October 30, 2008

God and the stone too heavy to lift

APOLOGIA By Hendrik van der Breggen
(The Carillon, October 30, 2008)

God and the stone

Some objectors to God’s existence ask: If God is all-powerful, can God make a stone so big God can't lift it? If you say Yes, then God is not all-powerful, because God can't lift the stone. If you say No, then God is again not all-powerful, because God can't make the stone. Thus, according to this objection, an all-powerful God doesn't exist.

The objection is mistaken, and here is why.

That God is all-powerful means God can do anything. This doesn't mean, however, that God can do anything you say.

Consider these strings of words: "square circle", "triangle with four right angles", "married bachelor." The concepts to which the individual words refer cancel each other out, because they are logically contradictory. As a result, the strings of words fail to refer to anything, and cannot refer to anything. Hence, the strings of words are unintelligible nonsense, of the order of blah-blah-blah.

But this means that when we intelligibly say God can do anything, we mean by "thing" or "thing to be done" some task whose description is not contradictory.

Of course, an all-powerful God can do things we don't understand, because of those things' immense complexity. However, to ask God to do a thing or task the description of which is contradictory is to ask God to do what is in principle un-understandable (even by God). Such a "thing" is, by definition, not a thing—i.e., not a genuine possibility—since the description fails to refer and cannot refer.

To hold God in disrespect for not doing such a thing or task is like asking a waiter to “blah-blah-blah,” and then getting upset with the waiter because both you and he don't know what you are talking about!

The objector asks: Can God make a stone God can't lift? But this is to ask whether God can create a situation in which the following two forces co-exist simultaneously: (1) a force that is in every respect most powerful; and (2) another force that is in one respect more powerful.

In other words: Can God make it true that, with regards to this particular respect, the most powerful force is, at the same time, not the most powerful force?

That is: Can God make X and not-X true at the same time and in the same respect? But this is to ask: Can God make a blah-blah-blah?

In other words, the objector’s question contains a contradiction. Therefore, the objection fails because it fails to qualify as intelligible discourse.

For an objection to succeed, it must at least make sense.

(Hendrik van der Breggen, PhD, is assistant professor of philosophy at Providence College, located in Otterburne, Manitoba, Canada.)

12 comments:

Pvblivs said...

     I find typical claim of omniscience is rather satisfyingly self-defeating. Consider the sentence, "'does not yield a sentence regardard as true by god when preceded by its own quotation' does not yield a sentence regarded as true by god when preceded by its own quotation." The phrase "preceded by its own quotation requires a bit of explanation. I feel it best to use an example. "Is a sentence fragment" preceded by its own quotation yields "'Is a sentence fragment' is a sentence fragment," which turns out to be a true sentence.
     An omniscient being would be able to determine the truth or falsity of any meaningful sentence. The sentence that I asked you to consider states only that "god" would not determine that it was true. If he determines it true, then it is meaningful, and it is false; which means that "god" is in error. If he determines it false or he determines it has no meaning, then it is meaningful and true; which again means that "god" is in error. If he can make no determination, then he is not omniscient, as his knowledge is incomplete. The sentence itself can only be meaningless if the term "god" does not refer to any being.

Dr. V said...

Pvblivs,

Thanks for your interesting comment on omniscience. It's one that will require some pondering. I will try to provide a thoughtful reply when my schedule permits.

Best regards,
Hendrik

Dr. V said...

Hello Pvblivs,

Sorry for taking so long to attend to your puzzle which purports to show that God either is not omniscient or doesn’t exist. Your puzzle is an intriguing one, and worth some careful thinking. Here (finally) is my response.

Pvblivs wrote:

I find typical claim of omniscience is rather satisfyingly self-defeating. Consider the sentence, "'does not yield a sentence regardard as true by god when preceded by its own quotation' does not yield a sentence regarded as true by god when preceded by its own quotation." The phrase "preceded by its own quotation requires a bit of explanation. I feel it best to use an example. "Is a sentence fragment" preceded by its own quotation yields "'Is a sentence fragment' is a sentence fragment," which turns out to be a true sentence.

An omniscient being would be able to determine the truth or falsity of any meaningful sentence. The sentence that I asked you to consider states only that "god" would not determine that it was true. If he determines it true, then it is meaningful, and it is false; which means that "god" is in error. If he determines it false or he determines it has no meaning, then it is meaningful and true; which again means that "god" is in error. If he can make no determination, then he is not omniscient, as his knowledge is incomplete. The sentence itself can only be meaningless if the term "god" does not refer to any being.

