The Modal Ontological Argument Begs the Question

[aleph naught]

Btw, 'water' and 'H2O' don't mean the same thing, and yet everything that's true of water is true of H2O. This is metaphysical equivalence, which is even stronger than logical equivalence, and yet even then it doesn't entail that the words mean the same thing.

[cnearing]

<<That's totally backwards. It has to be possible for God to exist in order for God to exist. If it's impossible for God to exist, then God does not exist. >>

Well, you're wrong.  As I have proven.  You do not understand the modal ontological argument.

Instead of just flatly rejecting the conclusion of my logical proof, try actually engaging the argument.

[cnearing]

<<
Arguments do not beg the question. People beg the question. >>

Not only is this wrong, it's irrelevant.  I could just as easily say that "Craig begs the argument with the MOA."

And that would also be entirely true.

[cnearing]

This means, definitionally, that they have identical entailments and therefore identical extensions--literally, identical literal meanings.

That's false. Just because P and Q are logically equivalent, it doesn't follow that they mean the same thing. <>T is only logically equivalent with T on S5, it's not logically equivalent on S4. But obviously it's not a matter of semantics whether or not S5 or S4 are the proper modal logic system to do metaphysics in.

They aren't logically equivalent.  They are identical in extension given S5--and, yes, S5 is precisely a matter of semantics.  It follows specifically from what is meant by a certain *possible world semantics* (or, precisely, set of definitions regarding what it means to be a possible world, what it means to be possible, and what it means to be necessary).

It is entirely a matter of semantics, and given the semantics in use, the MOA trivially begs the question--exactly as I have proven.

[ParaclitosLogos]

<<
Arguments do not beg the question. People beg the question. >>

Not only is this wrong, it's irrelevant.  I could just as easily say that "Craig begs the argument with the MOA."

And that would also be entirely true.

It is not irrelevant because you say so. And it is aside from relevant true.

[cnearing]

Well, look, OM.  If you can turn it into some actual objection to the logic of my argument, feel free.

If you are really planning to deny the premise in which I define "begs the question" though, I don't think I have any need to take that sort of head-in-sand approach seriously.

[ParaclitosLogos]

Well, look, OM.  If you can turn it into some actual objection to the logic of my argument, feel free.

If you are really planning to deny the premise in which I define "begs the question" though, I don't think I have any need to take that sort of head-in-sand approach seriously.

G I assume means God exists

<> G means possibly God exists.

They do not mean literally the same thing since your premise goes
5.) If a premise in an argument and the argument's conclusion have the same literal meaning, the argument begs the question.

It simply does not apply.


I also gave a counter example where premise 1 entails the conclusion and the conclusion entails premise 1, and, begging the question is not the case.

Also having identical entailments, and identical extensions does not entail nor imply having identical literal meanings, it is just the case that  in some sense both expresions have some semantic similarity, what exactly it is will depend on one´s semantic model used. In Plantinga´s model, speficically correferring terms can express semantic and epistemic inequivalent properties.

It does not even imply having identical meaning.

[cnearing]

<<It simply does not apply.>>

Of course it does.  It is a conditional statement, and the antecedent condition is met.

<<Also having identical entailments, and identical extensions does not entail nor imply having identical literal meanings.>>

Actually, literally, that is what it means.  That's actually just what the words "extension" and "literal" refer to.

They don't have identical *intensions*--that is, people respond, in a sort of emotional sense, to them in different ways.  People associate them, indirectly, with different things.  An example would be, for instance, a "benjamin" and a "hundred."  Both--literally--refer to a hundred dollar bill, but they have different connotations, or intensions. 

However, consider the argument:

1.) I have five benjamins.
2.) If I have five benjamins, I have five one-hundred-dollar bills.
3.) If I have five one-hundred-dollar bills, I have five hundreds.
C.) Therefore, I have five hundreds.

This argument still plainly begs the question, despite the difference in intension between the term used in p1 and the term used in the conclusion.  By definition, they have the same literal meaning, just as G and <>G have the same literal meaning, by definition.  (Specifically, the definition of "<>" as an operator in s5 modal logic and the definition of an MGB.)


<<I also gave a counter example where premise 1 entails the conclusion and the conclusion entails premise 1, and, begging the question is not the case. >>

No, you didn't.  You wrote this:

<<
1. Clark Kent is with louise at niagara falls

2.  Clark is superman (Clark Kent exists iff Superman exists.Clark is with Louis iff Superman is with Louise)

3. Superman is with louise at niagara falls
>>

Which does, in fact, trivially beg the question.  The only case in which it is not obvious that it begs the question is the case in which one exploits the audience's ignorance of the fact that the terms "Clark Kent" and "Superman" are being used to refer to the same person. 

