Math and Philosophy: Opposite yet Similar

Pondering on the Midterm Philosophy orals I had weeks ago made me realize a few things.

We had a discussion on how different Mathematics is from Philosophy. In math, one always has to prove the existence of statements through theorems and definitions. It is always about simplifying equations or infinites through rigorous calculations like integrals or summations. That is why phrases like “infinite yet countable” are so common to hear in mathematics classes.

In philosophy, however, I always hear that it is impossible to fully contain an experience or emotion. It is impossible because of the infinite meanings that go along with this experience, as mentioned by Paul Ricouer.

These two opposite viewpoints made me believed that the fields of Mathematics and Philosophy differ so much. One believes that infinites can be reduced to numbers, yet the other does not. But, instead on focusing on the difference, what I would want to point out  is that though these subjects are seemingly opposites, they are strikingly similar as well.

In mathematics, statements always start with assumptions. For example, consider a problem like this:

What is the probability of getting a heads when a coin is flipped? Assume that the coin is fair.

The answer to this question is obviously ½. One either gets a heads or a tails. However, this problem lies with the assumption made about the fairness of the coin. There is no such thing as a “fair coin” because all coins are born with tiny imperfections, minute deviations introduced by the fabrication process. Everybody knows that, over time, a coin will wear and tear, picking up scratches or dents. And everybody knows that these imperfections can affect the physics of the coin flip; thus, biasing the results by some infinitesimal amount which in practice we ignore. We ignore using the assumption that the coin is fair.

This practice of simplifying problems through assumptions show that math acknowledges that same idea that philosophy is also trying to tell us: reality is rich. It is simply impossible to reduce life to formulas and equations because as mentioned by Fr. Ferriols, “the abundance of reality will always be beyond the reach of our techniques.” The number of variables and factors to consider in every coin flip are so many that it becomes impossible for any human or computer to accurately know the probability of tossing a coin. Without assumptions, for example, one has to account for the wind direction and speed when the coin is tossed. More to that, one has to consider the dimensions of the coin!

This is why mathematicians need assumptions in order to solve problems. They use the word “assume” to get a grasp of reality but in the end, acknowledge that the answer they get can never be equated to life as a whole.

This insight I have with regards to math and philosophy made me realize a lot of things. Being an Applied Mathematics in Finance (AMF) student, I thought that math is the center of all sciences due to its ability to precisely calculate objects or situations. However, learning philosophy under Dr. Garcia made me see that I do not live in a mathematical world. There are things that cannot be defined or calculated, and that is why, “the stance of a human being facing reality has always to be a tension between a sense of knowledge and a sense of ignorance” (Ferriols).


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