The Ontological Arguments

[john_doran]

Hitetlen:

Of the other concepts, I tried to give a short and very general definition of the “world”, making as few assumptions as possible. If and when we can agree on a suitable definition, then we can attack the problem of “being” and “object” (they go hand-in-hand) and then we can contemplate the problem of “existence”.

by my lights, a world is a maximally consistent state of affairs, and a state of affairs, W, is maximally consistent if for every indexical state of affairs, S, W either includes S or precludes S.

this is plantinga’s definition, and it is the one to which i subscribe. different philosophers have different ideas (see, for instance, david lewis).

Hitetlen:

I don’t think so. These are all considered axioms, self-evident truths. They are considered “true” in this world, the only one we actually know of. If you wish to postulate that they are true across all the possible worlds, you have to argue for it and not assume it. I am convinced that in any “world” which contains thinking beings, those beings will arrive at these truths, and in that respect I think they are universal.

what do you think it means to be “self-evident”? can a self-evident proposition be disconfirmed by experience?

but at any rate you miss the point: our conviction in mathematical and logical truths is such that we do not generally believe that those truths could be different, and it is precisely this conviction that is the starting point for discussions of modality. in other words, “necessity” is the concept we use to describe things like math and logic, since the idea that we could find out tomorrow that 1+1=3 is inconceivable. and that’s precisely what it means to be necessary: cannot nor could not have been different.

if there are no necessary truths, however, this is exactly what turns out to be false, and there is nothing we believe that could not turn out to be false tomorrow.

Hitetlen:

But I don’t think that a question “Where were the rules of chess, before chess was invented?” (you see, I read the article you pointed out to me) is a valid question. By the same token one could ask: “Where was ‘East of Eden’ before Steinbeck wrote it?” Or “Where was the Rubik’s cube before Rubik thought about it?” These questions are sheer nonsense. I could take it a step further, and ask an even more absurd question: “Where is the variant of ‘East of Eden’ which Steinbeck would have written, if he had a constant migraine?” If one accepts the idea of “abstract objects” vs. “abstract concepts”, these questions are “legitimate”. I strongly deny this.

but what’s the difference between asking whether the rules of chess existed before they were discovered and whether the pythagorean theorem existed before it was discovered? i mean, pythagoras discovered the relation between the hypotenuse and the two other sides of a triangle, he didn’t make it up: any right-angled triangle had those geometric relations before pythagoras articulated them, and would have had those relations even if no one had articulated them.

Hitetlen:

Not independent of experience. The primitive people observed the world and one of them suddenly realized that “two” apples are more than “one” apple. That was the great conceptual breakthrough, and mathematics was “crerated”.

you miss the point. “independent of experience” does not mean independent of every scintilla of experience, it means independent of the experience involved in the proposition. which is to say that the realization that “1+1=2” does not depend on experience in the way that propositions like “it is raining” depend on experience.

what’s more, math is a formal science that is conducted without empirical experimentation (goldbach’s conjecture isn’t provable by experiment, nor is the continuum hypothesis, and fermat’s theorem wasn’t proved by appeal to empirical data), which is also what is meant by “independent of experience”.

Hitetlen:

What do you mean, they don’t “work”?

they fail to prove their hypothesis.

Hitetlen:

I disagree with the highlighted part. Absolute zero degree is a hypothetical limit of temperature; when the Brownian motion of molecules slows down, the temperature drops; but it can never actyally achieve this theoretical limit. So this limit exists as a conceptual limit, but it does not mean that it exists in a physical manner.

i’m not sure how this is relevant. the concept of “necessary being” isn’t empirical (any more than is the concept that every even number is the sum of two primes), so empirical (or, if you prefer, nomological) necessity is inapposite.

 

[john_doran]

Hitetlen:

Moreover this line of reasoning is distinctly tautological: A necessary being exists necessarily, because its existence is necessary.

perhaps, but so what? “a bachelor is an unmarried man” is tautological also, but no less true for all that.

 

[Hitetlen]

john doran:

perhaps, but so what? “a bachelor is an unmarried man” is tautological also, but no less true for all that.

If this sentence is used as a definition to explain the concept of “bachelor” to someone who never heard of this concept, then it is not tautological, it is simply expanding on the word, giving a different description to the hitherto unencountered word. If the listener never heard of the concept of marriage, then - as a definition - it is insufficient.

