Thomas Metcalf

Originally posted by HRG :

Indeed. It's always bothered me that OAs ask us to conclude a very synthetic proposition a priori, which is a related worry, I think. I don't see how God could possibly be a consequence of the existence of existence itself.

Hm. Maybe a maximally great being would be describable within 1st-order predicate calculus, if to be so describable is better than not to be. God's existence would be so... compelling, maybe... that it would follow from something as basic as the 1st-order calculus.

More generally, it certainly seems true to me that everything that exists satisfies some predicate(s), and that there's a primary-kind property "being God." It's not as if we're limited to within the predicate calculus for our description; successive translation of the elusive sentence in question would simply read "There is only one being that instantiates Godness," and then "There is only one God." We can certainly understand the meaning of these sentences, and that suggests to me that if they're direct translations of the sentence in the 1st-order predicate calculus, that sentence is meaningful as well.

Kenny

Indeed. In fact, in terms of philosophy of language, Saul Kripke’s theory of nonrigid vs. rigid designators and Hilary Putnam’s theory of natural kind words entail that statements such as “Necessarily, wherever water exists, water is composed of H2O molecules” are true and meaningful. Yet I doubt the phrase “wherever water exists, water is composed of H2O molecules” is a tautology of first order predicate calculus, especially since this statement represents an empirical discovery! If Kripke and Putnam are right (and there are some good reasons to think they are right or at least close to being right), then there are numerous necessary truths about the world that do not reduce to tautologies in first order predicate logic.

I think we have an equivocation fallacy going on here. You seem to be reading ‘true in all possible worlds’ as ‘true in all formal systems of logic.’ However, in terms of modal logic, at least as it is commonly used by philosophers, ‘true in all possible worlds’ means ‘true in all logically coherent states of affairs.’ Those are two completely different meanings.

God Bless,
Kenny

Kenny

I disagree with this on two counts.

First of all, I disagree that the statement “there is a logically possible world in which God exists” literally means that God exists in every possible world. In order for such to be the case, the former would have to entail, without the help of any additional premises, the latter. But clearly “there is a logically possible world in which God exists” does not entail that God exists in all possible worlds unless we add the premise that if God exists God necessarily exists. Otherwise, the ontological argument would only require one premise rather than two. Second, I don’t see why it should necessarily be any more difficult to prove that God exists or any “harder” for God to exist than it would any other necessary truth to be true.

Consider, for example, the statement “2+2=4.” I think that there are good philosophical arguments for accepting the premise that if “2+2=4” is true at all then necessarily 2+2=4. First, it is clear, however, that 2+2=4 does not literally mean that necessarily 2+2=4. In fact, there are some philosophers who accept the former while rejecting the latter (though I am aware of none who reject both the former and the latter ). Second, it's very easy to prove that there is a logically possible world in which the statement “2+2=4” is instantiated. I recall doing so sometime in my very early childhood (at the age of five or six perhaps?) by counting on my fingers. I don’t see how a proposition’s being necessary entails that it is somehow more difficult to prove. Nor do I see that it is somehow “harder” (I’m not even sure what that would mean in this context) for the statement “2+2=4” to be true simply because it is necessary.

God Bless,
Kenny

Bilbo

Earlier, I wrote:

"There is a possible world in which maximal greatness is instantiated."


To which Thomas responded:

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I don't like that formulation, because then the statement seems to me to be patently false. Maximal greatness can't be instantiated "in" a possible world, because what's in the world itself has nothing intrinsically related to other possible worlds.
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The reason I introduced this way of stating the premise was to hedge out problems that arise in modal contexts when singular terms occur in negative existential statements.

In any case, you take umbrage with the convention of locating property instances in (or at) worlds. I don’t know what mileage you hope to gain by adopting that stance, or how it is relevant to your earlier suspicions about the difficulty in accepting one modal premise over another, so feel free to clarify.

Its also somewhat puzzling that you take an opposing stance, and then appear to grant the conventional usage later in the same post.

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Maximal greatness doesn't exist in possible worlds; it ranges over possible worlds.
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It appears we differ substantially on the terminology and concepts involved, so we should address those issues. As I see it, If we take a (broadly) realist stance on properties, and possible worlds (as initially sketched by Kenny), and we take maximal greatness as a property (actually, a conjunction of *world-indexed* properties), then we would certainly want to say that maximal greatness, (or any other property for that matter), exists in (or at) a world. Of course a distinction will be made between a property *existing* in a world (or all the worlds) and a property being *instantiated* at a world. The issue surrounding the "existence” of the property of maximal greatness then, is not to the point.

