Sean at common sense philosophy discusses the sentence: "Caesar is a prime number."
Apparently some people (including Carnap) think this claim is not false. They don't think it's true either, of course, but rather meaningless -- just like "Caeser is and." Though I agree about the latter, I think the former sentence is simply false. This is because, as Sean points out, there is a set of all prime numbers, and Caesar is not among its members. This undeniable fact immediately entails that Caesar is not a prime number, and hence "Caesar is a prime number" is false. I wonder if some might be tempted to deny it meaning simply because it is so very false, necessarily and obviously so, that no-one would ever even dream of seriously entertaining the thought that it might be true. Then, rather like how something might be so cold that it "burns", so some sentences might be so false that they no longer seem it. Very odd.
Despite the failure of this particular example, there are some sentences that seem genuinely meaningless despite syntactic conformity, such as Chomsky's famous example: "Colourless green ideas sleep furiously." Though I'm actually tempted to just call that one false too. It is not the case that colourless green ideas sleep furiously. Ideas don't sleep -- furiously or not, and whatever shade of colourlessness they might come in!
What do people usually make of claims about non-existent subjects, e.g. "The present king of France is bald." False or meaningless? Is there any sort of consensus on this issue?
What is it about a sentence that makes it meaningful (or not)? Consider the condition that a sentence either violates syntactical requirements or else contains nouns that fail to refer. Is that condition necessary for meaninglessness? Is it sufficient? Are there any better criteria you can offer?
Wednesday, November 23, 2005
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I would suggest that truth or falsity is only really meaningful when applied to well formed statements, e.g.
ReplyDelete1) If X is the present king of France then X is bald
2) There exists X such that X is the present king of France
Statement 1 is true and statement 2 is false. So the question is what logical meaning should we take from an English statement such as "The present king of France is bald."
I would suggest that the quoted sentence implies a conjunction of 1 and 2 above so is false. But it would be quite hard to argue with someone who insisted that only 1 is implied. There's no real way to conclusively resolve this because ordinary English is just not that precise.
What Nigel proposes is, of course, roughly Russell's approach. Frege seems to have thought sentences with non-referring expressions are meaningless, and I believe Strawson agreed, though I think that these days even people who would question the details of Russell's theory of descriptions would mostly prefer to call sentences like this false rather than meaningless.
ReplyDeleteHi, I just recently started reading your blog. I enjoy it, so I thought I'd post. As regards claims of non-existent subjects, I think there might be a sort of fallacy being committed so as to render the statement meaningless. I'm not aware of any particular fallacy that applies, but I think it would be along the lines of a complex question. I have witnessed such (fallacious?) statements similar to the one suggested by you (i.e., "The present king of France is bald"). For example, I have heard "Santa Clause lives in the North Pole. Yes or No?" It should be noted that this statement was made in reference to this actual world (not a fictional word). I think both of these statements—"The present king of France is bald" and "Santa Clause lives in the North Pole"—like a complex question, assume something not true, thus, in my opinion, rendering them meaningless. The first statement assumes that France has a king, which is not true. The second statement assumes that Santa Clause really exists, which, while it breaks my heart to say it, is not true (although I'm still hopeful).
ReplyDeleteWell, now that I rethink it, the statements might or might not be meaningless, depending on one's interpretation of what that means. Although the statements might somehow still be fallacious, although I'm not exactly sure what that would mean for a statement and if that means that the statement is meaningless (or just "very false," as you say). I think the question "Are those statements false?" can be answered, but that the answers should not misused. For example, in answering that question in regards to both of the statements made, I would say the answer is "Yes, those statements are false." So, what I mean by the answers should not be misused is this: "The present king of France is bald" is a false statement not because the present king of France is not bald (or has hair) but because there is no present king of France.
"Caesar is a prime number" seems like it has to be a false statement; Caesar is clearly not a prime number.
ReplyDeleteThe objection Sean encounters is this: "He claims that if we were to say that this is a meaningful, false statement, that we would be committed to saying that Caesar is divisible by another whole number."
I fail to see how we would be bound to say any such thing. Caesar is a name, a person, and quite clearly not a prime number. Non-prime numbers are also not prime numbers. Am I missing something?
However I want to say that your example, "The present king of France is bald," is meaningless.
In this case, "present king of France" should be considered as a single signifier. It's a group of words denoting one idea. That said, since there is no current French king, it's also a meaningless signifier. Isn't it? If a signifier refers to a non-existant signified, it seems to follow that the signifier is meaningless.
So we might as well say "Snozzberril is bald." Surely we would then all agree that the sentence is meaningless--if we would, how can we not say the same thing for "The present king of France is bald?"
I'm not sure one should dismiss the thought so quickly - which of the following are simply false, and which are nonsense?