Hendrik’s reply:

Okay, let’s first look at your example: “Is a sentence fragment” is a sentence fragment.

Yes, this is a meaningful sentence, and it’s true. I have no problems with this. The phrase “is a sentence fragment” is mentioned and then it’s used, and the result is a grammatically correct sentence that turns out to be true.

Okay, let’s now look at the sentence you think defeats omniscience or shows that “god” has no referent: “Does not yield a sentence regarded as true by god when preceded by its own quotation” does not yield a sentence regarded as true by god when preceded by its own quotation.

Here’s my assessment.

First, some clarification.

The phrase “its own quotation” in the second half of the sentence refers to the sentence as a whole (i.e., the field of reference includes the portion in quotes plus the rest which isn’t in quotes). For the sentence as a whole to be preceded by its own quotation, it would have to look like this:

‘“Does not yield a sentence regarded as true by god when preceded by its own quotation” does not yield a sentence regarded as true by god when preceded by its own quotation.’ “Does not yield a sentence regarded as true by god when preceded by its own quotation” does not yield a sentence regarded as true by god when preceded by its own quotation. (Notice that the whole sentence is quoted and precedes the original sentence.)

Now, keep in mind that the phrase—“Does not yield a sentence regarded as true by god when preceded by its own quotation”—is a sentence fragment, not a sentence.

So far, so good.

Now, if the whole sentence is preceded by its own whole quotation (as above), then the sentence fragment mentioned in the original sentence, which is the subject of the original sentence, doesn’t yield a sentence, never mind a true sentence. The sentence fragment per se doesn’t yield a sentence, period, because the sentence fragment remains a sentence fragment—i.e., a non-sentence—even when the whole original sentence is preceded by itself in quotes. Because it (the sentence fragment) isn’t a sentence, it can’t be a candidate for being a true sentence, a false sentence, a meaningful sentence, or a meaningless sentence. Again: it’s not a sentence. Thus, the original larger sentence, which is about the fragment, is true, because the fragment cannot yield a sentence at all, let alone one that can be regarded (by anyone, god or no god) as true.

But you claim that “If [god] determines it [the original larger sentence] true, then it is meaningful, and it is false; which means that ‘god’ is in error.” Well, as I’ve shown, we can see quite clearly that the sentence is true and (because we can see it’s true) meaningful. Also, I’m pretty sure that if a finite and fallible mind such as mine can figure this out, then an omniscient/all-knowing god could too. Surely, then, because the sentence is true and meaningful, it’s not false. So, contrary to what you would have us think, this god would not be in error. Nor would this god’s existence be logically precluded.

Therefore, the puzzle impinges neither on the issue of omniscience nor on the question of whether “god” has a referent.

Pvblivs, I think that what I’ve argued is reasonable, and I’m hoping that it’s helpful. I think that the puzzle is puzzling because the example/illustration—“Is a sentence fragment” is a sentence fragment—misleads us into thinking that the puzzle is like it, when in fact it’s not. Unlike the sentence in the example/illustration, the sentence in the puzzle involves a referential function to itself as a whole which gets missed, thereby causing the puzzlement/confusion.

Of course, I could be missing something important—and as a result be way off target!

Thanks for the puzzle. It was fun to think about. (Okay, so I need to get a life…)

With best regards,
Hendrik

Pvblivs said...

     Hmmm... It looks like blogger ate my reply. The sentence does, indeed, refer to itself, but only insofar as it is the result of applying the specified operation to the named string of words. It says nothing about when the entire sentence is preceded by its own quotation. It speaks of the result of preceding a particular string of words by its own quotation (which happens to yield the original sentence) and states that this result will not be regarded as a true sentence by the supposed omniscient being.

Dr. V said...

Pvblivs,

Thanks for your reply – it’s good to hear from you. You mention that you sent a previous reply. For the record, none was received at my end.

Here’s my response to your latest comment.

Pvblivs wrote:

The sentence does, indeed, refer to itself, but only insofar as it is the result of applying the specified operation to the named string of words. It says nothing about when the entire sentence is preceded by its own quotation. It speaks of the result of preceding a particular string of words by its own quotation (which happens to yield the original sentence) and states that this result will not be regarded as a true sentence by the supposed omniscient being.

