# The Relation Projection Fallacy and the purpose of life

I bet most people here have realized this explicitly or implicitly, but this comment has inspired me to write a short, linkable summary of this error pattern, with a name:

The Relation Projection Fallacy: a denotational error whereby one confuses an n-ary relation for an m-ary relation, where usually m<n.

Example instance: “Life has no purpose.”

This is a troublesome phrase. Why? If you look at unobjectionable uses of the concept <purpose> --- also referenced by synonyms like “having a point”—it is in fact a ternary relation.

Example non-instance: “The purpose of a doorstop is to stop doors.”

Here, one can query “to whom?” and be returned the context “to the person who made it” or “to the person who’s using it”, etc. That is, the full denotation of “purpose” is always of the form “The purpose of X to Y is Z,” where Y is often implicit or can take a wide range of values.

This has nothing to do with connotation… it’s just how the concept <purpose> typically works as people use it. But to flog a dead horse, the purpose of a doorstop to a cat may be to make an amusing sound as it glides across the floor after the cat hits it. The value of Y always matters. There is no “true purpose” stored anywhere inside the doorstop, or even in the combination of the doorstop and the door it is stopping. To think otherwise is literally projecting, in the mathematical sense, a ternary relation, i.e., a subset of a product of three sets (objects)x(agents)x(verbs), into a product of two sets, (objects)x(verbs). But people often do this projection incorrectly, by either searching for a purpose that is intrinsic to the Doorstop or to Life, or by searching for a canonical value of “Y” like “The Great Arbiter of Purpose”, both of which are not to be found, at least to their satisfaction when they utter the phrase “Life has no purpose.”

Likewise, the relation “has a purpose” is typically a binary relation, because again, we can always ask “to whom?”. “<That doorstop> has a purpose to <me>.”

In some form, this realization is of course the cause of many schools of thought taking the name “relativist” on many different issues. But I find that people over-use the phrase “It’s all relative” to connote “It’s all meaningless” or “there is no answer”. Which is ironic, because meaning itself is a ternary relation! Its typical denotation is of the form “The meaning of X to Y is Z”, like in

• “The meaning of <the sound ‘owe’> to <French people> is <liquid water>” or

• “The meaning of <that pendant> to <your mother> is <a certain undescribed experience of sentimentality>”.

Realizing this should NOT result in a cascade of bottomless relativism where nothing means anything! In fact, the first time I had this thought as a kid, I arrived at the connotationally pleasing conclusion “My life can have as many purposes as there are agents for it to have a purpose to.”

Indeed, the meaning of <”purpose”> to <humans> is <a certain ternary functional relationship between objects, agents, and verbs>, and the meaning of <”meaning”> to <humans> is <a certain ternary relationship between syntactic elements, people generating or perceiving them, and referents>.

When I found LessWrong, I was happy to find that Eliezer wrote on almost exactly this realization in 2-Place and 1-Place Words, but sad that the post had few upvotes—only 14 right now. So in case it was too long, or didn’t have a snappy enough name, I thought I’d try giving the idea another shot.

ETA: In the special case of talking to someone wondering about the purpose of life, here is how I would use this observation in the form of an argument:

First of all, you may be lacking satisfaction in your life for some reason, and framing this to yourself in philosophical terms like “Life has no purpose, because <argument>.” If that’s true, it’s quite likely that you’d feel differently if your emotional needs as a social primate were being met, and in that sense the solution is not an “answer” but rather some actions that will result in these needs being met.

Still, that does not address the <argument>. So because “What is s the purpose of life?” may be a hard question, let’s look at easier examples of purpose and see how they work. Notice how they all have someone the purpose is to? And how that’s missing in your “purpose of life” question? Because of that, you could end up feeling one of two ways:

(1) Satisfied, because now you can just ask “What could be the purpose of my life to <my friends, my family, myself, the world at large, etc>”, and come up with answers, or

(2) Unsatisfied, because there is no agent to ask about such that the answer would seem important enough to you.

And I claim that whether you end up at (1) or (2) is probably more a function of whether your social primate emotional needs are being met than any particular philosophical argument.

That being said, if you believe this argument, the best thing to do for someone lacking a sense of purpose is probably not to just say the argument, but to help them start satisfying their emotional needs, and have this argument mainly to satisfy their sense of curiosity or nagging intellectual doubts about the issue.

• Main is <-- way, I think you accidentally ended up in Discussion. ;)

• Don’t the higher powers promote articles to Main?

