On 25 Dec 2013, at 22:29, LizR wrote:
Bruno assumes a very minimal maths (peano arithmetic I believe)
many variant are possible, but for the ontology I like to take
Robinson arithmetic, which can be roughly presented in this way:
0 ≠ s(x)
s(x) = s(y) -> x = y
x+0 = x
x+s(y) = s(x+y)
x*0=0
x*s(y)=(x*y)+x
Then I modelize the reasoner/observer by PA, which is RA + the
induction axioms, that is
0 ≠ s(x)
s(x) = s(y) -> x = y
x+0 = x
x+s(y) = s(x+y)
x*0=0
x*s(y)=(x*y)+x
+ (for all arithmetical formula F) the infinity (one for eaxh formula
F) of induction axioms:
(F(0) & Ax(F(x) -> F(s(x))) -> AxF(x)
It is the strongness of those induction axioms which makes PA into a
Löbian machine, that is one having the G* "theology".
But I put them already in the epistemology. Just to help not mixing
ontology and epistemology.
PA = RA + the infinity of axioms (F(0) & Ax(F(x) -> F(s(x))) -> AxF(x)
Note that PA machines:numbers can be proved, by RA, to exist (in
arithmetic). Like the UD, RA can also emulate the PA, and so we can do
the interview of the infinitely PAs in arithmetic.
RA can imitate PA, like Hofstadter can imitate Einstein by running his
brain, or the Searle guy can imitate a chineese, that is without
understanding it, nor becoming the people imitated.
which I think can be found in reality. BECs for example appear
capable of doing elementary arithmetic. Or are you suggesting that
addition and multiplication don't exist in "reality maths" ?
(Let me respectfully suggest you check out what Bruno is saying
before deciding whether he's right or wrong -
Thanks Liz. It is crazy how people forget to begin by the beginning,
and to end with the ending, of a text, before saying what they think
about it.
though god knows you will have plenty of company in the camp which
says "Bruno must be wrong because - well, because he must be! I
don't need to analyse the logic of his arguments, I can see they're
wrong because ... well .... they just are. Because I say so! No, I'm
not listening, la la la!" etc).
That's a good summary of the usual counter-arguments. You forget the
shoulder shrugging and the eyes looking at the sky :(
Of course sometimes they are genuine misunderstanding, and the subject
is very complex. But some seem to judge without doing the home work,
and that is sad/weird.
Eventually they do the home work and just need to continue to deny, by
fear of looking like behaving stupid, but of course that is when they
do *look* stupid, and that is more sad/weird.
Bruno
http://iridia.ulb.ac.be/~marchal/
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