On 05 May 2014, at 21:38, Craig Weinberg wrote:
On Monday, May 5, 2014 10:26:27 AM UTC-4, Bruno Marchal wrote:
Then you can study how to define sequence in that theory.
Only because you have an a priori expectation of sequence which can
be inferred. Otherwise nothing is defined and you have only
unrelated statements. You need sense to draw them together and match
your intuition.
No. Logic is the art of making derivation without sense.
There is no art without sense.
Then substitute "art" by "mean".
If logic could be accomplished without sense then it would be
impossible to make an error in logic.
That does not follow. Logic don't use sense, but the machine or the
theory can use it at another level. The physical lwas does not make
error, nut an altimeter in a plane can be wrong when referring to the
plane altitude.
There would be no need to formalize logic because it would be
inescapable in every state of consciousness.
It is still needed when you communicate to others.
That isn't what we see though. In fact, logic is very tenuous and
requires a particularly sober intellect which is focused on modeling
concepts in an impersonal sense.
That is even why so many people think that a machine which can
reason is just doing syntactical manipulation without understanding,
and at the low level, that's correct.
A derivation, in a formal theory, is valid or non valid,
independently of any of its possible interpretation (all those terms
are well defined).
Syntactical manipulation is still sense, it just has relatively
limited aesthetic qualities.
You are not trying to understand.
Gödel is the fist who did that. He invented the "Gödel beta
function", based on a generalization of a famous chinese "lemma",
about set of modular equations in arithmetic.
Eventually (not easy exercice) you can define from the axiom and the
chine lemma a representation of the exponential function, and with
its you can define a sequence in arithmetic by using the unique
factorization of the natural numbers.
But "eventually" means that you must follow a sequence of steps to
do your defining. You smuggle the expectation for sequence in from
the start.
Hmm, ... I will not insist here, as this will be the object to the
next post in the math thread.
It is not the existence of arithmetic, it is the existence of 0,
s(0), etc. + the basic relation that you can derive from the axioms.
"Derive" requires sequence and sense.
Not at all.
Does that mean that dead people would be good at deriving relations
from axioms?
Apparently ... in your theory. You are the one saying that my sun in
law is a zombie, death as far as his consciousness is concerned.
It is the same capacity to reason which tells me that 5-3=2 which
tells me that sequence can exist without arithmetic but arithmetic
cannot exist without sequence.
It is a bit imprecise. I can define sequence in *any* turing
complete language, and they are all equivalent for computationalism.
You can define a notion of sequence as primitive, instead of
numbers, yes. That is the case for LISP, somehow, which is close to
combinators and lambda calculus.
Yo have never provide any theory, so I can't figure what you talk
about.
The theory is that logic and arithmetic are particular continuations
of sense, not the other way around.
Sense is a vague term. Not two human being understand it in the same
way. It is a bit like God. Important notion, but hardly usable in
theories.
If theories can't use sense, and sense is important, then surely it
is the theories that should change.
No. It is like "god". We can talk about it without referring to it to
assert a proposition, when we want make a rational communication,
which was what we were talking about. Of course in daily life, we
don't do rational communication all of the time. You change the
subject, and confuse level of discourse. []p does not refer to sense,
but []p & p does, for example.
Bruno
http://iridia.ulb.ac.be/~marchal/
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