Variable Question Fallacies

"This often confuses undergraduates (and postmodernist professors) who discover a sentence with more than one interpretation; they think they have discovered an unstable portion of reality."

I don't really know how to read this sentence. Are you claiming that there is a fixed, stable reality? Are you claiming that the postmodernist professor is implicitly claiming the existence of a fixed reality?

I think the more articulate postmodernist professor would claim "we cannot make reference to a fixed interpretation of phenomena outside of an assumed cultural reference." -You're- the one talking about "reality."

You are using terms like "proposition," "question," etc. very loosely. Could you please clarify what the pertinent "question" that the huntergatherer and the astronomer are trying to "answer" is? What "propositions" do they assert?

I would make two claims. First, I claim that everyday people going about their everyday business are not trying to answer claims/make propositions. Second, I think that "truth" as a linguistic concept exists only in very specific contexts.

"Have you stopped beating your wife?" has well-defined true-or-false answers. It's just that people are generally too stupid to understand what the no-answer actually indicates.

"Is this sentence false?" is problematic only if we presume that it's meaningful. All things are dividable into the categories of sensible and nonsensical. The sensible portion is then further dividable into the categories of true and false. Nonsense is outside the bounds of the true-false distinction.

Actually, you can't quite escape the problem of the excluded middle by asserting that "This sentence is false" is not well-formed, or meaningful; because Gödel's sentence G is a perfectly well-formed (albeit horrifically complicated) statement about the properties of natural numbers which is undecidable in exactly the same way as Epimenides' paradox.

Mathematicians who prefer to use the law of excluded middle (i.e. most of us, including me) have to affirm that (G or ~G) is indeed a theorem, although neither G nor ~G are theorems! (This doesn't lead to a contradiction within the system, fortunately, because it's also impossible to formally prove that neither G nor ~G are theorems.)

More to the point: (P or ~P) isn't a theorem, it's an axiom. It is (so far as we can tell) consistent with our other axioms and absolutely necessary for many important theorems (any proof by contradiction— and there are some theorems like Brouwer's Fixed Point Theorem which, IIRC, don't seem to be provable any other way), so we accept a few counterintuitive but consistent consequences like (G or ~G) as the price of doing business. (The Axiom of Choice with the Banach-Tarski Paradox is the same way.)

OK, I've said enough on that tangent.

"Have you stopped beating your wife?" has well-defined true-or-false answers. It's just that people are generally too stupid to understand what the no-answer actually indicates.

It's usually given as "Have you stopped beating your wife yet?" (Emph mine). The problem is the presupposition that you have been beating your wife. Either answer accepts (or appears to accept) that presupposition.

It's a different sort of bad question than the underconstrained questions. The Liar Paradox OTOH is a case of underconstrained question because it contains non-well-founded recursion.

I think the trouble about "Have you stopped beating your wife?" is that it is not about a state but about a state transition. It asks "10?", and the answer "no" really leaves three possibilities open (including that the questionee has recently started beating his wife). The sentence structure implies a false choice between answers 10 and 11, because we are used to asking (and answering) yes/no questions about 1-bit issues while here we deal with a 2-bit issue. But you probably knew all that... =)

Oh, and the Liar Paradox makes much more sense once we overcome our obsession about recursion: If we take the equally valid stance of viewing it as an iteration, it is easy to see that the whole problem is that the proposition does not converge; that's all there is to it.

it's not as simple as "Say, do you think Z + 2 equals 6?"

Except, of course, when it is. And sometimes that isn't simple either.

A friend tells the story of being asked (by a stranger at a bus stop) "Is ten percent about two dollars?" "It depends," says she. "Ten percent of what?" "A mop," the stranger explains helpfully. "Um," says she, re-evaluating her understanding of the conversation. "How much does the mop cost?" "Twenty dollars." "Well, then, yes. Ten percent of twenty dollars is two dollars."

"Well," comes the huffy reply, "why didn't you say so in the first place, then?"

This is admittedly largely irrelevant to the point of your post, but I often remember that story when conversations seem to break down. Sometimes the word we have different interpretations of didn't even get spoken in the first place.

"Oh my gosh! 'The Sun goes around the Earth' is true for Hunga Huntergatherer, but for Amara Astronomer, 'The Sun goes around the Earth' is false! There is no fixed truth!" The deconstruction of this sophomoric nitwittery is left as an exercise to the reader.

Am I correct that this sophomoric nitwittery can be solved by taking Earth as a fixed point? Then sun really will go around it. So will the moon. All other planets will go around the sun.

If not, well... you can imagine why I didn't get an A in that philosophy where a teacher meant it literally (as in relativism)

Have you stopped beating your wife?

I'd just like to point out that there is a definite answer to this. If a person has never started beating his or her wife, then they cannot stop and the answer must be no. Is there a flaw in this reasoning? Or am I not using the common definitions?

Martin told Bob the building was on his left.

Here, too, I see a definite answer. The word "left" is possessed by the word "his." In the English language, the pronoun "his" (and similarly "him," "her," "it," etc.) always refers to the nearest possible preceding sensible noun. In this case, "building" is not a sensible word for "his" to refer to. The next nearest noun is "Bob," which does make sense for "'his" to refer to. Therefore, "his left" must refer to Bob's left. Of course, given context, the interpretation of "sensible" could change. If, say, Bob was giving Martin directions, and Bob just asked Martin to tell Bob what Martin saw (note that pronouns would more typically be used; I used names to allow a more certain answer upon careful reading), then "his left" would refer to Martin's left. Of course, this example is widely more open to interpretation, and I myself am not convinced.

"Oh my gosh! 'The Sun goes around the Earth' is true for Hunga Huntergatherer, but for Amara Astronomer, 'The Sun goes around the Earth' is false! There is no fixed truth!" The deconstruction of this sophomoric nitwittery is left as an exercise to the reader.

An apt way to put it. That this worthless dimestore philosophy so often underlies contemporary contemplative discourse by relatively intelligent people never ceases to bewilder and sadden me. (see example below)

Variable truth-value (VTV) of a sentence is a technical thing in formal semantics - it means that the truth-value of this sentence depends on the little thingy called variable assignment. While the term might seem misleading, it is useful for explaining why we still claim "He walked in" has a truth-value - it first has the VTV, and then we find some "discourse" assignment that converts VTV to truth-value. Also, variable assignment can be manipulated from within the sentence (anaphora, movement, you name it).