But exploiting ignorance regarding the meanings of your terms does not salvage the argument from begging the question. 

[ParaclitosLogos]

<<It simply does not apply.>>
Of course it does.  It is a conditional statement, and the antecedent condition is met.

<<Also having identical entailments, and identical extensions does not entail nor imply having identical literal meanings.>>

1) Actually, literally, that is what it means.  That's actually just what the words "extension" and "literal" refer to.

They don't have identical *intensions*--that is, people respond, in a sort of emotional sense, to them in different ways.  People associate them, indirectly, with different things.  An example would be, for instance, a "benjamin" and a "hundred."  Both--literally--refer to a hundred dollar bill, but they have different connotations, or intensions. 

However, consider the argument:

1.) I have five benjamins.
2.) If I have five benjamins, I have five one-hundred-dollar bills.
3.) If I have five one-hundred-dollar bills, I have five hundreds.
C.) Therefore, I have five hundreds.

This argument still plainly begs the question, despite the difference in intension between the term used in p1 and the term used in the conclusion.  By definition, they have the same literal meaning, just as G and <>G have the same literal meaning, by definition.  (Specifically, the definition of "<>" as an operator in s5 modal logic and the definition of an MGB.)


<<I also gave a counter example where premise 1 entails the conclusion and the conclusion entails premise 1, and, begging the question is not the case. >>

No, you didn't.  You wrote this:

<<
1. Clark Kent is with louise at niagara falls

2.  Clark is superman (Clark Kent exists iff Superman exists.Clark is with Louis iff Superman is with Louise)

3. Superman is with louise at niagara falls
>>

Which does, in fact, trivially beg the question.  The only case in which it is not obvious that it begs the question is the case in which one exploits the audience's ignorance of the fact that the terms "Clark Kent" and "Superman" are being used to refer to the same person. 

But exploiting ignorance regarding the meanings of your terms does not salvage the argument from begging the question.

Please, can you reference the literature where having the "identical extension" and "literal meaning" is the same in modal logic? I haven´t found it.

Also

The reference where
If a premise in an argument and the argument's conclusion have the same literal meaning, the argument begs the question.

** See the quote below from fallacy files.

However, consider the argument:

1.) I have five benjamins.
2.) If I have five benjamins, I have five one-hundred-dollar bills.
3.) If I have five one-hundred-dollar bills, I have five hundreds.
C.) Therefore, I have five hundreds.

This argument still plainly begs the question, despite the difference in intension between the term used in p1 and the term used in the conclusion.  By definition, they have the same literal meaning, just as G and <>G have the same literal meaning, by definition.  (Specifically, the definition of "<>" as an operator in s5 modal logic and the definition of an MGB.)

To formally show an argument begs the question one needs to make explicit the support for the premises, and show that the only reason one believes one or more of the premises is because one believes the conclusion.

All you are showing is that the argument is circular, not all arguments that are circular beg the question or are vicious

Exposure:

Unlike most informal fallacies, Begging the Question is a validating form of argument, that is, every argument that begs the question is valid―if this seems surprising or confusing to you, see the Q&A, below. Moreover, if the premisses of an instance of Begging the Question happen to be true, then the argument is sound. What is wrong, then, with begging the question?
First of all, not all circular reasoning is fallacious. Suppose, for instance, that we argue that a number of propositions, p1, p2,…, pn are equivalent by arguing as follows, where "p → q" means that p implies q:
p1 → p2 → … → pn → p1

Then we have clearly argued in a circle, but this is a standard form of argument in mathematics to show that a set of propositions are all equivalent to each other.

So, when is it fallacious to argue in a circle?
For an argument to have any epistemological or dialectical force, it must start from premisses already known or believed by its audience, and proceed to a conclusion not known or believed.

Premise 2 does not depend on prior believe in C, but it can be a-posteriori, for example for a foreigner like me.
The person can start from an a-posteriori support of P2 to the previously unknown conclusion.

The same goes for the MOA.

For an agnostic, that comes to evaluate the 1st premise with out knowing the conclusion,  conclude tha the premise is plausible (through some support of Necessary moral truths, the necessary truth of mathematics, modal intuition based on conceivability, modal intuition based on Understanding, etc...), and, from it arrive at the previously unknown conclusion.


All you are pointing to is to the circularity of the argument, and, pressuposing everyone begs the question because of it.



On the superman example, yes I did.

When I explained the support of the premises independent of the conclusion.

..Support for 1. Louis Lane is with Clark at niagara falls on an assignment.

Sport for 2. when Louis went at Niagara Falls with Clark he felt onto fire and did not burn, and his eyeglasses fell(his wonderful disguise), at all, and, after all he looks like superman.

