[lit-ideas] Re: "p & p"

 
 
Donal McEvoy writes (re: Geary's "f* you and f* you):
 
>had thought maybe it was an interesting question in philosophical  logic
>that was being broached re is it redundant or tautological or  something to
>propose 'X & X'. I should have known by the fact the  fella from Argentina 
had
>posted nothing. 
 
Some hope.
 
And then, R. Paul adds:
 
>Formal logicians have never known what to do with conjunctions, even  though 
as
>the 'logical constants,' they are supposedly their bread and  butter. It's a
>scandal that ordinary propositional logic cannot deal with  the temporal 
sense of
>'and'.
 
Re McEvoy's concern:
 
While it is not tautological to say "p & p", it is interesting to note  that 
it is a _theorem_, and thus a tautology, to say:
 
     "if p, (then) p & p"
 
as the truth-table below shows:
 
 p ->    p & p
 
 1  1   1  1  1
 0  1   0  0  0

 
where the column for the conditional yields 'true' values only.
 
R. Paul connects this with the 'temporal' sense (or 'usage' as I prefer) of  
'and'.
 
Indeed, 
 
    "She talks and she talks"
 
may be understood temporally, and thus not really a case of "p &  p".
 
The real crux is to find an example of a natural context for things  like:

"The dog is black and the dog is  black."
 
It can be suggested that what is at play here is some illocutionary  raising:
 
      "The dog is black and the dog is  black"
 
-- would implicate, "and that's it: there's nothing more to it, or nothing  
we can do about it"
 
But in this case, I propose, the _iteration_ involves _not_ the fact  
reported (the dog's being black) but the fact that the utterer is _repeating_  
what 
is repeated. The explicit formalization being:
 
      I say "the dog is black and I say it again:  "the dog is black". Got it?
 
It may be said that 'and' _requires_ that the two conjuncts are _not_  
identical. But surely that's the wrong assumption to make what the standard  
logical 
system being what it is, where "if p, p & q" remains a theorem. To  
constraint the system to block these utterances would involve changing the 
rules  of 
the game, and I don't think there is no need for that.
 
Better, with Grice, to provide a pragmatic explanation.

Thus, when dealing with
 
    "She had a child and got married"
 
vs.
 
    "She got married and had a child"
 
Grice proposes that it's the pragmatic rule, 'be orderly', which is at  play.
 
For 
 
    "The music is loud and the music is loud"
 
the rule being, "Don't repeat yourself -- unless you must and feel in the  
emphatic mood".
 
Cheers,
 
JL
 


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