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Disputing Definitions

48 Post author: Eliezer_Yudkowsky 12 February 2008 12:15AM

Followup toHow An Algorithm Feels From Inside

I have watched more than one conversation—even conversations supposedly about cognitive science—go the route of disputing over definitions.  Taking the classic example to be "If a tree falls in a forest, and no one hears it, does it make a sound?", the dispute often follows a course like this:

If a tree falls in the forest, and no one hears it, does it make a sound?

Albert:  "Of course it does.  What kind of silly question is that?  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?"

In this example, Barry is arguing with Albert because of a genuinely different intuition about what constitutes a sound.  But there's more than one way the Standard Dispute can start.  Barry could have a motive for rejecting Albert's conclusion.  Or Barry could be a skeptic who, upon hearing Albert's argument, reflexively scrutinized it for possible logical flaws; and then, on finding a counterargument, automatically accepted it without applying a second layer of search for a counter-counterargument; thereby arguing himself into the opposite position.  This doesn't require that Barry's prior intuition—the intuition Barry would have had, if we'd asked him before Albert spoke—have differed from Albert's.

Well, if Barry didn't have a differing intuition before, he sure has one now.

Albert:  "What do you mean, there's no sound?  The tree's roots snap, the trunk comes crashing down and hits the ground. This generates vibrations that travel through the ground and the air. That's where the energy of the fall goes, into heat and sound.  Are you saying that if people leave the forest, the tree violates conservation of energy?"

Barry:  "But no one hears anything.  If there are no humans in the forest, or, for the sake of argument, anything else with a complex nervous system capable of 'hearing', then no one hears a sound."

Albert and Barry recruit arguments that feel like support for their respective positions, describing in more detail the thoughts that caused their "sound"-detectors to fire or stay silent.  But so far the conversation has still focused on the forest, rather than definitions.  And note that they don't actually disagree on anything that happens in the forest.

Albert:  "This is the dumbest argument I've ever been in.  You're a niddlewicking fallumphing pickleplumber."

Barry:  "Yeah?  Well, you look like your face caught on fire and someone put it out with a shovel."

Insult has been proffered and accepted; now neither party can back down without losing face.  Technically, this isn't part of the argument, as rationalists account such things; but it's such an important part of the Standard Dispute that I'm including it anyway.

Albert:  "The tree produces acoustic vibrations.  By definition, that is a sound."

Barry:  "No one hears anything.  By definition, that is not a sound."

The argument starts shifting to focus on definitions.  Whenever you feel tempted to say the words "by definition" in an argument that is not literally about pure mathematics, remember that anything which is true "by definition" is true in all possible worlds, and so observing its truth can never constrain which world you live in.

Albert: "My computer's microphone can record a sound without anyone being around to hear it, store it as a file, and it's called a 'sound file'. And what's stored in the file is the pattern of vibrations in air, not the pattern of neural firings in anyone's brain.  'Sound' means a pattern of vibrations."

Albert deploys an argument that feels like support for the word "sound" having a particular meaning. This is a different kind of question from whether acoustic vibrations take place in a forest—but the shift usually passes unnoticed.

Barry:  "Oh, yeah?  Let's just see if the dictionary agrees with you."

There's a lot of things I could be curious about in the falling-tree scenario. I could go into the forest and look at trees, or learn how to derive the wave equation for changes of air pressure, or examine the anatomy of an ear, or study the neuroanatomy of the auditory cortex.  Instead of doing any of these things, I am to consult a dictionary, apparently.  Why?  Are the editors of the dictionary expert botanists, expert physicists, expert neuroscientists?  Looking in an encyclopedia might make sense, but why a dictionary?

Albert:  "Hah!  Definition 2c in Merriam-Webster:  'Sound:  Mechanical radiant energy that is transmitted by longitudinal pressure waves in a material medium (as air).'"

Barry:  "Hah!  Definition 2b in Merriam-Webster: 'Sound:  The sensation perceived by the sense of hearing.'"

