[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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