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Arguing "By Definition"

38 Post author: Eliezer_Yudkowsky 20 February 2008 11:37PM

Followup toSneaking in Connotations

"This plucked chicken has two legs and no feathers—therefore, by definition, it is a human!"

When people argue definitions, they usually start with some visible, known, or at least widely believed set of characteristics; then pull out a dictionary, and point out that these characteristics fit the dictionary definition; and so conclude, "Therefore, by definition, atheism is a religion!"

But visible, known, widely believed characteristics are rarely the real point of a dispute.  Just the fact that someone thinks Socrates's two legs are evident enough to make a good premise for the argument, "Therefore, by definition, Socrates is human!" indicates that bipedalism probably isn't really what's at stake—or the listener would reply, "Whaddaya mean Socrates is bipedal?  That's what we're arguing about in the first place!"

Now there is an important sense in which we can legitimately move from evident characteristics to not-so-evident ones.  You can, legitimately, see that Socrates is human-shaped, and predict his vulnerability to hemlock.  But this probabilistic inference does not rely on dictionary definitions or common usage; it relies on the universe containing empirical clusters of similar things.

This cluster structure is not going to change depending on how you define your words.  Even if you look up the dictionary definition of "human" and it says "all featherless bipeds except Socrates", that isn't going to change the actual degree to which Socrates is similar to the rest of us featherless bipeds.

When you are arguing correctly from cluster structure, you'll say something like, "Socrates has two arms, two feet, a nose and tongue, speaks fluent Greek, uses tools, and in every aspect I've been able to observe him, seems to have every major and minor property that characterizes Homo sapiens; so I'm going to guess that he has human DNA, human biochemistry, and is vulnerable to hemlock just like all other Homo sapiens in whom hemlock has been clinically tested for lethality."

And suppose I reply, "But I saw Socrates out in the fields with some herbologists; I think they were trying to prepare an antidote.  Therefore I don't expect Socrates to keel over after he drinks the hemlock—he will be an exception to the general behavior of objects in his cluster: they did not take an antidote, and he did."

Now there's not much point in arguing over whether Socrates is "human" or not.  The conversation has to move to a more detailed level, poke around inside the details that make up the "human" category—talk about human biochemistry, and specifically, the neurotoxic effects of coniine.

If you go on insisting, "But Socrates is a human and humans, by definition, are mortal!" then what you're really trying to do is blur out everything you know about Socrates except the fact of his humanity—insist that the only correct prediction is the one you would make if you knew nothing about Socrates except that he was human.

Which is like insisting that a coin is 50% likely to be showing heads or tails, because it is a "fair coin", after you've actually looked at the coin and it's showing heads.  It's like insisting that Frodo has ten fingers, because most hobbits have ten fingers, after you've already looked at his hands and seen nine fingers.  Naturally this is illegal under Bayesian probability theory:  You can't just refuse to condition on new evidence.

And you can't just keep one categorization and make estimates based on that, while deliberately throwing out everything else you know.

Not every piece of new evidence makes a significant difference, of course.  If I see that Socrates has nine fingers, this isn't going to noticeably change my estimate of his vulnerability to hemlock, because I'll expect that the way Socrates lost his finger didn't change the rest of his biochemistry.  And this is true, whether or not the dictionary's definition says that human beings have ten fingers.  The legal inference is based on the cluster structure of the environment, and the causal structure of biology; not what the dictionary editor writes down, nor even "common usage".

Now ordinarily, when you're doing this right—in a legitimate way—you just say, "The coniine alkaloid found in hemlock produces muscular paralysis in humans, resulting in death by asphyxiation."  Or more simply, "Humans are vulnerable to hemlock."  That's how it's usually said in a legitimate argument.

When would someone feel the need to strengthen the argument with the emphatic phrase "by definition"?  (I.e. "Humans are vulnerable to hemlock by definition!")  Why, when the inferred characteristic has been called into doubt—Socrates has been seen consulting herbologists—and so the speaker feels the need to tighten the vise of logic.

So when you see "by definition" used like this, it usually means:  "Forget what you've heard about Socrates consulting herbologists—humans, by definition, are mortal!"

People feel the need to squeeze the argument onto a single course by saying "Any P, by definition, has property Q!", on exactly those occasions when they see, and prefer to dismiss out of hand, additional arguments that call into doubt the default inference based on clustering.

