Are there precise definitions for what a variable, a symbol, a name, an indeterminate, a meta-variable, and a parameter are?

In informal mathematics, they are used in a variety of ways, and often in incompatible ways. But one nevertheless gets the feeling (when reading mathematicians who are very precise) that many of these terms have subtly different semantics.

For example, an 'indeterminate' is almost always a 'dummy' in the sense that the meaning of a sentence in which it occurs is not changed in any if that indeterminate is replaced by a fresh 'name' ($\alpha$-equivalence). A parameter is usually meant to represent an arbitrary (but fixed) value of a particular 'domain'; in practice, one frequently does case-analysis over parameters when solving a parametric problem. And while a parameter is meant to represent a value, an 'indeterminate' usually does not represent anything -- unlike a variable, which is usually a placeholder for a value. But variables and parameters are nevertheless qualitatively different.

The above 2 paragraphs are meant to make the intent of my question (the first sentence of this post) more precise. I am looking for answers of the form "an X denotes a Y".

reallyphilosophical (anymore). Isn't this so basic that there should be definitions? – Jacques Carette Jun 25 '10 at 11:36notmathematical definitions. Unless mathematicians were proving things about variables, why would they need to define them precisely? – Carl Mummert Apr 27 '11 at 10:14