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Wrong Questions

32 Post author: Eliezer_Yudkowsky 08 March 2008 05:11PM

Followup toDissolving the Question, Mysterious Answers to Mysterious Questions

Where the mind cuts against reality's grain, it generates wrong questions—questions that cannot possibly be answered on their own terms, but only dissolved by understanding the cognitive algorithm that generates the perception of a question.

One good cue that you're dealing with a "wrong question" is when you cannot even imagine any concrete, specific state of how-the-world-is that would answer the question.  When it doesn't even seem possible to answer the question.

Take the Standard Definitional Dispute, for example, about the tree falling in a deserted forest.  Is there any way-the-world-could-be—any state of affairs—that corresponds to the word "sound" really meaning only acoustic vibrations, or really meaning only auditory experiences?

("Why, yes," says the one, "it is the state of affairs where 'sound' means acoustic vibrations."  So Taboo the word 'means', and 'represents', and all similar synonyms, and describe again:  How can the world be, what state of affairs, would make one side right, and the other side wrong?)

Or if that seems too easy, take free will:  What concrete state of affairs, whether in deterministic physics, or in physics with a dice-rolling random component, could ever correspond to having free will?

And if that seems too easy, then ask "Why does anything exist at all?", and then tell me what a satisfactory answer to that question would even look like.

And no, I don't know the answer to that last one.  But I can guess one thing, based on my previous experience with unanswerable questions.  The answer will not consist of some grand triumphant First Cause.  The question will go away as a result of some insight into how my mental algorithms run skew to reality, after which I will understand how the question itself was wrong from the beginning—how the question itself assumed the fallacy, contained the skew.

Mystery exists in the mind, not in reality.  If I am ignorant about a phenomenon, that is a fact about my state of mind, not a fact about the phenomenon itself.  All the more so, if it seems like no possible answer can exist:  Confusion exists in the map, not in the territory.  Unanswerable questions do not mark places where magic enters the universe.  They mark places where your mind runs skew to reality.

Such questions must be dissolved.  Bad things happen when you try to answer them.  It inevitably generates the worst sort of Mysterious Answer to a Mysterious Question:  The one where you come up with seemingly strong arguments for your Mysterious Answer, but the "answer" doesn't let you make any new predictions even in retrospect, and the phenomenon still possesses the same sacred inexplicability that it had at the start.

I could guess, for example, that the answer to the puzzle of the First Cause is that nothing does exist—that the whole concept of "existence" is bogus.  But if you sincerely believed that, would you be any less confused?  Me neither.

But the wonderful thing about unanswerable questions is that they are always solvable, at least in my experience.  What went through Queen Elizabeth I's mind, first thing in the morning, as she woke up on her fortieth birthday?  As I can easily imagine answers to this question, I can readily see that I may never be able to actually answer it, the true information having been lost in time.

On the other hand, "Why does anything exist at all?" seems so absolutely impossible that I can infer that I am just confused, one way or another, and the truth probably isn't all that complicated in an absolute sense, and once the confusion goes away I'll be able to see it.

This may seem counterintuitive if you've never solved an unanswerable question, but I assure you that it is how these things work.

Coming tomorrow:  A simple trick for handling "wrong questions".

 

Part of the sequence Reductionism

Next post: "Righting a Wrong Question"

Previous post: "Dissolving the Question"

Comments (125)

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Comment author: Paul_Crowley2 08 March 2008 07:04:07PM 1 point [-]

How do you apply this approach to questions like "to what extent was underconsumption the cause of the Great Depression?" No conceivable experiment could answer such a question, even given a time machine (unlike, say, "Who shot JFK?") but I think such questions are nevertheless important to our understanding of what to do next.

The best answer I have to such questions is to posit experiments in which we rewind history to a particular date, and re-run it a million times, performing some specific miracle (such as putting money into a billion carefully-chosen wallets) on half a million of those occasions, and gather statistics on how the miracle affects economic indicators.

Comment author: pnrjulius 30 April 2012 02:56:21PM 1 point [-]

I have a somewhat better way. Place economics on a sufficiently rigorous empirical foundation, so that it is (let us say) somewhere near the level of quantum physics.

Having done this (monumental) task, we can now answer questions about historical events in economics as well as we can answer questions about historical events in physics---e.g. "Why is that laser red?" "Why did those interference fringes form here and not there?"

Comment author: HalFinney 08 March 2008 07:51:09PM 1 point [-]

I can take a shot at a couple of these. For free will, suppose it turns out that neural activity is not fully determined by mechanistic principles, but is in some cases determined by thermal/quantum noise. And yet, it turns out that out of that noise, certain neural activity patterns appear seemingly magically. Neurons A, B and C fire together to make a decision, even though the most detailed investigation shows that whether they would fire or not was purely random. And yet these correlations appear persistently, too often for random statistical correlations to explain, and correspond to our subjective feelings of free will. A likely model is that there is another, otherwise inaccessible, realm which is influencing neural activity and that the brain is a specially-tuned "receiver" designed to amplify quantum chaos into determinate action. The free will comes from this other realm.

For why anything exists at all, one possibility is the Tegmark/Schmidhuber model where the universe is pure information, part of a much larger information world which has Platonic existence. In this concept, all information patterns and "information objects" have a form of existence, and sufficiently complex information objects look like universes such as the one we observe. These models then aim to impose a measure on information patterns, making some more prominent than others. Suppose these theories can be developed to the point that this measure can be computed, and it turns out to predict that there is by far one highest-measure information pattern which includes conscious entities. And further, that that information pattern corresponds in 100% agreement to our universe, even to the point where it computes that we ourselves, we human beings, are by far the most prominent conscious information patterns in the informational multiverse. Then I think this would be a very strong candidate for an explanation of why anything exists, and in particular why the observed universe and we observers exist.

Comment author: komponisto2 08 March 2008 09:13:06PM 5 points [-]

"to what extent was underconsumption the cause of the Great Depression?"

Tabooing the word "cause", one finds that this question is a disguise for something like "Given the economic data of the period immediately preceding the Great Depression, can we prevent an economic collapse by making sure we don't underconsume?"

Comment author: JulianMorrison 09 March 2008 12:34:42AM 6 points [-]

As I was putting the "free will" question to myself, I decided to re-frame it as "would an AI have free will" Answer: obviously not, it's an optimization process. Then I thought: an AI is different from a trivial arithmetic solver, the AI's search strategy is not fully determined by the goal. What would an AI be like whose strategy was wholly undetermined? It would thrash around randomly. So, insight: the uncertainty in our strategy is another name for our ignorance of the search domain. At the one end, zero information, total randomness. At the other, full information, determinism. In the middle, a "free" (meaning: ignorant) choice of search strategies which corresponds to the feeling of free will.

