Mathematics: A Tool For Philosophical Thought
Mathematical Entities Are Idealized Mental Abstractions
In a study by Rafael E. Nunez on the nature of mathematics, he states
"Mathematics is a highly technical domain, characterized by the fact
that the very entities that constitute it are idealized mental
abstractions."^{1}
According to Professor Fred L. Wilson of the the Rochester
Institute of Technology^{2},
"Plato was fond of mathematics because of its idealized abstractions
and its separation from the merely material." Furthermore, Professor
Wilson states "Nowadays, of course, the purest mathematics manages to
be applied, sooner or later, to practical matters of science. In
Plato's day this was not so, and the mathematician could well consider
himself as dealing only with the loftiest form of pure thought and as
having nothing to do with the gross and imperfect everyday world." Is
it any wonder that it is widely believed that above the doorway to
Plato's Academy was written, "Let no one ignorant of mathematics
enter here."^{3}
^{1} Cognitive Science Program at Northwestern University
^{2} Professor
Fred L. Wilson  Rochester Institute of Technology
^{3} Wittenberg University Department of Mathematics and
Computer Science