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Just in case the argument is presented with that statement as a premise, I offer the alternatives:

"There is a possible world in which maximal greatness is not instantiated."

"There is a possible world in which 'exists necessarily' and 'is a unicorn' are satisfied by the same object."

I see just as much reason to accept these propositions as I do to accept their cousin.
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These are interesting claims, and ones worth exploring.


I then wrote:

"I'm not sure that its "hard to support the modal premise", if we understand it in terms of possible property instantiation. As Kenny suggested earlier, it seems quite reasonable to say that the premise is (at worst) properly basic for some people."


To which you respond:

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I think the illusion of proper basicness occurs because of a confusion between epistemic and alethic modality. "There is a possible world in which maximal greatness is instantiated" is true if "possible" is epistemic possibility, but we have no way to tell whether it's true if "possible" is alethic modality.
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I assumed it was understood that when theistic philosophers talk about “possibility” with regard to the modal ontological arguments, they typically have Broad Logical Possibility firmly in mind. This understanding of modality is to be distinguished from other types of “possibility”; Narrow Logical Possibility, “epistemic” possiblity, as well as wider notions like nomological and “physical” possibility.


Given these distinctions, I’m not sure where you think that “confusion” arises with regard to a persons belief regarding modal propositions, in this broadly logical sense. You claim that “we” (you?) have no way to tell whether a given proposition or its negation is true, but neglect to expand on why you think that is so, or why it is true for others.

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When you evaluate your intuitions about the alethic version, ask yourself whether your intuitions suggest that maximal greatness is instantiated in all possible worlds, because that's what the statement literally means.
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That’s as good a piece of advice as I’ve received in a while

Regards,

Bilbo.

HRG

Yes, it is - if you stick in the definition of "water" = "that which is composed of H2O molecules".

If someone talks about "water" as a "natural kind word", he is not doing philosophy, but linguistics, cognitive psychology etc.

Depends on the definition of "water". Either you define water as above (then it is not a discovery) or you define it as "the main component of Earth's oceans" - or similarly -, then it is not necessarily true. I can imagine an Earth, under different physical and chemical laws, whose oceans are mainly composed of NH3. I can also imagine a desert tribe which doesn't even know the concept of water since they satisfy their liquid requirement from nutritious roots.

I would be interested in those good reasons, as my first reaction is that they are abusing the term "necessary".

Not so. The formal system of logic is but the language we use to talk about the possible worlds. My quantification runs over all worlds, not over all systems of logic.

See above - and what decides whether a conceivable state of affair is logically coherent, if not a system of formal logic ?

regards,
HRG.

HRG

Isn't "necessary" usually included in the definition of "God" ?
Any valid mathematical theorem is a tautology, hence necessarily true.
In formal systems like mathematics, it does. There is no conceivable world in which a valid mathematical theorem is not true - like there is no conceivable world in which a bishop could move to a square of different color in chess.
IHMO, this is not an instantiation of the mathematical statement 2+2=4, aka =+SS0SS0SSSS0 (in Polish notation, S = successor). It is experimental evidence that some collections of objects are modelled by the natural numbers, if addition models juxtaposition.

If you had "added" 2 drops of water to 2 drops of water, you'd have gotten a (bigger) drop. Thus, numbers plus addition model the behavior of fingers, nuts or dimes, but they do not model the behavior of drops.

The distinction between "2+2=4" and "2 fingers juxtaposed to 2 fingers make 4 fingers" may sound trivial, but it isn't. It is the same as a distinction which is made since Gauss, Riemann and Einstein: mathematical geometry (that which is deduced from axioms) versus physical geometry (that which described the behavior of rigid rods and light rays). That the former (in its Euclidean version) models the latter to a good approximation does not prevent the essential distinction between the two.

Regards,
HRG.

Kenny

According to Kripke and Putnam’s theory, one would not have to have a conception that such was the definition of water in order for the phrase “Necessarily, wherever water exists, water is composed of H20 molecules” be true. According to their theories, the meaning of water is fixed by repeated instances of members of a certain social linguistic community pointing to various representative exemplars and saying “this is water.” The speakers need not be aware of all the properties that water has or that water is composed of H2O for the meaning of water to include ‘that which is composed of H20 molecules.’ According to this theory, meanings are not just fixed by concepts in the minds of certain speakers but in terms of how words actually refer to objects in the world. In other words, the world and not just the interior mental states of language speakers, contributes to meaning.

