of necessity, since that very being is what makes the difference between something and nothing.

Dominik,

I'll focus on your argument, since I think it illustrates where we might be able to make progress here. Your (2) and (3) are ambiguous. They can mean either:

(2*) No essential property of T can be gained *while T exists*.
(3*) No essential property of T can be lost *while T exists*.

or:

(2**) In all past moments, T has its essential properties.
(3**) In all future moments, T has its essential properties.

Let's consider (2*) and (3*) first. They are both obviously true, but they leave open the possibility that T didn't always exist and T will not always exist. And so, (2*) and (3*) at most show that:

(4*) If existence is an essential property of T, it's always an essential property of T *while T exists*.

(4*) is true, but renders the argument invalid since (5) has a different antecedent than (4*)'s consequent. To keep the argument valid, we need replace (5) with:

(5*) If existence is always an essential property of T *while T exists*, then T's non-existence is impossible.

But while this makes the argument, the problem is that (5*) is false since T's non-existence is compatible with it always having existence while it exists.

So let's consider (2**) and (3**) next. The advantage of these premises is that they do support (4). But the problem is that these premises are true *only if* T is an everlasting being (exists in all times). But why think that any being whose existence is identical to its nature is an everlasting being? This substantial claim needs further argument.

But suppose all the above problems can be solved so that (4) is true. The argument has another problem.

(5) is also ambiguous. It can mean either:

(5*) If existence is always an essential property of T, then T's non-existence is impossible *in any world T exists*.

or:

(5**) If existence is always an essential property of T, then T's non-existence is metaphysically impossible (i.e. T exists in all possible worlds).

Let's consider (5*) first. I could accept it if the antecedent means "T has existence at all moments", but this would make the argument invalid since the consequent of (5*) isn't the same as the antecedent of (6). To keep the argument valid, (6) needs to be replaced with:

(6*) If T's non-existence is impossible *in any world where T exists*, then T exists of necessity.

The problem is that (6*) is false, since the fact that T's non-existence is impossible *in any world where T exists* is compatible with T not existing in some possible worlds.

As for (5**), it just seems false. The fact that T always has existence doesn't show that T exists in all possible worlds. Further premises are needed to make this connection.

So the argument you gave has multiple problems. Maybe it can be revised to avoid the problems raised above, but as is, I still fail to see why (A*) should be accepted.

M. L.,

how closely did you read Bill's book? I invite you to take a look back at pages 57-59, preferably until 64. You're the perfect example of someone talking about pseudo-existence; you're not talking about the topic at hand and make an illegitimate distinction between existence and actuality. The relevant section of my last comment wasn't this argument, but section 3 (and 1 to a lesser extend) which you ignored. If you had paid sufficient attention to the points there, you'd know your mistake. Your view makes it impossible to give an account of what the difference for an entity is if existence is essential or accidental to it. This should give you pause. In addition, talk about possible worlds doesn't add anything interesting here, since the contingency of a being is a matter of its nature and not primarily about the quantity of possible worlds in which it exists or not. The latter is a consequence of the former. So we should concentrate on what it is in the former that makes it either necessary or contingent.

But before we can get to that we apparently have to once again go over terminology. The existence of a thing is its actuality. If actuality is possessed by its nature, so that it's in the nature of the thing to be actual, then there's no room for speculation of possible worlds in which it isn't actual, since its actuality is always a consequence of that what it is.

Additionally, an essential property of T is a property that couldn't be different. An accidental property contingently belongs to an underlying substance, but the substance prevails whether that property is actual or not, since it doesn't make the substance what it is. Existence normally is not a quidditative property, it carries no determinate content and to contingent beings it's always accidental. In Bill's book it's the unification of properties, the necessary being is identical with said unification and due to its lack of composition with anything that could be in need of unification, it exists a se. It is existence and essentially so, since it's its very nature.

Here comes your equivocation: You want to say that this only proves that it exists/is identical to existence in the world in which it exists. But, with the definitions of existence above and in several comments before in mind and with the definition of essential properties, this just means that you have changed the subject. Existence is that which makes something be instead of nothing. If God is identical with it, it just means that God carries that which distinguishes him from nothing essentially within him. If you want to say that this is only so in some worlds you either 1) don't understand what an essential property is, 2) changed the subject to pseudo-existence (I'll come back to that when talking about your objections) or 3) once again moved existence back into the realm of accidental properties, thereby changing the argument of your interlucor.

Confused? The points will become clearer:

Your (2) and (3) are ambiguous. They can mean either:
(2*) No essential property of T can be gained *while T exists*.
(3*) No essential property of T can be lost *while T exists*.

or:

(2**) In all past moments, T has its essential properties.
(3**) In all future moments, T has its essential properties.

I accept the formulations as entailed by mine, but your reformulations do no metaphysical lifting here.

They are both obviously true, but they leave open the possibility that T didn't always exist and T will not always exist. And so, (2*) and (3*) at most show that:

(4*) If existence is an essential property of T, it's always an essential property of T *while T exists*.

No, and this is what I meant with you dealing in pseudo-existence. For T to have existence is for T to be. If T is contingent, then it has existence accidentally, after all it's not in its nature to exist.
The way you formulated it you made T into a contingent being. And now we landed in an utterly bizarre scenario:

Per hypothesis, T has necessary existence as an essential property. Since T exists in some, but not all possible worlds, it's contingent, which is what your claim entails. Since it exists contingently, existence is accidental to T. Since it's the accidental instance of existence that determines T's mode of being, the essential property of necessary existence can't mean actuality. So what is that misnamed property doing exactly? Whatever it does, it is not doing what existence is described as doing, which is why I say that you keep equivocating. I suggest that the reason why you don't see why an entity that essentially possesses existence or is identical with it, must necessarily exist is because despite claiming so, you actually don't pay attention to existence being an essential property.

