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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 Technology2, "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 

 

 

 

 

 

 

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