|How open is the meaning of the term "parallel lines"?|
Rank amateur philosophy of language hat on here, but I think Mr. Ludlow is obfuscating a key distinction between the micro-languages within the language we speak and the languages within the language -- formal, informal, scientific, artistic, etc. For example, when he goes on to say the meaning of a term like "parallel lines" remains open to some extent, I suspect the degree to which it is open, if really at all, is insignificant. We can use metaphor and other conversational tools to make it mean something different in conversation, but there is a static definition in the English language we use for mathematics that doesn't brook playfulness or shift. We can teach geometry in American English today just as we could 25 years ago and the meaning of the term "parallel lines" is equally as clear. (Unless I'm very much mistaken and my geometry is out-of-date, in which case I need to rethink my whole understanding of language, too.)
Word meanings are dynamic, but they are also underdetermined. What this means is that there is no complete answer to what does and doesn’t fall within the range of a term like “red” or “city” or “hexagonal.” We may sharpen the meaning and we may get clearer on what falls in the range of these terms, but we never completely sharpen the meaning.
Words certainly do shift in meaning: the words that are fashionable to use for the same meaning change, and we gain and lose the need to express certain meanings over time. How quickly something can happen in a micro-language which changes the language (a meme is born, and suddenly everybody is saying things in a new way -- a process the internet may be accelerating) is fascinating, but I don't think the dynamism crosses from the conversational to the mathematical in a way that makes it meaningful to say the term "parallel lines" is fuzzy. It looks as sharp as an acute angle to me.
Where I do wholeheartedly agree with Mr. Ludlow is in thinking Justice Scalia's philosophy of language is as simplistic, useless, and wrong-headed as his philosophy of law.