But this is not what you did. You propose a statement: “There exists a necessary being”, and when you are asked “why?” your reply is: “because if it did not exist, it would not be a necessary being”. That is meaningless tautology. It does not substantiate anything, merely repeats what you said before.

 

[Krebsbach]

Hi guys,

It is said that No Thing Can Be Necessary. But can the same be said about propositions in general? I.e. Is it true that: No Proposition Can Be Necessary (true under all conditions)? That is self-contradictory, so there must some proposition(s) that are necessary. There are some necessarily true propositions. Might a necessarily true proposition affirm the existence of some thing? That has to be entertained as a possibility, at least at this point in the inquiry.

So if it is granted that some there are some necessary propositions (which Hitelen does not), must it then follow that they could be of the type which affirms the existence of some thing? Many folks say no. It seems absurd to say “It is necessarily true that Bill Clinton exists in all possible worlds or under all conditions”, for example. It just doesn’t work to take a fully specified and concrete thing and argue for its necessary existence. Bill Clinton will always be a concrete and contingent being.

But the whole point of the OA in whatever form it takes is that God is in a category by himself. He is unique in that he is necessary and contingent. He is wholly abstract and concrete. All this is captured in the expression “necessarily somehow actual.”

 

[Hitetlen]

john doran:

by my lights, a world is a maximally consistent state of affairs, and a state of affairs, W, is maximally consistent if for every indexical state of affairs, S, W either includes S or precludes S.

I certainly do not understand this. “State of affairs”? What the heck does that mean? Whose “affairs”? What is the state of affairs between a neutrino and a positron? What does all this have to do with our universe? I am calling the “emperor is naked” on this definition, until I hear more.
john doran:

but what’s the difference between asking whether the rules of chess existed before they were discovered and whether the pythagorean theorem existed before it was discovered? i mean, pythagoras discovered the relation between the hypotenuse and the two other sides of a triangle, he didn’t make it up: any right-angled triangle had those geometric relations before pythagoras articulated them, and would have had those relations even if no one had articulated them.

Until someone conceptualized the abstract concept of a triangle, and the abstract concept of a square and/or multiplication, there was no such theorem, even though the possibility to recognize it was there. Some actual, real-world pieces of wood, arranged in a suitable fashion would have fulfilled an approximate equation of a^2 + b^2 ~ c^2, (if someone would be able to measure those pieces an perform the calculation) and that would be it. If our physical world would not be so close to an Euclidean flat surface, this theorem would not even be true. In a Riemann geometry or a Gauss-Bolyai-Lobatchevski geometry type of world the theorem of Pythagoras would not be true. It is not true in all the universes.

So, going back where is the abstract “object” which would have materialized if Steinbeck would have had a migraine while he was writing “East of Eden”? Or a different one if he had a toothache? Since there are infinitely many ways “East of Eden” could have turned out, if Steinbeck had some outside influence while conceiving and writing this novel, it is simply crazy to say that all of these possible outcomes somehow “exist” in some latent state, waiting to be actualized.

Even though mathematical and geometrical laws are somewhat “independent” of the discoverer (in some ill-defined manner), they are still the product of the person’s mind who first formulates them. This is even more obvious with the pieces of literature, which are also abstract constructs. If one wishes to argue that Pythagoras’ theorem was “there”, and Pythagoras merely discovered it, the same must be applied to literary works, and it must be argued that Steinbeck somehow “discovered” East of Eden, which was “out there” somewhere in a latent, virtual form. And that is simply nonsense.
john doran:

you miss the point. “independent of experience” does not mean independent of every scintilla of experience, it means independent of the experience involved in the proposition. which is to say that the realization that “1+1=2” does not depend on experience in the way that propositions like “it is raining” depend on experience.

But it does. Someone had to realize that putting two identical items on the ground is more than one item. The words “one” and “two” are artificial constructs, they just describe the intuitive notion that eating two apples is more satisfying than eating one apple.

 

[Hitetlen]

adamlsp:

Yes it is self-contradictory. It is similar to saying “morality is subjective.” This statement desubjectifies morality. It makes a claim outside of the moral system that applies to all moral systems. Therefore it is an objective statement of morality which contradicts itself. So effectively by saying “nothing is necessarily true,” you intend to make this statement necessarily true, that is, true in all possible worlds. Hence the self contradiction. MAth physics, chemistry, all exist when we are not here. By these were we formed. It is just the understanding of them that does not exist when we are gone if you choose to go forth under your thoughts-don’t-exist-outside-the-mind banner.

