On 19 Dec 2012, at 20:55, John Mikes wrote:
I tried to identify the meaning of "axiom" and found a funny solution:
as it looks, "AXIOM" is an unprovable idea underlining a theory
otherwise non-provable.
In most cases: an unjustified statement, that, however, DOES work in
the contest of the particular theory it is serving.
Better definitions??????
It is quite good, imo. Nuances can be added according to the nature of
the theory (formal, informal, etc.), but that is quite OK. Unless the
context asks for precision I take as quasi synonymous the following
things:
axioms,
beliefs,
theorems,
hypotheses,
theories,
mind constructs,
assumptions,
etc.
Sometimes I have to distinguish the given axioms, from the
consequences, but consequences of hypotheses remains hypothetical.
Then there are theories where everybody agree on the axioms (except
Sunday Philosophers), like elementary arithmetic axioms, or group
theory axioms, etc. And theories, often intended to apply on some
reality where we can disagree, like set theory, analysis, theories in
physics, biology, chemistry, etc. Now I have never met a chemist
doubting QM, but they can diverge on some assumption in QM, like
notably the collapse, etc.
Bruno
John M
On Tue, Dec 18, 2012 at 12:50 PM, meekerdb <meeke...@verizon.net>
wrote:
On 12/17/2012 11:53 PM, Quentin Anciaux wrote:
Is there a logic that does not recognize a proposition to be
true or false unless there is an accessible proof for it?
Accessible is hard for me to define canonically, but one could
think of it as being able to build a model (via constructive or
none constructive means) of the proposition with a theory (or some
extension thereof) that includes the proposition.
If you include the proposition as an axiom, then it is trivially
true, but you don't work anymore in the same theory as the one
without that proposition as axiom.
Quentin
It seems like just defining a new predicate "accessible" which means
"provable or disprovable" which you attach to propositions. Then it
doesn't need be an axiom and it still allows an excluded middle.
Brent
--
You received this message because you are subscribed to the Google
Groups "Everything List" group.
To post to this group, send email to everything-list@googlegroups.com.
To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com
.
For more options, visit this group at http://groups.google.com/group/everything-list?hl=en
.
--
You received this message because you are subscribed to the Google
Groups "Everything List" group.
To post to this group, send email to everything-list@googlegroups.com.
To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com
.
For more options, visit this group at http://groups.google.com/group/everything-list?hl=en
.
http://iridia.ulb.ac.be/~marchal/
--
You received this message because you are subscribed to the Google Groups
"Everything List" group.
To post to this group, send email to everything-list@googlegroups.com.
To unsubscribe from this group, send email to
everything-list+unsubscr...@googlegroups.com.
For more options, visit this group at
http://groups.google.com/group/everything-list?hl=en.