Interesting corollary: more knowledgeable people must be less free. To them, strategies we might try are obviously useless.

Comment author: TheOtherDave 03 November 2010 09:42:21PM 12 points [-]

more knowledgeable people must be less free.

Larry Niven plays with this idea in Protector... the idea being that if you're really smart, the right solution presents itself so rapidly that you simply don't have any choices.

I suspect this is nonsense in any practical sense. Sure, any increase in intelligence will force you to close off some options which you now realize are bogus, but it will likely also make you aware of options you weren't previously able to recognize.

In my own experience, increased understanding leads to a net gain of options. Perhaps the curve is hyperbolic, but if so I live on the ascending slope.

Comment author: pnrjulius 30 April 2012 02:59:47PM 4 points [-]

Do you feel any less free because it never occurs to you to bash your head against a wall, or slit your throat with a steak knife?

I certainly don't; it would be a terrible inconvenience to have to go through all the really stupid options of things I could do at any given moment before arriving at the reasonable ones.

How much more so, then, for a superintelligence; it does not have to wonder about the stupid questions we humans often ask, but instead can focus on the really interesting decisions that remain to be made. (If you imagine that the space of possible decisions is finite, perhaps it could run out eventually... but my sense is that no intelligence small enough to fit in our universe can run out of possible decisions in our universe.)

Comment author: TheOtherDave 30 April 2012 03:13:11PM 0 points [-]

It does occasionally occur to me to kill myself, and in my really bad periods I do experience myself as prevented from choosing an eminently desirable path by my own earlier precommitments. But that's neither here nor there.

Leaving the particulars aside... if there exists some question Q such that intelligence I1 finds Q difficult to answer and I2 finds Q easy to answer because I2 is a superintelligence with respect to I1, then I2 may well at some point consider Q, answer Q, and then move on to the next thing. Or, of course, it might never do so, depending on the relevance of Q to anything that occurs to I2.... as you say, the space of possible decisions is enormous.

I fail to see what follows from this. Can you unpack your thinking a bit, here?

Comment author: RichardKennaway 30 April 2012 03:34:00PM 2 points [-]

"Do you know, can you comprehend, what freedom it gives you if you have no choice? Do you know what it means to be able to choose so swiftly and surely that to all intents and purposes you have no choice? The choice that you make, your decision, is based on such positive knowledge that the second alternative may as well not exist."

-- Rafael Lefort, "The Teachers of Gurdjieff", ch. XIV

Quoted before here.

When you have a purpose, you must act to achieve it. If you do not, you did not have that purpose.

If you are driving a car, you are not free to do anything you like with the steering wheel. You must use it to direct the car along your intended route.

You are only faced with choosing when you do not know the right choice. When you do know, you no longer have that choice. You cannot make your choice and have it still.

Comment author: Jason_Brennan 09 March 2008 12:49:55AM 0 points [-]

This reminds me of logical positivism.

Here's a question: "Are there such things as wrong questions, and is there some sort of test to help me identify them?"

Interestingly, I couldn't imagine any concrete, specific state of how-the-world-is that would answer that question.

Comment author: pnrjulius 30 April 2012 03:01:48PM 2 points [-]

No, we can manage this where the positivists could not.

A good heuristic test for a wrong question: We've been trying to resolve it for thousands of years, and there are two (or more) camps that vehemently insist their solution is exactly right, but none of them have any evidence that would persuade an impartial observer.

Free will certainly qualifies, as does "Why does anything exist?", as does the Hard Problem of consciousness.

One might think that religion qualifies as well---but in this case, the atheist camp actually has some pretty good evidence.

Comment author: Cyan2 09 March 2008 02:41:34AM 3 points [-]

Jason Brennan,

Suppose the state of how-the-world-is is that over time, beings with certain biased decision-making algorithms have evolved. As products of evolution, the algorithms are pretty good for making sure the beings running them have offspring, but are less good at obtaining representations of the "true" state of the world or at processing complex information. Such beings are likely to form queries which contain false assumptions, category errors, or other flaws.

Comment author: Ian_C. 09 March 2008 03:01:45AM 5 points [-]

The screwy concept in "Why does anything exist at all?" is not existence, it is "why." There's nothing wrong with "why" as such, it just doesn't apply to existence. That's what makes for wrong questions: pairing up words that don't apply to each other, such as "What is the sound of blue?"

"Why" only applies when there is an alternative that could have been, but nothingness can't be (as soon as it tries it becomes something) so there's no alternative to existence.

Comment author: Psy-Kosh 09 March 2008 09:11:23AM 3 points [-]

Ian: I don't follow. Why is it that there simply couldn't have been, well, nothing at all. No reality of any form in any way at all in any sense existing. No subjective experiences and nothing to experience and no one to do the experiencing?

Just... nothing.

So I'm not sure the "why" question is invalid for existance. Sure seems like a reasonable question. In other words, how is it that you figure that the question of existance is such that "why?" or "how is it that existance came to exist?" or "how is it that anything at all exists?" or any question of that form is invalid?

Comment author: mitchell_porter2 09 March 2008 09:48:47AM 4 points [-]

Hal, in effect you're saying "Our world exists because it is an information pattern, and all information patterns exist". But why do they all exist?

Comment author: Latanius2 09 March 2008 12:02:52PM 1 point [-]

Psy-Kosh: let's Taboo "exist" then... What does it exactly mean? For me, it's something like "I have some experiences, whose cause is best modeled by imagining some discrete object in the outer world". The existence or non-existence of something affects what I will feel next.

Some further expansions: "why": how can I predict one experience from another? "world": all the experiences we have? (Modeled as a discrete object... But I can't really imagine what can be modeled by the fact that there is no world.)

So the question "why does our world exist" becomes something like "what is the experience from which we can predict we will have any experiences at all... Sounds a little bit more controversial than the original.

By the way, have we tried this transformation in the opposite direction? Turning the question "what is the sound of blue" to one which seems to make sense...

Comment author: Psy-Kosh 09 March 2008 05:38:55PM 3 points [-]

Latanius: I was including the issue of subjective experience. As in "Why is there any subjective experience at all?" ie, why is there _ANYTHING_, including subjective experience. Your answer doesn't leave me with a "okay, now the question has been answered" sense.

Actually, as near as I can tell, you're trying to answer a different question, specifically, it looks like you're trying to address the question of "how do I know my experiences in any way correlate with the Real World(tm)? Maybe I'm just hallucinating everything? Maybe there's nothing but dreams?" etc etc etc...

