Variable Question Fallacies

Followup toWords as Mental Paintbrush Handles

Albert:  "Every time I've listened to a tree fall, it made a sound, so I'll guess that other trees falling also make sounds.  I don't believe the world changes around when I'm not looking."
Barry:  "Wait a minute.  If no one hears it, how can it be a sound?"

While writing the dialogue of Albert and Barry in their dispute over whether a falling tree in a deserted forest makes a sound, I sometimes found myself losing empathy with my characters.  I would start to lose the gut feel of why anyone would ever argue like that, even though I'd seen it happen many times.

On these occasions, I would repeat to myself, "Either the falling tree makes a sound, or it does not!" to restore my borrowed sense of indignation.

(P or ~P) is not always a reliable heuristic, if you substitute arbitrary English sentences for P.  "This sentence is false" cannot be consistently viewed as true or false.  And then there's the old classic, "Have you stopped beating your wife?"

Now if you are a mathematician, and one who believes in classical (rather than intuitionistic) logic, there are ways to continue insisting that (P or ~P) is a theorem: for example, saying that "This sentence is false" is not a sentence.

But such resolutions are subtle, which suffices to demonstrate a need for subtlety.  You cannot just bull ahead on every occasion with "Either it does or it doesn't!"

So does the falling tree make a sound, or not, or...?

Surely, 2 + 2 = X or it does not?  Well, maybe, if it's really the same X, the same 2, and the same + and =.  If X evaluates to 5 on some occasions and 4 on another, your indignation may be misplaced.

To even begin claiming that (P or ~P) ought to be a necessary truth, the symbol P must stand for exactly the same thing in both halves of the dilemma.  "Either the fall makes a sound, or not!"—but if Albert::sound is not the same as Barry::sound, there is nothing paradoxical about the tree making an Albert::sound but not a Barry::sound.

(The :: idiom is something I picked up in my C++ days for avoiding namespace collisions.  If you've got two different packages that define a class Sound, you can write Package1::Sound to specify which Sound you mean.  The idiom is not widely known, I think; which is a pity, because I often wish I could use it in writing.)

The variability may be subtle:  Albert and Barry may carefully verify that it is the same tree, in the same forest, and the same occasion of falling, just to ensure that they really do have a substantive disagreement about exactly the same event.  And then forget to check that they are matching this event against exactly the same concept.

Think about the grocery store that you visit most often:  Is it on the left side of the street, or the right?  But of course there is no "the left side" of the street, only your left side, as you travel along it from some particular direction.  Many of the words we use are really functions of implicit variables supplied by context.

It's actually one heck of a pain, requiring one heck of a lot of work, to handle this kind of problem in an Artificial Intelligence program intended to parse language—the phenomenon going by the name of "speaker deixis".

"Martin told Bob the building was on his left."  But  "left" is a function-word that evaluates with a speaker-dependent variable invisibly grabbed from the surrounding context.  Whose "left" is meant, Bob's or Martin's?

The variables in a variable question fallacy often aren't neatly labeled—it's not as simple as "Say, do you think Z + 2 equals 6?"

If a namespace collision introduces two different concepts that look like "the same concept" because they have the same name—or a map compression introduces two different events that look like the same event because they don't have separate mental files—or the same function evaluates in different contexts—then reality itself becomes protean, changeable.  At least that's what the algorithm feels like from inside.  Your mind's eye sees the map, not the territory directly.

If you have a question with a hidden variable, that evaluates to different expressions in different contexts, it feels like reality itself is unstable—what your mind's eye sees, shifts around depending on where it looks.

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.

"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.

And yet, even I initially found myself writing "If X is 5 on some occasions and 4 on another, the sentence '2 + 2 = X' may have no fixed truth-value."  There is not one sentence with a variable truth-value.  "2 + 2 = X" has no truth-value.  It is not a proposition, not yet, not as mathematicians define proposition-ness, any more than "2 + 2 =" is a proposition, or "Fred jumped over the" is a grammatical sentence.

But this fallacy tends to sneak in, even when you allegedly know better, because, well, that's how the algorithm feels from inside.


Part of the sequence A Human's Guide to Words

Next post: "37 Ways That Words Can Be Wrong" (sequence guide)

Previous post: "Words as Mental Paintbrush Handles"

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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.

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... =)

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.)

No, it's not the same. Gödel sentences can be resolved by adding axioms. You can't add axioms to resolve 'This sentence is false'.

