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.
Axioms of arithmetic were enunciated after experience with arithmetic.
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