Sciences Participating with Arts & Culture in Education

Few activities, in truth, can rival it. Mathematics have become the indispensable tool of the modern man.                                                                        

EVANDER (questioning):

But is it only that, a tool?

BASIL:

What else could it be? Think only of accountants, physicists, doctors, architects, or even cashiers, all of whom need math in order to function. I could list a number of other examples, Evander, but I believe that I have made my point.

EVANDER:

I understand you perfectly. However, it is not true that mathematicians use math in the same way as those other people you just mentioned. On the contrary, mathematics as a discipline, though it possesses myriad practical applications, is inherently abstract. Look at physics, for instance. Physicists use math in order to uncover the principles of the universe. Mathematicians, on the other hand, study math purely for its own sake, exploring the nature of concepts like quantity, space and change. They pursue knowledge for knowledge’s sake. That is why we call their branch of math pure. And that is exactly the point of philosophy.

BASIL (dismissive):

A branch of mathematics which cannot be directly applied to any field of work is surely meaningless.

EVANDER:

Far from it, my friend! Such abstraction is precisely math’s strength.                                                                                                               

BASIL:

How do you mean?

EVANDER (explaining):

Well, you would agree that math is essentially a deductive system, that is, it comes to conclusions based on a set of initial, logical propositions, which are independent of observation. To give you a trivial example, if I say that 2 + 2 = 4, this statement is true regardless of how many times I conduct this operation. In other words, its validity does not derive from experimentation.

BASIL:

That much is clear to me.

EVANDER (CONT’D):

It is precisely this independence from empirical facts which opens the door to a plethora of otherwise unimaginable worlds. In the past fifty years, for instance, mathematicians have become interested in the study of multiple dimensions. Of course, humans are absolutely incapable of touching, seeing, or in any way experiencing such dimensions, but they can certainly attempt to understand them using mathematics. What mathematicians are interested in are not the effects that, say, a fourth dimension might have on the real world. They do not rely on empirical evidence. Yet they manage to make incredible discoveries nonetheless.

BASIL (thoughtful):

According to you, then, math is really a branch of philosophy?

EVANDER (smiling):

I would not go so far as to say that, although there are certainly many parallels to be made. And once you realize this, Basil, you will see that the respect you owe mathematics should encompass all other branches of philosophy, given that the difference between them is not one of spirit, but of form. In fact, just because math is written differently does not imply that its object is different too, for who would deny the kinship of two brothers though they look nothing alike. Similarly, what some fail to appreciate is that in all cases and regardless of its form, philosophy has one goal, namely the study of that which lies beyond human observation.

BASIL:

I’m afraid I must disagree. What of those disciplines which fit under the umbrella of practical philosophy, such as ethics and politics? You cannot seriously claim that these things bear no relation to the world of observation!

EVANDER:

To a certain degree, I admit that they do. Ethicists and political philosophers necessarily deal with concrete realities. But it is when they try to conceptualize these realities that their true philosophical nature emerges. For what is ethics if not the pursuit of the good? Or politics if not the pursuit of the right?

BASIL:

That is what they are.

EVANDER (inquisitive):

Then can you tell me, Basil, where in the world of the senses can I observe the good? Or the just? Is it written on someone’s face when he performs a given deed? What kind of observation makes us conclude that something is good or bad, just or unjust? What empirical criteria does one meet to merit these terms?

BASIL

I have no answer ready.

EVANDER:

Then can it be that the good and the just, by their very definition, are things separate from the world of matter, things which can be known or felt, but not observed?

BASIL:

I must admit, Evander, that I find it most difficult to refute these claims. The study of mathematics is most certainly a philosophical endeavour. However, I still find myself unconvinced that philosophers, like scientists, make any use of empirical data.

EVANDER:

My dear Basil, I fear that is because we differ in our understanding of the word “philosophy”. You seem to refer to the word merely as an academic discipline or career. In reality, it has a much deeper meaning. Above all, philosophy, at least in the Western tradition, refers to a particular way of thinking, a conceptual framework grounded in the laws of logic. In this sense, things like medicine, chemistry and astronomy — sciences which most certainly fit under your idea of empirical — are really all highly philosophical.

BASIL (indignant):

Many of your past claims have been quite outlandish, Evander, but this seems far too outrageous! Nevertheless, I will lend you my ear at the risk of being persuaded by your arguments.

EVANDER (amused):

It is most gracious of you to keep an open mind. Tell me, are you familiar with Stoicism?

BASIL: 

Vaguely, though I can tell from the expression on your face that it is something I should recall. Let me see...The Stoics were philosophers known for their unique ethical theories, were they not?

EVANDER:

Indeed, but their ethics are not what I am most concerned with at the moment. Instead, I would rather focus on the Stoic criterion for truth, as well as the influence that it had on the many disciplines of the ancient Greeks and Romans.

BASIL:

The Stoic criterion for truth?

EVANDER:

The Stoics had a particular method of assessing the validity of factual claims, especially when it came to examining the cosmos. In short, they believed that the senses and reason must be used together to discover truth. Cleomedes, a Greek astronomer, philosopher and teacher from the fourth century AD was a key proponent of this method. Using observation, he inferred that the cosmos was spherical, but also explained that this hypothesis must be proven using principles of Stoic logic.

BASIL (curious):

How so?

EVANDER:

Quite simply, Cleomedes referred to the fact that if a person were to look some distance ahead, he would notice the heavens meeting the horizon in a curved line. This, he believed, is visual — although not conclusive — proof that the cosmos is spherical in shape.

BASIL:

Why, this is exactly the same procedure we use back at the lab! My colleagues and I observe certain phenomena, but only with the help of reason and logical principles can we justify our observations.

EVANDER (smiling):

You have completed my point yourself, Basil. Stoic philosophers developed a criterion for truth which served a great number of disciplines. As such, Stoicism was much more than a set of ethical doctrines or metaphysical principles. It embodied a method of study which even today contributes to scientific thought.

Evander pauses and takes a sip of water. Meanwhile, Basil is seated in quiet contemplation, taking in all that has been said.

BASIL:

As always, Evander, our discussion has proved fruitful. Your insight is refreshing, and the confidence with which you speak is admirable. You have answered many questions this evening, and I am at a loss to how I, and many others, could have spent our entire lives in ignorance of the evidence you have provided here. After all, there is no denying that the earliest philosophers were in fact natural scientists, and that their theories, just like those of their modern counterparts, often came into conflict with religion. Furthermore, your discussion of mathematics has helped me realize that philosophy, as a discipline, is truly rigorous and objective, while in a broader sense, “philosophy”, the pursuit of knowledge, is constantly influencing many aspects of our human lives.

EVANDER:

You give me far too much credit, Basil. My theories are but seeds, useless if not for a rich and fertile mind in which to grow.                                 

BASIL (flattered):

Perhaps you are right. In any event—

Basil’s cell phone rings.

BASIL (slightly embarrassed):

Excuse me, my friend, but I must take it.

(speaking into his phone)

Yes. I see. He did what? I’m on my way. 

He rises from his chair.

BASIL (to Evander):

I am truly sorry, Evander, but I must go. It was a genuine pleasure seeing you. I truly regret leaving.

Evander rises as well.

EVANDER:

There’s no need for farewells just yet. I’ll accompany you as far as you need to go, and then will be off myself. (He gazes at the window) It’s getting quite dark out.

BASIL:

I appreciate the company. (He grins) Though I must insist you stay as close to me as possible: we wouldn’t want you getting lost in the dark now, would we?

EVANDER:

What a dreadful thought! How in the world would you manage without me?

Evander pays the waiter and the two leave the café.