Monday, December 04, 2006

Josh Parson's Wittgenstein Tractatus Prose Generator

Is here.

Sunday, December 03, 2006

Follow the Bouncing Coloured Existential Ball.

"On Existentialism" from Plantinga (no introduction required, the title says it all...)

(N.B. if your wondering why certain words are in colour, it's because I find it very difficult to keep all the examples of propositions distinct from the objects. No the use of italics are not good enough! So the use of colour keeps them visually and mentally ungarbled.)

Existential Thesis:

Singular propositions (thisnesses) are ontologically dependent upon contingent objects (exemplifications)

Part of the argument against the Existential Thesis:

(3) Possibly Socrates does not exist

(4) If (3) then the proposition Socrates does not exist is possible

(5) If the proposition Socrates does not exist is possible, then it is possibly true

(6) Necessarily, if Socrates does not exist had been true, then Socrates does not exist would have existed


(7) Necessarily, if Socrates does not exist had been true, then Socrates would not have existed

from (3), (4) and (5):

(8) Socrates does not exist is possibly true (i.e. the proposition could have been true)

from (6) and (7):

(9) Necessarily, if Socrates does not exist had been true, then Socrates does not exist would have existed and Socrates would not have existed

from (8) and (9):

(10) It is possible that both Socrates does not exist and the proposition Socrates does not exist exists

Therefore, the existential thesis is contradicted.

My confusion is with the denial of (6), the Pollock or Pollockian Existentialism, or anti-serious existential actualism, or serious anti-actualism with existential flavour, or …, objection. I don’t know what to call it nor do I get what it is exactly. Plantinga tries to clarify the position by adding another slew of premises, but I think (12) is supposed to sum it up:

(12) Necessarily for any object x, possible world W, and property P, if x has P in W, then x exists in W.

I get (12) and I get (6), but it gets a little hazy when you use existence as the property in the support of (12) in order to deny (6). Which seems to be what is going on, at least I think?

Perhaps I shall back up a bit and plug-in Socrates into premise (12):

(12*) Necessarily for any object Socrates, possible world W, and property existing, if Socrates has existence in W, then Socrates exists in W.

This seems to sound okay. But I can’t understand how given (12*) there is a denial of (6) and (7),

(6) Necessarily, if Socrates does not exist had been true, then Socrates does not exist would have existed


(7) Necessarily, if Socrates does not exist had been true, then Socrates would not have existed

Is Pollock (or the anti-serious existential actualist) saying that if we take Socrates does not exist as true then it conflicts with Socrates having the property of existing at W? If so, then they aren’t upholding the existentialist mantra of singular propositions being dependent on contingent objects. It’s the other way round, at least I think? I thought that you couldn’t take the does not exist part to conflict with Socrates having the property of existing at W. That would mean that the contingent object (Socrates) is dependant on the singular proposition (does not exist). Exemplifications are not dependent on thisness. If your following the bouncing coloured ball, red is not dependent on green, but green is dependent on red. Or as Plantinga says from the get go on the existentialist’s behalf:

“… thisness are ontologically dependent upon their exemplifications. Take any thisness t and the object x of which t is the thisness; t could not have existed if x had not. … Every thisness has essentially the property of being exemplified by the object that does not exemplify it. More exactly, the thesis in question is that it is necessary that every thisness has that property; it is not as if there could have been thisness that could have lacked the property in question.” (159)

Yeah… well... the point is that I don’t understand how (6) and (7) conflict with (12). Perhaps if the whole thing was turned into a black and white movie with French subtitles then I’d get the anti-serious existential actualist’s point of view, but as it is explained here, I’m at a loss.

The Great Marriage

I will concern myself with one question:

A randomly selected person, may, when asked, say that he believes that marriage exists, but deny that fictional characters exist. If we say that abstract things such as marriage and promises exist, ought we to admit that fictional characters exist as well?

The answer to this question may lie in figuring out WHY a person would admit the existence of marriage and deny the existence of fictional characters. There are several possible components to this reasoning:

A)"I say marriage exists because I know people who ARE married."
Resp) this is not a good reason. It treats marriage as a property, e.g. "Blaine is married". In the same way we can say, "Blaine is tall": but most people do not believe that "Tall" (or "Tallness") exist. Existence of properties is unclear, and may require a Platonic ideal to understand.

B)"I say marriage exists because it is a concept that can be actualized".
Resp)This response treats marriage in the proper way. But this response leans towards Platonism. What grounds does a Platonist have for believing in the existence of abstractia without being a fictionalist?

