Is “Caesar is a Prime Number” Meaningless
The other day I came across a passage in Carnap’s “The Elimination of Metaphysics” where Carnap was describing what kinds of sentences or phrases we should think of as meaningless. The first example he gave was “Ceaser is and.” Now clearly this is meaningless, no problem (or at least it seems obvious to me that such a serious break of syntax leads to that result.) However, Carnap then presents the second meaningless sentence, “Caesar is a prime number.” Carnap’s analysis of this statement is that it is meaningless in virtue of it being neither true nor false. 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. Since Caesar is neither a prime number nor divisible by another whole number, the statement, “Caesar is a prime number,” is, not false, but meaningless. But why think a thing like that? Surely, we would instead want to say that there is a set of all prime numbers and that, in virtue of Caesar not being identical to any member of that set, the statement “Caesar is a prime number,” is false. Clearly this is an instance of a category mistake but don’t we know to call it a category mistake in virtue of the fact that we know we know what the statement means? And further, my professor thinks that Carnap would claim that the statement “Caesar is not a prime number” is true. But how could this be the case if its negation is false?
Several members of the class agreed with Carnap as did my professor and I just cannot make any sense of it. Any help would be greatly appreciated.
Sean,
I’ve also been thinking about this a great deal since Thursday, and as far as I can tell, this question is one that should be answered empirically. Whether a statement/proposition/sentence is meaningful is not so much a normative claim as a descriptive one. Consider
(1) Caesar is and.
Now clearly, this is meaningless, but what does it mean to call it meaningless. Seemingly, it means that descriptively (1) is without meaning. We might even say that it is presciptively meaningless - we just ought not utter such statements. But is it a good idea to value meaningfulness in such a way? Carnap clearly did because in the case of
(2) Caesar is a prime number
he declared it to be meaningless even though its syntactic structure is meaningful. I suspect this is where the disjunction between you and Carnap occurs. If we are to take Carnap seriously then we must assert that meaningfulness has a normative aspect, such that when we utter meaningless statements and descriptively attribute meaning to them (as is the case with (2)) we are mistakenly doing something that we ought not.
But, I think that commonsense approach to understanding meaningfulness is that of description. To say that (1) is meaningless is simply to say that it has no meaning, not that it should not be attributed meaning. Similarly, to say that (2) is meaningful is simply to say that it has meaning, not that we ought to attribute meaning to it.
So who determines meaningfulness? I would be quite happy to let the folk decide what’s meaningful and what is not. They are the primary users of the language, and I suspect, mainly due to their apparent success in communication, that they are pretty good arbitrators of meaningfulness. So lets hook them up to those brain machines and read ‘em a variety of statements (including (1) and (2)) and see if they respond to (2) in the same way that they do to meaningful statements like “apples are red,” or see if they respond to (2) in the same way that they do to meaningless statements like “Caesar times 17 is purple.”
I think that not attributing normativity to meaningfulness is one way out, so there you go, but there are probably some significant mistakes with that response.
Comment by Justin — November 20, 2005 @ 8:01 pm
I think I tend to agree with you. However, (and this might seem silly), perhaps it depends on the stress in the sentence.
If I say “Ceasar is not a *prime* number”, then it might be thought that I’ve said that Caesar is a number but is not prime - which is plausibly meaningless.
However, if I say “Caesar is not a *prime number*”, perhaps this is the statement that Caesar is not a prime number, but may a non-prime number, or indeed, not a number at all.
Perhaps your natural reading (and mine) is the latter, whereas Carnap et al’s is the former, and this is the source of the disagreement.
(Perhaps its more obvious in the following case: “I am not a black man” - does that imply that I’m not black, not a man, or both? Again, it seems to me that it depends on hows its said, and that can’t be discerned from the formal structure of the sentence)
ps. Your comment box is a little small - a preview button might be handy.
Comment by Alex Gregory — November 21, 2005 @ 7:53 am
Piggly wiggle tiggle
Sean Martin at common sense philosophy and Richard Chappell at Philosophy, et cetera have lately been puzzling over the claim that so-called sentences, such as…
Trackback by Geekery Today — November 28, 2005 @ 10:17 pm
My take on the matter (and I’m sure someone has probably said this already) is that Carnap inappropriately limits the scope of things to either prime or composite numbers. Why suppose, as Carnap does, that if X is not a prime number, then X must be divisible by another whole number? The denial of “Caesar is a prime number” is not “Caeser is a non-prime number,” but simply, “It is not the case that Caesar is a prime number,” which seems intuitively true to me, for reasons Sean points out above.
Comment by Jim Sias — December 29, 2005 @ 2:05 pm