Thomas Metcalf

Originally posted by Kenny :

I'd say that's built into God's definition. Otherwise, you'd have this ontological argument:

(1) There is a possible world in which maximal greatness (except for alethic necessity) exists.
(2) If there is a possible world in which maximal greatness (except for alethic necessity) exists, then maximal greatness (except for alethic necessity) exists in every possible world.
(3) Therefore, maximal greatness (except for alethic necessity) exists in every possible world.

1 is true, and 2 is false (or at least unsupported). The alternative, of course, has the reverse problem.

(1') There is a possible world in which maximal greatness is instantiated.
(2') If there is a possible world in which maximal greatness is instantiated, then maximal greatness exists in every possible world.
(3') Therefore, maximal greatness exists in every possible world.

1' is false/unsupported while 2' is true. Both 3 and 3' entail the truth of theism.

Hm. I'm trying to express this point. I meant more that it's easier for them to fail to be true. We have to estimate their background probability to be lower, maybe, at least in the case of synthetic propositions like "God exists." (I hope you'll join me in supposing that "God exists" is synthetic. I think if you don't, the MOA looks worse for it.)

Here's a synthetic proposition: Our sun has nine planets. I would estimate the chance that it obtains in some randomly selected possible world to be about 0.5. And I would estimate the chance that it obtains in every possible world to be very low indeed. Necessarifying a synthetic proposition makes its background probability lower, right? I realize this isn't exactly the same issue, but I want to see if you'll agree to that. That's kind of what I'm trying to get at.

HRG

I must confess that I am not at all familiar with Kripke and Putnam and I am grateful to you, Thomas Metcalf and others for plugging a hole in my education

But I still have some nagging suspicion that they use the word "necessary" in a different way than logic does, modal or not.

BTW, do you (or does anyone) know if there has been a consistency proof for the various systems of modal logic ? If not, then they may lead us to paradoxes just as naive set theory did (Burali-Forti - set of all ordinal numbers, Russell - set of all sets which are not elements of themselves etc.)

Fine so far, and I'm glad to see Kripke and Putnam agreeing with me
Still fine.

However, this interpretation is strictly tied to one possible world, to wit, our universe. It refers to a "certain social linguistic community".

I thus question whether it can be used when discussing modal necessity - which implicitely requires an abstraction from the properties of any individual universe.
Thus, if I amplify K/P-s claim a bit, we are talking about the proposition "In our world, the substance which a certain social linguistic community calls water is composed of H20 molecules"; and I doubt it can be called modally necessary. It is meaningless in other universes than ours.

I'll follow your admonition and stop here, before making a long post!

Regards,
HRG.

HRG

Information please - what is an alethically possible world ? I doubt it denotes a world without the River Lethe

Thanks,
HRG.

Thomas Metcalf

Originally posted by HRG :

You just know "alethically possible" as "modally possible" or "ontically possible," perhaps, and it's closest to "logically possible." Alethic modality is the modality of truth or existence in possible worlds. It's only called "alethic" to distinguish it from other possibilities, necessities, and contingencies, like epistemic possibility, conceptual possibility, metaphysical possibility, etc.

You're correct that it has nothing to do with the River Lethe. The etymology is the same as it is for "dialetheism"; the root is the word for truth.

Kenny

There is no philosophy education without gaps. Philosophy is simply too big. Though I had some vague awareness of Kripke’s and Putnam’s views regarding these matters, it was only very recently that I have explored them seriously. In terms of my philosophy education, philosophy of language has been a major gap – one which I’m trying to fill in a little. I must say, though, that I find myself warmly drawn to Kripke’s and Putnam’s views here. Given that I’m already an externalist with respect to my views on epistemology, an externalist view of meaning in philosophy of language suites me just fine.

Well, if you think that way, just replace the term “necessary” with “true in all counterfactual scenarios” or something along those lines.

Honestly, I don’t know. If not, I would say that the axioms of modal logic S5 are sufficiently intuitive that the burden of proof would fall on the one doubting their inconsistency. I realize the same could have been said of naïve set theory, but the burden of proof in that case was met. Also, since we’re talking about philosophy here, we might hope for in some cases, but should not demand, the same sort of rigor we do in mathematics.

Well, if you agree that ‘water’ means ‘that which is composed of H2O molecules’ (or, at least, to not completely gloss over Bilbo’s concerns, ‘some set of objects which bares a certain sameness relation, sameL, with various exemplars referred to by members of our social linguistic community as ‘water’) by virtue of how the word ‘water’ is used by members of our social linguistic community to refer to the world, then it readily follows that necessarily water is composed of H2O molecules.

