Oh. If that’s the case, then he should recuse himself altogether from the argument, and in fact from any argument where truth is contingent. The axiom does not require that you accept the existence of anything at all; it merely requires that you accept the possibility of necessary existence.
That’s because you’re looking at it from the point of view of the world (in isolation) and not from the point of view of the Being (for Whom all worlds are accessible). All you see is a leg, and the Being has legs in many worlds. Your world might not contain all truths.
Eris
Okay.
That’s the only assertion that is reasonable, Eris. It is either make that assertion or recuse myself from the argument as you have done (or should do).
Tell me, please, when you have ever before required or been required to prove an axiom. That is simply outrageous. And you know that. Should Ayn Rand have been forced to prove that existence exists? Should Peano have been forced to prove that every number has a successor? Should Euclid have been forced to prove that all right angles equal one another?
Why do you introduce that burden in this case?
Okay, I’ll cut you the slack because you’re you. But I think reject is too strong a term. I think it implies that you do know that it needs rejecting.
I demonstrated it as best I could, but you know very well that I can’t prove it any more than I can prove that A is A.
Ok, first of all I apologise if what I say in this post has already been said. I tried to read every post in this thread, but I ended up skimming a lot of them.
First of all, I know this has already been mentioned but I didn’t see a response to it. Why should the greatest possible existence exist? Or rather, of all the possible existences, why should there be a greatest one? There are many things which don’t have any greatest element. For example, consider all the negative real numbers (not including 0). Given any negative number x, x/2 is greater than it. Many other similar examples. Or, if you prefer a concrete example, the longest rod of finite length: Given any rod you can add an inch to it’s length, and you will have a longer one. I’m not saying you can’t have a greatest possible existence, merely that this needs proving. i.e. Axiom 2 is by no means certain.
Secondly, can you always compare two objects and say ‘which of these is greater?’. For example, take a spoon and a fork. Which one of them is the greater object? (It is of course irrelevant as a spork is superior to both, but it’s just an example. ). In mathematical terms, greatness is a partial order but not a total one. So essentially what you’ve proven is that a god exists, but there may be more than one. (Minor nitpick I know). So your definition of god as the greatest possible being should really be modified to god as a greatest possible being.
Thirdly, I’d like to know what you mean by ‘existence’ and ‘possible world’. For example, does a world in which the only true statements are tautologies count? What would god be in such a world? What about the game of life - That would seem to be in a sense possible, but there is no god in it. For that matter, how would you define greatness in either of these worlds?
I’m not sure how interesting it is to prove that god must exist anyway. If I find myself convinced by an argument for the existence of a god, I will merely define myself to be god - There’s no real reason to conclude that this universe exists anywhere outside of my own imagination, therefore I must be the greatest possible being, as everything else is merely a figment of my imagination. (No, I don’t really believe that, but I just don’t think it’s a terribly useful definition).
For the record, I too don’t believe in the validity of modal logic for establishing existance. I don’t believe that anything except tautological statements exist neccesarily.
Incidentally, a nitpick: please don’t say G=G. That’s wrong, as it means you have a sentence that is not well defined. G=>G is a perfectly well defined statement.
Libertarian:
“Preguntas
That was actually cute. It’s going around the world to get to your elbow. But it’s cute (and invalid). Can you and I kiss and make up?”
What is invalid? This isn’t the apology I deserve. Remember you were the one who exploded at me. Not the other way around.
Do you see why it is necessary to prove Brouer’s theorem? I see it as the heart of the argument. In Tisthammer’s proof of Brouer’s theorem, I think the sound interpretation of worlds and possibility renders the proof invalid. One of the statements is nonsense, and symbolic manipulation of nonsense cannot be a valid proof.
I think your condescending tone deserves a like response. I think you don’t have as deep an understanding of the proofs here as I do. You seem to have completely forgot that Tisthammer’s proof used ~G=>~G. You say:
“Where the hell did I say, what is it, “~G => ~G”?”
as if you’d never seen it before. If you had really thought about Tisthammer’s proof, how could this have happened? Why didn’t you recall this? Also you wrote:
“Brouer’s Theorem is not proved (at least I’ve never seen it proved) with Becker’s Postulate.”
Since Tisthammer’s proof is a proof of Brouer’s theorem, you obviously did not think about the proofs long enough to realize the equivalence. I have no desire to continue a discussion at your pace. So that is why I won’t post to this thread again.
