Arguing "By Definition"

Good post. So how do you usually respond to invalid "by definition" arguments? Is there any quick(but honest) way to disarm the the argument or is there too much inferential distance to cover?

It seems that there simply are no definitions - especially those based in sensory primitive concepts.[4]
It seems as though there can be cases where our ignorance or error about a class means that we either don’t know the definition of a concept, or have incorrect notions about what a definition of a particular concept might entail.[4]
Quine's argument against analyticity in Two Dogmas of Empiricism also holds as an argument against definitions.[4]
Some concepts have fuzzy membership. There are items for which it is vague whether or not they fall into (or out of) a particular referent class. This is not possible in the classical theory as everything has equal and full membership.[4]
Rosch found typicality effects which cannot be explained by the classical theory of concepts, these sparked the prototype theory.[4] See below.
Psychological experiments show no evidence for our using concepts as strict definitions.[4]

Can you recall how Feynman used "by definition" correctly?

Geddis:

No, but botogol used it correctly here.

When someone says X is Y "by definition," the fundamental mistake they are making is thinking that the definition decides what belongs in a particular concept. No, the similarity between the objects relative to those around them (as recognized by our brain) is what decides.

The definition is just a reminder, a mental tool to help us keep the sets separate and organized within the context of our knowledge. Due to this, the definition can change as our knowledge grows, and we have the need to make finer separations. But the set doesn't change.

(Definitions also serve a role in human communication.)

Eliezer, I have been following your blog since a while now. I greatly appreciate your posts and am astounded at how you have the time and enthusiasm to keep writing such quality stuff so regularly.

I remember that I have gone through times where I found myself strongly convinced by person X's arguments but finally going to "person X had been wrong in so-and-so regard etc". For instance, you could put X as Ayn Rand.

I would have probably gone to deify you too, if not for the fact that you are trying your best to keep your readers from turning into blind followers and that you have an open comment system where interesting discussions follow your post, many of them opposing your arguments, and thus, allowing the reader to have a more rational understanding.

However, I have to constantly perform introspection to see if I have avoided the Happy Death Spiral.

Cheers, Sudeep

Thanks, Sudeep! I've always felt that it's okay to be imperfect, but not so imperfect that even other people notice.

But if you never try to do anything that feels impossible, you'll never grow - so keep trying to find my flaws! Don't give up just because it seems futile!

You wouldn't feel the need to say, "Hinduism, by definition, is a religion!" because, well, of course Hinduism is a religion. It's not just a religion "by definition", it's, like, an actual religion.

I really, really love this blog.

I've noticed that this recent series from Eliezer over the last two weeks has slowed things down. And while it's not the same breakneck pace of explanation, I think it really suits the subject matter to have it all laid out like that. That inferential gap can never be overestimated!

Godel, Escher, Bach just arrived on my desk at work - a second-hand copy from an eBay bookshop in the States. Looks terrifying!

Eliezer, I must admit I really don't get your problem with definitions. Or, more precisely, I can't get myself to share it. It seems to me you attack definitions mainly because they enable malignant (and/or confused) arguers to do a bait-and-switch. Without defining what is being talked about, there is no obvious switching anymore, so that seems to be your solution. But to me that is like leaving an important variable unbound, which makes the whole argument underdefined and therefore practically worthless. IMHO it is precisely because two people have a common conception of what they are talking about that they can communicate at all. Definitions help to make important key concepts sharply and clearly - uhm - defined. When someone uses a "definition" which makes little or no practical sense, just go and call 'em on that! When someone does a bait-and-switch, call 'em! But when people argue without defining what they're arguing about, what you gonna do? Apart from that, both "I can define that thing any way I want." and "It's in the dictionary." have a smell of straw-men. If someone goes "I can define that thing any way I want." then just insist on the exact same definition when they draw their conclusions - be a djinn! Don't give in to what they wish (or think) they had defined, but to what they did, and tread rickety would-be conclusions to shambles! If someone goes "It's in the dictionary.", ah well... find someone else to talk to... =)

I'll second Frank Hirsch's comment and add one point. I don't get this obsession with 'dictionary definitions' either. An etymological dictionary is endlessly fascinating precisely because it shows you the evolution of thought processes, concepts, and word usages, in action. Very much the opposite of the sort of table thumping that dictionaries are here supposed to give rise to. Eliezer's examples seem to be taken from a pretty toxic discussion environment

tcpkac, you mean like a blog comment thread?