Hendrik’s reply:

Okay, I think I’m seeing what you’re getting at. Let’s look again at our sentence: “Does not yield a sentence regarded as true by god when preceded by its own quotation” does not yield a sentence regarded as true by god when preceded by its own quotation.

I interpreted the “it” in “its own quotation” to refer to the sentence as a whole. It seems reasonable to think that if this is the interpretation at hand, then the puzzle doesn’t work. (I could be mistaken in this, but that’s what I’ve argued above, and I don’t think it’s a bad argument, given my interpretation of “it.”)

You are pointing out to me that the “it” in “its own quotation” should be interpreted as referring to the string of words following the quotation, which then, when placed in quotation marks, precedes this string of words.

So, to get rid of the ambiguity, the sentence should read (on your interpretation) as follows: “Does not yield a sentence regarded as true by god when the quotation in the sentence is constituted by the string of words after the quotation” does not yield a sentence regarded as true by god when the quotation in the sentence is constituted by the string of words after the quotation.

I think that the above states our puzzle’s sentence much more clearly in the way you intend, thereby ruling out the interpretation that I noticed previously.

Okay. I still think that the problem I outlined previously remains, but with some slight adjustments.

First some clarification. Keep in mind that the phrase—does not yield a sentence regarded as true by god when the quotation in the sentence is constituted by the string of words after the quotation—is a sentence fragment, not a sentence. (When it is in quotation marks, the fragment is mentioned; when it is not in quotation marks, the fragment is used.)

Okay, now, if the sentence fragment is preceded by its own quotation, then the sentence fragment mentioned in the sentence, which is the subject of the sentence, doesn’t yield a sentence, never mind a true sentence. The sentence fragment per se doesn’t yield a sentence, period, because the sentence fragment remains a sentence fragment—i.e., a non-sentence—even when the whole original sentence is preceded by itself in quotes. Because it (the sentence fragment) isn’t a sentence, it can’t be a candidate for being a true sentence, a false sentence, a meaningful sentence, or a meaningless sentence. Again: it’s not a sentence. Thus, the larger sentence, which is about the fragment, is true, because the fragment cannot yield a sentence at all, let alone one that can be regarded (by anyone, god or no god) as true.

But you claim that “If [god] determines it [the original sentence] true, then it is meaningful, and it is false; which means that ‘god’ is in error.” Well, as I’ve shown (or at least it seems to me that I’ve shown), we can see quite clearly that the sentence is true and (because we can see it’s true) meaningful. Also, I’m pretty sure that if a finite and fallible mind such as mine can figure this out, then an omniscient/all-knowing god could too. Surely, then, because the sentence is true and meaningful, it’s not false. So, contrary to what you would have us think, this god would not be in error. Nor would this god’s existence be logically precluded.

Therefore (and again), the puzzle impinges neither on the issue of omniscience nor on the question of whether “god” has a referent.

Pvblivs, I could (again) be missing something important—and be (again) off target. Also, I realize that I have run the risk of misrepresenting your original sentence by my rewording of it. Nevertheless, I do think that I’ve correctly captured your intended meaning in my rewording. If not, please do let me know. (I don’t like being misrepresented, and I’m sure you don’t either.)

Thanks again for the puzzle.

Best regards,
Hendrik

P.S. I notice that your blogger profile says you live in the United States. I hope that it’s not too personal of me to ask this, but here goes anyway: In which city and state do you live? I’m curious. Also, besides being curious, I think it’s nice to make a bit more of a personal connection when I have a philosophical discussion with someone. I think a personal element is important in discussions that have to do with deeply personal stuff such as God (or no-God), ethics, etc. Also, it’s more fun to argue with another person if you realize that you could do so over a beer or a coffee. (I would have to stick to coffee, because I used to drink way too much beer….) But if this is too personal, no problem.

Pvblivs said...

