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Re: [ontolog-forum] Ontology, Information Models and the 'Real World': C

To: Pat Hayes <phayes@xxxxxxx>
Cc: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Ingvar Johansson <ingvar.johansson@xxxxxxxxxxxxxxxxxxxxxx>
Date: Sat, 02 Jun 2007 15:25:51 +0200
Message-id: <46616FDF.1060506@xxxxxxxxxxxxxxxxxxxxxx>
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 truth-table 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 truth-functional. 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 
'one-stone-plus-two-stones-make-three-stones' 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 
self-contained 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 
philosophical-pedagogical 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 formal-logical 
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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