the importance of a knowledge that is non-temporal and not based on the senses but is simply consciousness, or self-evident knowledge that consists of ideas whose being involves their being true, it is natural and logical that both should make much of the mathematical method of proof or of what may be better termed “mathematical knowing.” For we cannot say that self-evident ideas are proved at all. What is meant by mathematical demonstration is that mathematics, arithmetic and geometry, constitute a discipline that leads the mind from the sensible or material to the intellectual or spiritual. It is a method rather of illumination.
We can simplify the subject by observing that the theory we are now dealing with, had its origin with Plato. He says: “Geometry, no doubt, is a knowledge of what eternally exists.”[1] We recall his famous requirement made of students who would enter his lecture hall: No one should enter here who is not versed in geometry.[2] The reason such a condition was made by Plato should be obvious to all students of his philosophy. The reason is that geometry is a means of discipline to the mind, teaching it how to pass from objects of sense to objects of thought.
Prof. Paul Shorey makes good his contention against Zeller's interpretation of Plato, namely, that “the mathematical principle * * * stands midway between material objects and the ideas.”
