Re: [escepticos] ¿Por qué iba a aceptar un axoma si no es autoevidente?. Era imposibiblidad de demostrar una negación.

[Pedro J. Hdez]

El día 7 de agosto de 2008 17:49, Eloy Anguiano Rey
<eloy.anguiano en gmail.com> escribió:
> El jue, 07-08-2008 a las 17:46 +0100, Pedro J. Hdez escribió:
>> El día 7 de agosto de 2008 17:14, Pepe Arlandis
>> <pepe.arlandis en gmail.com> escribió:
>> > La autoevidencia no es ninguna propiedad exigible a los axiomas,
>>
>> ¿Y deseable?.
>
> Tampoco.

Algunas citas algo más largas que tu "tampoco" donde sospechosamente
la palabra auto-evidentes aparece

Wikipedia dice al respecto

"In traditional logic, an axiom or postulate is a proposition that is
not proved or demonstrated but considered to be either self-evident,
or subject to necessary decision. Therefore, its truth is taken for
granted, and serves as a starting point for deducing and inferring
other (theory dependent) truths.

In mathematics, the term axiom is used in two related but
distinguishable senses: "logical axioms" and "non-logical axioms". In
both senses, an axiom is any mathematical statement that serves as a
starting point from which other statements are logically derived.
Unlike theorems, axioms (unless redundant) cannot be derived by
principles of deduction, nor are they demonstrable by mathematical
proofs, simply because they are starting points; there is nothing else
from which they logically follow (otherwise they would be classified
as theorems).

Logical axioms are usually statements that are taken to be universally
true (e.g. A and B implies A), while non-logical axioms (e.g, a + b =
b + a) are actually defining properties for the domain of a specific
mathematical theory (such as arithmetic). When used in that sense,
"axiom," "postulate", and "assumption" may be used interchangeably. In
general, a non-logical axiom is not a self-evident truth, but rather a
formal logical expression used in deduction to build a mathematical
theory. To axiomatize a system of knowledge is to show that its claims
can be derived from a small, well-understood set of sentences (the
axioms). There are typically multiple ways to axiomatize a given
mathematical domain."

Cuando la gente habla del axioma de elección utiliza la palabra auto-evidente.
http://plato.stanford.edu/entries/axiom-choice/
Y por cierto. Éste parece un buen ejemplo en el que la gente no se
pone de acuerdo si es autoevidente, no lo es, si es verdadero o falso
y pone en jaque en montón de demostraciones previas.

O Penrose por ejemplo

But what is a mathematical proof? A proof, in mathematics, is an
impeccable argument, using only the methods of pure logical reasoning,
which enables one to infer the validity of a given mathematical assertion
from the pre-established validity of other mathematical assertions, or from
some particular primitive assertions—the axioms—whose validity is taken
to be self-evident. Once such a mathematical assertion has been established
in this way, it is referred to as a theorem.

saludos

Pedro J.

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-- 
Pedro J. Hdez
Ecos del futuro
ecos.blogalia.com