The question at hand is more "why is there anything? At all. Including subjective experience. ie, how is it that there's something at all other than, well, nothing?"

Maybe the question is deconstructable, but it doesn't seem like it's been deconstructed here yet.

Alternate form of the question, used by some physicists: "What breaths fire into the equations?" Great, there're some equations that are good at describing reality. Are they so compelling that there actualy need be a reality/set of subjective experiences/whatever for them to describe?

It may be just some form of mental confusion on my part. But as of yet, it sure seems like a real question to me.

Comment author: HalFinney 09 March 2008 11:11:10PM 0 points [-]

Mitchell, that's a good point. My scenario might be considered *evidence* that all information patterns exist, and that we live among them, but can not really answer the question of why this is true.

One issue is that the question of "why", and of reasons why things are true, has many different interpretations and variations. Sometimes just giving evidence for something can be considered to answer a "why" question. For example, if someone asks for reasons why Macs are better than PCs, he is usually asking for evidence that Macs are better. But in other cases, people want more, and certainly someone asking why anything exists would be one of those.

Comment author: Latanius2 09 March 2008 11:52:18PM 1 point [-]

Psy-Kosh: Maybe I really tried to approach the meaning of the question from the direction of subjective experience. But I think that the concept of "existence" includes that there is some observer who can decide if that thing we're talking about does really exist or doesn't, given his/her stable existence.

Maybe that's why the question can't be easily answered (and maybe has no answer at all) because the concept of "world" includes us as well. So if we want to predict something about the existence of the world (that is what the word "why" means, I think), we haven't observe anything: it's a logical truth that any world in which this question is asked really does exist.

But if we statisfy the two assumptions in the question (the existence of the world is observable by us, and is repeatable, so we can make predictions about it), it starts to make sense, but it becomes less mysterious somehow. Some possible answers: because the previous one did already collapse in an anti-big-bang, I've just seen that..., or we usually have to wait for it to recreate itself, therefore nothing exists right now... Or it exists because I was bored and created a new one, or maybe because I was bored and started Half-Life (which also fits our new world-concept in some way)... etc.

And... physical equations are definitely _something_ which differ from nothing. Some rules for a... world... But I think if something is becoming so blurry like the concept of "world" just now, we better ask what subsystem in our mind is applied for the wrong problem, and what are those problems which it is intended to solve.

Comment author: Ian_C. 11 March 2008 01:41:54PM 1 point [-]

Psy-Kosh: "So I'm not sure the "why" question is invalid for existance. Sure seems like a reasonable question. In other words, how is it that you figure that the question of existance is such that "why?" or "how is it that existance came to exist?" or "how is it that anything at all exists?" or any question of that form is invalid?"

I believe that, like all concepts, we get "why" by abstracting away from our experiences in this universe, and that it is therefore this universe that gives the concept it's meaning. It doesn't make sense to step outside the universe to compare it to another alternative universe beside it and try an use concepts from our universe in that space. They don't have any meaning there.

Comment author: Jaco_van_der_Westhuizen 24 June 2008 01:35:19PM 0 points [-]

I believe that you are correct about the concept of existence, that it is not a real thing, but rather an artifact of our perception.

Which is why positivists say that something is only real if it can be perceived, directly or indirectly. They say that we only need to take into account things that can be perceived, because if it affects us, we are perceiving it.

Now that I think of this again, I see one possible flaw, if something is imperceptible now, it might still become perceptible later. For physical objects there might be a law to protect us, but our knowledge of non-physical (i.e. mental) objects leave much to be desired.

Comment author: AndyCossyleon 08 November 2010 09:39:14PM *  0 points [-]

The state of affairs (not State of Affairs) wherein nothing exists cannot possibly by inconsistent, for it contains nothing. The question is, why this populated, consistent world (presumably it is not inconsistent) and not the other?

Perhaps this question is a wrong question because nothing, in fact, does exist. I'm envisioning something beyond the multiverse, alternate realities that are exactly that, other realities, totally disjoint from ours, inaccessible in every possible and impossible way. Like the universe under your fingernail... except it's not under your fingernail, it is Nowhere. Some of these realities are empty; nothing exists. But some, like ours, are not.

We talk of the origin of existence. What if it originated multiple times? Basically, let's assume the statements "nothing exists" and "something exists" are both true. Where does that take us?

These alternative realities do not exist, because they do not conform to our mode, our universe's (or multiverse's) mode of existence; but they conform to their own mode. Or do they? Nes or yo?

Comment author: dlthomas 29 March 2011 11:47:56PM 0 points [-]

To my mind, I have free will to the degree that there is an "I". My decision is determined by my environment and my self. Were there, hypothetically, some other individual in my place they might well make a different decision. So I determine my actions, and can therefore be said to have free will.

It is true that my state follows from my history and my genetics (arguably a part of my history, in a sense), but I assert that this is irrelevant because of our main reasons for caring about "free will." In my experience, people care about whether we have "free will" for two reasons. The first is a sort of despair in the face of inevitability that echoes the determinism of classical Greek mythology - the gods have something planned and no matter what you do it will happen. This, of course, is not a feature of physical determinism - what you do is a part of the system, and if you had done something else things might have turned out considerably differently. What you will do is determined, but it's determined through who you are, not in spite of it.

The second reason people care about free will is to allow us to reason about responsibility and blame. This can also be dealt with by much of the above, however, along with an observation that blame and praise, and the brains expecting these, are themselves a part of the system.

Comment author: potato 20 September 2011 06:30:48PM *  0 points [-]

And if that seems too easy, then ask "Why does anything exist at all?", and then tell me what a satisfactory answer to that question would even look like.

And no, I don't know the answer to that last one. But I can guess one thing, based on my previous experience with unanswerable questions.

What if we take "X exists" to simply mean "X was not made up, i.e., not a fiction, hallucination, illusion, or delusion"? Then the question becomes "Why is anything not a fiction, hallucination, illusion, or delusion at all?" Well, if everything was made up, we would be in the rather awkward position of every made up thing being made up by another made up thing, which must have also been made up by some other made up thing, etc. That's not quite a solution, but it prohibits you from imagining a world in which nothing existed, as an empty black void.

There's also the classic analysis of the question "Why is there something rather than nothing?" which seems somewhat related. Well, when we say that anything which can take the value x is a something, we also imply "there is x". X having the value of a something is sufficient for the truth of "There is X." And similarly "nothing" is the term that we apply when we are presented with a list of properties which no object has, e.g., nothing is a circular square. This is not to say that there is this object, nothing, out there in the universe which is both circular and square, obviously. So the reason that it can't be that there is nothing, is because "nothing is" is English's short hand for negated existential quantification, so of course it is never positively quantified.

