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Re: ZFC and God
Posted:
Jan 22, 2013 9:37 PM
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On Jan 21, 1:07 pm, Zuhair <zaljo...@gmail.com> wrote:
> Harvey Friedman had presented several formulations of theories using
> some concepts in theology relative to which ZFC is provable to be
> consistent!
To prove something consistent, you have to define what it means for it
to be consistent. To prove a system of formal wffs consistent, we
have a (recursive) function f over wffs that maps a wff into its
negation, and it is not consistent iff there is a w such that w and
f(w) are provable. But how does this apply to ZFC? ZFC is a
collection of statements that are best expressed in English - attempts
to formalize them create debate as to what a particular expression
means. In other words, where is the formal syntax that precisely
specifies the axioms and rules of ZFC? There are none - it is not
that formal.
C-B
> So some kind of mentioning of the supernatural (or what is
> mutually interpretable with it!) is needed to prove ZFC's
> consistency.
>
> See:http://www.cs.nyu.edu/pipermail/fom/2013-January/016881.html
>
> Doesn't that say that mathematics following ZFC is only grounded in
> Mythology driven principles!
>
> Doesn't that mean that ZFC based mathematics is too imaginary that
> even if consistent still it is based and rooted in fantasy that cannot
> really meet reality!
>
> Why should one follow such a system so grounded?
>
> With the scientific triumph it looks that mathematics is ought to be
> revolutionized to parallel science instead of absolutist tendencies of
> the old era of Religion and mythology as it seems to be currently
> rooted in?!
>
> Zuhair
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