Adam

The definition of morality is simply the written and unwritten rules that a particular society establishes for describing the means of acceptable conduct. As such there is no absolute morality (it is established by the society), and that does not lead to any type of contradictions. The statement “there is no absolute morality” is a meta-moral statement, which does not apply to itself.

You are simply playing with a modified version of the famous Russell-paradox; which, in its simplest form says: “This sentence is false”. This is a corollary of the “set-of-all-sets” type of constructs, which allow you to create similar self-contradictory statements; a nice linguistic game. In any formal (axiomatic) system we can find equivalents of this. It is a “weakness” of all axiomatic systems.

 

[adamlsp]

Hitetlen:

The definition of morality is simply the written and unwritten rules that a particular society establishes for describing the means of acceptable conduct. As such there is no absolute morality (it is established by the society), and that does not lead to any type of contradictions. The statement “there is no absolute morality” is a meta-moral statement, which does not apply to itself.

You are simply playing with a modified version of the famous Russell-paradox; which, in its simplest form says: “This sentence is false”. This is a corollary of the “set-of-all-sets” type of constructs, which allow you to create similar self-contradictory statements; a nice linguistic game. In any formal (axiomatic) system we can find equivalents of this. It is a “weakness” of all axiomatic systems.

Social contract theory does not explain morality. Cultural norms (sociological definition) are not the same as morals. Some of them may be formed by morals but not all. In some societies it is rebels who go against these cultural norms that are looked upon by individuals suffering in that society as heros. Do you then not believe that a society can be corrupt. Like Nazi Germany for instance. Would you say based on your definition that that system of morality was right for them? Were we then wrong to enter WWII? People have consciences. Consciences are not simply memories of norms for if they were then the individuals who rebeled did it for what reason? I’m not trying to form an ironclad case just a general picture.

That sentence is clearly self-contradictory. That’s easy. If that’s true then the statement about there-are-no-necessary-truths is also self-contradictory. You are nitpicking, which is good to refine points but you are not abolishing anything. Clearly there must be necessary truths then. Do you have another argument against this or do you wish to continue refining this one?

Adam

 

[john_doran]

Hitetlen:

But this is not what you did. You propose a statement: “There exists a necessary being”, and when you are asked “why?” your reply is: “because if it did not exist, it would not be a necessary being”. That is meaningless tautology. It does not substantiate anything, merely repeats what you said before.

for one thing, a tautology is a statement that is analytically true, or true by definition, not false or meaningless.

so, if my statement is tautologous, then it is true by definition. which, a fortiori, means it’s true. which means there’s a necessary being. right?

but whatever - this is not what i did at all.

let me rehearse what i said:
john doran:

a necessary being is either necessary or impossible (it cannot just happen to begin to exist, nor can it just happen to cease to exist); if it is not impossible, then it exists (whatever it is, and however many of them there may be); but the concept of “necessary being” is not impossible (i.e. logically contradictory); therefore there is at least one necessary being.

now let’s look at it carefully. what i actually said is that a necessary being is necessary or impossible, which gives you precisely the additional conceptual content you’re looking for - it is a disjunctive argument, not a definition.

a definition would be: a necessary being is a being that exists in all possible worlds.

a tautology would be: a being that exists in all possible worlds exists in all possible worlds.

what i think you might have meant was that i offered a circular argument - i.e. i used the conclusion as a premise. but did i? it may look like i did, in that what i said was, formally (A v B); ~A; B, and B appears in the major premise of the syllogism. but, as i said, the argument is disjunctive, and this is the exact form of a disjunctive syllogism.

if you want to demur, then you’re going to have to demonstrate that the initial disjunction is unsound (e.g. there are other alternatives that i haven’t considered).

 

[Hitetlen]

adamlsp:

Social contract theory does not explain morality. Cultural norms (sociological definition) are not the same as morals. Some of them may be formed by morals but not all. In some societies it is rebels who go against these cultural norms that are looked upon by individuals suffering in that society as heros. Do you then not believe that a society can be corrupt. Like Nazi Germany for instance. Would you say based on your definition that that system of morality was right for them? Were we then wrong to enter WWII? People have consciences. Consciences are not simply memories of norms for if they were then the individuals who rebeled did it for what reason? I’m not trying to form an ironclad case just a general picture.