Albert and Barry, chorus:  "Consarned dictionary!  This doesn't help at all!"

Dictionary editors are historians of usage, not legislators of language. Dictionary editors find words in current usage, then write down the words next to (a small part of) what people seem to mean by them.  If there's more than one usage, the editors write down more than one definition.

Albert:  "Look, suppose that I left a microphone in the forest and recorded the pattern of the acoustic vibrations of the tree falling.  If I played that back to someone, they'd call it a 'sound'!  That's the common usage!  Don't go around making up your own wacky definitions!"

Barry:  "One, I can define a word any way I like so long as I use it consistently.  Two, the meaning I gave was in the dictionary.  Three, who gave you the right to decide what is or isn't common usage?"

There's quite a lot of rationality errors in the Standard Dispute.  Some of them I've already covered, and some of them I've yet to cover; likewise the remedies.

But for now, I would just like to point out—in a mournful sort of way—that Albert and Barry seem to agree on virtually every question of what is actually going on inside the forest, and yet it doesn't seem to generate any feeling of agreement.

Arguing about definitions is a garden path; people wouldn't go down the path if they saw at the outset where it led.  If you asked Albert (Barry) why he's still arguing, he'd probably say something like: "Barry (Albert) is trying to sneak in his own definition of 'sound', the scurvey scoundrel, to support his ridiculous point; and I'm here to defend the standard definition."

But suppose I went back in time to before the start of the argument:

(Eliezer appears from nowhere in a peculiar conveyance that looks just like the time machine from the original 'The Time Machine' movie.)

Barry:  "Gosh!  A time traveler!"

Eliezer:  "I am a traveler from the future!  Hear my words!  I have traveled far into the past—around fifteen minutes—"

Albert:  "Fifteen minutes?"

Eliezer:  "—to bring you this message!"

(There is a pause of mixed confusion and expectancy.)

Eliezer:  "Do you think that 'sound' should be defined to require both acoustic vibrations (pressure waves in air) and also auditory experiences (someone to listen to the sound), or should 'sound' be defined as meaning only acoustic vibrations, or only auditory experience?"

Barry:  "You went back in time to ask us that?"

Eliezer:  "My purposes are my own!  Answer!"

Albert:  "Well... I don't see why it would matter.  You can pick any definition so long as you use it consistently."

Barry:  "Flip a coin.  Er, flip a coin twice."

Eliezer:  "Personally I'd say that if the issue arises, both sides should switch to describing the event in unambiguous lower-level constituents, like acoustic vibrations or auditory experiences.  Or each side could designate a new word, like 'alberzle' and 'bargulum', to use for what they respectively used to call 'sound'; and then both sides could use the new words consistently.  That way neither side has to back down or lose face, but they can still communicate.  And of course you should try to keep track, at all times, of some testable proposition that the argument is actually about.  Does that sound right to you?"

Albert:  "I guess..."

Barry:  "Why are we talking about this?"

Eliezer:  "To preserve your friendship against a contingency you will, now, never know.  For the future has already changed!"

(Eliezer and the machine vanish in a puff of smoke.)

Barry:  "Where were we again?"

Albert:  "Oh, yeah:  If a tree falls in the forest, and no one hears it, does it make a sound?"

Barry:  "It makes an alberzle but not a bargulum.  What's the next question?"

This remedy doesn't destroy every dispute over categorizations.  But it destroys a substantial fraction.


Part of the sequence A Human's Guide to Words

Next post: "Feel the Meaning"

Previous post: "How An Algorithm Feels From Inside"

Comments (42)

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Comment author: brent 12 February 2008 01:23:13AM 4 points [-]


"Abortion is murder because it's evil to kill a poor defenseless baby."

I am so sick of arguing with people who's definition of the issue constitutes 99% of their argument, and who aren't willing to acknowledge that their definition needs consensus before their point is even meaningful let alone valid.