She does not believes 1 because she believes 3, nor believes 2 because she believes 3...

And you are indavertently misrrespresenting when begging the question is really fallacious.

[ParaclitosLogos]

Semantics, in the sense of a theory of meaning, is, of course, more than a definition of truth in a model, and an accompanying theory of logical truth. To state the truth conditions of sentences one must also specify the intended model, without which the nonlogical vocabulary will remain uninterpreted. For each sentence S, we are after a statement, For all world-states w, ‘S’ is true at w iff at w, P, that specifies what the world must be like if S is to be true. It is standard in possible worlds semantics to take this ‘must’ to have the force of metaphysical necessity, and the world-states quantified over to be metaphysically possible. However, if what I have said is correct, this isn’t quite right. In addition to metaphysically possible world-states (all of which are also epistemically possible), the intended model must also include epistemically possible, but metaphysically impossible, states. Hence, the semantic theory should tell us, for each S, what it is for S to be true at an arbitrary epistemically possible world-state.


 Although these truth conditions are stronger, and more informative, than those provided by Davidson, they aren’t enough to establish the theories generating them as theories of meaning. Since sentences true in the same epistemically possible world-states may differ in meaning (consider any two necessary, apriori truths), knowledge even of these strengthened truth conditions is not sufficient for understanding a language. Nor can we identify the meaning of S with the proposition it expresses, if, as is often done in possible worlds semantics, the latter is taken to be the set of world-states at which S is true. It is no small thing to have a theory that specifies the modal truth conditions of sentences; for many philosophical purposes, nothing else is needed. But we still have no justification for taking such a theory to be a theory of meaning.

Soames, Scott (2010-07-26). Philosophy of Language (Princeton Foundations of Contemporary Philosophy) (p. 56). Princeton University Press.

 

As of today we are still looking for a true theory of meaning. Semantic equivalence is  rather a model of sorts, but, it is not even close.

This is why one can see it is obvious two terms that are semantically equivalent can mean two very different things.

(i.e. Clark Kent and Superman)

[cnearing]

I think it is nonsense to say that two things can be semantically equivalent and mean two very different things.  Clark Kent and Super Man are either semantically equivalent or they mean different things.  Not both, and what matters is precisely what is meant by both.

However, in the case of the MOA, the *only* thing they can be meant by <>G is something that is equivalent to G.  Indeed, were this not the case, the argument would not be sound.

Indeed, it is trivial (as I already explained) that one *does in fact* need to affirm God's existence in order to be justified in claiming <>G.  There is, by definition, no sufficient support for <>G other than a demonstration that G actually does exist in every possible world.  Every other argument would fall well short of constituting justification for <>G.

You are right that circular arguments are not necessarily problematic--thry can be used, as the four first premises in my argument are, to show that several different terms are equivalent.

But the MOA does not do that.  It's conclusion is not that <>G and G and []G are equivalent.  That is true, as I have proven, and if that were actually the conclusion to the MOA, I would have no problem with the MOA at all.

But it isn't.

The MOA concludes with G.

And it does so by leveraging both the fact that G and <>G are equivalent and the fact that <>G *looks* (to the audience who does not understand the meaning of the meaning of <> and MGB) SS though it bears a lesser burden--that it is easier to justify, epistemically, or can be justified epistemically by different means than, G.

But this is at best incompetent and at worse deeply dishonest.

<>G and G require exactly the same sort of justification, because, by definition, one must be justified in asserting G in order to be justified in asserting <>G, and one must be justified in asserting <>G in order to be justified in asserting G.

This, of course, is because (as we have proven) G is a necessary condition for <>G and <>G is a necessary condition for G.

[cnearing]

We can see this pretty easily.

A proposition is possible--true in some possible world only if it does not contradict any necessary fact.  However, the set of necessary facts is not well defined.  In particular, we know incorrigibly (by definition) that "[]G xor[](~G)" for the definitions of these terms under which s5 operates.

So.  Is it []G or [](~G)?  Well, that is precisely the question we are here to discuss, simply phrased in the language of the possible world semantics in question, here.

However, in order to assert <>G, one must assume ~([](~G)).

That's trivial.  It is explicitly required by the definition of the possibility operator.  G is possible only if G does not contradict any necessary facts, and G does explicitly contradict one of the alleged necessary facts that sits right at the heart of the overall debate.

In every sense, then, asserting <>G is begging the question, and the only way one could avoid this charge is by claiming to not really know what the language in the argument actually means (in which case one isn't really arguing at all, but just reciting something they don't understand, much as a toddler might recite some science fact overheard from an older sibling).

[ParaclitosLogos]

I think it is nonsense to say that two things can be semantically equivalent and mean two very different things.  Clark Kent and Super Man are either semantically equivalent or they mean different things.  Not both, and what matters is precisely what is meant by both.