You’ve chosen to call it an axiom, and when we accept it as an axiom, the proof follows. No one is disputing this at all.
I do not feel that it is a “good” axiom, since ~<>G seems to be just as viable to me, within the context of the proof, whose only other assumption is G->G.
Now, you want to impose more meaning into G->G and say that “G” is equivalent to “God exists”, making G->G represent “If God exists, God exists necessarily”. You then proceed to bring in your next assumption, <>G, which would translate as, “I can construct (or, alteratively, there exists) a logical world where God exists [which may or may not be this world.]” Do you not see that this is the assumption that has caused many of us so much grief here?
Now, let’s look at our definitions. “God is the greatest possible being.” “Greatest” has no home in modal logic. We are interpreting “greatest”, modally speaking, to mean that the only existence God can have is necessary existence, or that “G->G”. Fine. But that doesn’t represent “God is the greatest possible being”, it represents that “God’s only type of existence is non-existence or necessary existence.”
Now, we also want to say, “God is possible”. This presents us with no problem in English, and I agree in English. God is possible. In modal logic, though, you are saying that there is a logical world where G is true. Typically, in all the logic I’ve studied, and in all the math I’ve studied, existence declarations like this are proved, not assumed. Typically. It seems to be quite a mouthful to say “There exists a logical world where God exists.” The average theist already takes this on faith, and says that this logical world is our world. The average atheist demands a demonstration of this. Translating it into symbols doesn’t remove the necessity or burden of proof.
Again, if you are forcing me to accept it as an axiom, then you are correct in your assessment (as far as I can tell). So what? I can make anything an axiom and demand you accept or reject it. And I think that is what you’ve done here.
We don’t know that god is possible as in “<>” because we don’t have a logical description of God within the proof, we have your semantics assuring us that it must be so because “The greatest possible being must be possible by definition.” Not in logic, man, not that I’ve ever seen.
No, you can’t. And that’s why the argument cannot be used to prove what is the greatest possible spoon. The argument is about modalities of existence: possibility, necessity, and actuality.
Existence can mean one of three things: true in at least one possible world; true in every possible world; true in an actual world. Existence and truth may be considered as synonyms. Worlds without truth do not exist.
A possible world is a world with at least one true statement.
That depends, I suppose, on what you mean by God and what you find to be interesting. In this case, the meaning of God is unequivocal: He is the Supreme Being, and capable of all possible capabilities. Whether you find that interesting or not is itself interesting, but not relevant to the argument.
I take it, then, that you don’t believe what you just said. It was not a tautology.
Huh? Since when does a definition have to be a wiff (well formed formula)?
Preguntas
Don’t get too carried away with yourself. You can’t just grab an inference from here and another from there and go, “Oy! I have a syllogism!” It doesn’t work that way. One inference has to follow from another.
Oh, okay. It seems to me that some people are disputing that, but if you aren’t, then I have no quarrel with you on that.
You’re entitled. But you have not explained to my satisfaction (not that you have to) how the modal status ~<> might be compatible with the modal status .
But that’s backwards. G -> G follows <>G. It doesn’t precede it.
It is unfortunate that plain English and formal language have entwined, I grant you. But as Plantinga said, “It does not take a neo-Platonist to agree that the greatest or most supreme being intended in the argument is certainly one whose powers of existing are maximal or whose mode of being is, as existence qua existence goes, supremely perfect.”
But one thing is certain: unless none of us exist, then necessary existence cannot be equivalent to (nor ORd with) nonexistence.
I think what the average theist takes on faith is the argument’s conclusion (that God exists in actuality), not the argument’s axiom (that God exists — having been defined as necessary existence — in at least one world).
At any rate, I don’t understand why you say that such statements on existence are not typically offered as axioms. I don’t know how Rand’s “existence exists” could be less existence-centric. Likewise, Peano’s assertion that there “exists” a successor to every number and zero is making an existential claim.
Well, no. Once I understood that you were uncomfortable with either accepting or rejecting possibility, I allowed that you may recuse yourself from the argument. You shouldn’t comment one way or the other about its validity or soundness in that case. Wouldn’t you agree?
If it’s proved, then there were inferences before it. I’ve never seen an axiom proved. Not in logic, man, not that I’ve ever seen.
No, that would be a proof that things neccesarily exist. Further the statement it demonstrates exists neccesarily is a tautology. I said “Why should the greatest possible existence exist?” Infinite sets with a partial order on them don’t neccesarily contain a maximal element.
ok. So let’s be clear on this. What do you mean when you are comparing greatness of concepts? The number (well, cardinality - It will be infinite in most cases) of possible worlds in which it exists? In which case it’s still not a total order - It’s quite possible to have distinct concepts which exist in an equal cardinality of possible worlds.