But that is all arguing from definition, which I know is silly when you are dealing with finding a truth, but what about when dissolving a question?

Comment author: Philip_W 04 October 2012 06:43:12PM 0 points [-]

Existence is not the property that all things that are not made up have. There are an uncountably infinite amount of conceivable universes which have not been conceived and also don't exist. You're confusing "not X" and "the (phenomenological) opposite of X".

Well, when we say that anything which can take the value x is a something, we also imply "there is x".

So you would say numbers exist? "Five exists" sounds like a type error to me - it's a mathematical concept, not an object.

X having the value of a something is sufficient for the truth of "There is X."

I don't get what you're trying to say here.

So the reason that it can't be that there is nothing, is because "nothing is" is English's short hand for negated existential quantification, so of course it is never positively quantified.

You've befuddled the question, not dissolved or answered it. While I don't follow your reasoning exactly, it sounds like an argument against the validity of the null set.

I hope you're somewhat mathematically inclined, because what follows below is an attempt to express what's wrong with your reasoning:

Consider the program

if(N=0){ return 1};

where N is the sum over the array na containing the amounts in existence ni of all objects a_i which belong to the set A of objects relevant to the question, and the returned value is the truth value of the statement "nothing is A".

For example: Let A = the set of all circular squares. Then A = {null}, na = {null} N = sum ni over all i = 0. Therefore "nothing is a circular square" is true.

"Why is there something rather than nothing?" then becomes "Why is ni not equal to 0 for all objects ai?". (note: Tegmark multiverses can also be considered objects).

But that is all arguing from definition, which I know is silly when you are dealing with finding a truth, but what about when dissolving a question?

When dissolving a question you are trying to find the truth. Specifically, you're trying to find the true state of your mind which caused the question to arise. When you start using definitions, you don't look at your mind anymore.

As for the original question, I obviously don't have the answer, but a path that sounds plausible to me is that, information-theoretically, "everything existing" and "nothing existing" are identical: a fully connected graph is the same as a fully unconnected one. Humans don't think this way naturally because there's a physical difference between connected and unconnected neurons, and because we're working solidly in the low-level-of-connections part of the spectrum (only 10^16 out of (10^12)! possible connections are present in the brain).

So if it turns out that Tegmark's Mathematical Universe Hypothesis is correct (that the existence of all mathematical objects is consistent with our observations), then the question would be dissolved; there would be no mathematical rules which work upon mathematics itself to determine which parts of it "exist". The only question would then be "How is the MUH consistent with our observations?" - which is a mathematical and physical problem for which a clear answer exists. (If you prefer "existence" to have a use in language still, because it's a word, and words are used and defined by human consensus, and because by intuitive usage the Invisible Flying Teapot does not exist even though it's clearly a mathematical object, you can use "existence" to refer to things which can affect our universe, or something like that).

Comment author: kremlin 31 May 2012 09:22:06PM 6 points [-]

Some people were talking about The Ship of Theseus -- the question "If a ship's parts are replaced one-by-one over time, after each part is replaced is it still the same ship?" First thing that came to my mind was that this was a wrong question. I saw it fundamentally as the same mistake as the Blegg/Rube problem -- they know every property about the ship that's relevant to the question, and yet still there feels like a question left unanswered.

Am I right about this?

Comment author: Oscar_Cunningham 31 May 2012 09:49:33PM 5 points [-]

Yep.

Comment author: rkyeun 28 August 2012 02:44:31AM 0 points [-]

How many nothings do you expect to exist? Zero of them?

Comment author: satt 09 April 2013 11:37:29PM 0 points [-]

And if that seems too easy, then ask "Why does anything exist at all?", and then tell me what a satisfactory answer to that question would even look like.

And no, I don't know the answer to that last one. But I can guess one thing, based on my previous experience with unanswerable questions. The answer will not consist of some grand triumphant First Cause. The question will go away as a result of some insight into how my mental algorithms run skew to reality, after which I will understand how the question itself was wrong from the beginning—how the question itself assumed the fallacy, contained the skew.

Yup, basically. See

Comment author: Swimmer963 10 April 2013 02:41:55AM 1 point [-]

The fact that this linked to a PDF that wasn't behind a paywall made me very happy... It looks interesting. Currently converting the saved .pdf to .epub and putting it on my iPhone for later reading. Thanks!

Comment author: MugaSofer 10 April 2013 09:55:05PM -3 points [-]

OK, firstly, I'm curious as to whether the question actually feels dissolved to you now?

Secondly, that linked ... piece ... is terrible. Really terrible. I wrote a truly marvelous rebuttal, which this comment box is too small to contain, partly because I was quoting heavily and partly because there's just so much wrongness. I'll probably stick it in Discussion.

Comment author: MugaSofer 10 April 2013 10:49:18PM -2 points [-]

Actually, on reflection, I find my main criticism is pretty simple:

The author has dissolved the wrong damn argument. It is perfectly true that, having explained both A and B, A-and-B does not require a separate explanation. However, the actual problem is not that he cannot explain A-and-B, it's that he can only explain A and B by describing how they are produced by other things, which he does not explain.

This is, I had thought, pretty basic philosophy; although, to be fair, it's so damn long I can't blame anyone for not realizing that's his core argument.

Also, yes, the word "thing" is pretty vague. No, this does not render all sentences containing it meaningless. Especially when it's part of the compound word "anything".

Comment author: satt 11 April 2013 02:42:46AM 0 points [-]

Didn't originally see this comment. (That's what I get for leaving a tab open for hours before bothering to reply.)

to be fair, it's so damn long I can't blame anyone for not realizing that's his core argument.

Your second paragraph differs from my understanding of Maitzen's core argument, but it's possible I misread him.

Also, yes, the word "thing" is pretty vague. No, this does not render all sentences containing it meaningless. Especially when it's part of the compound word "anything".

Maitzen doesn't say all sentences containing "thing" or "anything" are meaningless. On p. 62 he writes,

In many ordinary contexts we may implicitly understand the true sortals over which ‘thing’ is generalizing; consider "Exactly how many things did you buy today?" said to someone just home from a shopping spree. So it’s perhaps unsurprising that we’d carry that implicit understanding into unrestricted metaphysical contexts where it doesn’t hold.

People automatically attach an implicitly understood meaning to the word "things" (or "anything") when it shows up in everyday sentences, and that often works OK. But given the atypical question "Why is there anything?", it's not obvious which meaning they should substitute in, and their brains start flailing. Or so Maitzen speculates.

Comment author: MugaSofer 11 April 2013 02:34:36PM *  -1 points [-]

Didn't originally see this comment. (That's what I get for leaving a tab open for hours before bothering to reply.)