I would disagree, but you never defined what the word “morality” means to you. Different moral systems are not necessarily compatible with each other. Today cannibalism is usually morally unacceptable, but when the plane went down in the Andes, and the only way to survival was resorting to cannibalism, it was not considered immoral, at least not by the majority of the people. In ancient times it was a generally accepted practice, and some tribes also practiced it until quite recently.

adamlsp:

That sentence is clearly self-contradictory. That’s easy. If that’s true then the statement about there-are-no-necessary-truths is also self-contradictory.

1. The statement “There is no absolute morality” does not lead to a contradiction, because it is not a moral statement.
2. What is the truth value of the statement “This sentence is false”?
3. And when you answer that, please give me one example of a necessarily true statement, one which you think is necessarily true.

adamlsp:

You are nitpicking, which is good to refine points but you are not abolishing anything. Clearly there must be necessary truths then. Do you have another argument against this or do you wish to continue refining this one?

I am not just nitpicking, I am trying to establish a common communication ground, so we can lessen the chances of miscommunication. I am asking you again, just give me a “necessary true statement”, to substantiate that there are such statements.

This statement has to be true ABOUT all possible worlds. Observe, I did not say “IN” all possible worlds, since it is not necessarily true that ALL possible worlds would have hypothetical entities, capable of expressing ideas, or statements. Some may contain inanimate objects only, and in those worlds there are NO statements at all, true or false.

Furthermore, you use the law of contradiction in an incorrect manner. The law of contradiction only says that a statement AND its negation cannot be both true in the same time and in the same context. It does not say: "if a statement if false, then its opposite is true". There are statements which cannot be assigned a true or false value, notably among them is the one I already stated several times: “This sentence is false”. It has no true or false value assiciated with it, and neither has its negation: “It is not true that this sentence is false”.

There are two things we have to consider about the statement: “There are no necessarily true statements”. One is that it is a meta-statement - a statement about statements. That means that only meta-logical laws can be applied to it. The other one that is the purported answer to the question: “Are there necessarily true statements?”, and some questions simply do not have an answer. One example: “When did you stop beating your wife?” It looks like a correctly formed question but has no answer if you never attempted beating your wife.

 

[john_doran]

Hitetlen:

I certainly do not understand this. “State of affairs”? What the heck does that mean? Whose “affairs”? What is the state of affairs between a neutrino and a positron? What does all this have to do with our universe? I am calling the “emperor is naked” on this definition, until I hear more.

i’m afraid i don’t have the time or the inclination to keep going, man - i figured that the next question would be about states of affairs (which is why i didn’t provide more elaborate definitions of possible worlds in the first place), and then after that perhaps actualism and serious actualism, and so on…

you can look here for an overview, if you like:

plato.stanford.edu/entries/states-of-affairs/

Hitetlen:

Until someone conceptualized the abstract concept of a triangle, and the abstract concept of a square and/or multiplication, there was no such theorem, even though the possibility to recognize it was there.

sure, if by “theorem” you mean something like “a mathematical relationship recognized, transcribed, and proved by someone”. but the relationship existed, and was the thing that was perceived by pythagoras. the relationship is what is expressed by the theorem - it is the meaning, or sense, of the theorem.

Hitetlen:

If our physical world would not be so close to an Euclidean flat surface, this theorem would not even be true. In a Riemann geometry or a Gauss-Bolyai-Lobatchevski geometry type of world the theorem of Pythagoras would not be true. It is not true in all the universes.

absolutely false: the pythagorean theorem is a mathematical equation, and says absolutely nothing about the world - it says that the relationship holds in euclidean space, but doesn’t say whether real space is flat. that’s the job of physics.

the pythagorean theorem holds in every possible world, because it is the expression of a(n abstract) mathematical relationship that holds for geometrical figures in euclidean spaces in every world, whether or not the real space of any particular world is euclidean or riemannian or whatever.