     A sentence fragment, when preceded by its own quotation can yield a sentence. Consider if my example sentence had been "'is a sentence fragment' does not yield a sentence regarded as true by [god] when preceded by its own quotation." This is a complete sentence, although its subject is a sentence fragment. To analyze this sentence, we consider what happens when we apply the operation to the subject. The subject is "is a sentence fragment." When preceded by its own quotation, it yields "'is a sentence fragment' is a sentence fragment." So, the example sentence means the same as "''is a sentence fragment' is a sentence fragment' is not a sentence regarded as true by [god.]" Since "'is a sentence fragment' is a sentence fragment." is readily seen as true, it would be regarded as true by any god that might be referenced and the full statement is false.
     Now, the actual sentence I used was "'does not yield a sentence regardard as true by god when preceded by its own quotation' does not yield a sentence regarded as true by god when preceded by its own quotation." The analysis starts the same way. The subject is "does not yield a sentence regarded as true by god when preceded by its own quotation." This is a sentence fragment. But it yields a complete sentence when preceded by anything that can serve as subject. Its own quotation ("'does not yield a sentence regarded as true by god when preceded by its own quotation'") can serve as a subject. When the subject of the sentence is preceded by its own quotation, it yields the original sentence. So, although it takes a roundabout method to get there, the sentence I used as demonstration asserts that it is not a sentence regarded as true by whatever entity "god" is supposed to mean. It would be easier to say "This sentence is not regarded as true by god." But it might be objected that "this sentence" is meaningless in the context rendering the entire sentence meaningless. The roundabout method constructs a meaningful sentence even if one tries to claim that its subject is meaningless. (That would just render the full sentence true.)

Pvblivs said...

     Oh, yes. I didn't think that you got the comment that I said blogger ate as I never got the "your comment has been saved..." message. My tastes are someone different. I like a level of anonymity. (Even when I am "out and about" I tend not to reveal personal information. That's just me.)

Dr. V said...

Pvblivs,

Thanks for your thoughtful response to my response to your previous thoughtful response (etc.). I must say that I appreciate your fine mind. You are forcing me to think—very hard. Thanks. (If I were still a drinker, I would have to have a drink or three…)

Okay, here’s our original sentence (with spelling correction): “does not yield a sentence regarded as true by god when preceded by its own quotation” does not yield a sentence regarded as true by god when preceded by its own quotation.

As a result of your clarifications, I believe that I better understand that a sentence fragment can be used as a subject and can yield a complete sentence. I understood this previously, especially with respect to the example/illustration, but now I’m clearer on it with respect to our original sentence. In the case of the original sentence, then, I stand corrected on this—and I appreciate your helping with this. So I’m now on the same page as you regarding our original sentence and the fact that a sentence fragment (as that in our original sentence) can yield a complete sentence. So far, so good.

But, Pvblivs, I’m still troubled. I’m back to being troubled by the reference of “it” in “its own quotation.” I know that you want me to think that “it” refers to the string of words after the second quotation mark (in our puzzling sentence), the string of words that’s used and then gets mentioned (via quotes) at the beginning of the sentence. However, it seems to me that the word “it” is doing something suspicious. When I say, does not yield a sentence regarded as true by god when preceded by its own quotation, it is not clear to me what the referent is of “it” in “its own quotation.” Please bear with me as I try to explain.

Think of this simpler example (of yet another sentence fragment): does yield a sentence preceded by its own quotation.

Regarding this simpler example, I know that you want me to think that the “it” in “its” (possessive form of “it”) refers to the sentence fragment. But it seems to me that the sentence fragment itself actually doesn’t direct us to do this. In the context of the sentence fragment itself, the word “it” seems very much to refer to the (whole) sentence that results (is yielded) when we precede the fragment by a quotation. This seems reasonable. Of course, though, we need the context of the complete sentence to make better sense of the fragment.

But things get worse when we place the fragment in quotes and in front of the original fragment: “does yield a sentence preceded by its own quotation” does yield a sentence preceded by its own quotation. It seems to me that, now, the referent of the word “it” in the predicate is no longer clear. The word “it” seems not to have a referent, or too many referents.

You want to say “it” refers to the string of words that’s not yet quoted, i.e., the string of words that’s being used in the sentence. Yes, that’s one possibility. But, as I’ve argued, the word “it” in “its own quotation” seems like it can also refer to the sentence.