So too with the argument "X, by definition, is a Y!"  E.g., "Atheists believe that God doesn't exist; therefore atheists have beliefs about God, because a negative belief is still a belief; therefore atheism asserts answers to theological questions; therefore atheism is, by definition, a religion."

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.

Atheism does not resemble the central members of the "religion" cluster, so if it wasn't for the fact that atheism is a religion by definition, you might go around thinking that atheism wasn't a religion.  That's why you've got to crush all opposition by pointing out that "Atheism is a religion" is true by definition, because it isn't true any other way.

Which is to say:  People insist that "X, by definition, is a Y!" on those occasions when they're trying to sneak in a connotation of Y that isn't directly in the definition, and X doesn't look all that much like other members of the Y cluster.

Over the last thirteen years I've been keeping track of how often this phrase is used correctly versus incorrectly—though not with literal statistics, I fear.  But eyeballing suggests that using the phrase by definition, anywhere outside of math, is among the most alarming signals of flawed argument I've ever found.  It's right up there with "Hitler", "God", "absolutely certain" and "can't prove that".

This heuristic of failure is not perfect—the first time I ever spotted a correct usage outside of math, it was by Richard Feynman; and since then I've spotted more.  But you're probably better off just deleting the phrase "by definition" from your vocabulary—and always on any occasion where you might be tempted to say it in italics or followed with an exclamation mark.  That's a bad idea by definition!

 

Part of the sequence A Human's Guide to Words

Next post: "Where to Draw the Boundary?"

Previous post: "Sneaking in Connotations"

Comments (34)

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Comment author: PK 21 February 2008 12:21:00AM 8 points [-]

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?

Comment author: [deleted] 13 June 2014 10:37:47AM -2 points [-]

You can start by explaining what it means for something to have a definition by reducing to the idea of a 'concept':

''

The classical theory of concepts, also referred to as the empiricist theory of concepts,[2] is the oldest theory about the structure of concepts (it can be traced back to Aristotle[3]), and was prominently held until the 1970s.[3] The classical theory of concepts says that concepts have a definitional structure.[1] Adequate definitions of the kind required by this theory usually take the form of a list of features. These features must have two important qualities to provide a comprehensive definition.[3] Features entailed by the definition of a concept must be both necessary and sufficient for membership in the class of things covered by a particular concept.[3] A feature is considered necessary if every member of the denoted class has that feature. A feature is considered sufficient if something has all the parts required by the definition.[3] For example, the classic example bachelor is said to be defined by unmarried and man.[1] An entity is a bachelor (by this definition) if and only if it is both unmarried and a man. To check whether something is a member of the class, you compare its qualities to the features in the definition.[2] Another key part of this theory is that it obeys the law of the excluded middle, which means that there are no partial members of a class, you are either in or out.[3]

The classical theory persisted for so long unquestioned because it seemed intuitively correct and has great explanatory power. It can explain how concepts would be acquired, how we use them to categorize and how we use the structure of a concept to determine its referent class.[1] In fact, for many years it was one of the major activities in philosophy - concept analysis.[1] Concept analysis is the act of trying to articulate the necessary and sufficient conditions for the membership in the referent class of a concept.[citation needed] Arguments against the classical theory

Given that most later theories of concepts were born out of the rejection of some or all of the classical theory,[4] it seems appropriate to give an account of what might be wrong with this theory. In the 20th century, philosophers such as Rosch and Wittgenstein argued against the classical theory. There are six primary arguments[4] summarized as follows:

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]

Prototype theory

Main article: Prototype theory

Prototype theory came out of problems with the classical view of conceptual structure.[1] Prototype theory says that concepts specify properties that members of a class tend to possess, rather than must possess.[4]Wittgenstein, Rosch, Mervis, Berlin, Anglin, and Posner are a few of the key proponents and creators of this theory.[4][5] Wittgenstein describes the relationship between members of a class as family resemblances. There are not necessarily any necessary conditions for membership, a dog can still be a dog with only three legs.[3] This view is particularly supported by psychological experimental evidence for prototypicality effects.[3] Participants willingly and consistently rate objects in categories like ‘vegetable’ or ‘furniture’ as more or less typical of that class.[3][5] It seems that our categories are fuzzy psychologically, and so this structure has explanatory power.[3] We can judge an item’s membership to the referent class of a concept by comparing it to the typical member - the most central member of the concept. If it is similar enough in the relevant ways, it will be cognitively admitted as a member of the relevant class of entities.[3] Rosch suggests that every category is represented by a central exemplar which embodies all or the maximum possible number of features of a given category.[3] Theory-theory