No worries, I was offline anyway. Came back to find both your comments.

Your second paragraph differs from my understanding of Maitzen's core argument, but it's possible I misread him.

This is why my original, obscenely long comment contained quotes for every point.

Naturalists point to the many phenomena we used to attribute to supernatural agents but can now explain scientifically: the change of seasons, the course of a disease, the orbits of planets, and on and on. Their theistic opponents often admit that natural science has discovered not only good piecemeal explanations of the existence of particular phenomena but even good integrated explanations of the existence and operation of entire systems. In this sense, the opponents concede that natural science can answer not only mechanistic ‘‘how’’ questions but also existential ‘‘why’’ questions, such as ‘‘Why are there penguins?’’ or ‘‘Why is there cancer?’’ Yet they hasten to point out that natural science hasn’t explained why there exists anything at all: not specific things or kinds of things but anything in the first place, anything in general.

[...]

Properly put, then, the challenge to naturalism is that natural science may do a fine job accounting for particular contingent, concrete things and kinds of things, but it isn’t equipped or even meant to tell us why any such things exist at all.

Other philosophers regard the challenge as well-posed but sufficiently met if natural science can explain the existence of each given contingent, concrete thing. Their spokesman is Hume’s Cleanthes: ‘‘Did I show you the particular causes of each individual in a collection of twenty particles of matter, I should think it very unreasonable, should you afterwards ask me, what was the cause of the whole twenty. This is sufficiently explained in explaining the cause of the parts.’’

[...]

The nature of my complaint may become clearer if we imagine the following exchange:

A: Why is there anything?

B: What do you mean? Are you asking why numbers exist?

A: No. If numbers exist, they had to exist. Why is there anything that didn’t have to exist?

B: So you’re asking why there are any contingent things. Well, there are pens, which are contingent things, and here’s how pens come to exist—

A: —No! I’m not asking why there are any pens.

B: All right then. Penguins exist, and they’re contingent. Penguins evolved from—

A: —No! I’m not asking why there are penguins either. I’m asking why there are any contingent things at all.

B’s answers may seem deliberately obtuse, but they bring out the emptiness of A’s questions: A rejects each of B’s attempts to supply determinate content to the dummy sortal ‘contingent things’, but without such content there’s no determinate question being asked. Once ‘contingent things’ takes on content (e.g., in one of the ways B suggests), the resulting question becomes empirical and scientifically answerable. Or suppose I mention pens, plums, and penguins. You then ask me, ‘‘Why are there any of the things you just mentioned?’’ but tell me you don’t want explanations of the existence of pens, plums, or penguins in particular; instead, you want to know why there are any of the things I just mentioned (with table-pounding emphasis on ‘any’) rather than none at all. Clearly your attitude is perverse: ‘the things I just mentioned’ is only a covering term for pens, plums, and penguins; it doesn’t pick out a category of thing requiring an explanation beyond those I was already prepared to give and you didn’t want to hear. Likewise for ‘contingent things’ and the other dummy sortals I’ve discussed: there aren’t any contingent things whose explanations outstrip the explanations available for the individuals covered by the covering term ‘contingent things’. For the same reason, we can see that the question ‘‘Why does the Universe exist?’’ taken in the way that objectors to naturalism must intend it, also poses no unanswerable challenge to naturalism, for it amounts to asking (again) ‘‘Why are there any contingent, concrete things at all?’’ or (again) ‘‘Why are there these contingent, concrete things rather than none at all?’’ or perhaps ‘‘Why are there these contingent, concrete things rather than other such things?’’ Once we substitute true sortals (‘pens’, ‘plums’, ‘penguins’, etc.) so that those latter questions have more sense than the question ‘‘Exactly how many contingent, concrete things are you holding in your hand?’’ they seem to admit of naturalistic answers. If, moreover, the explanatory challenge to naturalism should consist of a long disjunctive question—‘‘Why are there pens, or plums, or penguins, or…?’’—then of course naturalism can offer a long disjunctive answer.

The closest he comes to answering the actual question is this...

At this point, defenders of supernaturalism might counter that naturalistic explanations must ultimately bottom out at brute, unexplained posits. But I see no reason naturalistic explanations can’t go forever deeper. One bad reason for concluding that they can’t is the notion that x can’t explain y unless x itself is self explanatory. I don’t see that notion as at all implied by our ordinary concept of explanation, which allows that x can explain y even if something else altogether explains x. Moreover, there are grounds for thinking that naturalistic explanations not only could but must go forever deeper. A common attitude among scientists is that the more they discover, the more there is yet to discover—the more they know, the more they realize they don’t know—a pattern there’s no reason to think won’t continue indefinitely. Indeed, scientific discoveries routinely raise at least as many questions as they answer. Biologists have described some 80,000 species of roundworm, for example, but suspect there might be a million species. More generally, having discovered organisms in places they didn’t think could support life, biologists now worry that they lack even a rough idea of the total number of species; knowing more shows us we know less than we thought we knew. Furthermore, history teaches, just when some scientists begin to think the explanatory end is in sight, a revolution comes along to open domains of further inquiry. Maxwell gives way to Planck and Einstein, and Hilbert gives way to Go¨del. Jonathan Schaffer usefully catalogues several other examples of this kind.

... which, naturally, misses the point. Yes, we can imagine something infinitely old and fractally complex existing - although there may be some technical reason why it's impossible, I don't know of any - but we can also, counterfactually, imagine it not existing, and declaring it's turtles all the way down does not explain why this counterfactual is not true (in fact, I think it probably is true, because blah blah complexity bah blah Occam's Razor.)

People automatically attach an implicitly understood meaning to the word "things" (or "anything") when it shows up in everyday sentences, and that often works OK. But given the atypical question "Why is there anything?", it's not obvious which meaning they should substitute in, and their brains start flailing. Or so Maitzen speculates.

Except that you don't need to substitute in something specific for "anything", since it's just the set of all things - including all those possible things he lists. This might be clearer if we said "everything" or "something"?

Comment author: satt 12 April 2013 01:19:18AM *  0 points [-]

I think I understand better where you were coming from now. Your complaint (about how solving the A and B vs. A-and-B issue doesn't address the infinite regress issue) seems like it's basically answered by TOD.

Except that you don't need to substitute in something specific for "anything", since it's just the set of all things - including all those possible things he lists. This might be clearer if we said "everything" or "something"?

Talking about "the set of all things" can be quite problematic in itself! But brushing abstract set theory paradoxes aside, I think once you pin down "the set of all things" or "everything" or "something" tightly enough, you have effectively substituted in something specific: you've given me enough information to discern precisely what you're asking about, and rendered the question well-posed. At that point TOD's reply kicks in.

