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

[Shane Mage <shmage@xxxxxxxxxxxx>]

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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