C)"Because fictional characters resemble concrete objects that may or may not exist, I am scared to admit that fictional characters exist".
Resp)I believe this is a common reason why people deny the existence of fictional objects - I shall call fictional characters humanoids because they claim to have (disregard van Inwagen) properties that humans have. Most laypeople would fear being called a fool if they would say that Henry IV does not exist because he is dead, and then go on to say Falstaff does exist because Shakespear created him. In the same way, people may be scared to admit that fictional objects exist because of their similarity to mythical objects: try convincing a scientific community that Vulcan exists!

Of course, fear is not a good reason to decide the way things actually are. But no other reasons have been given to say why we should accept one and not the other. That is why I believe that all Platonists should be inclined to be fictionalists. Of course, if one is a Platonist, one should be sure that they hold their views because of (B) and not (A).


In Plantinga's article "On Existentialism" I couldn't find a posative argument for serious actualism, but it looked like rather he was defending it from a couple objections. In any case, his argument against the inference from actualism to serious actualism confused the heck out me. Here's a brief look at some of the confusion.
"(12) Necessarily for any object x, possible world W, and property P, if x has P in W, then x exists in W"
Oh yeah, actualism too:
"(13) There are no nonexistent objects"
After a couple steps he gets
"(15) Whatever has P, exists" (where P is any property)
I get hazy about the point where he derives
"(18) whatever does not exist, exists".
I'm not sure where he gets 18 from. I'm not sure why he's objecting to the argument from actualism to serious actualism in the first place (it doesn't seem to suit is purposes). But playing along, where did 18 come from? And more importantly, why does he have a problem with it? I'm tempted to say that he plugs in the property of non-existence into (15), but this doesn't seem right. At worst it's a trivial statement. By (13) there are no nonexistent objects to fill the first clause of (18) anyway. You certainly can't prove that Zeus exists from (18) for instance. By (13) there is no such thing a Zeus (in the actual world), so it can't be an instance of something that does not exist.
Also, he states that Socrates is one of the things that are, but perhaps not in W. Is he using something other than common domain semantics? Or did I miss something? Priest allows something to BE at world W without existing at W, so I'm (perhaps mistakingly) taking that as standard.
So, given that I don't understand his objection to the inference from actualism to serious actualism, I find myself perplexed to the state of thinking that such an inference is valid. I'm sorry Plantinga!

Tuesday, November 28, 2006

Readings for Monday

For Monday, please read Plantinga, "On Existentialism" and "Reply to Pollock" (copies available in the philosophy department). There are some issues not directly relevant to our main concern in these papers. Look at them with an eye toward extracting Plantinga's two arguments for seriousness (serious actualism, in particular). Next it is worth looking at Bergmann's short paper, "A New Argument from Actualism to Serious Actualism" and Hudson's reply, "On A New Argument from Actualism to Serious Actualism". Then, if you haven't had enough, a good next stop would be Yagisawa's recent paper, "A New Argument Against the Existence Requirement" (an argument against seriousness) and Caplan's reply, "A New Defence of the Modal Existence Requirement". I'm putting a copy of another recent reply to Yagisawa in the department box: McCarthy and Phillips, "No New Argument Against the Existence Requirement".

This is a lot of stuff to work through. I don't expect everyone to read it all. The main objective is to try to distill some arguments for/against seriousness from the above. So it is not necessary to read every word of every paper. Also, this issue is hard. So don't be surprised if the reading is difficult. It's better for you to have a good grasp of one argument than a poor grasp of several.

Sunday, November 26, 2006

Noneist Existence Predicate

I’d like to present an objection to noneism from a very recent van Inwagen paper, “McGinn on Existence”. (Colin McGinn is a noneist and van Inwagen is criticizing him. The objection can be extended to Priest, however.)

Non-noneists accept the following:

~upside down 'A'x~ Fx iff backwards 'E'x Fx
E!a iff backwards 'E'x (x = a)

('E!' is the existence predicate.) Noneists employ U and G quantifiers and define upside down 'A' and backwards 'E' in terms of these and E!. But notice that noneists cannot go on to define E! in terms of backwards 'E'. So noneists employ a predicate that does not make sense to non-noneists. Or if sense is made of it, sense can no longer be made of U and G.

Concerns with Creatures

I will post a few of my worries that I have with Van Inwagen's "Creatures of Fiction".