I’d suggest this be promoted.

• I’ve seen the beings of higher intelligence promote things to main, but I don’t think it’s particularly reliable.

• I bet most people here have realized this explicitly or implicitly

A maybe tangential comment: what I often appreciate on Lesswrong is the capability of certain posts to put order to some vague ideas or concept I have in my mind. This is one of those posts. Good work!

• After reading how to measure anything, I suspect of people when they say something could not be measured or defined, in principle. And one of the most useful things is how vague notions could be tabooed or replaced.

• Suppose I find a piece of strange-looking code on my computer and ask, “Does this code have a purpose?” The following seem to be reasonable possible answers:

1. Yes, it was written to serve some useful function.

2. No, it’s a functionally null piece of code that the programmer forgot to remove.

3. No, it seems to be the result of some kind of copying error.

4. Yes, it’s a backdoor deliberately inserted by a previous intruder.

5. No, it’s a security vulnerability that the original programmer accidentally created.

The following do not seem to be reasonable answers:

• a) Yes, it’s an accidental vulnerability whose purpose for an attacker is to use it to hack my machine.

• b) Yes, its purpose is for me to show off my testing/​debugging skills to my boss.

It seems that at least in some cases when I ask “Does this thing have a purpose?” the kind of answer I’m looking for includes “someone deliberately created it” but excludes “it’s valuable for someone”. If “Does life have a purpose?” is like this, whether or not other people value my life wouldn’t to be relevant to answering it.

• There’s a stick lying on the ground in the woods. It previously was unknown by any agent, so it was purposeless.

I pick it up and start using it to steady myself as I hike. Now, it’s a walking stick. Its purpose to me is to help me walk. I didn’t create it. But I started using it, thereby creating a new entity—though the stick itself is physically unchanged.

In the computer example, the vulnerability gains purpose the moment that an intruder becomes aware of it. Previously, it merely had potential purpose.

What you’re calling the act of “creation” can be as simple as the creation of an “intent to use” connection in the mind of an agent.

• It seems that at least in some cases when I ask “Does this thing have a purpose?” the kind of answer I’m looking for includes “someone deliberately created it” …

… for a purpose? Was, but is no more, valuable for someone? Was a byproduct of something valuable? Honestly, this comment confuses me. If there’s some insight to be had from it, as many people seem to think, I’d be happy if someone explained it to me, because apparently I’m too simple to get it.

If “Does life have a purpose?” is like this, whether or not other people value my life wouldn’t to be relevant to answering it.

What would satisfy the question if life was created for a purpose but has later become obsolete for its creator?

• It seems that at least in some cases when I ask “Does this thing have a purpose?” the kind of answer I’m looking for includes “someone deliberately created it” but excludes “it’s valuable for someone”.

Can you give a more concrete example of what you’re looking for in those cases?

Maybe I misunderstood your point, but I feel “somebody deliberately created it”* is at least as weird a usage for “purpose” as the mistake pointed out in the op. Anything delibrately created or not can serve a purpose, original or not, on the condition there’s an agent deciding so. Something created for a purpose can also become obsolete over time.

*yeah this isn’t exactly what you said, but still...

• The following do not seem to be reasonable answers:

They seem like reasonable purposes to me.

It seems that at least in some cases when I ask “Does this thing have a purpose?” the kind of answer I’m looking for includes “someone deliberately created it” but excludes “it’s valuable for someone”.

To me, the purposes of a thing are all purposes that purposeful agent have for the thing. What purpose does X have for Y? Among those questions, you can always ask “What purpose does the creator of Y have for Y?”

If “Does life have a purpose?” is like this, whether or not other people value my life wouldn’t to be relevant to answering it.

It’s irrelevant because you have a purpose for your life (presumably), so any additional purposes for your life are superfluous to the question—we’ve already concluded that your life has a purpose by noting your purpose for it.

• Well, it’s extremely unlikely for a piece of code (or things like that) to be there by accident and still be useful to its user. (This is more or less why [HPMOR spoiler] Uneel fcrphyngrq gung zntvp jnf vagryyvtragyl qrfvtarq ol Ngynagrnaf.) This doesn’t seem to generalize. (Think of “the purpose of X” as “the reason not to get rid of X”. In realistic situations, a given piece of code either has been placed there deliberately by someone or there’s no good reason to keep it. This doesn’t obviously apply to most other things, including life.)

• If we’re naming fallacies, then I would say that this post commits the following:

The Linguistic Consistency Fallacy: claiming, implicitly or otherwise, that a word must be used in the same way in all instances.

