Lizzie Borden took an axiom, And gave her theory forty wacks-iom?
On Sun, Dec 28, 2008 at 3:54 PM, Shane Mage <[email protected]> wrote: > > On Dec 28, 2008, at 12:42 PM, Jim Devine wrote: > > Definitions aren't _meant_ to convince anyone. Rather, the point of > definitions is to facilitate communication. > > A definition is also not an axiom. If you'll allow me, here's another > definition: an axiom is a "self-evident and necessary truth; a > proposition which it is necessary to take for granted; a proposition > whose truth is so evident that no reasoning or demonstration can make > it plainer." (from the Wiktionary) Instead of "self-evident," I'd say > "true by general agreement in the context being discussed." > > In geometry, one defines a "line." But an axiom might say something > like "two parallel lines never intersect." (Obviously, though this > axiom may be "self-evident," it may not be true. Non-Euclidean > geometry allows parallel lines to intersect, as on the surface of a > globe.) > > That definition seems unsatisfactory. The nature of an axiom, as I > understand it, is that it follows with absolute certainty from the > definitions of its terms. Thus, the Euclidian "Parallel Lines" is defined > as two straight lines such that at all points in one the perpendicular line > between them will have equal length. The axiom that "two parallel lines > never intersect" is "self-evident" because for it to be untrue would > contradict the definition of "parallel." "Non-Euclidian" geometry differs > from "Euclidian" geometry in its definitions, from which different axioms > necessarily follow. > > Shane Mage > > This cosmos did none of gods or men make, but it > > always was and is and shall be: an everlasting fire, > > kindling in measures and going out in measures." > > Herakleitos of Ephesos > > _______________________________________________ > pen-l mailing list > [email protected] > https://lists.csuchico.edu/mailman/listinfo/pen-l > > -- Sandwichman _______________________________________________ pen-l mailing list [email protected] https://lists.csuchico.edu/mailman/listinfo/pen-l
