Thursday, February 14, 2008

Does every proposition have a negation?

Some philosophers have held—as Wittgenstein seems to in the Tractatus—that if some (apparent) statement is meaningless then so is its “negation”, and conversely that if the negation of a statement is meaningful then the negated statement must be meaningful too. Thus some have held that, since statements such as “It is not the case that Jones is identical to himself” are (so they think) obviously meaningless, then “Jones is identical to himself” is likewise meaningless. On the other hand, some have supposed that since statements such as “Jones is identical to himself” are (so they think) obviously meaningful, then so is “It is not the case that Jones is identical to himself”; it’s just that the latter is necessarily false. What has never been questioned, so far as I know, is that every meaningful statement has a negation. I think one might reasonably maintain something like the following: Suppose you think the meaning of a declarative sentence is the proposition it expresses. In that case you could say that while a given declarative sentence, say “Jones is identical to himself”, expresses a proposition, the sentence which results from prefixing a negation operator to it, say “It is not the case that Jones is identical to himself”, expresses no proposition. One could thus maintain that there are necessary truths but no necessary falsehoods. I think many would see this as beneficial, since if we could grasp the meaning of a necessarily false statement—that is, if we could understand full well what things would be like if it were true—what would we mean by calling it necessarily false or impossible? On the other hand, since we would still believe in necessarily true propositions, we could (at least potentially) accept the existence of a priori knowledge. We could also avoid a major pitfall of theories which reject (apparently) necessary truths as pseudo-propositions, namely, that on such theories a statement like “Every genuine statement has its truth value contingently” would seem not have its truth value contingently.

Such, I think, are the merits of this view. But what do you think? Is this view tenable, or does it suffer from problems comparable to those of the rival views discussed above? I have my suspicions, but for now I’m just interested in your own opinion.