Like you say - most of the time an argument is completely settled once/if everyone agrees one the terms being used.

Comment author: DanielLC 08 July 2011 05:08:21AM 7 points [-]

I would say that if it is evil to kill a poor defenseless unborn baby, then murder should probably be defined to include abortion. The problem is when people say "It's evil to kill a poor defenseless baby because abortion is murder."

Comment author: po8crg 24 March 2012 01:56:31PM 14 points [-]

The problem is that it begs the question - using "unborn baby" defines it into the same ethical category as a born baby, different only in location. When you dig down enough, usually that's the point at dispute - is the thing growing in a womb entitled to rights in the manner of a (born) baby, or is it not so entitled.

There are some property-rights thinkers who do hold that it is the location that matters, i.e. the baby is trespassing on the mother's womb, and she's entitled to use deadly force to remove it, but that's not the usual argument.

Comment author: TheOtherDave 24 March 2012 02:25:07PM 4 points [-]

Upvoted entirely for using "begs the question" correctly.

But, to respond to the comment -- there is also the position that the extent to which we should act to prevent my life from ending depends significantly on the costs of sustaining my life and who bears those costs, and since the cost equation typically changes significantly for an 35-week-old fertilized egg and a 45-week-old fertilized egg, it's reasonable to reach different conclusions about what acts are justified in those two cases.

And one can adopt that position whether the 35-week-old fertilized egg is called an "unborn baby," a "fetus", a "uterine growth", a "upcoming blessed event", a "little leech," or whatever. (All of which are terms I've heard pregnant women use to describe their fertilized egg at various stages of gestation.

The same principle suggests that we don't treat a 45-week-old fertilized egg the same as a thousand-week-old fertilized egg.

But I agree with your implicit point that many thinkers on the subject, as well as many speakers on the subject who may or may not be doing much thinking at the time they speak, respond primarily to the connotations of those terms.

Comment author: snewmark 23 December 2016 05:45:34PM 0 points [-]

Upvoted entirely for using "begs the question" correctly.

Ha, did you really praise the proper use of an ancient expression in the midst of a definition debate?

(Sorry about posting this 4 years later, I just had to get that out.)

Comment author: Doug_S. 12 February 2008 03:35:56AM 18 points [-]

Suppose I order a blegg from a mail-order catalog. As it turns out, the object I received is blue and is furry, but it is cube-shaped, does not glow in the dark, and contains neither vanadium nor palladium. I am disappointed and attempt to return the object, claiming that it is not, in fact, a blegg. The seller refuses to give me a refund or exchange the object for another. Annoyed, I decide to take the seller to court.

Would I win the lawsuit?

(This is why arguments over definitions have real-world consequences.)

Comment author: halcyon 07 April 2012 06:34:55AM 10 points [-]

Sorry, just... no. I realize it's been four years, but I had to create an account just to register my disapproval. The question remains, what did you want from the blegg? Vanadium or Palladium? Its glow-in-the-dark property? A gestalt effect arising from the combination of certain salient features? What does any of this have to do with consensus-based definitions?

Comment author: ete 26 April 2014 10:26:28PM 4 points [-]

I find it quite interesting that despite the two above posts having very strongly contradictory points they both a large number of upvotes are are both at 100% positive (15 and 8 at the time of writing). I wonder whether the community's opinion has shifted over the years, or whether lw voters just think both points are well put and are very reluctant to downvote things based on disagreeing with a point.


Comment author: samcoy 21 November 2015 12:39:54PM 2 points [-]

I think it's very much a case of well-put arguments.

I can certainly see how pragmatically, definitions can clearly matter. Heck, we have laws that are very picky about them, because we need a very specific set of rules so that crinimals/those falsely accused are clearly in one category or another, and to make the law above debate.

At the same time, asking whether something is against the law, whether it fits into the category of "murder" for example, is simly arguing whether it is case considered worthy, by those who wrote the law, of punishment.

Both arguments are very well explained by the two comments.