Comment author: MugaSofer 12 April 2013 09:01:10PM -3 points [-]

Talking about "the set of all things" can be quite problematic in itself!

Sorry, I of course meant the set of all actual things.

At that point TOD's reply kicks in.

I guess I'll have to reply to that, then.

Your complaint (about how solving the A and B vs. A-and-B issue doesn't address the infinite regress issue) seems like it's basically answered by TOD.

That link is to a list of all his comments. Could you point me at where he refuted me?

Comment author: satt 12 April 2013 11:43:47PM 0 points [-]

I guess I'll have to reply to that, then.

No problem.

That link is to a list of all his comments. Could you point me at where he refuted me?

Apologies, I meant to link to this specific comment.

Comment author: TheOtherDave 12 April 2013 11:46:25PM 1 point [-]

Note that MugaSofer replied to that comment.

Comment author: satt 13 April 2013 12:07:45AM 0 points [-]

Indeed, and I think their line of argument is a reformulated cosmological argument. I'm still thinking on it, though.

Comment author: MugaSofer 13 April 2013 12:02:35AM -2 points [-]

Ah, thanks. I've already replied to that by now, but we're still haggling over the details. I assume you were referring to this paragraph?

If I try to answer that question generally, I get "Everything that exists, exists as a consequence of the way everything that existed a moment earlier existed, and all of that stuff existed as a consequence of the way everything existed a moment before that, and so on and so on." Which is unsatisfyingly general, as expected, but accurate enough. (Or, to quote Lorraine Hansberry: "Things as they are are as they are and have been and will be that way because they got that way because things were as they were in the first place!")

Comment author: satt 13 April 2013 12:57:38PM 0 points [-]

That paragraph and the one after it, yeah. But as you say, you've already replied to it. I'll probably post a reply to your reply in a bit.

Comment author: lukeprog 15 April 2013 04:46:38PM 0 points [-]

You might be misinterpreting Maitzen's argument. His newer article, Questioning the Question, may be clearer. And, the volume in which it appears may be of interest to you.

Comment author: MugaSofer 19 April 2013 02:27:40PM *  -2 points [-]

Thanks for the link; it's certainly possible I went astray somewhere, it's a pretty long article.

I'll respond more fully when I've read the linked article.

Comment author: satt 11 April 2013 02:16:51AM 0 points [-]

The question certainly feels dissolved. Maitzen's basic argument reads like a reasonable one to me: either the questioner supplies some actual semantic content for the word "anything" in "Why is there anything?", or they don't. If they do, the question presumably has a naturalistic answer (even if science don't know that answer). If they don't, the question's ill-posed, and dissipates in a cloud of underspecification. (Strictly speaking, only the latter counts as dissolving the question, but then it's only the latter form of the question that ties people up in philosophical knots, so I'm counting it.)

Of course, the argument might be really terrible even though it passes my smell test. I'll keep an eye out in Discussion for your counterargument.

Comment author: MugaSofer 11 April 2013 01:23:09PM -2 points [-]

The question certainly feels dissolved.

Huh. Fair enough.

Maitzen's basic argument reads like a reasonable one to me: either the questioner supplies some actual semantic content for the word "anything" in "Why is there anything?", or they don't. If they do, the question presumably has a naturalistic answer (even if science don't know that answer). If they don't, the question's ill-posed, and dissipates in a cloud of underspecification. (Strictly speaking, only the latter counts as dissolving the question, but then it's only the latter form of the question that ties people up in philosophical knots, so I'm counting it.)

Well, here's my counter-dissolution rephrasing: "Why is there everything? Including the things you assume exist when providing a naturalistic explanation of, say, penguins?"

Of course, the argument might be really terrible even though it passes my smell test. I'll keep an eye out in Discussion for your counterargument.

As you know, I actually ended up posting a pared-down version here, but I would have posted a link here anyway.

Comment author: TheOtherDave 11 April 2013 03:12:05PM 1 point [-]

If someone asks me a question too general for me to answer in a non-facile way, like "Why do people do what they do?" or "Why do we make buildings out of the materials we make them out of?" or "Why do we write with the things we write with?", I have two basic strategies I can adopt if I want to answer it.

One option is I can try to answer the question in its general form, which generally results in facile non-answers, like "Because of their various properties and the constraints of their environment," which turns out to answer all three of those questions equally well (or poorly).

Or I can try to replace the general question with a series of representative specific questions, which I then try to answer, in the hopes of either thereby jointly exhausting the original set, or of thereby finding a general strategy for answering specific questions that I'm confident can be applied to members of the original set as I encounter them.

Of course, someone smarter than me might be able to skip the specific-questions stage altogether and construct such a general strategy or itemized explanation solely by analyzing the general question... but if I'm not that smart, I'm not that smart.

If someone responds to the break-it-down-to-specifics strategy by insisting that the specific questions are irrelevant, the way Maitzen describes , they are in effect asking me a question and then refusing to let me try and answer it. I have no problem saying that their question is meaningless, because they are asking it meaninglessly.

That said, I agree with you that the question needn't be meaningless. Someone who doesn't approach it the way Maitzen's foolish interlocutor does could ask it meaningfully.

So, OK. You ask:

"Why is there everything? Including the things you assume exist when providing a naturalistic explanation of, say, penguins?"

If I try to answer that question generally, I get "Everything that exists, exists as a consequence of the way everything that existed a moment earlier existed, and all of that stuff existed as a consequence of the way everything existed a moment before that, and so on and so on." Which is unsatisfyingly general, as expected, but accurate enough. (Or, to quote Lorraine Hansberry: "Things as they are are as they are and have been and will be that way because they got that way because things were as they were in the first place!")

If I want a more satisfying answer, I either ask someone much smarter than me, or I start breaking it down into particulars. Why are there penguins? If my answer to that assumes that A exists, why is (or was) there A? Etc., etc., etc. In the hope of thereby finding a general strategy for answering specific "Why is there X?" questions that I'm confident can be applied to everything that exists.

Would you disagree with any of the above?

Comment author: MugaSofer 12 April 2013 09:12:34PM *  -2 points [-]

Would you disagree with any of the above?

'fraid so.

One option is I can try to answer the question in its general form, which generally results in facile non-answers, like "Because of their various properties and the constraints of their environment," which turns out to answer all three of those questions equally well (or poorly).

I think it would be more helpful to explain why the properties and constraints of their environments led to the actual result, wouldn't it? Rather than describing what kind of explanation how a result might have, in general terms.