1)The use of existence/non-existence as as attribute on par with other attributes. We see this in Van Inwagen's assumption about Meinongians, p.299a. He says, "They mean to assert that there are, there really are, certain objects that have, among attributes (such as jollity and rotundity), the attribute of non-existence". My worry is that Van Inwagen is treating existence as a first order predicate, a big no-no according to Kant in his objection to Anselm's Ontological Argument. Kant, in his Critique of Pure Reason, writes "BEING is evidently not a real predicate, that is, a conception of something which is added to the conception of some other thing. It is merely the positing of a thing, or of certain determinations in it. Logically, it is merely the copula of a judgement". If we treat existence as an ordinary attribute there is no stopping the Ontological Argument to prove God's existence, a priori. Because the Ontological Argument appears fishy to most people, we should accept that Kant was right in his assessment of the existence predicate. I have not yet thought out the consequences for Van Inwagen, among others, nor am I convinced that he thinks this way. However, I put forth the concern.

2)"I do not see how it is I am supposed to use (Ix, [supposedly the same as (Crazy Ux]) and (Backwards Ex)" (300). This solution is simple according to Priest's set up. We just read Ix as applying to all worlds, and only commit to existence in the use of (Backwards Ex).

3)"If the Meinongian is asked, 'About your Mr. Pickwick--has he an even number of hairs on his head?,' he will answer... 'He neither has nor lacks the property of having an even number of hairs on his head; he is therefore what I call an incomplete object" (300). - Meinongians say that an object is incomplete because it does not exist. Surely if Mr. Pickwick existed he would have either an even or odd number of hairs on his head, but a Meinongian cannot say this. Van Inwagen faults Meinongians for this--yet his own solution is to say that when an author writes about some attribute of a character, e.g. Mrs. Gamp's fatness, she does not have this characteristic in the normal sense, but somehow bears a "certain intimate relation to fatness"(305). In the case of hairs on head, she would bear no relation if the number was not specified, so Van Inwagen's answer is the same as the Meinongian's.

4)The scope of existence. I believe Van Inwagen wants to say that Creatures of Fiction exist in the general sense of existence. He says "Anyone who said that there were such things as characters in novels, and went on to say that there was no such thing as Mrs. Gamp would simply be factually ignorant. He would be like someone who said that there were such things as irrational numbers, but no such thing as [pi]" (302). I am not sure that his solution guarantees this, though. First, notice how he phrases the above sentence. He always says "characters in novels". Now, it seems that even a Meinongian will say that characters would exist if the world of the novel was the actual world. This response, of course, does not entail that we say Mrs. Gamp exists in this world. What I believe is that all of Van Inwagen's references to the existence of characters fall within the scope of the world of the fiction. See, for example, all of his logical renderings of sentences 4-7. His later solution affirms this when he says, "The proposition commonly expressed by 'Mrs. Gamp is fat' we may express by 'A(fatness, Mrs. Gamp, Martin Chuzzlewit)'" (305). Only a later change suggests we can fill in 'x' for 'Martin Chuzzlewit', but this variable seems to be crucial to our interpretation of the relationship. For example, if x is a fiction like 'War and Peace', we cannot ascribe new things to the physically existing (in some higher sense, supposedly) persons, like Napoleon. So it seems we NEED to locate the character within his proper world. Therefore, there is no guarantee that the character exists in our own.

A Confessional About How a Priest Lacks Virtue.

I have a confession to make… most of my confusion while reading Towards Non-Being stems from the odd sentence or two (not the whole thing as a conjunction thereof, ha!) that Priest chucks out that lack any argument. He takes for granted certain claims as undeniable, then leaves things the way they are full stop and carries on. Today, I shall harp on one of these priceless Priestly moments which can be found in the chapter on Fiction (second paragraph of 6.2).

I have another confession to make… The ‘p’ word, as in phenomenological, makes me queasy. It’s similar to the word intuition. I find both words to be nebulously vague (yes, nebulous & vague, not either or) when used to define something, and when used, lend to more questions than clarifying answers. So, I’ll use (and hopefully Priest is using the term in the same manner) it as is defined in the Stanford Encyclopedia’s entry on phenomenology:

“Phenomenology is the study of structures of consciousness as experienced from the first-person point of view. The central structure of an experience is its intentionality, its being directed toward something, as it is an experience of or about some object. An experience is directed toward an object by virtue of its content or meaning (which represents the object) together with appropriate enabling conditions.”

