Re: Godel Was No Aristotle

On Apr 19, 3:58 pm, Aatu Koskensilta <aatu.koskensi...@xxxxxxxxx>
wrote:
On 2007-04-19, raydpratt wrote:
I remember reading that in logic history some mathematician had been
devastated by Godel's logic-of-sets question about whether a class of
all-things-not-a-member-of-a-class would itself be a member of such a
class, and I thought I remembered that the liar's paradox was a Godel
line of thinking along similar lines that also came from Godel.

You're quite confused. The class of all classes that are not members of
themselves appears in the so-called Russell paradox, due to Bertrand Russell.
This paradox demonstrated that the logical system of Gottlob Frege, as
presented in _Grundgesetze der Arithmetik_, is inconsistent.

No. Russell and Frege concluded that not every property defines a
set, but that is obviously nonsense: What keeps us from defining
property to be synonymous with set and thus there is a flaw in the
reasoning? This is obvious, but the solution to the problem of
explaining away the set of all sets that don't contain themselves is a
little more complex.

So I guess some people like to believe the simplest explanation,
although not necessarily the correct one or the one that makes sense
when we are willing to view it with a critical eye.

"is not an element of itself" is not a property! (This is shown quite
clearly if we formalize the discussion - which is fairly easy to do if
we use a Computationally Based Logic.)

C-B

Russell
discovered the paradox in 1901 and communicated it to Frege in 1903; Göde,
who was not born until 1906, had nothing to do with.

GÃdel is also not responsible for the liar paradox which is considerably
older, dating back, in essentially its modern form, to 400 BC. It is usually
attributed, in different forms, to Eubulides and Epimenedes, the former being
responsible for the "I'm lying" variant and the latter for badmouthing
Cretans. Lying Cretans were around at about 600 BC, admitted liars being
the more recent invention from 400 BC.

Before attempting to solve age old conundrums and logical problems it's a
good idea to acquaint oneself with the history and literature on the subject.

--
Aatu Koskensilta (aatu.koskensi...@xxxxxxxxx)

"Wovon man nicht sprechen kann, daruber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus


.

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