are you saying that because the definition of a heap is vague, there are multiple feasible definitions of a heap, so some people (using one definition) would call a candidate heap a heap and other people (using another definition) would say it isn't a heap?
Not that they are necessarily using multiple definitions, but the common definitions themselves do not specify an exact range in quantity in which a cluster of things could be considered a heap. Two people could disagree about whether something is a heap despite using the same vague definition of "heap". They may be comparing the candidate heap relative to things that they have experienced being called heaps in the past. I suppose you could still treat this as being a difference in their personal definitions of "heap". However, I don't think that if pressed to define "heap", that people would be likely to state an explicit quantity range. They would most likely give vague qualitative definitions. The same person may even use inconsistent definitions at different times or forget to include certain aspects that they would consider to be important defining characteristics. People don't normally think in terms of definitions when classifying things. They usually just classify based on what feels correct, and definitions are after-the-fact attempted explanations of their classifications.
Almost all terms introduce a simplification, not just the vague ones.
Doesn't the introduction of a simplification itself give a term some vagueness, because then you don't know the details of the relevant characteristic, just a qualitative judgment? For "heaps", the simplification is one that keeps the exact quantity obscured while providing a qualitative description instead. Even if you had a different quantity term that, unlike "heap", didn't have fuzzy boundaries, it could still be considered vague in a different sense if multiple quantities could fulfill its definition (assuming an exact quantity really did exist in reality). It would certainly at least be considered somewhat ambiguous. For example, the category "integers" has seemingly clear boundaries, but calling an unknown number an integer is still vague if it doesn't express all the relevant information.
vague terms have a wider array of meanings than non-vague terms
Yes, terms can be vague in that way too.
Not that they are necessarily using multiple definitions, but the common definitions themselves do not specify an exact range in quantity in which a cluster of things could be considered a heap. Two people could disagree about whether something is a heap despite using the same vague definition of "heap". [...]
Ahhh, I think I understand. Yes, that makes sense.
Doesn't the introduction of a simplification itself give a term some vagueness, because then you don't know the details of the relevant characteristic, just a qualitative judgment?
Yes,...
It's that time of year again.
If you are reading this post and self-identify as a LWer, then you are the target population for the Less Wrong Census/Survey. Please take it. Doesn't matter if you don't post much. Doesn't matter if you're a lurker. Take the survey.
This year's census contains a "main survey" that should take about ten or fifteen minutes, as well as a bunch of "extra credit questions". You may do the extra credit questions if you want. You may skip all the extra credit questions if you want. They're pretty long and not all of them are very interesting. But it is very important that you not put off doing the survey or not do the survey at all because you're intimidated by the extra credit questions.
It also contains a chance at winning a MONETARY REWARD at the bottom. You do not need to fill in all the extra credit questions to get the MONETARY REWARD, just make an honest stab at as much of the survey as you can.
Please make things easier for my computer and by extension me by reading all the instructions and by answering any text questions in the simplest and most obvious possible way. For example, if it asks you "What language do you speak?" please answer "English" instead of "I speak English" or "It's English" or "English since I live in Canada" or "English (US)" or anything else. This will help me sort responses quickly and easily. Likewise, if a question asks for a number, please answer with a number such as "4", rather than "four".
The planned closing date for the survey is Friday, November 14. Instead of putting the survey off and then forgetting to do it, why not fill it out right now?
Okay! Enough preliminaries! Time to take the...
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[EDIT: SURVEY CLOSED, DO NOT TAKE!]
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Thanks to everyone who suggested questions and ideas for the 2014 Less Wrong Census/Survey. I regret I was unable to take all of your suggestions into account, because of some limitations in Google Docs, concern about survey length, and contradictions/duplications among suggestions. The current survey is a mess and requires serious shortening and possibly a hard and fast rule that it will never get longer than it is right now.
By ancient tradition, if you take the survey you may comment saying you have done so here, and people will upvote you and you will get karma.