ReplyDelete(1) Caesar is a number.
(2) Caesar is prime.
(3) Caesar is divisible only by itself and 1.
Whilst (1) is just false, I'm not sure what to say about the others; I suppose those who are for pro-meaningless might suggest that it makes no sense to say of something that isn't a positive integer that it is divisible only by itself and 1.
Nigel and Joe, your comments are nice responses to each other. The key question is how to analyze non-referential definite descriptions. Are they like names, and hence claims about them are as meaningless as "Snozzberril is bald"? Or are they existential claims (noting that "There exists X such that X is the present king of France -- and X is bald" is straightforwardly false). I'm not entirely sure, but one reason to favour the latter is that the definite description ("the present king of France") is clearly meaningful. It doesn't refer, because as it happens there is no present king of France. But it's a clear and precise description nonetheless. We can all recognize what conditions must be realized for the phrase to successfully refer, and we can easily identify the referent in other possible worlds (or, e.g., a story where modern France has a monarchy). But this is still consistent with the first option, i.e. the whole sentence might still be meaningless, if we analyzed it as the simple predicate BALD(k), where 'k' refers to the present king of France (and hence fails to refer).
ReplyDeleteDJ, for what it's worth, my intuition is that "Santa Clause lives in the North Pole" is simply false of the actual world. That's not to say he lives elsewhere. (No more than "I'm not sure that God exists" entails "I am sure that God doesn't exist"!) See also my comments below about the scope of negation.
Joe: "I fail to see how we would be bound to say any such thing. Caesar is a name, a person, and quite clearly not a prime number. Non-prime numbers are also not prime numbers. Am I missing something?"
I agree with you. As described, it sounds like Carnap was simply misunderstanding the scope of negation. The negation of "X is a prime number" is not "X is a non-prime number", but rather, "it is not the case that X is a prime number", that is, "either X is not a prime, or X is not a number". Caesar satisfies this requirement in virtue of not being a number.
Sumguy: But is that really senseless, or is it just very false? Consider the set of objects which are divisible only by themselves and by 1 (i.e. the set of prime numbers). Is Caesar a member of this set? No. So it's false that Caesar is a member of this set. So it's false that Caesar is divisible only by itself [himself?] and 1.
Note: I'm taking "divisible only by themselves and by 1" to entail that said object is divisible by itself and by 1. If we instead interpreted it in a purely negative sense, as meaning "not divisible by any non-itself, non-1, integers", then I suppose this description would actually be true of non-numbers. After all, other objects presumably aren't divisible by anything (only numbers are). So they satisfy the truth conditions. Very odd.
Things are only false in relation to other facts. So Caeser is a prime number depends on how you define prime numbers and how you define Caeser. Just as sumguy has looked at it we are fairly close to being able to call caeser a prime if we strech the definition a little.
ReplyDeleteIt is possible using the imprecision of english to assume that any question's answer is the one with hte nearest possible assumptions - then whether it has an answer or not depends on how bright you (the person answering it) is.
For example someone might ask me "is golem bad?" and I might say "false" on the basis golem doesnt exist but realy the apropriate answer would be a deeper analysis. similarly IF we make certain assumptions we could say ceaser is not a prime or caeser is a prime baised on asuming he is a number and that it is legitimate to discuss him in that context.
On a certain level, Nigel is right to say that a statement is meaningful iff it is well-formed. The problem with English is that it isn't a formal language, so whether or not a statement is "well-formed" in the technical sense simply doesn't come into play. As I see things, "meaningless" is a term of art when applied to natural English, and not too much emphasis should be placed on the borderline cases. The real question for me is: if we can rationally reconstruct English in whole or in part as a formal language (or set of formal languages), then what are the possible candidates for replacing an expression like "Caesar is a prime number", and which if any of those expressions are well-formed?
ReplyDeleteNow, Carnap wrote in this kind of framework, and this is probably the question he was asking. (After all, the full title of his paper, as I recall, was something like "The Elimination of Metaphysics _Through the Logical Analysis of Language".) He is not interested not so much in English as given in grammar textbooks as in the so-called "logical form" of English statements, or (less dogmatically) in epistemically equipotent reconstructions. Furthermore, the Carnap of those days was working within the logistic system of Principia Mathematica, which contained a system of types (which are, in a way, roughly the same as Ryle's "categories", or the young Carnap's "object spheres") for (among other things) determining which expressions are well-formed. I don't know much of anything about how type theory actually works, but I _think_ that numbers and people are of different types (at least in PM), so the statement "Caesar is a prime number" is meaningless. I think so, anyway.
