vagueness solved!

haha, just kidding. vagueness poses a critical problem for many branches of language theory. but, after writing a paper on it, and losing a lot of sleep over it, here are my thoughts on vagueness:

1. vagueness is an essential part of the functioning of language. no two objects are precisely the same, so for a word to apply to many similar objects immediately requires vagueness. without vague (and i realize i'm using the term vaguely here) extensions, words could only apply once, and then language wouldn't really function as a language at all.

2. the meanings of words are conventional. everyone says this, but what does it mean? well, David Lewis's book Convention goes a long way toward explaining it in terms of game theory. In a nutshell, Lewis defines convention as: we all want to continue doing the same action provided most other people continue also, but if the majority started doing some alternative action, we would want to switch to that alternative. But he uses it to describe the meanings of whole sentences. If his theories were applied to words, they might usefully describe how vaguenesses and ambiguities and such arise. we use a word to describe a thing only when we think other speakers will do the same. for example, our only way of knowing whether a man is bald or not bald is to consider whether others would apply the word 'bald' to him.

3. The above example is not just meant to demonstrate that the application of a term to an object is vague. The meaning of the word itself changes based on how speakers would choose to apply it. i'm not really sure how to articulate this difference, but it's very important.

that's all for now. hopefully posting will be more frequent now that we're all settled at home.

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