So, with this definition in the back of our minds, imagine me on the bus eavesdropping on two chicks, and their conversation goes something like this:

“blah, blah, … yeah I remember hearing this story about a kid whose family decided to emigrate over to Canada from India. So they managed to hitch a ride on a boat that was carrying a bunch of circus, or zoo, or something, animals on it. But, the boat shank and the kid had to survive on a dingy for like months with a bunch of animals. Crazy, eh!”

On overhearing this story I’m struck with many intentional states, like admiration for, sadness for, etc., about the kid in the story. Then the conversation goes on:

“Yeah that’s crazy. So where did you hear this? An who was the kid?”

“I think his last name was Patel or something. Someone wrote a book about it a few years ago called The Life of Pi.”

Now I, being reasonably up on my Canadianna, am darn well aware that The Life of Pi is a work of fiction cooked up by an author named Yann Martel. There is no kid named Pi Patel who endured a heroic journey as described from India to Canada. And my intentional state about some object, in this particular case the kid Pi, has dramatically changed. The admiration for, sadness for, etc., I felt is now of a lesser degree.

It’s important to note, that Priest does not claim that you cannot have intentional states based on the existential status of a fictional objects, he claims quite the opposite, that we can have the same full bodied experience about a fictional object as we would about an existent one. What he claims is that the existential status of an object “is completely immaterial phenomenologically.”(117) But, if the status of a fictional object is completely immaterial, then why did my admiration for, sadness for, etc. change? Perhaps, this point is more in the domain of aesthetics with reference to such classic examples as Carroll’s Loath Letter (a personal fav.!) or Moore’s Glass Flowers, which do not illustrate directly the issue of existence vs. non-existence. But, do show that our intentional states about an object can vary or flux depending on that object’s phenomenology.

Our intentional states (or experience of or about some object O) is by virtue of O’s content or meaning (it’s representation or phenomenology). One is not immaterial to the other.

To compound the issue further, if Priest wishes to define existence as just another thing in the set of properties (as seen in the Proof of Arbitrary Existing Entities below) to get out of the mess that CP causes for Meinongians, then he will have to give an account as to how the existence property can be prized out of the set before, during, whenever, it is connected with a representation. Properties, intentional states, and representations are all connected by virtue of each other. In this case virtue does make a world of difference!

Saturday, November 25, 2006

Necessary Existence Revisited

Accepting premise 1 that we can quantify over everything, let's look at premise 2: If (1) then it's not possible that there's something such that, possibly, absolutely everything is distinct from it."
I think, in its current form, premise 2 may be denied. Indeed, there isn't actually something such that absolutely everything is distinct from it, however it may be possible that there is something such that, possibly everything is distinct from it. Take an arbitrary x in the domain (which includes all existent things).

1. It is not necessary that x be in the domain (that x exist)
2. If (1) then (3)
3. It is possible for x to not be in the domain
4. If (3) then (5)
5. It is possible for everything in the domain to be distinct from x
6. If (5) then (7)
7. There is something such that possibly, absolutely everything is distinct from it
8. If (7) then (9)
9. It is possible that there is something such that possibly, absolutely everything is distinct from it

Why is this argument able to fly in the face of the good reasoning that gave us premise 2? I think the answer lies in the notion of "possible". To say something possibly doesn't exist is roughly equivalent to saying that possibly everything that exists is distinct from it. For any existent object this obviously isn't the case, but that doesn't exclude the possibility for it being the case. Note, that the case in which the possibility is fulfilled, it is not contradictory to the necessity of identity. If the object were to not exist, it wouldn't be in the domain anyway, and thus would need not be distinct from itself. The argument for Necessary Existence depends on a rigid domain, but the notion of possible non-existence depends on the domain being flexible. So clearly, if we hold the domain rigid in our logic, it will look like the domain can't possibly be other than it is.
So, let's reformulate premise 2 of the original argument to see if it can still cause trouble:

2*: If (1) then it's not possible that there's something such that absolutely everything is distinct from it.

Here I removed the possibility operator I exploited in my argument. If we follow the original argument through using 2* instead of 2 we get the conclusion:

C: Necessarily everything exists.

Let's rephrase that in terms of the domain (which still includes all existing things).

C*: Necessarily, everything in the domain is in the domain.

This is beggining to look a little less threatening let's rephrase it one more time.

C**: Necessarily, for every x in the domain, x is in the domain.

Does this still say that necessarily everything that exists exists? No, this is little more than the law of identity applied to the domain itself. It doesn't exclude the possibility of different things being in the domain, but if those things are in the domain they better be in the domain.

