Fair question. Perhaps it's more precise to say "Because sometimes it's better not to. Sometimes there is no canonical choice that follows from our definitions

Fair question. Perhaps it's more precise to say "Because sometimes it's better not to. Sometimes there is no canonical choice that follows from our definitions, and it doesn't help to assign an arbitrary value that doesn't help solve any related problems." What is "x" equal to? In general, I mean, not in the context of any equation like "x+1=2". You could say "x=7 in the study of free variables over integers when no other constraints are given", and that is completely consistent with the rest of mathematics, and yet would not be particularly useful and introduces an ugly (philosophical weasel word, yes) asymmetry in the theory (I'd say it introduces a gauge invariance (https://secure.wikimedia.org/wikipedia/en/wiki/Gauge_theory https://secure.wikimedia.org/wikipedia/en/wiki/Gauge_theory), but I'm really not qualified to discuss that in a rigorous way.) Someone like Scott Aaronson could put this claim on more solid footing, but I would state that, intuitively, "assigning a value to an indeterminate form leads to a more complex definition of a mathematical system" in some formal complexity-theory sense.