A Tired response -Reply

[GONZALO FONSECA <FONSECA@xxxxxxxxxxxxx>]

Paul Davidson says: "[W]hen you claim that axioms can be derived from
other axioms you are talking gibberish.  They are universal truths that are
believed and do not derive from other axioms.  Statements that can be
derived from (other) axioms are logical conclusions or deductions -- they
are not axioms!"

     I am in complete agreement with the dictionary (and your) definitions
of axioms, assumptions and deductions and I used them consistently.
If you believe I have not, then I am afraid then you have misunderstood
my point.   Firstly,  I repeatedly pointed out that your "classical axioms"
(note the quotation marks) are NOT axioms by the dictionary definition as
they are NOT self-evident.   My second point is that they are not logical
conclusions either for they cannot be deduced from axioms.  As I
claimed, they are "unjustified assumptions".
     The gist of my first point was that often economists assume what are
actually unjustified assumptions to be axioms.  My dispute was on how
"axiomatic" these assumptions actually are (i.e. how " fundamentally
self-evident").    The second point was that even when they recognize
that these assumptions are not axiomatic (i.e. they are deductions),  few
take the time to actually spell out the axioms which underly them and
proceed with the logical deduction.   Neo-Walrasian economists (Arrow,
Debreu, McKenzie, Sonnenschein et al.) have actually bothered to do so
and, (surprise, surprise) the assumptions are NOT deducible from the
axiomatic structure they propose.   A third point I made was that EVEN
the Neo-Walrasian axioms are not really that fundamentally self-evident
either.

So much for Neoclassicals.  What I asked of you was to reevaluate your
assumptions (which you consider axiomatic).  I was (and am) arguing
they are not axioms as they are not self-evident and that they are not
logical deductions either for you have never specified the axioms upon
which they are derived.   My proposition, nonetheless, is that your
assumptions COULD be proved to be deductions if we bothered to go  to
the nanoworld and set up our axioms there - and that complexity theory
can provide much of the in-between.

Gonzalo Fonseca
New School for Social Research