"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)

I think the main problem is in "goes around", although HH::the Sun != AA::The Sun and HH::the Earth probably != AA::the Earth, the latter two shouldn't matter as much.

HH believes "HH:(text X)" is true and AA believes "AA::(text Y)" is true, which isn't interesting. What's interesting are three things: that AA::(text X) has meaning, AA::(text X) != AA::(text Y), and if AA::(text X) then NOT AA::(text Y).

Basically, yes. From the earth's perspective, the earth spinning on its axis while the sun is (relatively) stationary looks exactly the same as the sun going around the earth.

So they look identical, but Amara the Astronomer knows that this illusion is simply a misunderstanding of how the heavenly bodies interact.

Hunga Huntergatherer doesn't know the earth spins. If he did he'd probably be able to figure out that the sun isn't circling the earth if he thought about it for a while.

Well in that case Earth doesn't really go around the sun, it just goes around the center of this galaxy on this weird wiggly orbit and the sun happens to always be in a certain position with respect to...... ouch! See what I did? I babbled myself into ineptness by trying to be "absolutely technically correct." I just can't. Even if I finished that "absolutely technically correct" sentence, I'd probably be wrong in some other way I haven't even imagined yet.

So let's accept the fact that not everything that is said which is true is "absolutely technically correct." (True with respect to The Simple Truth, ugh, this semantics is tiring so I'll quit).

The not-technically-correct truth for Hunga Huntergatherer and the not-technically-correct truth for Amara Astronomer seem to verbally contradict each other in the same way that Albert::sound verbally contradicts Barry::sound. Is the solution to it that one is false and other is true? You take the side of Amara Astronomer (and so do I) because the maps in our heads resemble this view better than the other.

The fact that these two notions seem contradictory is not because they are contradictory, but because our minds are trying to map them both into the same spot.

Your solution brings us back to analyzing maps. Its analogue is defining Albert::sound to be correct. I don't believe that the point of the article was to define truth. It's practically impossible to do so (see my fumble above). I think the point of the article was that contradictions in our ill-defined language (and concepts and maps that come with it) do not imply contradictions in reality.

I believe you missed my point entirely.

I was simply discribing why Hunga Huntergatherer might not have realized that it is the earth that goes round the sun.

Hunga's map is still extremely useful, particularly for getting your bearings. The old saying "the sun rises in the east and sets in the west" is still useful even though it is the earth spinning to create the effect rather than the sun actually moving around the earth (which is implied in the saying).

It's worth noting that Hunga's map is included in Amara's map, not eliminated by it. Albert's map also includes Barry's map, just like Einstein's map of gravity includes Newton's map.

They're all still just maps though, and should be treated as such.

True, but what you imagine to be territory may just be another layer of maps.

If you need to think that there is a territory down there somewhere in order to keep from drowning in relativism, then go ahead and think that. But be careful not to imagine that you have actually seen the territory. You haven't. All you have access to (by way of science) are some mighty fine maps.

I pause. “Well…” I say slowly. “Frankly, I’m not entirely sure myself where this ‘reality’ business comes from. I can’t create my own reality in the lab, so I must not understand it yet. But occasionally I believe strongly that something is going to happen, and then something else happens instead. I need a name for whatever-it-is that determines my experimental results, so I call it ‘reality’. This ‘reality’ is somehow separate from even my very best hypotheses. Even when I have a simple hypothesis, strongly supported by all the evidence I know, sometimes I’m still surprised. So I need different names for the thingies that determine my predictions and the thingy that determines my experimental results. I call the former thingies ‘belief’, and the latter thingy ‘reality’.”

The map is not the territory, and the territory is not the map. My hypotheses about it might be wrong, but the territory is still the territory. How would a map determine my experimental observations?

That is a great quote from The Simple Truth. And what is more, it is perfectly responsive to what I was trying to say. Thank you.

As you may already know, Eliezer quoted that passage in Quantum Non-realism because QM makes it necessary to modify that argument slightly. The trouble is that in QM, your experimental results are no longer "determined" or at least not in the same sense. Oh, I agree with the basic message of that Quantum Non-realism posting that QM creates no problems for realism that MWI and a little fine print can't fix. But I think that the fact that QM forced a change to the argument does suggest that there may be even more changes needed down the road.

I need a name for whatever-it-is that determines my experimental results, so I call it ‘reality’. This ‘reality’ is somehow separate from even my very best hypotheses.