Hitetlen:

So, going back where is the abstract “object” which would have materialized if Steinbeck would have had a migraine while he was writing “East of Eden”? Or a different one if he had a toothache? Since there are infinitely many ways “East of Eden” could have turned out, if Steinbeck had some outside influence while conceiving and writing this novel, it is simply crazy to say that all of these possible outcomes somehow “exist” in some latent state, waiting to be actualized.

no, not really. it just means that there are an infinite number of abstract objects.

Hitetlen:

Even though mathematical and geometrical laws are somewhat “independent” of the discoverer (in some ill-defined manner), they are still the product of the person’s mind who first formulates them. This is even more obvious with the pieces of literature, which are also abstract constructs. If one wishes to argue that Pythagoras’ theorem was “there”, and Pythagoras merely discovered it, the same must be applied to literary works, and it must be argued that Steinbeck somehow “discovered” East of Eden, which was “out there” somewhere in a latent, virtual form. And that is simply nonsense.

no, it’s not. and certainly not just because you say so.

look, the existence of abstract objects is entailed by our most foundational beliefs about the world; if it so happens that another implication of such an entailment is that there are all sorts of additional abstratca, then so be it - it makes far, far more sense to accept such a conclusion than it does to give up our belief in the necessity of mathematical and logical truths.

it makes as much sense to abandon abstract objects because there must be an infinite number of them as it does to abandon a belief in the real world because the proposition “possibly, the real world is an illusion” is true.

 

[Hitetlen]

john doran:

let me rehearse what i said:
john doran:

a necessary being is either necessary or impossible (it cannot just happen to begin to exist, nor can it just happen to cease to exist); if it is not impossible, then it exists (whatever it is, and however many of them there may be); but the concept of “necessary being” is not impossible (i.e. logically contradictory); therefore there is at least one necessary being.

now let’s look at it carefully. what i actually said is that a necessary being is necessary or impossible, which gives you precisely the additional conceptual content you’re looking for - it is a disjunctive argument, not a definition.

a definition would be: a necessary being is a being that exists in all possible worlds.

a tautology would be: a being that exists in all possible worlds exists in all possible worlds.

what i think you might have meant was that i offered a circular argument - i.e. i used the conclusion as a premise. but did i? it may look like i did, in that what i said was, formally (A v B); ~A; B, and B appears in the major premise of the syllogism. but, as i said, the argument is disjunctive, and this is the exact form of a disjunctive syllogism.

if you want to demur, then you’re going to have to demonstrate that the initial disjunction is unsound (e.g. there are other alternatives that i haven’t considered).

OK, let’s get down to the details:

Here is your opening statement: “a necessary being is either necessary or impossible”. That statement is already incorrect. It should say:

“A being either exists in all possible worlds, or in some (but not all) possible worlds, or cannot exist in any possible world”.

In the first case, the being exists necessarily, in the second case it exists conditionally, in the third case it does not exist at all. Or putting it into a succint sentence:

“A being is either necessary, possible or impossible.”

You made two errors: inserted the word “necessary” before the word “being”, and left out the most probable case: “a being exists in some worlds, but not in others”.

The sentence you stated is circular: “a necessary being is either necessary or impossible”, you say something akin to: “a red apple is either red or green”. Since a red apple can only be red, your opening part of the syllogism already entails the result, thus it constitutes a circular argument.

If you would wish to make an utterance about a “necessary being” it could only be “a necessary being is necessary” (which would be tautological) or “A necessary being exists in all possible worlds”, which would indeed be a definition.

How could a necessary being be impossible? Your statement poses a bogus disjunction.

Now, if we get down to the correct form of the problem: “A being is either necessary, possible or impossible.”, then you can start to argue that there is one (or more) being that exists in all possible worlds, and thus it is necessary. Good luck. Formal logic will not help you here.

 

[Krebsbach]

Now, if we get down to the correct form of the problem: “A being is either necessary, possible or impossible.”, then you can start to argue that there is one (or more) being that exists in all possible worlds, and thus it is necessary. Good luck. Formal logic will not help you here.

Hey Hitester,

But I think Anselm can.

So we got the three possibilities: necessary, possible and impossible.

Let’s deal the the impossible kind first. If we conceive of an impossible being we really are saying the very idea of it is nonsense. Ain’t no way it is going to exist in any world. e.g. a round square.

A possibly existing being, aka contingent being, may exist in at least one world. It might exist in all worlds but not necessarily, and even if it did it conceivably could cease to exist in any or all of them.