But the question for us, who don't need types, is different. Genius has got it right - the answer to this question lies in how you define the terms. More than that, it's a question of the entire logical structure of your favorite rational reconstruction. Still, if you want to say that "is a prime number" means by definition "is a member of the set Prime Numbers", then "Caesar is a prime number" is just false (although you have to figure out some way of independently fixing the extension of the set). As for any other interpretation of "is a prime number", I think you're just going to have to do the dirty work of embedding the statement in a formal language in order to answer the question decisively.
By the way, Joe, it seems that you might want your analysis to preserve the intuition that 'Caesar is a prime number' is not true. But this does entail that 'Caesar is a prime number' is false. So it does not entail that Caesar is not a prime number. I might have gotten your intuition wrong, but it is consistent with the statement being either meaningful or meaningless.
Ian - what you say about Carnap (and your own views) is really interesting. Could you say a bit more? I suppose what I'm wondering is as follows: there are at least two different ways of cashing out why 'Ceasar is a prime number' is meaningless (if it is); on one hand, we could say it involves a category error; the meanings of the constituent expressions are such that they belong to different (logical) types, and the resulting combination, although syntactically correct, is (logically) ill-formed. Alternatively, we might say that it is meaningless because we cannot even understand the constituent expressions as having a meaning. Why? - because there is no plausible putative assignation of meaning for the constituent expressions such that the result is well-formed (these differences are intended to correspond to those Cora Diamond makes in 'what nonsense might be', but i don't have it to hand). Which of these is closest to Carnap?
ReplyDeleteFrom what you've written, it seems that Carnap might not be happy with our talking of english sentences as well-formed, but we could put the distinction by saying does Carnap think 'Ceasar is a prime numer' is meaningless either because (i) it's formal language candidate replacement sentence is ill-formed, or (ii) there is no plausible formal language candidate replacement sentence (or (iii), neither).
Hi Richard,
ReplyDeleteOn sentences with non-referential definite descriptions, I don't see any reason to consider them meaningless. On Russell's view, they involve an existential claim, and are therefore simply false. I believe the standard alternative to this is Strawson's view, on which a sentence like "The present king of France is bald" presupposes the existence of the king of France in order to have a truth value, and hence is neither true nor false; but that doesn't make it meaningless. Declarative sentences without a truth value can be meaningful on this approach, just as imperatives, questions, and other kinds of sentences can. The Russellian point of view, I imagine, would be based on assuming that a meanungful declarative sentence must express a proposition, and that propositions must be true or false.
The alternative position that you suggest of making sentences with non-referential definite descriptions meaningless seems highly impractical, as in many cases we don't know if our terms refer or don't. Suppose we are discussing a newly proposed scientific theory about some hypothetical particles, for example "preons". We can have a meaningful discussion about preons, arguments for and against their existence, experimental detectability, etc., without knowing if they exist, and perhaps never coming to know it.
I think the same is true also for proper names. In "Snozzberril is bald", the sentence is meaningless because no meaning has been attached to "Snozzberril", not because the name has no referent. Compare "Sherlock Holmes is clever" or "Santa Claus is fat". These are as meaningful as if we had descriptions instead of the names. Whether they are neither true or false, or simply false (in the actual world) is a different question.
To digress a little, and to talk about context:
ReplyDeleteWith regards to "Chomsky's famous example: 'colourless green ideas sleep furiously.'" In the current context, this sentence is obviously meaningless. In many contexts, however, it might not be meaningless, and there are ways of analysing it that bring out some meaning. It is true that ideas are not usually described as coloured, any more than they are described as asleep, and coloured things are not usually colourless, but still we could say that "colourless" implies a sort of paleness or emptiness (perhaps the ideas in question are wordless or weak in some way), that "green" suggests some kind of nature or harmony in the ideas, and that "sleep" reinforces the connotations of "colourless" and (to a lesser extent) those of "green." Perhaps these ideas, while calm on the surface, conceal some kind of "furious" activity, just as the serene face of a sleeper belies the nightmares that can thrash around in their head. Thus we can interpret this sentence in a "poetic" sort of way, and arrive at some meaning.
This might seem like a frivolous sort of exercise, and perhaps we can distinguish between "logical" meaning and "emotional" or "poetic" meaning, and discard the latter, but I think there is some merit in understanding this kind of “meaning", for two reasons. Firstly, many people would regard the second kind of “meaning” as stronger and more important than the first kind. Consider the following four statements. Two were composed by Dylan Thomas some time ago, and the other two were composed by me just now.
1) I had a short childhood that I enjoyed very much, and I regret the fact that it has gone.
2) Oh as I was young and easy at the mercy of his means,
Time held me green and dying
Though I sang in my chains like the sea.
Or:
3) Lots of people are intensely attracted to other kinds of people, and the people who are thus attracted are tempted and disturbed by the attraction.
