The definitions I have seen of "field" seem rather unsatisfactory. Wikipedia starts off by saying that a field is any function with spacetime as its domain, but this seems awfully broad, since there are 2|ℝ| number of functions with spacetime as a domain. Further down, Wikipedia basically says that a field will be the solution to certain differential equations, but that is circular, because in order to know which variable to select to solve for, one must be able to label it as a field. Other sources just cite well-known examples (usually electromagnetic field), which isn't a definition (or even a completely good hint, since one would want to look for a definition to cover scalar, vector or tensor fields). Srednicki's "Quantum Field Theory" doesn't give a definition. Daniel Fleisch ("A Student's Guide to Vectors and Tensors" claims there is no agreed-upon definition, which is odd, given the ubiquity of the concept. Can anyone give me a reasonable definition that is not circular, not too broad, not just listing the major fields, but that is giving a decent definition (giving conditions that are both sufficient and necessary to call a function a field).