"Caesar is a prime number"

------------By J. L. S.

From an online source:

"In “The Elimination of Metaphysics” Carnap describes what kinds of sentences or phrases we should think of as meaningless."

"The first example he gives is."

i. Caesar 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."

ii. 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."

---- Tomorrow.

--Personally, I don't see why we cannot name a number, "Caesar".

"Mary brought Caesar gifts to the party"

"3" as it happens.

"3" is indeed a number in some formal systems, no?

Harrison considers a different case:

"Snow is white"
"Arthur is white"

-- surely we could call "snow" "Arthur". But here the problem, Harrison notes, is that 'snow' is a natural kind. And natural kinds don't get to get names like those. Etc.

---

I agree with this student's professor that "Caesar is not a prime number" is true.

Etc.