I understand your point, but I do think there's a serious, deep-rooted bias here, which boils down to trying to fit reality into 'common usage' and mental categories. People slip up with this all the time, hence it's worthy of analysis and discussion.

Plus, if Eliezer was content to just disdainfully ignore the Ignorant Masses and talk to someone else, I don't imagine he'd be writing a blog entry here every day.

Frank, tcpkac:

What do you think of, say, philosophers' endless arguments of what the word "knowledge" really means? This seems to me one example where many philosophers don't seem to understand that the word doesn't have any intrinsic meaning apart from how people define it.

If Bob sees a projection of an oasis and thinks there's an oasis, but there's a real oasis behind the projection that creates a projection of itself as a Darwinian self-defense mechanism, does Bob "know" there's an oasis? Presumably Eliezer would ask, "for what purpose do we want to answer the question?" However, many philosophers would prefer to unconstructively argue what semantics are "correct". So my personal experience is that I don't think Eliezer's attacking a straw man here.

A similar example in grammar: many people think usage of "ain't" is somehow objectively wrong, rather than being just an uncommon and frowned-upon dialect.

This seems to me one example where many philosophers don't seem to understand that the word doesn't have any intrinsic meaning apart from how people define it.

I suspect it's more that they don't care.

Eliezer objects to Aristotelian syllogisms, saying that (for example) concluding that a human is mortal is silly because mortality is part of the definition of human.

This is a mistake. Mortality isn't part of the definition; it doesn't need to be. The point is that mortality has been observed to always apply to entities that possess the necessary defining qualities of humanity. This is a separate and distinct observation.

We don't need to see Socrates die to conclude that he was human. "Socrates is human" and "All humans are mortal" are very different and independent inferences. The data necessary for us to accept one as true have nothing to do with the data necessary for the other.

If we kept trying to kill Socrates, and failed despite meeting the conditions that we've found to normally kill people, we would then be confronted with an inconsistency, and would have to discard at least one of our prior assumptions. We could abolish the idea that all humans are mortal, since this being we recognize as human seems to be immortal. We could abolish the idea that Socrates is human. Or we could abolish both.

Which option we choose has a lot to do with the relative strength of the supporting arguments for each assumption.

Ben, Rolf, no problem, I just thought that 'people who look at dictionnaries' was starting to be a category subject to sneaky connotations.. :)

I believe Eliezer is developing a kind of Bayesian Positivism. He is attempting to describe a way of talking/thinking about things that is thoroughgoing, radically empirical, and thus grounded. I think these posts on language and definitions are essential for what he is trying to do. In this fashion, he should be able to cut through many of the Gordian Knots of philosophy. If Eliezer succeeds, and if people take notice, this could be an important moment in the history of thought.

And why Bayesian Positivism? Why now? For what purpose?

Eliezer recognizes the necessity for clear thought in the light of the unique challenges facing us in the years to come. We are going to need to make complex judgments about matters of existential risk and a common ground will help us avoid a quagmire of unproductive discussions.

Rolf: ,,What do you think of, say, philosophers' endless arguments of what the word "knowledge" really means?'' I think meh! ,,This seems to me one example where many philosophers don't seem to understand that the word doesn't have any intrinsic meaning apart from how people define it.'' Well, if they like to do so, let 'em. At least they're off the streets. =) What's worse is the kind of philosophers who flourish by sidestepping honest debate by complicating matters until nobody (including themselves) can possibly tell a left hand from a right foot anymore, and then go on to declare victory. Definitions belong to their toolset, too. But are we going to argue against knifes because the malignant can hurt others with them, and the ignorant or plain unlucky even themselves? We need them to carve the turkey, so if we want turkey slices we'll just have to operate carefully. I, for one, want to keep my knife! ,,Presumably Eliezer would ask, "for what purpose do we want to answer the question?" However, many philosophers would prefer to unconstructively argue what semantics are "correct". So my personal experience is that I don't think Eliezer's attacking a straw man here.'' He is if he is going to spill the baby with the bath. He'd have to write "Careless/malignant use of definitions is bad." not just "Definitions are bad." (which is my perception).