Comment author: PSissy 23 December 2016 02:51:50AM 0 points [-]

I hope you'll forgive me for creating an account two years later after you created one four years later.

If the catalog offered a "blegg" for sale, with no further information, then the definition of "blegg" itself would very much be an important issue in the ensuing lawsuit. If "blegg" generally means something that contains vanadium and is egg-shaped, but the one sold and delivered is neither, then the actual definition would be important in determining whether the buyer was scammed. The question is not "what did you want from the blegg", it's "what is a blegg, and is that what was sent by the company".

If I order a "bicycle" from a catalog and the product comes with one triangular wheel and no seat, then it very much matters that the commonly used definition of "bicycle" is "a conveyance with two round wheel and a place to sit", and that would be a valid basis for suing the fraudulent company. It doesn't matter "what I want from" the bicycle. I might want a convenient mode of human-powered transportation, or I might want a frame of welded metal. But the fact is the company did not deliver what was advertised.

Comment author: Caledonian2 12 February 2008 03:50:02AM 4 points [-]

Using different words to describe the same thing can produce a dispute where there is none, yes. But people also tend to use the same word to refer to totally different things, sometimes as a means of artificially avoiding conflict. Equivocation can be a powerful teaching tool and rhetorical device, but more often it serves as a way to lie plausibly, both to others and to oneself.

Meaningful communication is possible only when people are discussing the same ideas, and ensuring that everyone involved maps the same concepts onto the same words is necessary to bring that about.

Without concern for the proper use of words, language becomes useless.

Comment author: Eliezer_Yudkowsky 12 February 2008 06:30:36AM 15 points [-]

Would I win the lawsuit? This is why arguments over definitions have real-world consequences.

Technically, that's not so much an argument over a definition, as an argument over cognitive history: The seller's expectation of your expectation of what you would get in the mail; and the application of the law to those expectations.

I did mention that the remedy is not universal. If people have already taken actions, based on their previous communications, then the consequences are already set in motion - you can't go back in time and use the remedy.

Abortion is murder because it's evil to kill a poor defenseless baby.

Another time you can't just generate new words is when a category boundary like "person" or "human" or "baby" makes a direct appearance in your utility function.

Comment author: Ron_Hardin 12 February 2008 10:46:51AM 2 points [-]

People can agree about all the facts but argue about what the word means, which question is an empirical one. People don't know what their criteria are for something being a sound, and can only offer aspects that seem to count for it or against it. You have to try the argument and see if you can see it that way.

Perhaps in the end you can bring out what a sound is.

See Cavell on chairs, op cit. and derivatively Wittgenstein.

The people arguing are not making a mistake; the cognitive scientist is.

Comment author: Ben_Jones 12 February 2008 02:10:02PM 5 points [-]

Without concern for the proper use of words, language becomes useless.

A valid point, as long as you're careful that language work for you and not vice versa. The moment you find the expression of your concept being stifled by grammar or vocabulary or tradition, find another way. Invent a new word; define it using comparison, differentiation, pictures, hand signals, noises. Language should bend to incorporate reality; otherwise the tail is wagging the dog. Language has enormous power to make our world, hence the sort of typical argument Eliezer discusses. But we should never lose sight of the fact that it is our tool, and any rules should be enabling rather than restrictive - clarity of communication is the goal.

Comment author: thodirycgoyust 15 August 2011 09:08:23AM 2 points [-]

This is why I advocate the adoption of logical language(s). Those in the tradition of Loglan, for example, share vocabularies and grammars designed such that context can be made irrelevant given appropriate sentence construction (some other ambiguity reducing features as well), and tools to easily make temporary (ie: until end of conversation) extensions to their vocabularies where the base is insufficient while generally behaving like natural language.

Comment author: [deleted] 15 August 2011 09:23:41AM 1 point [-]

And yet as far as I'm aware, it's impossible to infer the place structure or semantics of a predicate. This is a massive problem in Lojban (who knows or cares if it's in Loglan -- the language is kept as a trade secret, after all).