This thesis is supported by the fact that individuals can actually refer to objects even when they have a completely false concept of them. One of Kripke’s own examples is to suppose that there is a man in the street whose only conception of the term ‘Godel’ is ‘the man who originally proved the incompleteness of arithmetic.’ Now suppose that, in fact, Godel plagiarized his famous incompleteness theorem from some other man, say Smith. The man on the street still refers to Godel (and says something false about him) even though his concept of Godel is actually wrong. Likewise, he does not refer to Smith, even though Smith actually fits his conception of ‘Godel.’

Well, I would say that large portions of these fields are still included in philosophy or at least have significant baring on philosophical issues. Kripke has recognized that there are some deep connections between philosophy of language and necessary truth.

Actually, it is. Because what fills the Earth’s oceans in the actual world is a substance composed of H2O molecules and it is reference to that substance which fixes the meaning of the word ‘water.’ We can still say, for example, with full propriety, “the substance which fills the Earth’s oceans may not have been the substance which fills the Earth’s oceans.” Just as we can say with full propriety, “The author of Hamlet may not have been the author of Hamlet.” In this later phrase, the fist occurrence of ‘the author of Hamlet’ designates the individual who actually wrote Hamlet – namely Shakespeare. However, it is possible that Shakespeare might not have written Hamlet (to be taken in a counterfactual sense, not in the conspiracy theory sense that Shakespeare didn’t actually write the plays attributed to him). Thus, the latter occurrence of ‘the author of Hamlet’ refers not to the individual who actually wrote Hamlet but instead ranges over a number of possible worlds in which there is either no author of Hamlet (because it was not written) or someone else rather than Shakespeare wrote Hamlet. In other words, the descriptor ‘author of Hamlet’ changes its scope in the midst of the sentence. Notice, however, that one could not say, with propriety, “the author of Hamlet is not the author of Hamlet,” since that involves a contradiction.

Likewise, when we say "the substance which fills the Earth’s oceans may not have been the substance which fills the Earth’s oceans” the first occurrence of ‘substance which fills the Earth’s oceans’ means ‘water’ whereas the second occurrence of ‘substance which fills the Earth’s oceans’ ranges over counterfactual scenarios in which some other substance besides water fills the Earths oceans. If this counter factual scenario had been realized, the substance which fills the Earths oceans would not have been water. That’s easy to confirm intuitively. Suppose some sufficiently powerful being were to empty the Earth’s oceans and replace their contents with NH3 molecules. We would then say that the Earth’s oceans no longer containe water, not that water is now composed of NH3.

Actually, Putnam employs a similar example in favor of his thesis rather than in opposition to it. Putnam asks us to image that there exists a place called Twin Earth. Twin Earth is nearly identical with earth – so much so, in fact, that there exists a large body of English speakers on Twin Earth. There is one significant difference between Twin Earth and Earth, however. On Twin Earth water as that which is composed of H2O molecules doesn’t exist. Rather, another substance, which is nearly identical to water in terms of its most readily apparent properties, but is composed of a more complex chemical formula, which shall be abbreviated as XYZ, exists. XYZ fills the oceans of Twin Earth, Twin Earthers drink it, etc. Furthermore, without sophisticated scientific testing, it is impossible to distinguish H2O on Earth from XYZ on Twin Earth. On Twin Earth, the inhabitants refer to XYZ, rather than H20, as ‘water.’

Now suppose that some English speaking scientists from Earth were transported to Twin Earth. On first impressions, having been told by be the inhabitants that what fills the lakes and rivers of Twin Earth is water, the scientists assume that the word ‘water’ on Twin Earth has the same meaning that the word ‘water’ does on earth. However, upon testing, the scientists discover that what is called ‘water’ on twin earth is actually composed of XYZ rather than H20. Putnam believes that the conclusion these scientists would draw (or at least should draw) is that what is called ‘water’ on Twin Earth isn’t water. Likewise, scientist from Twin Earth could say, in their dialect, “What is called ‘water’ on Earth, isn’t water.” This is because, although the two words ‘water,’ on both planets are identical in terms of spelling and phonetic sound, they are actually two different words with two different meanings with the meaning of the spelling or utterance of ‘water’ being determined by the dialect of the speaker or the writer.