If you want to call the whatever-it-is 'reality', that is fine with me. The whatever-it-is is definitely different from the best map that you know of. But it is possible, is it not, that the whatever-it-is is the whole tower of maps - including the maps you know of and the maps you don't even imagine yet.

How would a map determine my experimental observations?

A map doesn't determine observations. A whole tower of maps determines observations (modulo the necessary QM/MWI fine print). In much the same way that map-towers determine theoretical predictions. Maps, predictions, and observations are all made out of the same kind of 'stuff'. There is nothing mysterious about it. You only get into trouble if you somehow begin to imagine that experimental observations are somehow built out of some kind of 'reality stuff' which is ontologically different from map-tower stuff. They are not. Observations are very theory-laden.

Logical positivism had all this stuff covered fairly satisfactorily by 1970 or so (IMHO) but then somehow there was a change in the Zeitgeist and everyone agreed that positivism is dead. I am a contrarian who thinks something like it can be revived - along with a number of more academically serious anti-realist philosophers working in philosophy of science.

I'm not sure what you mean by this.

How does one make maps into a tower? What would such a tower of maps look like? How is this different from a "territory" containing a tower of maps?

I am taking the word 'map' to mean pretty much the same as what philosophers of science refer to as 'theories'. And 'territory' to mean 'reality'. So by a 'tower' of maps, I mean a series of theories, each reducing to a 'lower-level' theory. For example, one map might be a theory of infinitely divisible material bodies with state properties like density, temperature, and elasticity. At the next level down in the tower of maps, we might have an atomic theory with 92 elements. Next a theory in which the elementary particles include electrons, neutrons, and protons. Next down, we have the standard model with QCD. Then some super-symmetric Kaluza-Klein GUT. Etc.

Is there a base-level theory ('map') that reduces to an underlying 'reality', rather than to a lower-level map? I suppose we will never know - can never know - whether such a reality exists and what it 'looks like'. Certainly, we never know whether our current lowest-level map is the final one.

The thing that strikes me is that a 'reduction' is really a relation (a morphism?) between maps - an association between the entities and observables at one level with those at the next level down. In doing a reduction, we are constructing in our minds a relation or morphism between maps which also exist in our minds. I am simply saying that if you postulate a new kind of thing - a 'reality' or 'territory' that exists outside our minds, you may solve some philosophical puzzles, but you create others. For one thing, we need to have two kinds of reduction in our epistemology - one taking maps to territories, and one taking maps to maps. I say, "Why bother! Let's follow Occam's advice and stick to maps rather than adding this new entity - the 'territory' - without necessity."

I hope that explanation helped.

Is there any real evidence of this? I hear interesting conjecture but not one bit of evidence.

You know the saying, big claims require big evidence. These are very big claims.

These are very big claims.

Not to my mind. In fact, I'm not sure they are 'claims' at all. I'm suggesting a different way of looking at things - a way which has advantages and disadvantages. I think the advantages dominate. Your mileage may differ.

If I did make claims, it was in the last paragraph where I suggested that anti-realism is both a respectable and a populated position in ontology and philosophy of science. The wikipedia article should provide links to sufficient evidence to back those claims.

The Wikipedia article wasn't all that helpful other than to give a better idea of what the term means.

There seem to be two major types of anti-realism - one seems to be the idea that nothing is objectively real, and the other that no matter how much indirect evidence we have we can never know what is objectively real.

The first position doesn't seem to be useful for much of anything (to me, anyway), and the second seems to be pretty close to what "the map is not the territory" is all about, with the claim that the map well never be able to perfectly reflect the territory.

Since you like to argue about the map/territory, I can only assume you believe nothing is objectively real.

Am I misunderstanding you?

I can only assume you believe nothing is objectively real.

It would probably be more productive to assume that I have seen no evidence that anything is objectively real, and that I have noticed no particular advantage to forming a belief on the subject in the absence of evidence.

And since I don't expect to see or hear any evidence on the question any time soon, I follow Occam's advice and try to think of how I can live without that belief in the real existence of something called 'territory'.

I think I understand you, but what I don't understand is how the idea that our subjective observations do not have an objective cause is simpler than the idea that what we sense directly and measure indirectly is the objective cause.