Secondly, your claim that 2 or 3 at most show no gaining or loosing of essential properties while they exist is false and you'd see that by paying attention to premise 1:

If existence is part of T's nature, then it's an essential property of it.

If you weren't equivocating about the meaning of exist, you'd see the mistake. Existence is what keeps T in being, possessing existence in its nature means T keeps itself in being (aseity). The keeping in being isn't limited to temporal, per accidens causal series in which T keeps itself in being in worlds in which it exists, but also in a per se causal series, where it keeps itself from being nothing.

Thirdly, once again, you don't seem to understand essential properties. T's essential properties are identical across possible worlds, so if it includes existence, which is what makes its essence actual, then that actuality will be shared across possible worlds. The question for a world in which T is not would require that the essential part to T which is responsible for making it actual actually wouldn't be essential at all. This is my third complaint, you keep on putting accidents into the essential properties where they don't belong, thereby causing us to talk about completely different things.

(5*) If existence is always an essential property of T *while T exists*, then T's non-existence is impossible.

In my usage of the words, which is consistent across the argument, this is just a tautology. I already complaint above that the invoking of "while/if T exists" declares existence to be accidental as opposed to be essential, thereby changing the argument I made.

But why think that any being whose existence is identical to its nature is an everlasting being? This substantial claim needs further argument.

Because its existence is essential to it (it is existence after all) , therefore it possesses aseity and is the exhaustive reason for its own existence, being completely independent of every other item in our ontology.

I don't know if you have understood that part in my previous comment, but this is exactly what mere factually necessary beings a la Rowe, Swinburne, Hick or Plantinga are not. They are mere postulations of a first that lack the sufficient reason for themselves and could never be the answer to questions concerning contingent existence or "Why is there something rather than nothing?" because they themselves share the contingent mode of being and are thus as much in need of an explanation as every other entity, with the difference that there is no answer.

They aren't logically necessary, they aren't metaphysically necessary and existence is accidental to them. In the entity in question it is essential. What effect does this difference have? Your current answer would be "None!", but that can't be true.

(5*) If existence is always an essential property of T, then T's non-existence is impossible *in any world T exists*.

Same problem here, either equivocation on existence or wrong understanding of what an essential property is.
I won't rehash the rest line for line, my points should be clear. Obviously I don't see your objections applying in any way.

A last attempt to make the necessary existence in all possible worlds clear is a reference to O'Connors "Theism and Ultimate Explanation" pp. 86-91.

"Is the property of necessary existence something that results from the rest of its essential nature, or from some part of its nature? Apparently, neither of these can be the case, because then there being, ‘in the first place’, so to speak, a thing having the ‘base’ set of properties giving rise to necessary existence would itself be a contingent fact, which contradicts the assumption that NB is truly necessary. That is, there would be a problematic explanatory/ontological priority of these base properties relative to the property of necessary existence – the problem being that the existence of the putatively necessary being would be only conditionally necessary on the instantiation of some more basic features. So, the logic of the concept pushes us to conclude that necessary existence is not a derivative or emer-gent property of NB, but a basic one.
Might it be that, while necessary existence (N), and certain other proper-ties (call their conjunction ‘E’) are alike essential to NB, nonetheless N could have been conjoined to some other nature and not to E, as it actually is?
(That is, might N be only contingently connected to E?) It seems not. Were this so, there would be no explanation for the fact that N is actually connected to E. N is by hypothesis a final, ultimate locus of explanation. There is no getting behind it to explain any purely contingent connections it has with other features.
So, it seems, there must be an internal, necessary connection between N and the correlated nature, E. Which way or ways might the entailment go?
Might E entail N, but not vice versa, leaving open the possibility that there are two or more natures, E1, E2, . . . E20, each of which entails N while N entails none of them? Again, were this possible, E1 and E2 would be explanatorily prior to N. If we asked, Why do the natures E1 and E2 neces-sarily exist, and not some others (E20, say)? the answer would be, Because E1 and E2 – apart from N – are the sorts of nature that simply must be (whereas E20 is not). But this (contrary to intention) can only allow for the entities’ existing by a kind of conditional necessity: given that there is an E1, it exists ‘of necessity’. And this is inconsistent with the claim that the necessity is absolute. So, we conclude, N entails the nature E."

Sorry to Bill for the lengthy quote.
O'Connor doesn't exactly discuss what we're talking about, but it's close enough. He asks what the absolutely necessary being, the conclusion of a contingency argument, must be like.
On the most basic level of ontology, conceived as a layer cake, there must be existence. For Thomas Aquinas, Bill and I, after several lines of argument of course, this would be enough, since it's a concrete layer and no mere abstraction. On O'Connors view, existence is that which entails the rest of the nature of the necessary being. Its entailment by existence is that which enables the necessary being to self-explain its existence. Existence is an actual part, the most fundamental part of its nature. It is absolutely inseparable from it. It follows that this must be the case under all circumstances, otherwise we'd have an accidental property. And there couldn't be any hypothetical power that would make the necessary beings destruction possible, either, since existence is the most fundamental layer there is. There's no getting behind it. The disposition of it to entail certain other properties is the internal explanation of an a se existing being and if we accept that the internal explanation is given in one world, due to its essential being, it's given in every possible world.

I don't mean to suggest that the property of necessary existence is conceptually open to us, no we can't understand it. But the way it has been outlined is what the necessary being must broadly be like if it exists at all. Perhaps O'Connors approach is more intuitive.

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