In reading John Stuart Mill, A System of Logic (1843), it’s become clear to me that a lot of what I’ve found most useful in logic has been less what it’s ultimately trying to do and more what it must do as a means to its end.
In A System of Logic, Mill starts his analysis with names. For example, there are names like “country,” which are (in their spoken, written, and other forms) associated with indefinite “groups of individuals”—for the lack of a better term—and names like “England,” which are associated with definite “individuals.” What’s the difference, though, between a name and a word? A name is a kind of word. A name is always associated with an indefinite group of individuals, a definite group of individuals, or a definite individual, and a word is associated like that only insofar as it’s a name. For example:
- “Country” is a name because it’s associated with England, Germany, and every other country (whether past, present, future, or hypothetical).
- “The Axis” (in the context of the Second World War) is a name because it’s associated with Nazi Germany, Facist Italy, and Imperial Japan.
- “England” is a name because it’s associated with that country.
- “The” isn’t a name—at least it’s not a name in and of itself—because it’s not associated with an indefinite group of individuals, a definite group of individuals, or a definite individual. (“The country that I grew up in,” though, which has “the,” is a name.)
Mill also distinguishes between connotative and non-connotative names, “country” being an example of a connotative name because it connotes certain attributes (e.g., sovereignty) and “England” being an example of a non-connotative name. “Country” denotes England because England is sovereign etc., but “England” denotes that country regardless of its sovereignty etc.
After his analysis of names, Mill moves onto ontology, which is the analysis of the most fundamental categories: mind, body, etc. And then after ontology—I’ll forgo summarizing Mill’s ontological system in this essay—Mill moves onto an analysis of propositions (which presupposes names, for propositions are in part made of names): For example, in “snow is white,” the subject, which says what the proposition is about, is “snow,” and the predicate, which says something about what the proposition is about, is “white.” Such propositions, according to Mill, aren’t best analyzed as the category “snow” being included in the category “white things,” but as what’s in the category “snow” being attributed whiteness.
It’s only after analyzing names, ontology, and propositions (which gets at the form and substance of propositions) as a means to an end that Mill gets to what logic is ultimately trying to do: explain what propositions imply what other propositions, well what kinds of propositions imply what other kinds of propositions. I’ve always found the former more useful than the latter, whether in Mill or elsewhere.