Now suppose we rewind the history of Earth and Twin Earth so that we are at a time when the scientists on these planets have not yet discovered that the substance which each refers to as ‘water’ is composed of H2O or XYZ respectively. It would still be the case that what Twin Earthers refer to as ‘water’ differs from what Earthers refer to as ‘water.’

Its easy to test our intuitions against this. Suppose, in the real world, scientists were to discover the substance XYZ and initially mistake it for water. Upon finding out that it this substance consisted of XYZ molecules, the scientists would conclude that the substance they had discovered was not water but something else. They would not conclude that water could be composed of XYZ rather than H2O. Similarly, suppose a scientifically unsophisticated speaker (a child perhaps), in the real world, on Earth, who is unaware that water is composed of H20, mistook a flask of XYZ for a flask of water. We would want to say that said speaker’s identification was incorrect.

I gave many of those reasons above. Kripke grounds his argument in the long standing seeming paradox that it appears it can be shown that there are no contingent identity statements. The argument runs as follows (Kripke’s actual formulation):

Many philosophers have sought for someway to deny this conclusion because it seems so paradoxical. Statements like “Bush is the President of the United States” seem like contingent identity statements (after all, a few less hanging chads and perhaps it would have been Gore). But Kripke accepts the conclusion and offers the idea of changing scope introduced above to explain away statements like “Bush is the President of the United States.” Bush, in this sentence, is a rigid designator. It refers to a specific individual in the actual world. “President of the United” states, however, in this sentence, is a non-rigid designator that ranges over counterfactual situations. Consequently this sentence is not strictly an identity statement. Once again, we could say with full propriety, “the President of the United States may not have been the President of the United States” because the term ‘President of the United States” shifts in meaning from a rigid to a non-rigid designator.

Now, certain terms like ‘water’ Kripke argues, can only be used as rigid designators. ‘Water’ means precisely what can be abstracted from the set of representative exemplars referred to by a certain social linguistic community as ‘water.’ We can not say, with propriety, “Water might not have been water” because there is no room for the scope of the word ‘water’ to change from rigid to non-ridged. In Putnam’s terminology, ‘water’ is a natural kind word. Likewise, since the word ‘water’ obtains its meaning from its representative exemplars, water is genuinely identical with the set of properties all of those exemplars share in common, and consequently water is identical to H2O. This is true whether the speakers are aware of this identification or not. And it follows from the fact that there can be no genuine contingent identity statements that Necessarily, water is H2O.

But your talk concerns truth values in all possible systems of logic not possible states of affairs in the world. I guess I don’t see the necessary connection?

Well, I think Godel’s incompleteness theorem gives us reason to believe that logical coherence is stronger than any system of formal logical can capture. Furthermore, it would appear from Kripke’s and Putnam’s analysis that there are necessary truths about the world which must be empirically discovered and cannot be derived as tautologies in first order predicate logic.

God Bless,
Kenny

Whew, how do I get myself into making such long posts like this when I only want to make a few brief comments? You think I would have learned my lesson by now.

Christopher13

HRG, I was going to come here and invite you to join the Aquinas thread but am happy to see that you have already done so. It needs new blood.
I also notice that you carry over your confusion regarding the competency of modern science. I don't know yet if this is completely fair to you. But I knew without you saying that you suspect "ontological classifications" are just mental constructs. This, at least, makes you interesting and gives you grounds to discuss such things as Aquinas' concept of esse. On second thought, though, you might not be at home in the Aquinas thread. It depends on just how agnostic you turn out to be concerning metaphysics.
Regarding this thread, 1) it would be nearer the mark to say that an infinite series IS the contingency problem, 2) my statement about temporality and causation does not imply the identity of concepts you suggest, 3)science, though only in your humble opinion, is not capable of tackling the Thomistic proofs--as I have argued elsewhere, descriptive, natural science takes the being of things for granted, not addressing the why that concerned previous generations (like Aristotle's) but the what of things. Aquinas, also, did not adopt the peculiarities of Aristotle's notion of Prime Mover as Final Cause, for example, and does not depend for its validity on contemporary science. . . . But your perspective gives us something to talk about, which we might end up doing in the Aquinas thread.

