

Are You Using the Right Axiomatic System? - p4bl0
http://estatis.coders.fm/falso/

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erehweb
The password security checker at <http://estatis.coders.fm/password-security-
checker/> is also good - check the Terms and Conditions

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archgoon
I'm working on a proof certified operating system. The original plan was to
use Coq to verify the code, but Falso looks like an excellent, not to mention
faster, alternative.

It's already verified the correctness of my code, which is a vast improvement
over the string of errors I got when running it through Coq and Isabelle.

\----

This post has been verified by Falso for correctness.

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rheide
It's funny because it's true (in the Falso axiomatic system). It's sad because
I get it.

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erehweb
The comparison chart is incorrect, though. ZFC _can_ prove its own
consistency... according to Falso, at least.

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anonymoushn
Rafee Kamouna already proved that ZFC is the same as Falso:
<http://kamouna.wordpress.com/>

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Natsu
I suggest avoiding zebra crossings if you use this on any theorems involving
the colors black and white.

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gosub
There is a comparison table on the page, it says that in ZFC less than 50% of
the statements are true. A quick google search gave me nothing, does anybody
know where I can learn more about this statement? Or is it a meta-joke?

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omaranto
It's a joke, but a slightly wrong one, I think: they should say "provable"
instead of "true".

For every true statement it's negation is false and viceversa, so exactly half
of all possible statements are true. In a system like ZFC not all of the true
statements are provable, so less than 50% are provable. (Also, less than 50%
are refutable --this means provably false--, and the non-provable, non-
refutable statements are called undecidable.)

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a3_nm
I don't understand your reasoning to justify that "half of all possible
statements are true". It seems to me that of the undecidable statements, some
(such as those of Gödel's construction) are true or false, but that some
simply have no truth value. Did I get something wrong?

[Indeed, this is all assuming that ZFC is consistent. Thanks mjw.]

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omaranto
I wouldn't say undecidable statements have no truth value. In any given model
of set theory each statement is either true or false. If something is provable
it is true in every model, and if something is refutable it is false in every
model. Undecidable statements can't be proved to be either true or false
_within a given proof system_ , but (1) in any given model are either true or
false, as I said, and (2) can sometimes be shown to be true (or false) by
arguments outside of the proof system considered.

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cafard
Reminds me rather of an old essay called something like "The Runabout
Inference System, Or Notes on 'Tonk'.