Caledonian,

The point is that mortality has been observed to always apply to entities that possess the necessary defining qualities of humanity.

Read this through. Necessary defining qualities? Your whole post implicitly assumes the existence of these magical qualities, which presumably reside somewhere just outside reality. Decide on these, then write it as 'mortality has always been observed to apply to entities that possess x, y and z'.

Frank - agreed; I think we're all on the same page here. The point is about human brains, not ideal minds. The problem with placing things in mental boxes (even thorough ones) is that we start thinking about the world in terms of boxes, not things; simply because of how our mental hardware is wired up. How about "Good definitions are still, by definition, limiting and compressed. Bad, careless definitions are really, really bad." Has a nice ring I think.

Really missed a metaphorical trick there. Should have gone with; 'Just because idiots using knives often cut themselves, doesn't mean they're not sharp enough to cut smart people too.'

Ben: I think you're right, we are on the same page! =) How about "Useful definitions will still be distorted by our mental mechanisms. Malignant and careless definitions are bad no matter what."?

Spot on sir.

I don't see Eliezer on a rampage against all definitions. He even admits that argument "by definition" has some limited usefulness.

I think key is when we say X is-a Y "by definition", we are invoking a formal system which contains that definition. The further inferences which we can then make as a result of this are limited to statements about category Y which are provable within the formal system that contains that definition.

Once we define something by definition, we've restricted ourselves to the realm bounded by that formal definition. But in practice many people invoke some formal system in order to make a statement "by definition" and then go on to infer things about X, because it is-a Y, based on understandings/connotations of Y that have no basis in the formal system that was used to define X as a Y.

So let's say we have a locus of points X in a euclidian plain equidistant from some other point C in the plane. Well in euclidian geometry, that's a circle by definition, and we can now make a bunch of geometric statements about X that legitimately derive from that definition. But we can't go on to say that because it is "by definition" a circle, that it represents "a protected area in which ritual work takes place or the boundary of a sphere of personal power cast by Wiccans", or "a social group" or "The competition area for the shot put" or "an experimental rock-music band, founded in Pori, Finland in 1991" to throw out just things that are "circle"s by some definition I was able to find on the web.

In this case, the inference problem is terribly obvious, but often it is much less so, as Eliezer has described for "sound".

The problem with arguing "by definition" from a typical natural language dictionary, is that such dictionaries are not formal systems at all, even though some of their definitions may be based on those in formal systems. It is quite common for a word to have two different and conflicting common definitions, and both of them will end up in a dictionary. I'm pretty sure that you could argue that a horse is a spoon, or that pretty much any X is equal to any Y "by definition" with some creative chaining up of dictionary "definitions".

Frank, I think I would say, not so much that definitions are useless, but that we should sharply distinguish between communication problems and single-player inference problems. When people start violently arguing over their communication signals while they (a) understand what each other are trying to say and (b) are trying to do an inference that they could theoretically do as single players, something has gone wrong.

Hi, am back from the city, and a bit sleepy. I'll try my best with my comment. =) Michael: I was not so much commenting on this specific post as on the whole series. Your example seems to me to boil down to a case of bait-and-switch. Eliezer: ,,When people start violently arguing over their communication signals while they (a) understand what each other are trying to say'' Here the problem is already at full swing, and it's the same as philosophers arguing about the "real" definition of X. As soon as you have managed to get your point across, any further insistance, or even "violent arguing" only shows lack of insight or sincerity. ,,and (b) are trying to do an inference that they could theoretically do as single players, something has gone wrong'' I see no problem about inferences as long as it's clear to everyone what the inference is about (and nobody tries to sneak a switch later).

Read this through. Necessary defining qualities? Your whole post implicitly assumes the existence of these magical qualities, which presumably reside somewhere just outside reality.

No. Would it have helped if I had put 'human' in quotes?