Actually, that seems to be based on a pretty big assumption - That the only reasonable form of logic is the one we use. But that’s a side issue.
Now please explain to me what you mean by:
a) A world
b) The difference between a possible and an actual world.
My point was that you haven’t really shown anything, as a perfectly valid interpretation of the existence of god is this:
a) I am imagining everything in this world I percieve.
b) Therefore I am the only being in this world.
c) Therefore, as god exists in all possible worlds, I am god.
I said I don’t believe in neccesary existence of non-tautologies. Whether I believe in existence is still an open question.
Observe what happens if you’re not careful with making your definitions well formed.
Let S=(S=>G)
Suppose S:
S
S=>G (as S=(S=>G))
G (Modus Ponens on 1 and 2)
Therefore S=>G. Hence S. Hence G.
Look familiar? It’s from a thread we both participated in a while back. It’s a good example of this type of problem.
You cannot construct a finite sentence G=G .
This isn’t a problem for the argument itself, merely somewhere you have to be careful with notation.
What?!?! Why would it have to be compatible with ? Besides which, plenty of people have shown how they relate:
is equivalent to ~<>~.
So…? Besides which, you’re the one who demands we accept ~<>G if we reject <>G. Our last bout suggested we put in <>~G instead since, by all rights, it should be possible.
this is so at odds with everything you’ve said. First it was an axiom. Then it was a definition. Now it follows <>G? How does it follow it? What does that mean?
You’re right. It should have been necessary non-existence.
Please read and reread and reread that quote again and again until you see that you are asserting god’s own existence. Rub-a-dub-dub (oh Hail Eris), that’s what we’ve been telling you for a long time now. And that’ what you think this thing “proves”.
I didn’t say the never are. They usually are. And, certainly, the theological debate for the last two thousand years or so has focused on proving that god must logically exist. To prove this, you assume he exists.
CHRIST. I mean, this is really making me upset, Lib. I’m beginning to guess at ulterior motives here.
Bullshit! I reject accepting an “axiom” that god fucking exists! That’s it! I want you to prove that. If you cannot prove it, I will not accept it.
Here’s an axiom for you, Lib: I can describe a world where Eris exists. Oh, and here’s another, if she exists anywhere, she must exist everywhere. But she exists in my head! I can conceive of her! So she must exist in the world, too!
Infinite sets? It’s difficult to parse the syntax in your paragraph (I can’t find a subject for your “is”), so I might be way off base in what I’m understanding you to be saying. The proof I gave you (and its commentary) is unambiguously labeled as “Proof of Necessary Existence” and shows that necessary existence is true in every possible instance.
If your question is why must necessary existence exist (in other words, for what epistemological reason) then I would give the same answer that I’ve already given here. Certain statements are universally true, such as the Law of Noncontradiction, which is true in every possible world. You should know this intuitively since you value tautologies so much. The negation of a tautology is a contradiction.
Infinity again. I don’t know why you’re introducing a very unnecessary entity. This isn’t a discussion of Cantor’s theories. Greatness here is expressed ordinaly. (Have you read any of the thread? I covered this in detail more than once.) Greatness is merely a plain English description of degree of possibility. The greatest existence is existence such that ~<>~E.
Well, I assumed you were asking what the terms mean in the context of modal logic. Why on earth would you mean something else here in this thread?
I hope I’m not walking on glass here. You are asking what I mean by them in the context of this argument, right?
As I’ve explained before, once or five times, a world is a set of statements.
A possible world is a world that contains at least one true statement. (Didn’t I just answer that in the previous post?) An actual world is any arbitrary possible world that is specified as “having truth under [symbol]t[symbol]”, in other words a world that is known to have truth.
Sorry, but I don’t follow that at all. Can you form it into a tableau for my feeble mind?
I can imagine it would be.
It’s not an implication. It’s a definition. Is there such a thing as a definition that is not recursive?
Why, thank you for your sage advice. I’ll tread as carefully as, um, possible.
I’ll catch you in the morning, my friend. My lovely wife is home now and my eyes hurt. Until then, please consider that fact that necessary existence does not directly imply possible existence. There’s no axiom that states G -> <>G. (Although there is one that states <>G -> <>G, the so-called 5 Axiom.)