For example, buildings are made out of the materials we make them out of because we choose materials that won't collapse, people do what they do because (insert general theory of psychology here) and so on and so forth.

Or I can try to replace the general question with a series of representative specific questions, which I then try to answer, in the hopes of either thereby jointly exhausting the original set, or of thereby finding a general strategy for answering specific questions that I'm confident can be applied to members of the original set as I encounter them.

Of course, someone smarter than me might be able to skip the specific-questions stage altogether and construct such a general strategy or itemized explanation solely by analyzing the general question... but if I'm not that smart, I'm not that smart.

Apparently I'm even less smart, because I have no idea what you're saying here :(

You ask:

"Why is there everything? Including the things you assume exist when providing a naturalistic explanation of, say, penguins?"

If I try to answer that question generally, I get "Everything that exists, exists as a consequence of the way everything that existed a moment earlier existed, and all of that stuff existed as a consequence of the way everything existed a moment before that, and so on and so on." Which is unsatisfyingly general, as expected, but accurate enough. (Or, to quote Lorraine Hansberry: "Things as they are are as they are and have been and will be that way because they got that way because things were as they were in the first place!")

Right, but I'm asking for an explanation of that whole stack of turtles - not how an individual turtle stays up, or even how every turtle stays up, but why the universe is not in the counterfactual no-turtle state.

Maitzen makes a similar argument, which I rebutted in my earlier comment:

The closest he comes to answering the actual question is this...

At this point, defenders of supernaturalism might counter that naturalistic explanations must ultimately bottom out at brute, unexplained posits. But I see no reason naturalistic explanations can’t go forever deeper. One bad reason for concluding that they can’t is the notion that x can’t explain y unless x itself is self explanatory. I don’t see that notion as at all implied by our ordinary concept of explanation, which allows that x can explain y even if something else altogether explains x. Moreover, there are grounds for thinking that naturalistic explanations not only could but must go forever deeper. A common attitude among scientists is that the more they discover, the more there is yet to discover—the more they know, the more they realize they don’t know—a pattern there’s no reason to think won’t continue indefinitely. Indeed, scientific discoveries routinely raise at least as many questions as they answer. Biologists have described some 80,000 species of roundworm, for example, but suspect there might be a million species. More generally, having discovered organisms in places they didn’t think could support life, biologists now worry that they lack even a rough idea of the total number of species; knowing more shows us we know less than we thought we knew. Furthermore, history teaches, just when some scientists begin to think the explanatory end is in sight, a revolution comes along to open domains of further inquiry. Maxwell gives way to Planck and Einstein, and Hilbert gives way to Go¨del. Jonathan Schaffer usefully catalogues several other examples of this kind.

... which, naturally, misses the point. Yes, we can imagine something infinitely old and fractally complex existing - although there may be some technical reason why it's impossible, I don't know of any - but we can also, counterfactually, imagine it not existing, and declaring it's turtles all the way down does not explain why this counterfactual is not true (in fact, I think it probably is true, because blah blah complexity bah blah Occam's Razor.)

f I want a more satisfying answer, I either ask someone much smarter than me, or I start breaking it down into particulars. Why are there penguins? If my answer to that assumes that A exists, why is (or was) there A? Etc., etc., etc. In the hope of thereby finding a general strategy for answering specific "Why is there X?" questions that I'm confident can be applied to everything that exists.

The usual naturalist strategy for this is to describe how other things that exist result in X, but of course this fails when applied to everything that exists.

Comment author: TheOtherDave 12 April 2013 09:49:12PM *  5 points [-]

For example, buildings are made out of the materials we make them out of because we choose materials that won't collapse,

But that simply isn't an adequate explanation for why we build materials out of the materials we make them out of.

This can be easily demonstrated by listing the materials that go into the construction of any building in your town and ranking those materials by how resistant to collapse they are. You will find that lots of the materials involved -- glass, gypsum board, fiberglass insulation, etc, etc, etc. -- are not resistant to collapse; we pick those materials for other reasons.

Of course, someone might complain that I'm being unfair here... of course "because they won't collapse" isn't an explanation of why we choose all the materials we build buildings with, just why we choose sturdy materials like wood or metal or cement to build the framework of a building. Duh.

And, well, yes, this is precisely my point. If I want to usefully answer a question like "Why do we make buildings out of the materials we make them out of?" the most satisfying way to do so is to break it down into more specific questions. "We build frameworks out of these materials because..." "We build windows out of these materials because..." "We build interior walls out of these materials because..." and so forth.

And if someone interrupts us to impatiently say "No, no, no, I don't want to hear about frameworks and windows and interior walls, I asked about buildings!!! I want to know why we build buildings out of the materials we build them out of!!! All parts of a building!!!" all we can really do is encourage them to be less impatient, because we can't usefully answer the question the way they insist on having it answered.

Of course, someone smarter than me might be able to skip the specific-questions stage altogether and construct such a general strategy or itemized explanation solely by analyzing the general question... but if I'm not that smart, I'm not that smart.
Apparently I'm even less smart, because I have no idea what you're saying here :(

Well, for example, suppose Sam asks me "how do I choose what kinds of wine go with what kinds of main course?" I might reply "Well, if I'm serving beef, I serve these wines, and if I'm serving fish, I serve those wines," etc etc etc.

Then Sam, who is much much smarter than me, looks at all of that and goes "Oh! I see. The general rule is to calculate at the ratio between the alcohol content and the tannin content expressed in these units, take that number mod 7, then take the numeric equivalent of the first letter of the main ingredient of the dish in German and take that mod 7, and match wines to dishes based on those two matching numbers."

And I stare incredulously at Sam, perform that calculation for a bunch of main dishes and wines, and ultimately say "Holy crap! You're right!" And Sam says "Of course. Say, why did you choose to answer the question in such a piecemeal way? It seems inefficient."

To which the only answer I can give is "Because I'm not nearly as smart as you are, Sam."

Right, but I'm asking for an explanation of that whole stack of turtles - not how an individual turtle stays up, or even how every turtle stays up, but why the universe is not in the counterfactual no-turtle state.

Right.

And again, my only choices when answering such a general question are:

(1) Be uselessly general ("Things as they are are as they are and have been and will be that way because they got that way because things were as they were in the first place!")
(2) Approach the general question by breaking it down into specifics ("Turtle #1 stays up because of Turtle #2. Turtle #2 stays up because of Turtle #3. Etc."; "We build frameworks out of these materials and windows out of _these materials and etc,")
(3) Be really really smart and come up with a general explanation ("The way you pick a wine is...")

(Of course, another option is the one you adopted for buildings: "we choose materials that won't collapse". Which has the unfortunate defect of being false. The same has historically been true of general theories of human psychology. But, sure, someone really really smart could articulate an accurate general theory here, as per approach #3.)

