Pat Hayes schrieb:
>> Here comes a new question, one that I
>> guess different logicians have different answers to. But I would be
>> happy merely to get an overview of some possible positions. Here comes
>> the question (X is meant to be a variable for constructions such as
>> FOL):
>>
>> "For which parts (X) of formal logic does it hold true: 'any discussion
>> of propositions in English is really beside the point for X'?
>
> I would say, in the sense I intended that phrase, all of them.
>
> Of course it is true that all of formal logic is inspired by aspects
> of natural language. We give the logical 'and' the truthtable that we
> do because this is closest in meaning to the English word "and", and
> so on. But even this simple connection makes the logic only a pale
> shadow of the full English usage. Even a word like "and" has meanings
> which go beyond the purely truthfunctional. For example, one can
> conjoin two of almost any similar structures in English ("Joe is tall
> and heavy") , but the logical form of this is meaningless in most
> formal versions of FOL: ((Tall and Heavy) Joe) ?? My point is that
> being too free with English examples can lead one very quickly into
> areas of English meaning  such as how to express indexicals  which
> are well outside the purview of ontological formalisms. (01)
Thanks for answering Pat, (02)
I would be happy if some more people would like to answer. But before I
continue, I want to make it perfectly clear that I have no preconceived
pet idea of what is the true answer to my question. I have since long
been interested in the relationship between mathematics and mathematical
physics (or between numbers and physical dimensions); since some years I
think that mereologists take much too lightly on the problem of how to
apply mereology in various contexts (see the paper "Mereology and
Philosophy  for discussion" in section 0 on my home site); and I am
confused about how to answer the analogous question about the
relationship between formal logic and natural languages. To me it looks
like this. (03)
On the one hand there is the intuition (and Pat's view) that all formal
logic, even the propositional calculus, leaves natural language behind,
just as arithmetic leaves all introductory talk about
'onestoneplustwostonesmakethreestones' behind. On the other hand,
I have my view that since there are propositions in both parts of
natural languages and parts of formal logic, there has to be some kind
of connection. Of course, the existence of such a connection might be
quite consistent with the view that formal logic is as much a
selfcontained formal discipline as mathematics is. But then,
nonetheless, someone ought to be able to say something about this
connection. It is a bit astonishing to me that there is huge literature
concerned with the relationship between numbers inside and outside
arithmetic, but (to my knowledge) almost nothing about the relationship
between propositions inside and outside formal logic. (04)
As it happens, I think the answer to my question is of practical
philosophicalpedagogical interest. I believe that the way introductory
courses in logic are usually taught  with their problems of how to
formalize ordinary English in propositional logic and FOL  they give
many students the impression that there is a hidden formallogical
essence in ordinary language. If Pat is right, efforts should be made in
order to take such possible impressions away. (05)
Hoping for more reactions  best wishes,
Ingvar (06)

Ingvar Johansson
IFOMIS, Saarland University
home site: http://ifomis.org/
personal home site:
http://hem.passagen.se/ijohansson/index.html (07)
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