E.g., I could print pamphlets defining 'klama' as standard 'se klama' and it would take a while for anyone to notice the difference.

Comment author: lessdazed 15 August 2011 10:16:48AM *  1 point [-]

Let's discuss partial solutions.

Suppose you and random other English speakers were abducted by aliens and accelerating out of the solar system on their ship. You strongly suspect you will never be able to go back, and get to work on building a new society.

You are the smartest person in the group and convince everyone that language is important. They agree to reform the language, but aren't capable of constructing or learning a new one, and aren't interested in teaching their children one. What simple reforms might be a good idea?

I can suggest some:

It will no longer be correct to say that something is (a color or similar property). One must say it "seems" a color, as well as to whom. Not "Snow is white", rather, "Snow seems white to me".

"Rationalize" will be replaced by a word with a different root.

Comment author: PetjaY 03 May 2015 09:51:32AM 0 points [-]

"It will no longer be correct to say that something is (a color or similar property). One must say it "seems" a color, as well as to whom. Not "Snow is white", rather, "Snow seems white to me"."

I´d say this is not needed, when people say "Snow is white" we know that it really means "Snow seems white to me", so saying it as "Snow seems white to me" adds length without adding information.

My first fixes to english would be to unite spoken and written english with same letters always meaning same sounds, and getting rid of adding "the" to places where it does not add information (where sentence would mean same even without "the").

Comment author: Kindly 03 May 2015 04:49:15PM 1 point [-]

I´d say this is not needed, when people say "Snow is white" we know that it really means "Snow seems white to me", so saying it as "Snow seems white to me" adds length without adding information.

Ah, but imagine we're all-powerful reformists that can change absolutely anything! In that case, we can add a really simple verb that means "seems-to-me" (let's say "smee" for short) and then ask people to say "Snow smee white".

Of course, this doesn't make sense unless we provide alternatives. For instance, "er" for "I have heard that", as in "Snow er white, though I haven't seen it myself" or "The dress er gold, but smee blue."

Comment author: TheOtherDave 03 May 2015 08:55:41PM 1 point [-]
Comment author: Jiro 03 May 2015 09:46:24PM 1 point [-]

It isn't possible for someone to consistently assert "X is true, but X doesn't seem true to me". And it isn't possible for someone to consistently assert "X seems true to me, but X is false". [1] So even though "seems to me" and "is" are not logically the same thing, no human being can separate them and we have no need for a special word to make it convenient to separate them.

[1] Of course they can assert that if we use a secondary meaning for 'seems' such as "superficially appears to be", but that's not the meaning of 'seems' in question here.

Comment author: ChristianKl 03 May 2015 11:13:19PM 0 points [-]

A quarter of the worlds languages mark evidentiality at a grammer level. Indo-European languages like English don't do this but other languages do.

Comment author: Caledonian2 13 February 2008 12:04:25AM 0 points [-]

The moment you find the expression of your concept being stifled by grammar or vocabulary or tradition, find another way.

No. First, you must check to confirm that your concept is potentially expressible. Some 'concepts' are self-contradictory and cannot be further talked about for that reason. There is nothing more than can be said about "the encounter of an immovable object with an irresistible force" beyond that it is invalid. Trying to find another way either leads to the eventual recognition that nothing else can be expressed, or (more likely) ends in our using language as a screen to prevent the incompatibility from entering our awareness.

Comment author: o 13 February 2008 12:30:49AM 0 points [-]


I would just like to tell you I very much enjoyed this post. I love debate but find they often go awry in ways such as above. More like this. Or, can you post links to others like this from before?

Comment author: taryneast 10 December 2010 10:08:02AM *  1 point [-]

Just to say - I recognise this comment was left several years ago... and probably before the sequence page was written, but for those who follow after, you can follow along here:


Comment author: Ben_Jones 13 February 2008 09:20:18AM 1 point [-]

...the encounter of an immovable object with an irresistible force...