#3 is obviously preferable, but if I'm not smart enough to do it, I'm not smart enough to do it, in which case #2 is usually my best option.

And if someone impatiently says "No, no, no, I don't want to hear about turtle 1 and turtle 2 and turtle 3, I asked about the stack of turtles!!! I want to know how the stack stays up!!! The whole stack!!!" all I can really do is encourage them to be less impatient, because I can't usefully answer the question the way they insist on having it answered.

Comment author: MugaSofer 12 April 2013 10:18:40PM *  -1 points [-]

And if someone interrupts us to impatiently say "No, no, no, I don't want to hear about frameworks and windows and interior walls, I asked about buildings!!! I want to know why we build buildings out of the materials we build them out of!!! All parts of a building!!!" all we can really do is encourage them to be less impatient, because we can't usefully answer the question the way they insist on having it answered.

Well, I suppose the answer in that case is really to point to our cognitive alogorithms and say "because they say those are the correct materials" ;)

Then Sam, who is much much smarter than me, looks at all of that and goes "Oh! I see. The general rule is to calculate at the ratio between the alcohol content and the tannin content expressed in these units, take that number mod 7, then take the numeric equivalent of the first letter of the main ingredient of the dish in German and take that mod 7, and match wines to dishes based on those two matching numbers."

Well, sure, if you don't know the answer you can't answer; and if you only know a needlessly complex answer, naturally that's the best answer you can give. I'm not sure how that bears on the questions, though.

Right.

And again, my only choices when answering such a general question are:

(1) Be uselessly general ("Things as they are are as they are and have been and will be that way because they got that way because things were as they were in the first place!") (2) Approach the general question by breaking it down into specifics ("Turtle #1 stays up because of Turtle #2. Turtle #2 stays up because of Turtle #3. Etc.") (3) Be really really smart and come up with a general explanation ("The way you pick a wine is...")

#3 is obviously preferable, but if I'm not smart enough to do it, I'm not smart enough to do it, in which case #2 is usually my best option.

And if someone impatiently says "No, no, no, I don't want to hear about turtle 1 and turtle 2 and turtle 3, I asked about the stack of turtles!!! I want to know how the stack stays up!!! The whole stack!!!" all I can really do is encourage them to be less impatient, because I can't usefully answer the question the way they insist on having it answered.

But we have all three "types" of answer as far as I can see, and they're all answering a different question - talking about internal structure of the pile rather than how it got there.

(1) "Turtles are held up by other turtles below them."

(2) "The top turtle is supported by the second-from-the-top turtle; the second-from-the-top turtle is supported by the third-from-the-top turtle; the third-from-the-top turtle is supported by the fourth-from-the-top turtle ..." and so on ad infinitum.

(3) "It's an infinite stack of turtles, each held up by the one below it."

What we really want is (4) "We live in a thought experiment and infinite turtles is a common metaphor for recursive buck-passing."

Comment author: TheOtherDave 12 April 2013 11:14:38PM *  0 points [-]

Well, I suppose the answer in that case is really to point to our cognitive alogorithms and say "because they say those are the correct materials" ;)

Sure. Which is an equally good (or poor) answer to "Why do we write on the materials we write on?"

What we really want is (4) "We live in a thought experiment and infinite turtles is a common metaphor for recursive buck-passing."

(shrug) If I were actually looking at the stack of turtles, and Sam gave me answer #4 I would stare incredulously at Sam. If he then gave me grounds for believing #4 and I confirmed it, I would ultimately say "Holy crap! You're right!" And if Sam said "Of course. Say, why did you choose to answer the question in such a piecemeal way as #2? It seems inefficient." the only answer I could give would be "Because I'm not nearly as smart as you are, Sam."

Which is to say, your #4 is part of my #3.

Your #3 is also part of my #3, in that if I were in that world staring at the stack of turtles, I would not be smart enough to infer that it's an infinite stack of turtles... on what grounds would I conclude that? But Sam's sibling Pat, who is not quite as smart as Sam, might somehow just know the stack was infinite rather than merely longer than I was able to see.

None of which changes the fact that if I'm not as smart as Sam or Pat, the best I can do is #2. And if someone interrupts #2 by saying "no, no, no, I don't care about the turtles, I'm asking about the stack!", they are asking a question and refusing to listen to the best answer I'm capable of offering. They would do better to ask someone smarter, like Sam or Pat. And if nobody smart enough to give answer #3 is available, they do best to either listen to my answer, or give up on the question.

Comment author: MugaSofer 12 April 2013 11:28:04PM -1 points [-]

Sure. Which is an equally good (or poor) answer to "Why do we write on the materials we write on?"

Yup. To be fair, it's also pretty much useless unless I can actually explain how said cognitive alogarithm works.

Your #3 is also part of my #3, in that if I were in that world staring at the stack of turtles, I would not be smart enough to infer that it's an infinite stack of turtles... on what grounds would I conclude that? But Sam's sibling Pat, who is not quite as smart as Sam, might somehow just know the stack was infinite rather than merely longer than I was able to see.

To be fair, if there's a literal infinitely-high stack of turtles, I'm not even sure where you're standing, let alone how you can observe it's length. Maybe Sam's just familiar with the anecdote?

Which is to say, your #4 is part of my #3.

I still think #4 is distinct from #3, because it explains the presence of the stack as well as it's internal structure - which is what was being asked, originally. No amount of #2 will ever replace #4, because they answer different questions. Still, I suppose it sort of implies #3, so #3 is a subelement of #4, at that.

Anyway, we seem to have reached agreement that there is something I'm looking for that #2 does not provide, which will likely require someone smarter than either of us to solve. So I guess the Question stands as, well, an open question.

Comment author: [deleted] 13 April 2013 01:39:26AM 0 points [-]

"Oh! I see. The general rule is to calculate at the ratio between the alcohol content and the tannin content expressed in these units, take that number mod 7, then take the numeric equivalent of the first letter of the main ingredient of the dish in German and take that mod 7, and match wines to dishes based on those two matching numbers."

http://xkcd.com/1155/ :-)

Comment author: TheOtherDave 13 April 2013 01:42:34AM 1 point [-]

I spent an embarrassingly long time after that xkcd trying to devise "compact" directions to my house from various places.

Comment author: satt 12 April 2013 01:16:08AM 0 points [-]

TheOtherDave's answer seems close enough to what I'd have said here that I'll just point at what he wrote!

Comment author: MugaSofer 12 April 2013 09:15:05PM -2 points [-]

Then I guess I'll have to point at my reply to him ;)