True, because the meaning of our descriptions of counterfactual situations is fixed by the language which we acquire in the actual world. The fact that a Twin Earth speaker may be able to truthfully utter, in their dialect, “Necessarily, water is composed of XYZ molecules,” does not mean that “Necessarily, water is composed of XYZ molecules,” is true when uttered by one of us. Though these two utterances may be phonetically identical, their meanings differ depending on the dialect in which they are uttered. Consequently, these two utterances actually express two different propositions – one of which is true and the other of which is false.

This does not negate the fact that the language by which we speak of such abstractions is obtained in the actual world.

I think you are confusing metalinguistic possibilities with the meanings that our language actually conveys. Certainly, it is true that water might not have been called ‘water.’ If our language had developed differently, perhaps water would have been called ‘blabbersquak’ or some such thing. It is also true that the word ‘water’ might not have referred to water, but to something else. On Twin Earth, for example, ‘water’ does not refer to water but to XYZ. None of these metalinguistic possibilities entails that water may not have been water, however, or that what we refer to as water might not have been composed of H2O.

God Bless,
Kenny

Kenny

I disagree. It may be that God’s necessary existence is not strictly a consequence of the meaning of the word ‘God’ or ‘maximal greatness’ but that the premise ‘If God exists, then necessarily God exists’ follows from the meaning of the word ‘God’ in conjunction with other facts about modality. For instance, if worship worthiness entails self sufficiency and, when analyzed in terms of other facts of modality, self sufficiency entails necessary existence, it may be that the premise ‘If God exists, then necessarily God exists’ follows if God is defined as a worship worthy being. But, it follows from the conjunction of the meaning of ‘God’ with certain other facts about modality, not from the meaning of ‘God’ alone. If that’s the case, then the premise you list above would be necessarily false without it being the case that necessary existence is included in the meaning of ‘maximal greatness.’

I think the statement ‘2+2=4’ provides a clear example of a similar case. “Necessarily, 2+2=4” does not follow from the meaning of ‘2+2=4,’ but it does follow from the meaning of ‘2+2=4’ when conjoined with the premise that true mathematical propositions are necessary.

The only way I can think to make sense of this is to think of ‘background probability’ as referring to antecedent epistemic probability. Of course, the objective probability of any necessary proposition being true is 1. That being said, I still do not see how this claim follows.

I’m not sure how far the usefulness of the distinction between analytic and synthetic propositions extends. Is the statement ‘water is composed of H2O’ analytic or synthetic? I suppose one could make the case that if the meaning of ‘water’ includes ‘being composed of H2O,’ then the statement is analytic. But analytic statements are typically thought to be semantically empty and empirically unfalsifiable. Neither seems true of the statement ‘water is composed of H2O.’ The fact that water is composed of H2O represents an interesting empirical discovery about the world and thus it certainly would seem that ‘water is composed of H20’ has semantic content. Furthermore, the statement ‘water is composed of H2O’ is falsifiable. Suppose, for instance, that we were to encounter incredibly strong evidence that our current molecular theory is wrong in such a way that rendered the proposition ‘water is composed of H2O’ untenable. I also share Kant’s suspicion that mathematical statements are not tautologies, so should they be classified as examples of the synthetic a priori? I’m asking questions here for which I do not have fully developed answers myself.

No, I think the modal status of any proposition (provided that such status remains unknown) is irrelevant with respect to its (epistemic) background probability. If Putnam and Kripke are right and statements such as ‘water is composed of H2O’ represent necessary truths, then I fail to see how that bares on the issue of the background probability that water is H2O.

God Bless,
Kenny

Thomas Metcalf

Originally posted by Kenny :

So you would use the first form of the argument I gave.

(1) There is a possible world in which maximal greatness (except for alethic necessity) exists.
(2) If there is a possible world in which maximal greatness (except for alethic necessity) exists, then maximal greatness (except for alethic necessity) exists in every possible world.
(3) Therefore, maximal greatness (except for alethic necessity) exists in every possible world.

And you hope there's a way to derive alethic necessity from self sufficiency or something similar. I really don't think there is, but if you can find it, then please present it. I should say that simply not being possibly destroyed or possibly ceasing to exist is no guarantee of alethic necessity, because the being still might not have existed in the first place. I have a feeling that any argument you give to derive alethic necessity from some other of God's characteristics won't be able to cover the possible worlds in which God fails to exist from the start.