This is the part of the proof that I’m having lots of trouble with. Below this definition is a fairly straightforward proof, I don’t pretend to understand it 100% but I will assume it to be true for the moment. If the lower sections are valid, then anything that we can describe in the above manner will be proven to exist, whether it be God, Santa Claus, or a darn SuperPickle. (you know, “What’s red, white and green and is faster than a speeding bullet?”)
What is it specifically about God that separates it from Santa and SuperPickle? God is the greatest possible existance, Santa is the greatest possible gift-giver, and SP is the greatest possible pickle. Is God the only thing that meets this criteria? For some people, God is a construct very similar to Santa, nothing more than a fairy tale, why should God enjoy properties that Santa doesn’t? I have no problem with defining God as the “greatest possible existance” but what about that is more special than the “greatest possible pickle”?
Well then. In order to help you parse the grammar:
‘the statement it demonstrates exists neccesarily’ is a tautology. Therefore it doesn’t contradict my belief about neccesarily existence.
However (for the third time) I will explain what I am saying.
I am not arguing that neccesary existence is not possible. I don’t believe it is, but that’s irrelevant to this point.
You consider things which possibly exist. We can consider this as a set. This set is clearly infinite, as the set of tautologies is a subset of it and the set of tautologies is infinite.
You are comparing objects by saying one has greater existence than another. This is what is known as a partial order, in that it satisfies the following three properties:
For all X, X does not have greater existance than X
For all X, Y and Z, if X has greater existance than Y and Y has greater existance than Z, X has greater existance than Z.
For all X and Y, both of X has greater existance than Y and Y has greater existance than X.
Or, as you like symbolic logic, it can be written this way (using > to mean 'has greater existance than)
(x) !(x>x)
(x)(y)(z) (x>y)^(y>z) => (x>z)
(x)(y) !((x>y)^(y>x))
You will agree that it has all these properties?
Were it a total order, it would have an additional one:
4. (x) (y) (x>y)v(y>x)v(y=x)
However you can have things which exist in the same number of possible worlds and are of equal greatness, e.g. any two tautologies are true in every world, and thus have equal greatness.
…
Hold on. You’re looking for the greatest possible existence. i.e. Something that exists in all possible worlds. Say… for example the statement (x) x=x ? Anyway, I’ll continue with my explanation of my first objection as I know you won’t accept this one.
Now, you are defining god as the greatest possible existence. However, not every partial order has a greatest possible element. Examples have been given, but seeing as you don’t seem to have read the rest of those posts, I’ll repeat them:
The natural numbers. 1, 2, 3, 4, 5…
m > n iff there is a natural number k s.t. m = n + k. It’s trivial to show that this is a partial order (in fact a total order). Now assume there is a maximum natural number N. N+1 > N, so N wasn’t the maximum. There are many such examples.
My complaint is that you have automatically assumed that your ordering must have a maximal element. This is not a valid assumption. It may be true (I do not believe it is, but that isn’t the point), but the burden is on you to prove it.
I don’t particularily value tautologies, it’s just that I don’t believe anything else can be neccesary.
I’m introducing infinity and cardinality here because it’s an alternate way of looking at things.
Umm… The response I’dlike to make to that isn’t polite enough to include in GD, so I’ll just say “Have you?”
What my discussion of set theory is supposed to show is that it is by no means self evident that there should be such an existence that is non-tautological.
(Note: Coding corrected so the symbol shows. Hope this doesn’t count as misquoting you.)
ok. Good. That’s what I was after. Consider the following two worlds:
Each consists of the symbols A, !, => (and thus by the standard definitions, v and ^ as well).
World one consists of: !A and all logical consequences of it.
World two consists of: A and all logical consequences of it.
Consider a statement B which is true in both worlds. Either B is a tautology, or it is a consequence of both A and !A.
Therefore A=>B and !A=>B are both tautologies.
!B=>A
!B=>!A
By the contrapositive.
Thus !B=>A^!A
!B=>!(Av!A)
Av!A => B
But Av!A is a tautology (law of the excluded middle), so B is a tautology.
Therefore the only statements which are true in all possible worlds are tautologies of the standard statement calculus. Hence your G must be a tautology of the statement calculus, and thus not particularily interesting.