We refer to a particular category with the label 'human'. The presence of certain properties is sufficient for us to assert that a thing is a member of the category. Calling a thing by that label is an assertion that those defining properties are present.

We do not need to have mortality as one of those properties to observe that all the things we call 'human' are mortal. If we find something that is a member of the category, but isn't mortal, then we need to adjust our assumptions.

Speaking as a mathematician (well a grad student) I can positively say I frequently see 'by definition' used in arguments and use it myself in a substantive valid fashion. Sure, definitions don't support inductive inference but that doesn't mean they are always trivial. Fermat's last theorem follow by definition from the definition of the integers but it's certainly not a trivial fact that it does so. While rarely quite so complex arguments about philosophy, politics and other things can sometimes benefit from the nonobvious manipulation of definitions.

Also the notion of something following 'by definition' is of incredible use of rebutting a great deal of misguided philosophy. Quite frequently in philosophy one will see an analysis of a concept like, life, knowledge, or morality claiming to be a explication of the term we use in everyday language. However, it can be very useful to point out that no matter what the theoretical virtues of reducing 'moral good' to 'that which produces moral emotions in us' it's simply definitionally false. To the extent that we have a coherent notion of 'moral good' the sense that it refers to interpersonal facts that are more than mere feelings is inseperable from the concept. The word might change meaning but a theory which says there is nothing more to morality than moral feelings is by definition claiming that there are no moral facts not offering a materialist account of them.

Ironically in making this point I'm somewhat agreeing with Eliezer. The real benefit in using the definition like I did above was to combat the abuse of that definition in the original argument. Definitions are dangerous in arguments but not because people are inclined to say 'by definition' when they mean 'damn right' but because they let the presenter shift the flaw in their reasoning far away from the controversial results. Unless your used to evaluating complex mathematical arguments (and even then) a subtle flaw in a definition at the begining of an argument that has been forgotten by the time the conclusion is reached can be extremely misleading. Worse it harnesses the social awkwardness of being pedantic and insisting on details and rigor before the person has been allowed to get into the meat of their ideas to squash your ability to find the flaws (obviously these are side effects not purposeful choices)

This post prompted me to survey the "Sent" folder of my email archives looking at how I use the phrase "by definition". I plead guilty to a few illegitimate uses of the sort covered in the post.

There is also at least one type of legitimate usage "outside of math", which I resort to fairly often. It consists of reminding my interlocutors of some consequences of the definition of a term that we have previously agreed on as a shorthand for some complex intension.

Interestingly, some of the oldest examples are from when I was playing the game of Nomic over email - the game consists of making changes to its own rules, usually by voting on change proposals, and a common type of move consists of making up a definition of this type within a rule, e.g. "A player's Loudness shall be defined as the number of emails they sent to the list in the past seven days." The legal effects of a definition contained in a rule are derived from its literal wording, as opposed to its intended meaning, so you can use "by definition" to straigthen out someone who is appealing to an intuitive, but wrong, understanding of a term so defined.

Other examples revolve around "terms of art", a word that has a special meaning in a given context. In Agile software development, the term "velocity" has a technical definition, which is "the sum of the estimates originally assigned to all features which were fully implemented in the previous iteration". Novices sometimes overload that with other meanings, such as "how much work to plan for the next iteration", so they'll ask questions like "one of my developers is going to take a vacation next month, how much should I lower velocity" ? Then I might remind them that by definition velocity is something observed, not decided upon.

Re: "using the phrase by definition, anywhere outside of math, is among the most alarming signals of flawed argument I've ever found."

I can't say I've noticed. What I do see is a lot of people arguing with one another without bothering to check that they are defining words in the same way. So, IMO making definitions explicit often helps to resolve apparent disagreements.

When you say that something is so by definition, what you (most likely) actually mean is that something is so by default. If a human is defined as "a featherless biped"*, you can't say that Hermione, who has just had an unfortunate accident with Hedwig and a polyjuice potion, is no longer human because she's grown feathers. "A feathered biped" is only by default not human!