Now. Let me ask this about synthetic propositions. Suppose I give you some synthetic proposition P and ask you to estimate its background epistemic probability. Now suppose I ask you to estimate the background epistemic probability of []P. You wouldn't lower your estimate at all?

HRG

Not to be confused with dial-a-theism - a modern form of televangelism for Unitarians

Thanks for the info!
HRG (who is awfully glad that as a mathematician he had only to deal with true/false, resp. valid/invalid)

Kenny

No. If the meaning of ‘God’ or ‘maximal greatness,’ though it does not entail alethic necessity by itself, when conjoined with certain other facts about modality, entails alethic necessity, then (1) is necessarily false. One could not have all the other qualities of maximal greatness without alethic necessity following as a result. However, if what I have stipulated is the case, then alethic necessity would not itself be included in the definition of maximal greatness. The label ‘maximal greatness (except for alethic necessity)’ would, in fact, be quite meaningless. It would simply be a confusion of categories to regard alethic necessity as a property or predicate associated with maximal greatness that could be subtracted from other properties or predicates associated with maximal greatness.

Well, at the very minimum, if God might not have existed in the first place, then God depends on the fortunate happenstance that God did in fact exist in the first place for His continued existence. God could think to Himself, “I realize that I can’t cease to exist or be destroyed, but thank Me I existed in the first place in order to get the whole thing going.” Actually, He couldn’t even think “thank Me” since the whole thing would have been completely beyond His control. But if self sufficiency entails that a being does not depend on any contingent circumstances external to itself for its continued existence, then the logical possibility that God might have not existed would violate the definition of God as a self sufficient being. One could strengthen this analysis, I think, if one were to add good reasons for holding to the principle of sufficient reason. If God could have failed to exist and the principle of sufficient reason holds, then one would have to account for either the existence or lack of existence of God in terms of other contingent circumstances, but that would mean that God’s existence depends on the world being a certain way which in turn would imply that God is not self-sufficient.

That being said, I think I want to table this discussion for now, since (as I originally stated) I’m not interested in arguing for the truth of the premises of the ontological argument directly at the moment.

As I said before, my estimate of the background epistemic probability of a particular proposition, P, (in most cases anyway) would be independent of my estimation of the modal status it would have if it were true. I may hold, for example, “If water is composed of H2O molecules, then necessarily water is composed of H2O molecules,” but that has no effect whatsoever on my estimation of the background epistemic probability that water is composed of H2O molecules. I suppose the only cases where my estimation would be affected would be cases where alethic necessity is arbitrarily tacked on to the definition of a proposition. If, say, the existence of such things as eunicorns, which are defined as horse-like beings with a single horn protruding from their heads and who exist necessarily, were proposed, my estimation of the background epistemic probability of this proposal would be quite low (I would peg it at zero, in fact). But, I don’t think that the OA does or need involve tacking alethic necessity onto the definition of God arbitrarily – to construe things that way is simply to caricaturize the argument, in my opinion.

Now as to my estimation of the background epistemic probability of []P with respect to various synthetic propositions (or just propositions in general, as I have doubts about the extent to which the analytic/synthetic distinction is useful), I would say it would vary depending on the nature of the proposition. Since I find Kripke’s and Putnam’s arguments compelling, for example, I would regard the antecedent probability that necessarily water is composed of H20 to be equal to the antecedent probability that water is, in fact, composed of H2O. I would regard the antecedent probability that necessarily Bush is the president of the United States, on the other hand, to be quite low, given all that we know about the nature of the world in general and the circumstances surrounding the last election in particular. If we indulge the speculation that mathematical propositions are synthetic, then my estimation of the probability of the necessary status of unknown mathematical conjectures (such as the conjecture that every even number is the sum of two primes) would be the same as my estimation of the probability of the truth of those conjectures.

All in all, I don’t see how the fact that, in general, P -> []P should lower our background estimation of the probability of P.

God Bless,
Kenny

Kenny

Q: How many unitarians does it take to change a light bulb?

Unitarian Response: We choose not to make a statement either in favor of or against the need for a light bulb. However, if in your own journey you have found light bulbs work for you, that is fine. You are invited to write a poem or compose a modern dance about your personal relationship with your light bulb, and present it next month at our annual light bulb Sunday service, in which we will explore a number of light bulb traditions, including incandescent, fluorescent, three-way, long-life and tinted, all of which are equally valid paths to luminescence.