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 <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'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 <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 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."