The Pythagorean Experiment

A reader whom I somewhat insulted wrote me a rather nice letter in return, and, more importantly, asked about the kind of philosophical questions which delight me more than wine. I would answer the questions, except that his questions provoke more questions in me than answers. So I will lay these queries out for him or anyone else who cares to comment to answer.

For the sake of simplicity, I will not put all his questions in one piece, lest some thread the discussion be lost.

Also, I mean not to answer the questions in the order asked, but will answer the one that interests me most first. Let’s start in the middle!

Question Seven: How is the Pythagorean Theorem non-empirical? I can test it with a ruler and a protractor. I assume it’s true and all my math works out and the bridges I build with it don’t fall down, so I can feel confident in it’s factuality.

Webster’s defines “Empirical” to mean capable of being verified or disproved by observation or experiment. However, among philosophers, the word is a term of art with a more exact meaning: An empirical truth is a truth the senses (or logical deductions from them) have some tendency to prove or disprove.

Hence, an empirical truth is dependent on sense information, which means, a truth  which is true only when and where the senses (or logical deductions from them) confirm it, and which relies on no other basis but the senses (or logical deductions from them) for proof of their truth.

This is in contrast with a rational truth. A rational truth is a truth deduced by logic from first principles, and, if the first principles are true, and the reasoning valid, the conclusion must be true. Hence, a rational truth is dependent on the truth of the first principles on which it rests, and on nothing else. Since rational truth depends on nothing else, it is true under all times, places, and conditions, no matter what the senses says or seem to say.

That is the definition used  by all philosophers since the dawn of the discipline of philosophy. We cannot substitute another definition without running the risk of deception or confusion.

A thumbnail way to distinguish the two is by the imagination. If one can imagine conditions under which the conclusion is not true, then the conclusion is a conditional.

It is an empirical truth apple trees do not talk. Much evidence confirms it. However, if flown to Oz on a tornado, we might well encounter trees that grew apples, talked, and tossed their fruit in anger at little girls. While the talking apple tree of Oz is impossible in the sense that it cannot fit into the world as we know it, it is not impossible in the logical sense, that is, it does not violate the law of identity.

On the other hand, if the talking apple tree throws two apples with one limb and two with the other, then he has thrown four apples, and that conclusion is as rigid and inescapable in Oz as in Kansas, and nothing can be done to escape it.

There is no “Fiveland” where twice two is five, and it cannot be imagined, nor can logical deductions spring from the conclusion that twice two is five without contradiction other deductions equally as valid springing from the same conclusion.

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Originally published at John C. Wright's Journal. Please leave any comments there.