To sum up, I deny premise 2 of the argument previously presented in the blog, but maintain the necessity of identity. I do this with the simple obvervation that in possible scenarios, it's possible that the domain be different than it actually is.

Sunday, November 19, 2006

A Reluctant Defense of Quine

There are a few ideas in Quine's "On What There Is" that, if taken seriously enough to support better, might warrant a closer look than Priest gave. Quine "gives up" the word exists, but makes the fatal mistake of letting Russel keep it, and that's where Priest jumps on him:
2. Meinong believed that there exists a unique being who is chief god living on Olympus, and he lives on Olympus...
Meinong did not believe the Greek gods to exist any more than you or I do: he knew they were mythological." page 110
The criticism is that under Quine's strategy 2 comes out true. Priest, on the same page states the very thesis that undermines this objection:
"To be assumed as an entity is, purely and simply, to be reckoned as the value of a variable" Priest quoting quine page 110
While one is under no obligation to accept Quine's thesis, it is still true that if his thesis is true, than sentence 2 is true. Meinong DID believe a unique being who is chief god living on Olympus exists(by quine's definition of 'exists').
Now the issue comes down to simply what it means to exist. In essence, it's just the debate about seriousness. If one is "serious" than Quine's thesis isn't far-fetched at all. Just like Priest can demmand some sort of support for Quine's thesis, Quine make a counter demand for some justification on why he can have non-existent objects being quantified over. Priest would then call Quine prejudiced against non-existent objects, and Quine would find something to say back; then maybe give Priest a different name and start attributing to him theories he doesn't accept at all.

Priest has another issue with Quine that is perhaps a stronger one. That is, Quine's strategy for deriving meanings of empty names rests on replacing the name with a definite description. This makes him a targed of the modal&epistemic objections, as Priest points out. And as proff Tillman pointed out to me, it also makes him target of most, if not all, objections raised against Frege. Still, consider the two ways of referent fixing: 1) baptism by perceptual contact 2) reference fixing by description. Note that in the case of empty names, (1) is impossible. In the case of 2, the name is originally dependant on a definite description. It would take more research and space to flesh this out than a mere comment paper; but perhaps this can be exploited to get a plausible theory of descriptivism that applies to empty names only. If this can be done, Quine's method would be sort of plausible. And if this were so, it could solve the paradoxes of non-existence, while still allowing seriousness and a relatively small ontology (it would require at least past&presentism). Contingent on this massive project of empty-name descriptivism, Quine's may be the best theory on balance.

The Metaphysics of Idol Worship: The Paradox of the Ancient World

Well, I thought Priest's argument concerning his readings of Quine and Russell were sound, so in order to stir up some excitement this week I'll have to resort to making up a crazy theory of my own. If you are looking for something to comment about, feel free to attack this article, as I do not sincerely hold to the view that I will present below. I leave it up as merely a possible theory to consider.

We come to the problems surrounding the paradox of nonexistence. As discussed in class...

Homer worshipped Zeus
seems true.
The sentence is true iff the object denoted by 'Homer' bore the relation expressed by the word 'worship' to the object denoted by 'Zeus'.
One problem: Zeus does not exist.

The noneist has a ready answer to the paradox of nonexistence because they allow for the object denoted by 'Zeus' to be nonexistent. However, for those who take a different approach, the paradox presents a real concern.

I offer these opponents of Meinong a solution:

(1)Ramses worshipped the sun
It is clear that this sentence is clear of paradoxical worries. The object denoted by 'Ramses' bore the relation expressed by the word 'worship' to the object denoted by 'the sun'. The sun is a concrete, existing object and thus there is no problem here.

(2)Ramses worshipped Ra
'Ra' is the egyptian sun god. When Egyptians worshipped Ra, they worshipped the sun. The object denoted by 'Ra' is the sun. We see this in an egyptian hymn to Ra, which reads:

"Homage to thee, O thou who risest in the horizon as Ra,
thou restest upon law unchangeable and unalterable. Thou
passest over the sky, and every face watcheth thee and thy
course, for thou hast been hidden from their gaze. Thou dost
show thyself at dawn and at eventide day by day..."

Thus, this case, too poses no paradox.

But what about (3)?

(3)Ra raised Osiris from the dead.
It is obvious that the sun did not raise somebody from the dead, nor did the Egyptians intend it this way. Ra had characteristics and performed actions beyond that of the sun. Does this lead us into paradox? Consider the following...

(4)William Wallace shot bolts of lightning from his arse.
William Wallace, the real Scottish fighter, did not do this. The truth value is false. However in...