A word doesn’t always mean the same thing even if it looks the same. People who worry about the purpose of life aren’t going to be immediately reassured once you point out that they’re just missing one of the relata. “Oh, silly me, of course, it’s a three-place relation everywhere else, so of course I was just confused when I was using it here”. If you ask people who are worrying about the purpose or meaning of life, “Purpose for whom?”, in my experience they tend to say something like “Not for anyone in particular, just sort of “ultimate” purpose”. Now, “ultimate purpose” may well be a vague concept, or one that we get somehow tricked into caring about, but it’s not simply an example of people making a trivial mistake like leaving off one of the relata. People genuinely use the word “purpose” in different (but related) ways.

That said, the fact that everywhere else we use the word “purpose” it is three-place is certainly a useful observation. It might make us think that perhaps the three-place usage is the original, well-supported version, and the other one is a degenerate one that we are only using because we’re confused. But the nature of that mistake is quite different.

If you think I’m splitting hairs here, think about whether this post feels like a satisfying resolution to the problem. Insofar as I still feel the pull of the concept of “ultimate purpose”, this post feels like it’s missing the point. It’s not that “ultimate purpose” is just a misuse of the word “purpose”, which, by the Linguistic Consistency Fallacy, must be used in the same way everywhere, it’s that it’s a different concept which is, for various reasons, a confused one.

FWIW I think “2-Place and 1-Place Words” is a bit dubious for similar reasons. Both this post and that make the crucial observation that we have this confusing concept that looks like it’s a good concept “partially applied”, but use this to diagnose the problem as incorrect usage of a concept, rather than viewing it as a perhaps historical account of how that confused concept came about.

Like I said, sort of splitting hairs, but it makes all the difference if you’re trying to un-confuse people.

• The Linguistic Consistency Fallacy: claiming, implicitly or otherwise, that a word must be used in the same way in all instances.

I’m definitely talking about the concept of purpose here, not the word.

in my experience they tend to say something like “Not for anyone in particular, just sort of “ultimate” purpose”… That said, the fact that everywhere else we use the word “purpose” it is three-place is certainly a useful observation. It might make us think that perhaps the three-place usage is the original, well-supported version, and the other one is a degenerate one that we are only using because we’re confused. But the nature of that mistake is quite different. … If you think I’m splitting hairs here,

I don’t think you’re splitting hairs; this is not a word game, and perhaps I should say in the post that I don’t think just saying “Purpose to whom?” is the way to address this problem in someone else. In my experience, saying something like this works better:

“The purpose of life is a big question, and I think it helps to look at easier examples of purpose to understand why you might be looking for a purpose of life. First of all, you may be lacking satisfaction in your life for some reason, and framing this to yourself in philosophical terms like “Life has no purpose, because .” If that’s true, it’s quite likely that you’d feel differently if your emotional needs as a social primate were being met, and in that sense the solution is not an “answer” but rather some actions that will result in these needs being met.

Still, that does not address the . So because “What’s the purpose of life” may be a hard question, let’s look at easier examples of purpose and see how they work. Notice how they all have someone the purpose is to? And how that’s missing in your “purpose of life” question? That means you could end up feeling one of two ways:

(1) Satisfied, because now you can just ask “What could be the purpose of my life to ”, etc, and come up with answers, or

(2) unsatisfied because there is no agent to ask about such that the answer would satisfy you.

And I claim that whether you end up at (1) or (2) is a function of whether your social primate emotional needs are being met than any particular philosophical argument.”

• I’m definitely talking about the concept of purpose here, not the word.

I think bryjnar is saying there may be two different concepts of purpose, which share the same word, with the grammatically 3-nary “purpose” often referring to one concept and the grammatically 2-nary “purpose” often referring to the other. This seems plausible to me, because if the 2-nary “purpose” is just intended to be a projection of the 3-nary “purpose”, why would people fail to do this correctly?

• Why have brilliant people failed at these before?

Maybe 2-naryish thinking about intentions in general is somehow useful. Maybe this has something to do with how we come up with new uses for things and spot other optimizer-thingies before they kill us. Maybe the brain makes new discoveries by confusing language with new meanings from time to time but unfortunately this can be a failure mode too.

Maybe it really is just a simple logical fallacy. The brain came up with the 2-nary grammatical shortcut, and didn’t properly keep it separate from the original 3-nary concept.