Reread me Caledonian - this is a problem with logic; not a problem with language. You had no problem expressing it verbally, so it's not the kind of thing I'm talking about.

Comment author: tommyjohn 18 November 2011 09:58:30PM 0 points [-]

Is this a problem with logic or a linguistic expression of a paradox?

Comment author: gutzperson 13 February 2008 11:10:18AM 1 point [-]

Language (systems) can never be precise, only as precise as possible. At its best it is about the least misunderstanding; misunderstanding being inherent. Approximation comes into my mind. It is about agreements (also the breaking of these) and closed circuit situations. At its best it is about more or less successful feedback loops.

Comment author: Caledonian2 13 February 2008 02:22:57PM 0 points [-]

You had no problem expressing it verbally

1) There are still people who insist that if we can talk about it, it must be real.

2) Logic is just language used very, very precisely. Reinventing language in an attempt to make one's point may be useful, even necessary, but it tends to be a means to disguise contradictions in logic by hiding them within unfamiliar terms and usages.

But we should never lose sight of the fact that it is our tool, and any rules should be enabling rather than restrictive

Language is enabling only because it is restrictive. Remove the restrictions and you lose the meaning. Logic is a tool that we cannot command, only obey.

Comment author: Ben_Jones 13 February 2008 03:34:36PM 0 points [-]

That's easy for you to say.

Comment author: Richard_Hollerith2 13 February 2008 05:34:39PM 3 points [-]

Eliezer said that another time you can't just generate new words is when a category boundary like "person" or "human" or "baby" makes a direct appearance in your utility function.

Which gently suggests that when defining a utility function that might remain in force for billions of years, one should prefer functions that do not have category boundaries.

I would be happy to exhibit functions of that sort that have the property that even after an explosion of engineered intelligence, the humans probably retain enough expected utility to keep them flourishing and protected from exploitation although they probably do not retain enough expected utility to cause the majority of the future light cone's space, time, matter, free energy and other resources to be devoted to them.

Comment author: Fyrius 25 March 2010 08:04:45AM 2 points [-]

"Pickleplumber" is now my favourite swearword.

Comment author: drewski 16 May 2010 03:36:03AM *  1 point [-]

If only everybody would search for more clarity in communication.

I think in the words I speak in to create logic in my mind. So not only does using a words with fuzzy definitions, exaggerating or twisting sentences affect my ability to communicate clearly, it affects my ability to think clearly.

Barry and Albert could have avoided argument if they saw being proven wrong as something that should be celebrated because their mind has been raised to a new level of understanding. Rather than a defeat. Then their focus would have been on understanding each other rather than defending their position.

Comment author: DanielLC 08 July 2011 05:05:42AM 1 point [-]

So is this what that dispute was? I always thought it was more of a solipsism thing, but that doesn't make much sense because then the question should be "Does the tree actually fall, or is it up when you first see it, down later on, and nonexistent in between?"

Comment author: olalonde 25 April 2012 04:50:58PM *  3 points [-]

One way to get around the argument on semantics would be to replace "sound" by its definition.


Albert: "Hah! Definition 2c in Merriam-Webster: 'Sound: Mechanical radiant energy that is transmitted by longitudinal pressure waves in a material medium (as air).'"

Barry: "Hah! Definition 2b in Merriam-Webster: 'Sound: The sensation perceived by the sense of hearing.'"

Albert: "Since we cannot agree on the definition of sound and a third party might be confused if he listened to us, can you reformulate your question, replacing the word sound by its definition."

Barry: "OK. If a tree falls in the forest, and no one hears it, does it cause anyone to have the sensation perceived by the sense of hearing?"

Albert: "No."

Comment author: ToddStark 17 December 2012 05:51:29AM 1 point [-]

"... replace "sound" by its definition."