(5)Peasant Joe believed William Wallace shot bolts of lightning from his arse.
It is the case; this sentence is true. This poses no paradox, as Wallace was a real man. An untrue, and fanciful, statement (arse lightning power) was attached to the concrete being.

Such could be the answer to (3) - Ra is the concrete sun with a fanciful statement attached to it which is false. However, the Egyptians believed it to be true.

So we return to

(6)Homer worshipped Zeus.
As we have said, Zeus does not exist. However, there are today, and in the times of ancient Greece, what we would call 'idols' of Zeus, including the incredible statue at Olympia. When one such as Homer were to worship Zeus, he would be in front of a statue, or call to mind the mental representation of the carved god. It is clear where I am going: idols are concrete objects. Stories of deeds of the gods can be attached to the figure of an idol, without resulting in the paradox of nonexistence. Notice that something such as 'framus' has no idol or concrete representation. It is truly meaningless, whereas 'Zeus' is not.

Tuesday, November 14, 2006

Necessary Existence

Okay since we're not doing necessary existence, I'm going to present what I take to be a fairly upsetting argument that is discussed at length in the readings for the 'necessary existence' section of the course syllabus.

First, note that often when people use 'everything' and related quantifiers, they don't mean it. So a used car salesman may say 'everything is on sale' and not mean to imply thereby that my sweater is on sale. Similarly you might say 'there's no beer in the fridge' even if there's a tiny puddle of beer at the bottom of the fridge.

But in order to do metaphysics, it must make sense to use 'everything' to mean absolutely everything, rather than some restricted domain. So for example if you make a metaphysical claim, like 'God does not exist', and you're only quantifying over some subset of everything (like the used car salesman does), then you have not succeeded in making an appropriately metaphysical claim. That's because if your domain of quantification is restricted, then it is compatible with what you said that God does exist--he just is outside the domain you are quantifying over. Similar considerations apply to any other putative metaphysical claim.

I will assume without argument that it's actually possible to do metaphysics. Since this seems to require that we can quantify over absolutely everything, I'll infer from the assumption that we can do that too. So we have (1):

1. We can quantify over absolutely everything.

But if (1) is true, we can ask the following question: Is it possible that there's something such that, possibly, absolutely everything is distinct from it?

The answer is 'no'. Take any candidate. If it's possible that that thing is such that, possibly, absolutely everything is distinct from it, then it is possibly distinct from itself. (Remember, we're quantifying over absolutely everything.) But nothing is possibly distinct from itself. (That is, if a = a, then necessarily, a = a.)

So we established the following:

2. If (1), then it's not possible that there's something such that, possibly, absolutely everything is distinct from it.

By modus ponens, we may infer (3):

3. Therefore, it's not possible that there's something such that, possibly, absolutely everything is distinct from it.

But (3) is logically equivalent to saying that necessarily, it's not the case that there's something such that, possibly, absolutely everything is distinct from it. So we have (4):

4. If (3), then necessarily, it's not the case that there's something such that, possibly, absolutely everything is distinct from it.

But the consequent of (4) is logically equivalent to saying that necessarily, absolutely everything is such that, it's not the case that, possibly, absolutely everything is distinct from it. So we have (5):

5. If necessarily, it's not the case that there's something such that, possibly, absolutely everything is distinct from it, then necessarily, absolutely everything is such that, it's not the case that, possibly, absolutely everything is distinct from it.

But the consequent of (5) is logically equivalent to saying that necessarily, absolutely everything is such that, necessarily, it's not the case that absolutely everything is distinct from it. So we have (6):

6. If necessarily, absolutely everything is such that, it's not the case that, possibly, absolutely everything is distinct from it, then necessarily, absolutely everything is such that, necessarily, it's not the case that absolutely everything is distinct from it.

But the consequent of (6) is logically equivalent to the claim that necessarily, absolutely everything is such that, necessarily, something is identical to it. That is, necessarily, absolutely everything necessarily exists. So we have (7):

7. If necessarily, absolutely everything is such that, necessarily, it's not the case that absolutely everything is distinct from it, then necessarily, everything necessarily exists.

By (2-7) and multiple modus ponens, we infer the conclusion:

8. Therefore, necessarily, everything necessarily exists.


The ways out seem three-fold: deny metaphysics is possible (i.e., deny (1)), deny necessity of identity (i.e., deny (2)), or deny the logical equivalence between (2) and (8) (so deny one of (3-7)). Not an attractive set of options.