Theory-theory is a reaction to the previous two theories and develops them further.[3] This theory postulates that categorization by concepts is something like scientific theorizing.[1] Concepts are not learned in isolation, but rather are learned as a part of our experiences with the world around us.[3] In this sense, concepts’ structure relies on their relationships to other concepts as mandated by a particular mental theory about the state of the world.[4] How this is supposed to work is a little less clear than in the previous two theories, but is still a prominent and notable theory.[4] This is supposed to explain some of the issues of ignorance and error that come up in prototype and classical theories as concepts that are structured around each other seem to account for errors such as whale as a fish (this misconception came from an incorrect theory about what a whale is like, combining with our theory of what a fish is).[4] When we learn that a whale is not a fish, we are recognizing that whales don’t in fact fit the theory we had about what makes something a fish. In this sense, the Theory-Theory of concepts is responding to some of the issues of prototype theory and classic theory.[4]""

Comment author: DonGeddis 21 February 2008 04:24:01AM 5 points [-]

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

Comment author: Eliezer_Yudkowsky 21 February 2008 04:29:56AM 0 points [-]

Geddis:

No, but botogol used it correctly here.

Comment author: Ian_C. 21 February 2008 07:19:40AM 6 points [-]

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.)

Comment author: Sudeep2 21 February 2008 08:52:09AM 6 points [-]

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

Comment author: Eliezer_Yudkowsky 21 February 2008 09:52:05AM 8 points [-]

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!

Comment author: Ben_Jones 21 February 2008 10:42:20AM 4 points [-]

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!

Comment author: Frank_Hirsch 21 February 2008 11:07:47AM 1 point [-]

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... =)

Comment author: tcpkac 21 February 2008 11:58:26AM 1 point [-]

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

Comment author: Ben_Jones 21 February 2008 02:05:32PM 0 points [-]

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.

Comment author: Rolf_Nelson2 21 February 2008 02:06:07PM 5 points [-]

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.

Comment author: Caledonian2 21 February 2008 02:24:41PM 0 points [-]

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.

Comment author: tcpkac 21 February 2008 02:52:13PM 0 points [-]

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

Comment author: Adam_Safron 21 February 2008 03:17:40PM 0 points [-]

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.

Comment author: Adam_Safron 21 February 2008 03:34:26PM 0 points [-]

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.

Comment author: Frank_Hirsch 21 February 2008 03:38:53PM 0 points [-]

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).

Comment author: Ben_Jones 21 February 2008 03:49:20PM 0 points [-]

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.

Comment author: Ben_Jones 21 February 2008 03:56:51PM 1 point [-]

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.'

Comment author: Frank_Hirsch 21 February 2008 04:07:15PM 0 points [-]

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."?

Comment author: Ben_Jones 21 February 2008 04:14:58PM 0 points [-]

Spot on sir.

Comment author: Michael_Sullivan 21 February 2008 06:04:33PM 0 points [-]

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".

Comment author: Eliezer_Yudkowsky 21 February 2008 07:20:24PM 1 point [-]

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.

Comment author: Frank_Hirsch 21 February 2008 10:17:18PM 0 points [-]

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).

Comment author: Caledonian2 22 February 2008 12:52:40AM 0 points [-]

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.

Comment author: logicnazi 03 March 2008 06:43:59AM 0 points [-]

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)

Comment author: Morendil 04 October 2009 04:15:52AM 1 point [-]

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.

Comment author: timtyler 01 January 2010 09:32:32PM 2 points [-]

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.

Comment author: purpleposeidon 23 September 2010 01:38:05AM *  2 points [-]

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.

Comment author: ec429 19 September 2011 04:53:46AM 1 point [-]

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)

Comment author: Rixie 26 July 2013 09:39:53AM 0 points [-]

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

Is The Feynman Lectures on Physics still worth reading?

Comment author: army1987 26 July 2013 12:27:51PM 0 points [-]

Yes, even though some of the stuff there (e.g. about elementary particles) is outdated.

Comment author: shminux 26 July 2013 05:07:24PM -1 points [-]

Not as a primary textbook, but as a supplemental text, exploring some of the ideas skipped or glossed over in the standard texts.

Comment author: kremlin 27 January 2014 06:57:24PM 0 points [-]

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.