• Maybe the brain is confusing the linguistic shorthand for a conceptual one. An agent is usually assumed even if the expression is grammatically 2-nary.

• I’d really like to see someone taboo or at least write out what they mean with this 2-nary purpose. It surely got me confused before, and especially now after the op clarified my thoughts, it feels like a completely meaningless and incoherent utterance.

Can you give any other examples where purpose is used this way in common language with intended 2-nary meaning* except “the ultimate purpose”?

*edited, sorry for the confusing wording

• “What’s the point of that curious tool in your shed?”

“Oh, it’s for clearing weeds.”

The purpose of the tool is to clear weeds. This is pretty underdetermined: if I used it to pick my teeth then there would be a sense in which the purpose of the tool was to act as a toothpick, and a sense in which I was using it for a purporse unintended by its creator, say.

Importantly, this isn’t supposed to be a magically objective property of the object, no Aristotelian forms here! It’s just a feature of how people use or intend to use the object.

• Sorry if I worded my question confusingly.

I think the op already addresses this and is not simply projecting minds. The important part is that an agent can be assumed and queried. I was hoping for an example where an agent cannot be assumed as in “the ultimate purpose”.

Your example would make no sense at all if an agent could not be queried.

• Oh, I see. Sorry, I misinterpreted you as being sceptical about the normal usage of “purpose”. And nope, I can’t give a taboo’d account of it: indeed, I think it’s quite right that it’s a confused concept—it’s just that it’s a confused concept not a confused use of a normal concept.

• Actually, “the ultimate purpose” seems double-confused, lacking both the object and the optimization process :)

If the object is “life”, I can’t tell if it is supposed to mean life-in-general, or my life, or all our lives.

• I don’t think so.

He’s pointing out that the concept of purpose entails an agent with the purpose.

We don’t explicitly stating context for words all the time. But for words like purpose, people haven’t just dropped context, they don’t even understand the context, and think that their projections have singular meaning, and argue with other bozos suffering under the same confusion about a different singular meaning.

Meanwhile, when two people who understand the full context of the concept have dropped context, they may miscommunicate at first, but have no problem clarifying their commnication—they just identify the full context in which they’re speaking. “I mean Joe’s purpose for his life.” “Oh, I thought you were talking about my purpose for my life. Nevermind.”

As for the guy talking about “Ultimate Purpose”, the OP points out that the concept of purpose entails a agent with that purpose. If by your own statement “it’s not anybody’s purpose”, then you’re not really talking about a purpose at all, and are just confused. The OP can show them the way out of their confusion, but there’s not guarantee they’ll take the way. You can lead a horse to water, but you can’t make him think.

• I’d claim that there is a distinct concept of “purpose” that people use that doesn’t entail an agent with that purpose. It may be a pretty unhelpful concept, but it’s one that people use. It may also have arisen as a result of people mixing up the more sound concept of purpose.

I think you’re underestimating people who worry about “ultimate purpose”. You say they “don’t even understand the context”, as opposed to people who “understand the full context of the concept”. I’m not sure whether you’re just being a linguistic prescriptivist here, but if there are a whole bunch of people using a word in a different way to the way it’s normally used, then I’m inclined to think that the best way to understand that is that they mean something different than that, not that they’re idiots who don’t understand the word properly.

• Nobody is calling anyone an idiot here, brilliant people can be confused too.

I think it’s a feature of the brain to confuse new language with the originally intended concepts. We wouldn’t have most of philosophy without this feature.

• Anecdotal counter-evidence:

I used to fret about the “ultimate purpose” and then I thought about what it would MEAN for their to be some grand purpose, and it seemed like a dreadful prospect once I’d actually sat down and considered the idea that God might be Disappointed in me. The thing I wanted from my “ultimate purpose” was a guiding force, a Sign From God telling me what to do, and it’s obvious that this doesn’t exist. Even if there is a God, and even if He is deeply, deeply Disappointed in me, I’ve never been told—it can’t influence my decisions.

So now I embrace Discordianism, and the freedom to write my own purposes, and to just worry about disappointing myself and the people in my life. It’s really quite relaxing.

• What I think of the post as saying, rather than “purpose has only the meaning (to english speakers) of a ternary relation,” is that “when one normally asks about something’s purpose, one implicitly uses its structure as a ternary relation, and since you haven’t established a ternary relation here you aren’t going to get a satisfying answer that way.”