Very well.
a) What do I know about this world? Only what I observe and deduce from said observations, yes?
b) Therefore the existence of anything other than myself is an undecidable proposition. I could equally well be imagining it.
c) Therefore by considering the statements which are true only from what I can deduce from my consciousness and perception (without acknowledging that my perception corresponds to anything other than my own imagination) we arrive at a set of self-consistent statements.
d) These statements thus form a possible world.
e) In this possible world there is only one being - myself (or an exact copy of myself).
f) God is a being which exists in all possible worlds.
g) Therefore god exists in the possible world in d.
h) By e there is only one being in the world of d.
i) Therefore that being must be god.
j) Therefore a being exactly equivalent to myself in every way is god.
k) The being is exactly equivalent to me, and thus I too must be god.
l) Feel free to worship me any time. Donation box is at the door.
Wow. I almost feel offended there… Oh wait, no I don’t. Never mind.
I can’t think of any offhand, but that’s irrelevant. The point is that it’s not a proper recursive definition, in the same way as defining n recursively by n=n+1 is wrong.
Is this clear? Not really. Maybe G = (A = A). No, we must be clear on the fact that we are speaking of a greatest possible being. I will not argue here that G -> G does not apply to a greatest possible being, but I am saying that G -> G, on its own, could be interpreted as (A = A) -> (A = A). Interpreting it as the greatest possible being may in fact be extremely reasonable, but it is out of the domain of the proof.
Now that we are clear on the definition, we can discuss the one premise. <>G. Is it possible that there could be a greatest possible being? Is it possible that there could be a necessary being? At first it seems that it is possible, because you can imagine a world with a logically necessary being.
And here is where I am glad you mentioned Plantinga. Plantinga notes that it is a valid argument, but he does not argue directly that it is sound. Because the question of accepting <>G is the question of accepting the modal theist’s account of the nature of logical space. In other words, if you accept the modal theist’s account of the nature of logical space, then <>G is reasonable.
However, Plantinga notes that you should consider the following argument:
There is a possible world which has the property of no-maximality.
A world has the property of no-maximality if no entity in that world has the property of unsurpassable greatness–i.e. if no entity has the world-indexed properties of being-maximally-excellent-in-A for every world A.
(Hence) No-maximality is exemplified in every possible world–i.e. there actually exists no being who is omnipotent, omniscient, morally perfect, etc., and who has these properties in every world.
This is also a valid argument. The question is again whether you accept the premise. And again this is based on your account of the nature of logical space. One account makes the first argument seem reasonable, another account makes the second seem reasonable. Of course there are also people who do not believe that they know enough to accept either account. To these people, neither argument is reasonable.
Hmm… I thought the G = G definition was just a typo. If that is the actual definition it makes no sense. I’ll just assume it was supposed to be G -> G because then the argument is valid.
I also think it is interesting that Av!A => B is provable in modal logic, as Kitarak has shown.
Unicorns are described as mythological creatures. Irrational numbers have mathematic evidence supporting them. And materialism is generally described as a belief. And god is generally described as a belief and/or conception as well, instead of a solid fact. You say that god is the greatest possible existance. I say you’re assuming god is, since you have no evidence to support it. You’ve covered various fringe elements, but you still refuse to give solid support for the most basic of assumptions in your argument. Without support, your whole argument fails.
Big deal? I know what definition you’re using for supreme being. However, if you were using this definition (Which states pretty well that it isn’t a sure thing), then your argument is again flawed because it’s relying on an unknown value. If it’s true, the argument is true, if it’s false, the argument is false. Prove it’s true, or the argument doesn’t have an answer either way.
Wait a minute… Are you refusing to clarify your own possition? Or are you trying to imply I’m not going to listen to it if you did?
Your statement is not “self-evident.” As for the second half of the definition, if it’s “accepted” to be true only for the basis of the argument, then you have an argument that is true (Debatable) if the axiom is true. And it certainly doesn’t seem to be accepted as true, now does it?
So, again, prove that “god is possible” in that he exists in at least one world. Even if we accept the rest of your argument as completely true, without nailing that axiom down to a sure thing, all you’re saying is “if god is exists in one world, he exists.” That doesn’t say anything in and of itself if we don’t even know if he exists in any world.
Your axiom is most certainly not self-evident, a universally recognized truth, or an established rule, principle, or law. It is simply something you are assuming to be true. If I started a logic train with the “axiom” that “2+2=16 in all cases,” are you saying that any argument using that axiom is completely valid? And if I started up the exact same train of logic, but with the (Equaly valid) “axiom” of “god is not possible,” then we’ve neatly disproved god’s existance.
