FOM: What is mathematics?
gibi at pascal.dm.uniba.it
Thu Feb 14 04:30:07 EST 2002
Dear FOM members,
Recently I found a tentative answer, both cognitive and historical, to the
<What is mathematics? >
I found a good evidence for this answer and I am very happy to submit it to
Premise: In linguistics, to analyze the linguistical representation of
(copular) sentences, it is often made a distinction between 'communication
of events' ("The house is great", "The dog is brown") and "communication of
relations" ("That is John's brother", "Mary is fairer than Cathy"). For the
former the relationship between the parts of the sentence and the parts of
the represented fact is 1-1 (You should say that the sentence is an iconic
image of the fact, a noun with an object, an adjective with a property of an
object), for the latter the relationship is more complex, and we must deal
with 'wholistic' connections.
It is quite easy to realize that even the earliest mathematical and logical
sentences were "communication of relations": "there are two stars" ('two' is
not the property of an object in the fact), "those objects are equal"
('equal' is not the property of an object in the fact), "it is true" ('true'
is not a property of an object in the fact), "the triangle is isosceles"
('isoscles' is not a property of an object in the fact).
Hence: mathematics emerges from the natural language to deal with wholistic
"communication of relations".
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