I think I agree with you on at least one point, though, which is that “words” are really not the problem object; the sentence “what is the meaning of life?” is grammatically correct and not logically invalid and is somewhat a different use of the word purpose. The core object in these constructions I think is cognitive algorithms; in particular the “hear the word purpose, search for Z” algorithm breaks down when purpose changes meaning to no longer involve the same sorts of X,Y,Z.

• FWIW I think “2-Place and 1-Place Words” is a bit dubious for similar reasons. Both this post and that make the crucial observation that we have this confusing concept that looks like it’s a good concept “partially applied”, but use this to diagnose the problem as incorrect usage of a concept, rather than viewing it as a perhaps historical account of how that confused concept came about.

What do you mean by an incorrect use of a concept? If you curry a function, you get a new function, in this case a new concept that happens to be confused because the original function needs all 3 places to make sense. It says so right here in this post. I’m inclined to believe the disagreement you posit simply doesn’t exist.

Would the historical account be that it was a less of a hassle to drop the agent from used language, and over time some people dropped it from the underlying concept, and got confused?

• Elaboration on purpose

Statements similar to ‘the purpose of government is to keep citizens safe’. One way these statements can be confusing is because they don’t have the agent argument, but they can also be confusing in a different way. If Carol is an ordinary citizen, the phrase ‘the purpose of government to Carol is to keep citizens safe’ is not much better. The reason, I think, is that Carol probably has not optimized government very much for that goal. In fact she probably has not optimized government much for any goal since it’s generally out of her control.

Statements like ‘the purpose of government is Y’ imply that there is a process which has optimized the institution of government according to some criteria, but there is no obvious agent or process to have optimized it. If you take voter irrationality seriously anyway.

Using purpose as a synonym of has optimized for also makes sense of phrases like ‘the evolutionary purpose of cat tails is increased balance’, even though evolution is not an agent, since it seems quite plausible that evolution has optimized cat tails so they increase their balance.

Other examples:

‘The purpose of a doorstop is to hold open doors’. The manufacturer has optimized the doorstop to be good at holding open doors, and doorstop owners have optimized (by selection) for the same purpose.

‘The purpose of TV is to keep the masses distracted’. Implies some process has optimized TV for distracting the masses. What process that is, is not obvious.

• I think using the word “purpose” to describe optimizations by non-human agents makes it too easy to anthropomorphize the relevant agents and should be avoided. I am not sure what a good non-technical substitute word might be. Maybe “point”?

• (2) Unsatisfied, because there is no agent to ask about such that the answer would seem important enough to you.

This seems to suggest that compared to theism, atheism is inherently demotivating for some people (namely those whose “social primate emotional needs” are not being met), since they can no longer fall back to “God” as an agent whose answer would be important enough. So this could be another way that Being Okay with the Truth may be false.

• I wonder if this is ever true for people who’ve never been theists. No wonder nothing else seems important anymore after importance has been anchored to godhood.

• I have no trouble conjuring hypothetical extrapolated superintelligent friendly future versions of myself that have deity-like knowledge relevant to the first referent of purpose.

This gives me an acceptable substitute solution when I find an unknown object of unknown creation that may or may not have some purpose in the mind of some agents at some point(s) in time.

Is this a possible escape route?

• The Curry Fallacy.

• Partial application, actually… Currying is the transform on the function to make Partial application easy. What we are doing here is partially applying relations...

Maximum nitpick

• +1 nitpickiness.

And Eliezer makes the same mistake in the linked article too ;) Not that it exactly matters!

• Nice! Apart from “meaning” or “purpose”, what other words does this apply to?

• “want”, “desire”, “should”, “can’t”, and similar all come to mind as running in to similar failures.

• Value.

• 28 Dec 2012 4:34 UTC
4 points

Can you use n and m or j and k instead of k and n. I got confused. /​nitpick

Good post! Thanks for causing me to allocate a useful concept in my brain!

• Done :)

• (Warning: purely meta comment.) I suggest that one should go vote on the linked 2-Place and 1-Place Words, because it does indeed seem to be especially underrated considering the frequent use of the concept in LW. (The cause is of course that it is an OB-import article and so could not attract votes when originally posted.)

• Let’s say you think a property, like ‘purpose’, is a two parameter function and someone else tells you it’s a three parameter function. An interesting thing to do is to accept that it is a three parameter function and then ask yourself which of the following holds:
1) The third parameter is useless and however it varies, the output doesn’t change.
2) There is a special input you’ve been assuming is the ‘correct’ input, which allowed you to treat the function as if it were a two parameter function.