You say god either exists (<>G, correct?), or does not exist (~<>G), and that you have to pick one. But you don’t have to pick one. Logically, we can’t pick either without support. We don’t know which one is true.
And as for you complaining about me repeating myself so much, maybe if you’d address my questions instead of dodging them with vaguely related tidbits, I wouldn’t have to repeat myself so much. I’ve been spending a lot of time here, trying to be civil, and I don’t much appretiate all the hostility you are leveling when I don’t roll over and agree with your unsupported assertions.
Another thought occurs: you suggest that the entity does not (or does not choose: how could we tell the difference?) have to exercise its capacity for evil. But isn’t it also possible that it does not exercise its capacity for knowledge? Or power? Or consciousness? Or willful choice? Or anything? How would we know that it IS exercising these capacities AT ALL, to what degree, to do what, that would even make it meaningful to speak of as anything other than a potential entity?
The arguement concludes that there is a necessary existence can do anything (logically) possible. But, looking at it from the perspective you offer on maximally filled/unfulfilled capacity (or anything in between), I don’t see that the arguement for it existing AND indeed exercising its capacity for, say, power, is any stronger than it was before we even granted it existence. Indeed, looking at it in this way, it’s still not at all clear what has been granted existence, because it could in practice be litterally anything, within logical possibility. So aren’t we back where we started: something exists, and thus anything (logically possible) can happen… but what does? How would we know? And how does this proof help resolve any of those questions?
That is, in what way is the conclusion of this arguement different from a conventional statements of a) existence and b) logical possibility?
—Not only must G be in a possible world, it must be in every possible world including (what I suspect you’re reaching toward) its own “metaworld” which basically would be the world that consists of all possible true statements.—
That is exactly what I am contending against. I am suggesting that while G could be a true and meaningful statement, it is not a characteritic of any being in any possible world. In the context of how greatest existence is defined for the proof, you can only say G after noting/proving that it exists in every possible world (that is the greatest number it can exist in). But in each individual world it exists in, is not a legitimate attribute with regards to its existence.
If I’m wrong about this (and indeed I have no definative proof that I am right), then it would at least be worthwhile to me to know why, and I don’t think you’ve explained so to my understanding yet. Which, I guess, is not really your obligation. I can certainly understand your frustration in threads like this when new people are constantly popping up to say “the arguement assumes G to be true!” But I think it would behoove YOU far more than I to not simply pass off my suggestions as evidence of not using enough “concentration.”
—I’m not sure I understand what that means. What does “A” represent? —
Well, that was dumb of me: I changed only one thing to X, thinking it would make things more clear, and but not changing the second reference made it less clear. Though I think the context of my sentance should have resolved the ambiguity, with enough “concentration.” (Kidding!)
—Given two Worlds, Wa and Wb, say that there exists a truth in Wa, Ta, that does not exist in Wb. Say also that there exists a truth in Wb, Tb, that does not exist in Wa. What you’re saying, if I understand you correctly, is that Ta is not accessible to Wb, and Tb is not accessible to Wa. And you’re correct.—
Actually, that’s not what I was talking about at all (you’ll have to explain why what I said was about “contingency”): my suggestion was more along the lines of Kant’s response to the original ontological arguement: making claims about the proper use of “existence” as an attribute.
I was talking about the characteristics it is meaningful to give to an entity in a possible world. I’m suggesting that if something exists in two possible worlds, A and B, “existence in B” is not a characteristic of the entity in world A. It may well be a true statement about the entity, but it is only a characteristic of the entity in world B.
So I am suggesting that while necessary existence, likewise, may be proven true, it is potentially objectionable to confer as an attribute “necessary existence” onto that being in any particular world. The proof in question here, however, uses precisely that sort of attribution to establish necessary existence in the first place.
—A Being Who exists as a necessary Being is assignable any and all attributes that are true.—
This may be true for the specific being of this proof, but how is it true for ALL necessary beings, including those that could be have proofs yet undiscovered (as this one was until this century)?
My omniparticle example was an inquiry into whether one could simply assert that the original definition of “greatest” or “supreme” was operationally limited only to “greatest existence.” Indeed, one thing I just noticed is that while Tisthammer’s proof includes the idea of “being supreme in every possible respect” you sometimes seem to be talking here as if “necessary existence” was synonymous with with that concept, ignoring the need to make that part of the arguement (which isn’t a big deal to the soundness of the arguement, since its an easily incorporated step, but IS a big deal to the debate over what “necessary existence” implies).
