Question Is it possible for a statement to be partially true and partially false?

Accepted:
November 4, 2005

Comments

Yes and no.

But seriously, now. First, a "conjunction" (an and sentence) might have a true part and a false part: "2 > 1 and 7 > 9". But the usual view of logicians is that a sentence like that is simply false despite having a true conjunct: its truth requires precisely that both conjuncts be true, which is simply not the case. Similarly for "all natural numbers are either less than or greater than 3"---it's simply false, even if there's only one exception among the infinitely many natural numbers.

Second, a sentence can be ambiguous, and true on one way of understanding it, but not on another. "Bill Gates contributes generously to charities," for example, might be true if by "giving generously" we mean "giving a great deal of money" but false if we mean "giving so much as to make for a significant sacrifice on the part of the giver". I suppose that if we use this sentence without intending one of those meanings rather than the other---so that it remains ambiguous---it might be called "partially true", or "true in a sense", or something like that. Or it might just be called "too unclear to evaluate".

Probably a better candidate for partial truth and partial falsity is a sentence involving the application of vague terminology to a "borderline case". It might be that "Monterey is in Northern California" is a good example: it seems not quite true, and not quite false, because, to speak metaphorically, "Northern California" doesn't have clean boundaries, and the city of Monterey is covered by the smudge. But it's a big controversy among philosophers how to apply the concepts of "true" and "false" to sentences like that. Some horses in the race:

Degrees-of-truth Theorists: the sentence is true to a certain degree and false to a certain degree---perhaps 50-50 or 60-40.
Nihilists: the sentence is not true to any degree nor false to any degree. "Northern California" is too ill-defined to be used in true or false sentences.
Epistemicists: the sentence is completely true, or completely false; it's just that we don't know (and probably could never figure out) which, because the (clean!) boundary that delimits Northern California is an elusive little bugger.
Supervaluationists: we simply haven't bothered to settle on where exactly the clean boundary should be; still, we've narrowed it down to a limited neighborhood of okay ways of slicing it. The sentence is true if it would come out true however we slice it, false if false however we slice it, otherwise an intermediate status that we might call "indeterminate". Monterey, being included by some okay boundaries of "Northern California" but excluded by others, therefore makes for an indeterminate case.

The buzz-word for this issue is "vagueness"; it's a playground (or is it a morass?) for logicians, metaphysicians, and philosophers of language.

Question Is it possible for a statement to be partially true and partially false? Accepted:November 4, 2005

Question Is it possible for a statement to be partially true and partially false?

Accepted:
November 4, 2005