Peter Wood at the National Association of Scholars asked me to review Proof: The Art and Science of Certainty by Adam Kucharski. So I did. (His will is stronger than mine.) Read it here, please.
To entice you to click, which is always a burden, which I hate doing myself, but which I hope you do, here is an excerpt of “You Can’t Get There from Here: Tracing the Logic of Proof“.
Euclid is touted by Kucharski as a master of proofs, and so he is. His Elements are used to this day to teach how far pure reasoning can go. We learn that Lincoln thought so, too. He boned up on Euclid’s proofs so that he could become a better advocate against slavery. Kucharski spends a good portion of the book on this. Here is the result:
To show that person A could not legitimately enslave B, Lincoln first assumed that A could enslave B. This implied that a legitimate argument for creating slaves existed. B could therefore use the same argument to enslave A, which contradicted the original assumption that A was the enslaver of B. If one person had the right to enslave another, Lincoln concluded, then a person A could be both enslaved and the enslaved. Hence a person did not have the right to enslave another.
As a proof this succeeds. Not in proving slavery illogical, but that Lincoln should have put in a few more hours with Euclid.
Supposing B is enslaved by A, B telling A, “I have a right to be an enslaver, too” is unlikely to convince A that it is B’s turn to be the enslaver. B’s argument cannot be used to enslave anybody, and it doesn’t contradict the assumption A is the enslaver, because, of course, A is the enslaver. It’s only true that B could not simultaneously be enslaved by and also the enslaver of A, if slavery were legitimate. It is also a truth that fortunes change and B could end up on top.
Lincoln’s argument would be like if the Central Powers to escape their fate in 1918 tried arguing that since the Allied Powers were conquerors in WWI, the outcome would be as legitimate if the Central Powers were conquerors, therefore neither side had the right to be the conquerors. They would have had more success trying to prove the existence of humor-filled feminists.
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Which I did, and recommend others do too :-)
You don’t need a publisher. It’s just Godwin’s Law in action. For whatever reason, that seals the deal for most readers (p=0.00005), even though the mechanism is not well understood.
Lincoln’s ”Fragments on Slavery”
c. 1854
If A. can prove, however conclusively, that he may, of right, enslave B.—why may not B. snatch the same argument, and prove equally, that he may enslave A?
You say A. is white, and B. is black. It is color, then; the lighter having the right to enslave the darker? Take care. By this rule, you are to be slave to the first man you meet, with a fairer skin than your own.
You do not mean color exactly?—You mean the whites are intellectually the superior of blacks, and, therefore, have the right to enslave them? Take care again. By this rule, you are to be slave to the first man you meet, with an intellect superior to your own.
But, say you, it is a question of interest; and, if you can make it your interest, you have the right to enslave another. Very well. And if he can make it his interest, he has the right to enslave you.