FOM: Goedel: truth and misinterpretations

V. Sazonov V.Sazonov at
Wed Nov 8 10:35:03 EST 2000

Torkel Franzen wrote:
> V.Sazonov says, with reference to
>     (1) Even if ZFC is in fact consistent, it seems that most likely
>         no argument proving this to everybody's satisfaction will
>         ever be found.
>    >Will you confirm, please, that we both understand this (1)
>    >(which is strongly different from the former (1) about TRUTH)
>    >in the same "physical" way, as I explained above.
>   Naturally, if ZFC is consistent, no inconsistency will in fact be
> found. 

It is your and may be my personal believe. (However, I would be 
happy if a contradiction will be found in ZFC or even in PA; 
this would be a good lesson for all of us!). Our beliefs have 
no direct relation to scientific knowledge. At least they have 
a very specific status in discovering a knowledge. This is 
something from our kitchens hardly having a general value. 
Do you always show everything happening in your kitchen to your 
guests? Also, science is not getting a consensus or agreement 
between peoples (is f = m*a believable, or whether everybody 
agree to adopt this law?).  

> But the statement "ZFC is consistent" in (1) is not a statement
> about any physical events or possibilities, but is the mathematical
> statement that no inconsistency exists. 

I do not understand what does it ever mean. 
If you mean arithmetical formula Con[ZFC], then I could 
only repeat that I cannot (i.e. have no idea how) seriously 
discuss its TRUTH or FALSITY, if not from the point of view 
of provability. I understand that this formula can be provable 
in some other theory as Con[PA] is provable in ZFC. What could 
you say of SCIENTIFIC character (desirably something new) about 
the formula Con[ZFC]? 

> Such a use of mathematical
> statements 

Do you mean considering them as believably TRUE 
(with the mysterious for me meaning of "TRUE")? 

> is, as we know, unacceptable from a strongly antirealistic
> point of view, such as expounded by you 

My point of view may be exactly characterized as realistic 
one in the proper meaning of this word. (Cf. e.g. my treatment 
of (1) I gave in the posting to which you reply.) The 
philosophical term "realism", however having some history and 
noble [I am not sure in my English here] philosophical roots, 
seems to me extremely suspicious and ambiguous. 

> or by Wittgenstein. If you're
> interested in any further exposition of this from my point of view, I
> suggest that you look at my "Provability and truth", which is
> available online.

I will take a look. 

However, it is very pity that we did not agree on very simple 
realistic meaning of (1) I suggested. You also actually did not 
present your meaning of (1). Now I am full of pessimism. 
Do you really hope, that without giving us even a very preliminary 
idea only your "Provability and truth" will help? 

Vladimir Sazonov

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