Teaching Classical Arithmetic with Vegetables

March 2001

"Because of our realist assumptions in mathematics, we have come to believe that 15 + 20 = 35 is true. But it is evidently not true. 15 unicorns plus 20 unicorns will not get you 35 unicorns, try as you may. Of course, on the other hand, 15 turnips plus 20 turnips will result in 35 turnips, and it will do so every time. The structure of the addition table is sound, and the 'argument' is valid. And if unicorns existed, we would wind up with 35 of them. But this means the argument is valid, not true." –– Douglas Wilson, "The Great Logic Fraud," The Paideia of God, 85.

Comment: Wilson did not write this revealing essay to make the trivial point that arguments are valid (or invalid) and propositions are true (or false). He wrote it to deny that the proposition, "Fifteen plus twenty equals thirty-five" is true. Arithmetic, like logic, Wilson says, is a "great fraud."

John Robbins
The Trinity Foundation
March 14, 2001

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