Yes, that's exactly what happens in a reasonable dialog, at the point where people realze they are thinking of the same thing in different ways. The trick is recognizing what that difference is so you can expand on it and compare. It happens fairly quickly and easily in most cases when both people are mostly focused on inquiry. If they are arguing their own position, they are unlikely to be looking for the difference, they are probably looking for ways to deconstruct the other person's terms and find fallacies in their logic or problems with their evidence. They will resort to arguing for their own definitions.

When you end up in a game of duelling definitions, one valuable strategy is to ask the purpose of the definition. It serves a rhetorical purpose to use one definition vs. another in an explanation or question. If emphasizes different things. This is an important pragmatist principle coming from the slant that words are tools for thinking.


Q: Why bring the perceiver into the picture when talking about sound? What purpose does that serve?

A: The reason I define sound as something perceived is to distinguish the dark, silent physical world of wavelengths and vibrations and strings from the one constructed in human experience to operate on the world. I care about the human experience, not what is going on with atoms.

This exposes a great deal of the relevant conceptual background and current focus of each person so you know what they are arguing about and might be able to either collaborate more effectively, learn something from each other, or else identify that you aren't talking about the same thing at all. Rather than just fighting over which definition is better.

Comment author: chaosmosis 03 May 2012 04:11:43AM 2 points [-]

Well-done definition debates are still possible. But they're about the comparative usefulness of conceptualizing X in a certain way Y as opposed to a different way Z, and vice versa. Well done definitional debates can actually be really interesting though, although they don't crop up too much.

Comment author: [deleted] 13 June 2014 10:50:28AM -2 points [-]

Here's an alternative guide to words:

'' Component display theory M. D. Merrill’s Component Display Theory (CDT) is a cognitive matrix that focuses on the interaction between two dimensions: the level of performance expected from the learner and the types of content of the material to be learned. Merrill classifies a learner’s level of performance as: find, use, remember, and material content as: facts, concepts, procedures, and principles. The theory also calls upon four primary presentation forms and several other secondary presentation forms. The primary presentation forms include: rules, examples, recall, and practice. Secondary presentation forms include: prerequisites, objectives, helps, mnemonics, and feedback. A complete lesson includes a combination of primary and secondary presentation forms, but the most effective combination varies from learner to learner and also from concept to concept. Another significant aspect of the CDT model is that it allows for the learner to control the instructional strategies used and adapt them to meet his or her own learning style and preference. A major goal of this model was to reduce three common errors in concept formation: over-generalization, under-generalization and misconception.''

Comment author: [deleted] 28 March 2015 07:09:00PM 1 point [-]

On the one hand I understand many reasons for words. What words are for. You notice something, someone names it for you, you look up the word, you connect it to a definition, and voila, you have gained knowledge. Because you know at least some of it´s properties and perhaps also common purposes, from the defintion.

On the other hand I understand why arguing over defintions obviously is pointless in above mentioned example and the examples from How an Algorithm Feels From Inside.

Here is my problem. I have never bothered arguing definitions for the sake of it. I use them in a meaningful context. Or so I THINK. Could someone give me some more every day examples of where this may not be the case? If I can connect this to something more concrete (something I can relate to), I might be able to really understand the issue.

Comment author: TheOtherDave 29 March 2015 12:25:49AM 1 point [-]

Let's try it the other way: what are some examples of cases where you find yourself using definitions in what you think, but are not sure, is a meaningful context?

Comment author: MarsColony_in10years 05 November 2015 05:15:53PM 0 points [-]

So, all arguments which do not make different predictions are extensionally equal, but are not intensional. From the Wikipedia page:

Consider the two functions f and g mapping from and to natural numbers, defined as follows:

  • To find f(n), first add 5 to n, then multiply by 2.

  • To find g(n), first multiply n by 2, then add 10.

These functions are extensionally equal; given the same input, both functions always produce the same value. But the definitions of the functions are not equal, and in that intensional sense the functions are not the same.

Comment author: [deleted] 01 January 2016 07:12:43AM 0 points [-]