A necessary being would have to exist in all worlds at all times, supposing such a thing exists. (We are not doing anything more at this point than supposin’.)

But at this point we have to realize that if we deny the possibility of a necessary being, we are concluding that all existence is contingent. IOW, the very idea of a necessary being is nonsense (falls into the third category of existence which is no existence at all) All beings are merely possible beings. But if we take for granted that a necessary being exists, then it must be taken to exist, no question.

So does seem reasonable to say that God either exists necessarily or the very idea is impossible nonsense.

 

[Krebsbach]

What Anselm and his later progeny like Plantinga add to the whole argument is the logic of perfection and greatness. If God is the maximally greatest being (and we don’t think the very idea is absurd) and greatness entails necessary existence, then God’s gotta exist.

kordially,

karl

 

[Krebsbach]

It seems clear to me that folks who disagree with the OA believe that all existence must be contingent. That strikes me as highly unlikely.

 

[Hitetlen]

Krebsbach:

So we got the three possibilities: necessary, possible and impossible.

Let’s deal the the impossible kind first. If we conceive of an impossible being we really are saying the very idea of it is nonsense. Ain’t no way it is going to exist in any world. e.g. a round square.

A possibly existing being, aka contingent being, may exist in at least one world. It might exist in all worlds but not necessarily, and even if it did it conceivably could cease to exist in any or all of them.

A necessary being would have to exist in all worlds at all times, supposing such a thing exists. (We are not doing anything more at this point than supposin’.)

But at this point we have to realize that if we deny the possibility of a necessary being, we are concluding that all existence is contingent. IOW, the very idea of a necessary being is nonsense (falls into the third category of existence which is no existence at all) All beings are merely possible beings. But if we take for granted that a necessary being exists, then it must be taken to exist, no question.

So does seem reasonable to say that God either exists necessarily or the very idea is impossible nonsense.

I like your reasoning, but I have a few remarks to make. We don’t have to explicitly deny the possibility of the existence of a necessary being. We can just say that we have no evidence for such a being. Besides, why should a necessary being be called God? It may just as well be a subatomic particle, which just happens to exist in all those possible worlds. The idea of existing in all the possible worlds does not imply anything, except existence. It does not imply all those attributes that people like to associate with the concept of God.

I think that the phrase chosen for “existing in all the possible worlds” that is: “necessary existence” is an unfortunate choice. Just like the term “irrational number” or “imaginary number”. Such words have unintended and confusing connotations, which should be avoided. (Though, of course, philosophers thrive of obfuscation… God forbid that they would utter anything that has a clear meaning for the laymen. )

Furthermore, I am not satisfied that the words: “world”, “being” and “exitence” are properly defined. Does the word “being” somehow imply conscious existence? One would tend to use “being” in conjunction with a “living entity”. For other kinds we would use the word: “object”.

 

[Hitetlen]

Krebsbach:

What Anselm and his later progeny like Plantinga add to the whole argument is the logic of perfection and greatness. If God is the maximally greatest being (and we don’t think the very idea is absurd) and greatness entails necessary existence, then God’s gotta exist.

I think it is absurd, but that is just my opinion, which does not count.

So let’s examine the concept of “maximum greatness”: Among all the humans on Earth, there must be a tallest one, therefore there necessarily is a “tallest” human being (as long as there are any humans at all). There is also a heaviest one, so there is necessarily a fattest human being. Does it follow from this that there is a human being who is both the tallest and the fattest? Obviously not. Now these tallest and heaviest humans are not the maximally tall and heavy ones, but that is irrelevant, this is just an example to help with the rest.

No matter how one defines “maximally great” if it entails more than one attribute, it is quite possible that one being will be the maximal for one attribute, and another one will be maximal for the other attribute. For example: the maximally knowledgable being (omniscient) is not necessarily the most potent one (omnipotent). These two attributes do not depend on each other.

 

[Hitetlen]

Let’s revisit this argument:
john doran:

a necessary being is either necessary or impossible (it cannot just happen to begin to exist, nor can it just happen to cease to exist); if it is not impossible, then it exists (whatever it is, and however many of them there may be); but the concept of “necessary being” is not impossible (i.e. logically contradictory); therefore there is at least one necessary being

There are several other errors in the above reasoning. The phrase “not impossible (i.e. logically contradictory)” is an invalid assumption and relies heavily on the misleading terminology of:

1. necessary (exists in all possible worlds)
2. possible (exists in some but not all worlds) and
3. impossible (does not exist in any world).