4) ..This world is half the devil’s and my own,
Daft with a drug that’s smoking in a girl,
Curling round the bud that forks her eye…
Sentences 2) and 4) are “meaningless” in much the same way that Chomsky’s sentence is “meaningless”: people are not “green”, “Time” does not “hold” people, there is no “devil” and noone has a “bud” in their eye. Nevertheless, many people would regard sentences 2) and 4) as much more meaningful than the other two sentences, and any concept of “meaning” that ignores this second kind of meaning is guilty of misusing a word and of ignoring some of the most important functions of language.
These examples are not quite as extreme as Chomsky’s example, but they are still recognisably distinct from the kind of sentences that people use in philosophy. However, I don’t think it is always possible to make such a clear distinction, and this is a second reason for paying some attention to “poetic” meaning: lots of statements are a mixture of “logical” and “poetic” meanings, and in order to understand what people “mean” by a statement (and so in order to agree with them) we need to understand both kinds of “meaning.”
This comment is a “digression” because it ignores the unspoken boundaries of the discussion that were set out in the original post, and it might be regarded as a wasteful and irrelevant sort of digression. Nevertheless, I even if we are to follow the promptings of the context that was established in the above post and in the above comments, and hence ignore the “poetic” concept of “meaning”, it is important to remember that this interpretation of “meaning” is limited, that it is context-dependent, and that different contexts can produce different interpretations.
"'colourless green ideas sleep furiously."
ReplyDeletemight be meaningless only because chomsky wanted it to be meaningless.
Ie if my friend the artist had said it it might mean
"new ideas to this world that have no excitement to them will despite some enthusiasm (from their originators?) remain without influence."
Which I would, I guess, say is generally true.
Hmm oh wait Mike made this point already.. hmmm...
I don't have time to say much, but I wrote on a similar line of questioning by Peirce a few months back. To quote him:
ReplyDelete"Every phoenix, in rising from its ashes sings 'Yankee Doodle,'" will be, we may be confident, not in conflict with any experience. If so, it is perfectly true."
Sumguy -
ReplyDeleteIn the days in which Carnap wrote the paper that Sean was initially talking about, he probably had in mind your first interpretation of meaninglessness. Even without getting into all of the details, we can imagine a handful of possible macrostructures for languages that are rich enough to talk about Caesar and prime numbers. Given the logic of PM, we just can't make the statement. There are plausible strings of symbols that might replace the sentence, but these strings aren't going to be well-formed sentences.
Also, I think that your (i) and (ii) are dead on, although I can't imagine what (iii) would be like.
An exegetical note off to the side:
ReplyDeleteProtagoras: Frege seems to have thought sentences with non-referring expressions are meaningless, ....
This is a common misunderstanding of Frege's view, one that I suspect comes about from people reading Russell and Wittgenstein's thoughts about propositional meaning and truth-valuability back into Frege, who did not share their conclusions. Wittgenstein and Russell held that any significant proposition has a truth value, but what Frege explicitly states in "Über Sinn und Bedeutung" is statements with empty proper names express a thought but have no truth-value. Since Frege's claim is that the sense of a statement is the thought expressed by it, and the referent of a statement is its truth-value, this means that he regards them as having a sense but no reference, just as (he thinks) the empty designator in them has a sense but no reference. Here's the relevant passage:
"The thought, accordingly, cannot be the Bedeutung of the sentence, but must rather be considered as its sense. What is the position now with regard to the Bedeutung? Have we a right even to inquire about it? Is it possible that a sentence as a whole has only a sense, but no Bedeutung? At any rate, one might expect that such sentences occur, just as there are parts of sentences having sense but no Bedeutung. And sentences which contain proper names without Bedeutung will be of this kind. The sentence 'Odysseus was set ashore at Ithaca while sound asleep' obviously has a sense. But since it is doubtful whether the name 'Odysseus', occurring therein, has a Bedeutung, it is also doubtful whether the whole sentence does. Yet it is certain, nevertheless, that anyone who seriously took the sentence to be true or false would ascribe to the name 'Odysseus' a Bedeutung, not merely a sense; for it is of the Bedeutung of the name that the predicate is affirmed or denied. Whoever does not admit the name has a Bedeutung can neither apply no withhold the predicate. But in that case it would be superfluous to advance to the Bedeutung of the name; one could be satisfied with the sense, if one wanted to go no further than the thought. If it were a question only of the sense of the sentence, the thought, it would be needless to bother with the Bedeutung of a part of the sentence; only the sense, not the Bedeutung, of the part is relevant to the sense of the whole sentence. The thought remains the same whether 'Odysseus' has a Bedeutung or not." (32-33)
Hope this helps.
As for the questions raised in the post itself, I try to offer some considerations in favor of the meaningless-rather-than-false take, and answer some of the other questions off to the side, in GT 2005-11-28: Piggly wiggle tiggle.
ReplyDelete