*I don't think you'll ever find a definition like that in a dictionary. "homo: any living or extinct member of the family Hominidae characterized by superior intelligence, articulate speech, and erect carriage": If you're mentally disabled, stuttering, and hunch-backed, it doesn't mean that you aren't, by definition, human. You've got bad genes (or bad nurturing), but they're still Hominidae genes.

Would it be accurate, then, to say that any valid use of "by definition" can be replaced by "a fortiori"?

As in, "Socrates is a [mortal, featherless, biped]. Therefore a fortiori Socrates is mortal." is valid (though one might dispute the premise). But "Socrates is a [featherless, biped]. Therefore a fortiori Socrates is mortal." is plainly obviously nonsense, even to people who think they can argue "by definition!". The remaining problem, of course, being that not everyone accepts that a fortiori deserves the certainty that they have been claiming for by definition!.

(In classical logic, if A∧B, then a fortiori A. In Bayescraft, P(A) >= P(A∧B) a fortiori)

Hey, sorry, just an unrelated question here, but:

Is The Feynman Lectures on Physics still worth reading?

I was stumblin and I found this article, which I think graphically does a great job of making a similar point (although that point wasn't its explicit intention).

All of the graphs except 'tautology' limit the number of worlds you could be in.

I disagree. Agreeing on term definitions beforehand would solve all of these problems: The definition of religion is not "something that answers theological questions," therefore the By Definition argument is ineffective for proving that atheism is a religion. (Incidentally, if that were the definition of religion, then atheism would be a religion.) For Hinduism, if someone tried to tell me that it was not a religion, I would necessarily use the definition of religion to prove them wrong. If Hinduism did not fit the definition of religion, it would not be a religion.

I love this series. Except, I have very particularly been in an argument where I said the phrase, "Hinduism is, by definition, a religion." Isn't agreement on common usage useful if you want to communicate efficiently? Maybe Wiggin shouldn't be used commonly, but one person defining Wiggin in a manner that contradicts the dictionary definition certainly doesn't do anyone any favors. And I think it's fine for common usage to define humans as mortal, as long as it consistently assumes that Socrates is inhuman when he goes on living forever.

What you really seem to be complaining about here is the lack of ability to first AGREE on a definition, then stick to it when the definition is used against you. Quite frankly, given how you're referencing socrates without getting into plato's metaphysics (which deals exactly with your argument, trying to define what a person is given that physical characteristics can change.)

If I define a person as a being capable of building tools and using them... but you insist that only HUMANS can be a person, well that creates a categorical difference between our definitions. From your definition an extraterrestrial that comes in using a space ship isn't a person... by my definition many species of birds are also persons.

The underlying complaint here is that you THINK you made a good argument because you hold a different set of definitions than another person does. In real logic, establishing common definitions and beliefs is key... there is no way I am to know what YOU believe, hell you could disagree with everything I think you would agree with. There IS NO WAY for me to say "yep... I made a good argument because the only way Eliezer Yudkowsky [LW · GW] can refute it is by deflecting and ignoring what I said... cause since it's obviously correct to me it must be obviously correct to everyone right? (And there are a large amount of people who actually believe in self-evident truth and don't recognize it as a fallacy)

Let me emphasize that a self-sealing argument (which is similar to what you're trying to argue) is a fallacy. If you agree a definition is correct, someone uses that definition against you to question your belief ("featherless chicken is a human" why not) but the flow of logic is such that by the definition you agreed upon a featherless chicken does fit in with what a human is... then changing your definition ex post facto is using a logical fallacy.

A "by definition" argument is one of the strongest arguments you can make, in the socrates claim about a chicken is close enough (really sounds like we're about to get into plato's metaphysics) to be an obvious attempt to show a weakness in the definition from which if socrates honestly believed featherless chickens should be classified as humans then the accepted definition would have supported the claim. Instead socrates is clearly trying to point out that the definition is faulted and offers a point that both debaters would accept is false (a featherless chicken is not a human).

Sometimes people say: "Too much of X is bad for you". Well, that is true by the definition of "too much". You can use this to make the argument, that the actual important point that the person tries to convey is that it is possible, and probably not too hard and quite likely if you are not careful, to get so much that it is bad for you.