[lit-ideas] Re: Are all logical possibilities a result of some kind of logica...
- From: Jlsperanza@xxxxxxx
- To: lit-ideas@xxxxxxxxxxxxx
- Date: Wed, 29 Apr 2009 07:42:34 EDT
In a message dated 4/29/2009 7:21:38 A.M. Eastern Daylight Time,
donalmcevoyuk@xxxxxxxxxxx writes:
And, if so, is this right or wrong?
And, if not, how do we explain away certain statements therein?
-----
I wouldn't say _necessity_ although there is something to it. I think it's
the mechanism of _tautology_ rather.
In the context of atomism, "My brother fought in the war", "My brother
lost an arm".
These are two 'atoms', p & q. we Conjoin them. The order is inessential
for Wittgenstein, "My brother lost an arm. He fought in the war". equivalent
to "My brother fought in the war. Lost an arm". p & q
truth table
p q
1 1
0 1
1 0
0 0
"p & q" is only true when both p and q are true, i.e first row there.
So we say, 'p & q' is a tautology.
------ The mechanism behind is not as simple and involves premise and
conclusion, and metalogical symbol, 'therefore' or _ergo_.
The premises are "p" and "q", and "p & q" is the conclusion.
Now there is the method of the ASSOCIATED MATERIAL CONDITIONAL for a
tautology.
To check the TAUTOLOGICAL status of a tautology you need to CONJOIN the
premises (and turn them into the antecedent of a conditional), with the
conclusion as the consequent of the same conditional. That conditional itself
has to be a tautology:
p & q -> p & q
which is a tautology of the form, p --> p
p --> p
1 1
0 0
i.e. true regardless.
In this scheme we do not really need to speak of 'necessity', which this
type of system restricts to a specific operator -- the square, [ ] -- and
which operates over 'possible worlds'.
It's trickiest when involving individual and predicates.
Aa
for example
a has attribute A
suppose a is Jehova
and A
is
overpowering.
Jews may want to say that G-d is almighty. The predicate, 'almighty'
applies necessarily to G-d. God is not just almighty he _has_ to be almighty.
So
they symbolise that by
[ ] Aa
i.e. there is no possible world such that a is not A.
Perhaps in an analogous way we could say, 'there is no possible world
where 'p & q' is true in circumstances _other_ than p and q being both true'.
Maybe some chemist may want to say, that 'orange' is not really 'red and
yellow'.
Or Darwin that man is not really 'slow ape'.
Or that Russell and Whitehead _wrote_ the Tractatus, therefore Whitehead
wrote the Tractatus.
In this last case above, 'and' notably works in contexts _other_ than
'atomic' formulae of the type Wittgenstein was interested.
"Russell and Whitehead wrote the Tractatus" should be regarded as a
_simplex_ because it's not really equivalent to "Russell wrote (in part) the
Tractatus" and "Whitehead wrote (in part) the Tractatus". It's rather more
like
a cheap custom never known to the Greeks. Imagine if Homer wrote in part
the Homeric Hymns with Hesiod!
Cheers,
JL
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