I would think Occam's razor would require you to assume there is an objective reality causing all of your indirect observations. Even if all of reality is just a figment of our imagination, or just a part of some simulator (to take an extreme position), doesn't there need to be a cause of such figments, or a machine of some kind on which the simulation runs?

In other words, I could understand the position that our understanding of reality (our best maps, if you will) may be completely wrong, and I could even understand the position that the nature of reality may be impossible for us to discover, but it seems to me the fact of our existence is pretty significant evidence that some kind of objective reality exists, whether or not we have accurately mapped it. Furthermore, both positions seem far more complicated than the position that what we have seen and measured is reality. Both positions must explain all of our senses as well as having some larger thing that is an undiscoverable reality. Occam's razor seems to say the simplest answer is that what we have sensed directly and measured indirectly is reality (though not necessarily the fundamental reality).

Does that make sense?

Does that make sense?

It does. But I think you are underestimating just how much complication a belief in an unknown (or not yet known) reality brings with it. And it is an unsupportable position to claim "that what we have seen and measured is reality". Measurement is obviously theory-laden. Sense data is too, though the theories involved are in the field of psychology and the neurosciences.

it seems to me the fact of our existence is pretty significant evidence that some kind of objective reality exists

One thing I notice you doing that you may not notice yourself: you are using the words "objective" and "subjective" as a kind of praise or condemnation. And you seem to associate the adjective 'objective' with the noun 'reality' as if 'reality' has a natural right to that adjective. But I am taking the position here that the only 'reality' you have access to is a subjective one (or, at best, intersubjective).

I think we pretty much understand each other at this point. I'm not trying to convert anyone - just to open some minds. And I apologize for my "maps all the way down' crack that started the conversation. It came across as trollish, and I regret 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.

"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)

"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.

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.

"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.

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.

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?

It's technically accurate, but it fails to provide useful information. The question isn't impossible to answer on its own terms, it just turns a simple negative into non-Gricean communication.

Late to the party here, but:

Any English speaker who hasn't been brainwashed with prescriptivist poppycock will tell you that the sentence has two possible readings: one where 'his' refers to Martin, and one where it refers to Bob. In natural language, linear order or closeness tends to matter a lot less than you might think. (This is why many linguistic analyses represent sentences as hierarchical tree structures, and argue that the behavior of some word is predicted by its position in the tree.)

We can even see effects on the resolution of pronoun reference that apply across sentence boundaries:

Martin punched Bob in the face. He fell.

Martin punched Bob in the face. He was very angry.

There's a preference to interpret 'he' as Bob in the first case and Martin in the second (it's not absolutely impossible to interpret them the other way around, but there's a preference), and it comes not from syntax (we've kept that pretty constant) but from what we might nebulously call "the structure of the discourse". It's extremely hard to predict what the preferred interpretation will be in any given case.

However, I think that the example could have been better constructed for a different reason. There are actually two phenomena at work in the sentence: the deictic quality of the word 'left', and the problem of pronoun reference. The point could have been made with reference to either one individually. So it's not a very consequential confound, but it's worth separating the two effects nonetheless.

"Martin told Bob the building was on the left" still suffers from the problem that we don't know whose left is meant (Martin's, Bob's, the speaker's, maybe the addressee's?). In this case, I can't see any way of determining a definite answer, even one based on some word-counting bullshit.

There would still be ambiguity if we got rid of 'left' but kept the pronouns in:

Martin told Bob that the building was to the north of him.

('North' differs from 'left' in that it is defined relative to the entire earth, but the sentence has different truth conditions depending on who 'him' refers to.)

Or, with less grammatical awkwardness:

Martin told Bob that the Xbox was at his house.

Since "Either Martin told Bob that the Xbox was at his house, or Martin did not tell Bob that the Xbox was at his house" can be false if 'his' refers to Martin in the first clause and Bob in the second, it still fits the example, but the ambiguity comes from a different source.

"Have you stopped beating your wife?", as has been explained elsewhere, is simply an example of a question that has a presupposition. Linguistics grad students and the people who love them will sometimes answer "Presupposition failure" to questions, but this has yet to catch on in the general population. ;)

In the English language, the pronoun "his" (and similarly "him," "her," "it," etc.) always refers to the nearest possible preceding sensible noun.

Maybe where your from. In English where I'm at, Jim will use 'him' to refer to Bob if he wants.

Or am I not using the common definitions?

An answer of 'no' to that question would normally be interpreted "I am still beating my wife".

Descriptivism FTW.

"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.