In addition (and more problematic for the puzzle, it seems to me), “it” in “its own quotation” properly refers to the subject, which is the mentioning of the sentence fragment (“does yield a sentence preceded by its own quotation”). But if the referent of “it” is the mentioning of the phrase in question—which requires quotation marks to do this—then the phrase “its own quotation,” i.e., the quotation/mentioning of the referent of “it,” does double duty of the mentioning job. Why? Because the “it” that’s mentioned by quotation marks (in the subject) is being mentioned again (via the phrase “its own quotation”), and so should also be in quotation marks, since there is a mentioning of what’s mentioned. But then there’s a mentioning of what’s already been mentioned as mentioned, and so on.

Because of the deep ambiguity and deep lack of clarity that seems very much to be inherent in the sentence fragment and, especially, in the resultant sentence, I have trouble designating that resultant sentence as true, false, meaningful, or meaningless. Yes, it’s a sentence, to be sure; but it seems to me to be a sentence that needs much work before it can earn any of these labels.

I think that this is the case for our original sentence, too.

Pvblivs, the more we wrestle with the puzzle, the more I think that I’m getting clearer on the source of the puzzlement. Of course—and again—I could very well be missing something important and as a result be way off target. I’m confident that if I am off target, you’ve got the critical thinking skills to help me figure that out.

Best regards,
Hendrik

P.S. No problem, Pvblivs, about the anonymity. However, if I’m ever in your neck of the woods (e.g., visiting your college or university or near wherever you work) and you happen to recognize me, please do introduce yourself to me. You’ve made me puzzle much about your puzzle, which is great. But I’m pretty sure that there’s some sort of moral imperative deeply embedded in both nature and all cultures which says that you now owe me a large and expensive, frothy Starbucks-type coffee/vanilla latte.

Pvblivs said...

     Ah, I suppose it is the ambiguity inherent in the English language.If we adopt a more (closer to) mathematical framework, we could define a predicate Nb such that Nb(x, y) means that x does not believe y(x, y) to be true, where y is any given predicate. In that case, Nb([god], Nb) is what I am trying to get at.

Dr. V said...

Pvblivs,

I must confess to you that my facility for doing formal logic has waned over the years. When I was an undergrad, I took every formal logic course available (and I even worked as a logic tutor). But I became increasingly suspicious of formalization when I came to realize that sometimes some subtle meanings were lost in the formalization process. As a result, I focused my studies as a graduate student (master’s level) on informal logic and critical thinking, which, I found, was much more sensitive to the actual meanings of arguments found in natural language. All this to say: Would you mind (when/if you have time) translating your formalization a bit more into natural language? (Probably our readers, if any, would appreciate this too.) Or, maybe even better, could you simply refer me (and our readers) to any literature in which our puzzle is discussed? It might be more helpful, for me at least, if I could study what’s already been said about this puzzle (if it’s been discussed by others). This is not to say that what you’ve written hasn’t been helpful—it definitely has been helpful.

Cheers,
Hendrik

P.S. You still owe me that coffee/latte.

Dr. V said...

A closing comment.

I have reviewed Pvblivs's ongoing objection (see above). I believe that the problem is not due to the inherent ambiguity of language; rather, the problem is due to the misuse of the inherent ambiguity of language via the neglect of the distinction between use and mention. Therefore, formalization will not help here.

Lesson (for us all, including one of my Critical Thinking students who dismissed the use-versus-mention distinction as irrelevant to life): Obviously, failure to keep in mind the use-versus-mention distinction can keep thoughtful people away from truth about God.

Review of the use-versus-mention distinction (from philosopher Trudy Govier): "Note here that when we are speaking about a word, or mentioning that word, we put it in quotation marks or italics to indicate that we are talking about the world itself, as opposed to using the word in the normal way. If someone says, the word sunset has six letters, that person mentions the word sunset. If he or she says, 'The sunset was beautiful,' the word sunset is used. Here is another example: (a) Maria called, 'out.' (b) Maria called out. Statements (a) and (b) make different claims. Statement (a) asserts that Maria uttered the word out, whereas statement (b) asserts that Maria called out in the sense of vocalizing something, but does not specify which words she called out. In (a), the word out is mentioned. In (b), that word is used." (Trudy Govier, A Practical Study of Argument, 6th ed. [Belmont, CA: Thomson/Wadsworth, 2005], 94-95.)

This comment section is now closed.

With best regards,
Hendrik

Hendrik van der Breggen said...

To summarize in plain English: the can-God-make-a-stone-too-heavy-for-God-to-lift fails as an objection to God's existence.