As I said, these phrases are very misleading. The word “impossible” is heavily loaded with the connotation of “logically impossible”, but that is not the case at all.

A “vegetarian shark” or a “purple-green checkered elephant” are not logical impossibilities, but it is quite possible that they never happened to materialize in any of the worlds. Therefore it is a logical error to say: “if something never happened, it is because it is logically impossible”. And that makes the whole original argument invalid.

To clarify this, let’s drop the misleading terminology above and categorize all the entities in neutral terms:

1. category “C1” (exists in all possible worlds)
2. category “C2” (exists in some but not all worlds) and
3. category “C3” (does not exist in any world).

Any entity belongs to one and only one category, by definition. The premise (“a necessary being is either necessary or impossible…”) of original syllogism can now be translated into:

“an entity in category ‘C1’ either belongs to category ‘C1’ or category ‘C3’…”, which is clearly nonsense, because by the very terms of categorization it can only belong to category “C1”.

 

[Hitetlen]

Let’s go back to the S5 modal logic:

adamlsp:

I give a brief definition of the S5 axiom of S5 modal logic. Then I state that if one does not understand, one should further their research into S5 modal logic. Reading Karl’s posts just above should help you understand because those arguments work ffrom the same idea. Your example does not apply to this. If you read all of my first post it may help. Possibly necessarily true = necessarily true.

The highlighted text is the one which needs to be discussed.

The definitions:

1. A statement is possibly true, if it is true in some possible worlds, but not true in all the possible worlds.
2. A statement is necessarily true, if it is true in all the possible worlds.

Since this is a disjunction, a statement cannot be both “possibly true” and “necessarily true”, and therefore the proposition: “possibly necessarily true” is an empty statement, or a self-contradictory one. (pick your favorite adjective).

And some people actually declare it an “axiom”!

Of course, there is a way to get around this, if the word “possible” is used in an inconsistent manner, which method is intellectually dishonest.

If the word “possibly true” does not mean “sometimes true but not always true”, rather it is used as an everyday synonym of “maybe true, maybe not”, then there is no logical contradiction, but what we have is intentional obfuscation. And that is worse than being simply wrong, it is intentionally misleading and dishonest.

 

[Krebsbach]

Hey Hiteman,

Re yer post @ 155:

Let’s work with your categories:

1. category “C1” (exists in all possible worlds)
2. category “C2” (exists in some but not all worlds) and
3. category “C3” (does not exist in any world).

But let me amplify and clarify their definitions.

C1 refers to the individual who, when it comes to actual worlds, must exist therein, and when it comes to possible worlds, cannot be conceived of not existing therein, ever. Theists say God is the only logical candidate for C1.

C2 refers to beings who exist “normally” or contingently. In any given actual world, or in any possible or conceivable world, they may or may not exist. If existing, they might cease to exist. This includes you, me, and mah huntin’ dawg Zoe. I would also include in C2 any vegetarian sharks, which while practically impossible in the normal course, could still happen, say through genetic engineering. Not so farfetched. (I know of a vegetarian cat who only eats tomatoes, fresh, canned or any which way.)

C3 refers really refers to nothing, nonsense, or absurdities. e.g. round squares, or, if you are an anti-Anselmian, the maximally great being.

 

[Krebsbach]

The definitions:

1. A statement is possibly true, if it is true in some possible worlds, but not true in all the possible worlds.
2. A statement is necessarily true, if it is true in all the possible worlds.

Since this is a disjunction, a statement cannot be both “possibly true” and “necessarily true”, and therefore the proposition: “possibly necessarily true” is an empty statement, or a self-contradictory one. (pick your favorite adjective).

I think it is legitimate to use “possibly necessarily true” in this sense:

We are just ordinary folks striving for understanding. We have conceived of 3 modes of existence, C1-3. We haven’t yet determined through analysis whether our categories even make sense. So at this point we posit or suppose C1 and say C1 existence is possible.

But as we work through the analysis and come to the conclusion that C1 existence is meaningful, then we no longer can talk in terms of “possibly necessarily true.” That would be sel-contradictory.