Ways of Seeing
- Exploring Modern Metaphysics -

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MATHEMATICS - The Pure Science

Science uses more than just theories, observations, and experiments in its Method of discovering truth. It also uses reason and logic. It assumes much that is usually not specified, including such "obvious" ideas that something can not be both true and false in the same way at the same time.

Math is known as the "pure" science because it uses no observations or experiments in the world, but instead uses only reason and logic in the form of non-specific generalities. In arithmetic 1 + 2 = 3; if you have one apple and you get two more you end up with three apples. Or oranges, or cars, or whatever. Mathematics as a science is really the root of arithmetic, calculus, and other disciplines of calculation; it provides the foundation in the form of theorems or statements about what is true and what is not. These theorems, unlike the theories of worldly science, can be known as certain and true for all time, that is, as long as reason and logic as we understand them remain valid.

Each branch of math has an underlying set of assumptions that are explicitly stated. For instance, in arithmetic 1 + 2 = 3 is actually something like: if 1 is the first integer (strictly defined) and 2 is the second integer and "plus" is defined in a certain way, then (and here's the underlying logic) the value of the first integer plus the value of the second integer is equal to the value of the third integer. In this way the conclusions of math can be totally known and proven for all to see, but they are also in a sense self-defining. And they assume the if-then logic and reasoning, among other things, for which no real proof appears possible. The interesting question is how many of these assumptions are real in all cases, and how many are simply a product of our minds and of the way in which our minds are constructed?

For a more detailed discussion on the way theoretical mathematics can provide insight into interactions within the physical world, click here.


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