**From:** H.M. Hubey

**Message:** 473

**Date:** 2003-08-07

Piotr Gasiorowski wrote:

Axioms of arithmetic were enunciated after experience with arithmetic.07-08-03 18:22, Richard Wordingham wrote:

> --- In phoNet@yahoogroups.com, "hubeyh" <HubeyH@M...> wrote:

>

>> Axiom 3. The system should be hierarchical e.g. get the commonest

>> changes to form a kind of a skeleton and add the more exotic ones on

>> top of these. This is not much more than an approximation scheme

> that

>> is already in use in linguistics (as well as in many branches of

>> sciences).

>

> Is this an axiom or a principle for organising our knowledge?

More generally, how does one axiomatise an empirical science? You can't

tell the universe how it _must_ behave. An axiom is _stipulated_ to be

true and is not supposed to be negotiable or falsifiable, which is fine

in maths but not in a discipline where we first observe and then try to

generalise from our observations. Some of these "axioms" are in fact

such generalisations -- not necessarily adequate: for example, "Axiom 0"

is probably true but its formulation is (conveniently?) vague, whereas

"Axiom 1" is not _generally_ true. On the other hand, "Axioms" 3 & 4 are

methodological postulates, not statements about language change.

In other words, axioms (math), postulates (say, quantum physics) are enunciated to capture

in a concise and precise way the empirical knowledge we possess about the topic.

Piotr

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-- Mark Hubey hubeyh@... http://www.csam.montclair.edu/~hubey