Oftentimes when explaining how Math is very interesting in that we don’t derive the truths of Math from experience (you don’t need to “go out there” and see in the world that 2 + 2 = 4; you know this logically), I explain the difference between a priori and a posteriori statements and give the example of the sun rising from a certain direction. But yesterday I had a revelation that my example had been wrong. So, I will share my revelation with you. If you think what I am saying is banally simple, I don’t apologize.
So, is it an empirical question: does the sun always rise from the east on every planet? In order to answer this question, do you need to go out there and explore other planets, or can you answer it a priori — without any experience of the world?
Well, how do we know which side is east and which side is west on our planet? Or which side is north and south? Sure, for most civilized people, “north” is associated with “up there”, because most of us live in the northern hemisphere. But even though Australia is called “the land down under”, people living in Australia, surprisingly enough, don’t experience the world upside down. They can just as well think of the North Pole being “down there”.
If you think about it, it seems obvious that east and west (and, as a result, north and south) are just definitions — not definitions based on the particular physical parts of our planet, but definitions based on direction of the sun’s movement in the sky. Once we know what north and south are, based on that definition, we can figure out what is in our north and south: in the north, there is Greenland and Iceland and volcanoes and a bunch of socialist countries, and in the south there are penguins and a bunch of white racist landowners (I am talking about South Africa, not South Carolina).
Imagine that a couple of astronauts are sent by the Federal Government to another planet to figure out where the sun rises on that planet (it has to be Federal Government, since it would be the only one stupid enough to spend money on such a project). They arrive on the dark side of the planet and are waiting for the sunrise. Finally, they see the sun rising, and the following conversation happens:
— Nu what?
— Which side is the sun rising from?
— I dunno. Which side is that?
— Well, is that east or west?
— How can you tell?
— Well, ok, which way are the penguins?
— Actually, on this planet there are no penguins.
— No penguins? What a dump. What about socialists?
— Actually, this planet is inhabited by a much more advanced civilization than ours, and most people here are libertarians.
— OK, that’s it. I am getting out of here.
— What are we going to write in the report?
— “The study did not produce statistically significant results.”
Do you see the problem? With the planet being curved, there is no way to tell which way is objectively “up”. In fact, for ancient Jews, “up” was east. And “right” was south. That is why, the youngest son of Yakov Avinu, who was born in the South was called Binyomin — “son of the right hand”.
So, the sun always rises from the east — by definition. You don’t need to go “out there” and do any observations. You just know it. The same way that you know that all bachelors have no parents-in-law.
On the other hand, with the moon, it’s not so obvious. If you say “every planet which has life has a moon”, it’s an empirical statement. Even if you find one hundred planets that have life and a moon, you can’t be sure that one-hundred-first will definitely have a moon.
But with 2+2=4, you know it a priori. You don’t need to keep adding objects together to convince yourself of this. Any two objects and any two objects will add up to four objects — whatever the objects, the climate, or the political party in power.
Now, the question is: should economics be studied a priori, like Math, or a posteriori, like Natural Sciences? Is “all things being equal, instituting minimum-wage laws increases unemployment” an empirical statement that needs to be proven by observation, or is it a logical statement?
(To see why our moon is necessary for there to be life on our planet, read this post.)