However, in the case of the MOA, the *only* thing they can be meant by <>G is something that is equivalent to G.  Indeed, were this not the case, the argument would not be sound.

Indeed, it is trivial (as I already explained) that one *does in fact* need to affirm God's existence in order to be justified in claiming <>G.  There is, by definition, no sufficient support for <>G other than a demonstration that G actually does exist in every possible world.  Every other argument would fall well short of constituting justification for <>G.

You are right that circular arguments are not necessarily problematic--thry can be used, as the four first premises in my argument are, to show that several different terms are equivalent.

But the MOA does not do that.  It's conclusion is not that <>G and G and []G are equivalent.  That is true, as I have proven, and if that were actually the conclusion to the MOA, I would have no problem with the MOA at all.

But it isn't.

The MOA concludes with G.

And it does so by leveraging both the fact that G and <>G are equivalent and the fact that <>G *looks* (to the audience who does not understand the meaning of the meaning of <> and MGB) SS though it bears a lesser burden--that it is easier to justify, epistemically, or can be justified epistemically by different means than, G.

But this is at best incompetent and at worse deeply dishonest.

<>G and G require exactly the same sort of justification, because, by definition, one must be justified in asserting G in order to be justified in asserting <>G, and one must be justified in asserting <>G in order to be justified in asserting G.

This, of course, is because (as we have proven) G is a necessary condition for <>G and <>G is a necessary condition for G.

<>G and G require exactly the same sort of justification, because, by definition, one must be justified in asserting G in order to be justified in asserting <>G, and one must be justified in asserting <>G in order to be justified in asserting G.

This, of course, is because (as we have proven) G is a necessary condition for <>G and <>G is a necessary condition for G.

Here, you confuse a metaphysical fact with an epistemic matter.

Just stating that 

x1. if G is a necessary condition for <>G and <>G is a necessary condition for G then for any x , x can only have the same epistemic justification for both

x2. G is a necessary condition for <>G and <>G is a necessary condition for G

x3. for any x , x can only have the same justification for both

1st of all what is to say that G is a necessary condition for <>G and viceversa (what makes x 2 true?) and why is x1 has to be the case?if at all.



Just like in my example of Clark and Superman. What is epistemically required to justify and know 1.Clark Kent is with Louise at Niagar falls is not necessarily the same that is required  to Know 3 nor 2, in my example.

1. Clark Kent is with louise at niagara falls

2.  Clark is superman (Clark Kent exists iff Superman exists.Clark is with Louis iff Superman is with Louise)

3. Superman is with louise at niagara falls

To beg the question Louise needs to believe 1 or 2 because she believes 3.

S1.Support for 1. Louis Lane is with Clark at niagara falls on an assignment.

S2. Sport for 2. when Louis went at Niagara Falls with Clark he felt onto fire and did not burn, and his eyeglasses fell(his wonderful disguise), at all, and, after all he looks like superman.

She does not believes 1 because she believes 3, nor believes 2 because she believes 3

 ~S3. Sadly, afterwards Louise got a defeater for 2 since Clark Kent did not give up his facade and tried to save her when she jumped into the falls.

S1 and S2 are different from S3 and from each other.


One can formulate the MOA as follows

P1. If it is possible that God(MGB)  exists , then, God(MGB) exists

P2. it is possible that God(MGB) exists

P3. God(MGB) exists.

SM1. The support for P1, is basically  the 5 axiom of modal system S5, made explicit in Plantinga´s MOA formulation

SM2. And P2 can be supported by several resrouces provided by the epistemology of modality independent of P1 and  P3, like modal intuitions based on conceivability, or understanding, and, other considerations like explaining necessary moroal truths , or mathematical truths, etc...

SM3, could be the Leibnizian cosmologial argument, for example, the direct experience of God.

Neither is P1 asserted because one already knows or asserts P3

Nor is P2 asseted because  one already knows or asserts P3.

SM1 , SM2, SM3 are not necessarily the same.

[cnearing]

Simply, none of the things you mentioned constitute support for p2 in your simple reformation except where the constitute identical support for the conclusion.

Precisely, this is the case because one cannot be justified in asserting <>P unless one is justified in asserting ~([](~(p))) as I explained above.

This is true as per the definition of "<>."

No support for p2 which does not establish this fact could ever be sufficient for p2.

And once this fact is established, p2 is pointless.  The conclusion has already been reached.

[cnearing]

And, of course we see this illustrated nicely by the reverse MOA:

1.) If <>(~G) then ~G
2.) <>(~G)
C.) ~G

1, again, is just s5. 

On what grounds can you object to p2?

It is intuitively true.  The coherence of (~G) is not in question.