The Value of Philosophy

The Value of Philosophy

Reading "What Makes the Examined Life Worth Living" by Pruim I found the section regarding internal and external question very interesting. To explain the difference between these, Pruim analyzes three different areas; physics, mathematics and morality.

Let us begin with an example in mathematics. The question whether 2+2 equals 4 or 5 is an internal question in the field of mathematics, while asking ourselves if any of these numbers really exist is an external question; a question about mathematics, not a question of mathematics. Another example, of morality, would be: Is it wrong to steal? How do we know that certain actions are wrong, as a matter of objective fact? The former question is internal, while the latter is external. Certainly we find answering internal questions a lot easier than answering the external ones.

The methods applied to answer internal questions are therefore irrelevant when trying to answer the external.

Pruim also talks about two different views of how one could address these questions; the realistic and the instrumentalistic. While the realist is trying to explain how certain observations can provide us with evidence to prove the theorem in question, the instrumentalist is concentrating on the usefulness of thinking of things that does not really exist. Pruim's example of this is economic hardship.

I agree with Pruim on this up to a certain point. To totally put the faith in something that we do not know to exist, might not be very wise. One could easily be distracted from reality, and make bad decisions based on the invented idea of solution to one's problems. Though, I believe having faith in a greater future is what keeps many people continue to do good in the world. Perhaps finding a balance between total belief in our faith and

As a mathematics major I must object to some of the statements Pruim makes about numbers. What Pruim does not seem to be aware of is the origin of the numbers. They were not simply made up one day as rules to a game, which is how Pruim would like to put it. Numbers are built from scratch, and from there carefully defined, starting with the Natural numbers, then all of the Integers, and later on the Real numbers, the Complex, etc. After having done this, certain operations are defined for interaction between the numbers. The most common being +, -, *, /.

Further, I would like to clarify a significant difference between mathematics and physics, with regards to whether how the statements/theorems in the sciences are proved. To prove a mathematical theorem, mathematicians can only apply other theorems that have already been proved. Thus, ultimately every theorem can be tracked back to the definitions of the numbers and their operations. On the other hand, most theorems in physics are proved with a different approach; experiments and observations; the realistic approach. For instance, if I hold a soccer ball in my hands and then drop it, will it fall to the ground? A physician would try it a thousand times, and every time, the ball will hit the ground. If he/she would drop it again the probability of the ball falling down is now very big. Thus the physician will accept the idea of gravity.

It is the undisputable truth