Re: Logic and language WAS Re: Contradictory negation

On Fri, 27 Sep 2002 19:17:47 -0700, Marcus Smith <smithma@...> wrote:

>On Fri, 27 Sep 2002, Clint Jackson Baker wrote:
>
>> Here are a couple of examples of this.  If I say, "I
>> went to the store and bought some milk," the full
>> meaning of this sentence cannot be captured in
>> symbolic logic by a literal interpretation.  This is
>> because I really mean, "I went to the store *and then*
>> bought some milk."  Conventional logic schemes cannot
>> take into account this temporal factor, because it is
>> not carried by the connector *.
>
>Here's another example where grammar and logic part company:
>"Teachers and students are welcome here." Logically, this is something
>like (X is teacher or X is a student) --> X is welcome. If 'and' were
>interpretted as logical AND, X would have to be a teacher and a student to
>be welcome.
I was hoping someone more knowledgeable than myself would jump in here, but
I think this is a matter of ambiguity rather than pure illogic. When a
bunch of clauses are conjoined, English allows common elements to be
"factored out" or "distributed". If you say:
    Teachers are welcome here and students are welcome here.
the "and" is perfectly logical. With factoring this becomes:
    (Teachers _and_ students) are welcome here.
The ambiguity arises (I think!) because omission of relative pronoun +
copula is also allowed.

Jeff