Bilbo

This is a fine exposition of the so called "New Theory of Reference" as that theory pertains to natural kind identities. I’ll just chime in with a footnote or two


Kenny writes:
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First, the law of substitutive identity says that, for any objects x and y, if x is identical to y, then if x has a certain property F, so does y:

(1) (x)(y)[(x = y) -> (Fx -> Fy)]

On the other hand, every object surely is necessarily self-identical:

(2) x) [](x = x)

But

(3) (x)(y)(x = y) -> [[](x = x) -> [](x = y)]

is a substitution instance of (1), the substitutivity law. From (2) and (3) we can conclude that, for every x and y, if x equals y, then it is necessary that x equals y:

(x)(y)((x = y) -> [](x = y))
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A little more intuitively and informally, we can speculate just which pairs invalidate the above formula (actually a theorem of Ruth Barcan’s, later revived by Kripke). Certainly not two different things (for then the protasis is false) and certainly not the same thing (for then the apodosis is true).


quote:
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I can imagine an Earth, under different physical and chemical laws, whose oceans are mainly composed of NH3.
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Its easy to test our intuitions against this. Suppose, in the real world, scientists were to discover the substance XYZ and initially mistake it for water. Upon finding out that it this substance consisted of XYZ molecules, the scientists would conclude that the substance they had discovered was not water but something else. They would not conclude that water could be composed of XYZ rather than H2O. Similarly, suppose a scientifically unsophisticated speaker (a child perhaps), in the real world, on Earth, who is unaware that water is composed of H20, mistook a flask of XYZ for a flask of water. We would want to say that said speaker’s identification was incorrect.
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One of the unfortunate aspects of Putnam’s Twin Earth thought experiment is that the terms “water” and “H2O” typically function as mass nouns, (rather than count nouns), and mass nouns are ambiguous and incomplete when used in identity statements. After all, the chemical formula “H2O” is a simplification and an approximation of what water is. Because some substance isn’t literally H20 (according to one sortal specification), doesn’t necessarily mean that it isn’t water. Putnam conceeds this point in a later essay (“Possibility and Necessity”, in volume three of his collected papers), but emphasizes that the identity relation, or in this case – “similarity relation”, is still one of necessity, IF true.

So if it really is possible that water is XYZ in Twin Earth (ie Broad Logical Possibility), then water is not H2O on our earth, or any other earth for that matter (contraposition). Or, alternatively, if our present molecular theory does not accurately model The Real World, then we might one day come to realize that water was not-H20, indeed, that its impossible that water be H20.


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And it follows from the fact that there can be no genuine contingent identity statements that Necessarily, water is H2O.
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As I see it, the salient point with regard to this theory is that the proponent shouldn’t be viewed as making questionable, extravagant or suspiciously unscientific claims with regard to the necessary a posteriori, because the necessity in question is qualified, and in one sense relative to our common opinions about what is actually the case.


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Whew, how do I get myself into making such long posts like this when I only want to make a few brief comments? You think I would have learned my lesson by now.
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An excellent and satisfying post Kenny; if we can be pardoned for (temporarily) losing God in all this


Regards,


Bilbo.

Thomas Metcalf

Originally posted by Bilbo :

I'm just trying to avoid lending any illegitimate intuitive appeal to the idea that maximal greatness is instantiated in a possible world. Prima facie, it's quite easy to forget that when we say maximal greatness is instantiated in a possible world, we're saying that maximal greatness is instantiated in every possible world. It just seems easier, intuitively, to estimate that in at least one possible world, maximal greatness is instantiated. I hope to remind the intuiter that she's committing herself to more than seems immediately evident.

I'm not sure they're really worth exploring. We seem to have no epistemic access to the truth of the former, and the latter seems dubious.

I'm just diagnosing those who find the MOA appealing with taking alethic possibility in an epistemic way. It seems to them to be possible that maximal greatness is instantiated in one possible world, but that's not enough to confirm alethic possibility.

I said we have no way to tell whether this statement is true:

"There is an alethically possible world in which maximal greatness is instantiated."

But we know that this proposition is true:

"There is an epistemically possible world in which maximal greatness is instantiated."

When I say we have no way to tell whether the former is true, I only mean in practice. I don't know whether there is a sound argument for the existence of the Anselmian God, so I don't know whether we have epistemic access to the truth of the former in principle.