Re: [Pen-l] Re: money [was: Skidelsky on Keynes

[Sandwichman <lumpoflabor@xxxxxxxxx>]

Lizzie Borden took an axiom,
And gave her theory forty wacks-iom?


On Sun, Dec 28, 2008 at 3:54 PM, Shane Mage <shmage@xxxxxxxxxxxx> 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
>
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-- 
Sandwichman
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