by Carl Pierer
Often, people don't do a particular thing. Even if they are supposed to. Tamino didn't talk to Pamina, Kant didn't leave Königsberg and Peter Singer doesn't donate all his money (to the point of marginal utility) to charity. We like to take this not acting as evidence for something more. Tamino's silence for unrequited love. Someone never leaving their hometown as a conservative old bore. Singer's “selfishness” as falsifying his philosophy. While intuitively plausible, this reasoning is flawed. It is the lover's fallacy.
In Act 2, Scene IV, of the magic flute, Pamina hears Tamino playing on his flute and hurries to talk to him. But he, undergoing the second ordeal, is bound to remain silent:
“You're here, Tamino? I heard your flute and ran towards the sound. – But you are sad? Will you not say a word to your Pamina?”
Tamino motions her to go away.
“What? I am to keep away from you? Do you love me no more? Oh, this is worse than an offence – worse than death.”
Pamina, deeply disappointed, reasons: “There are two possibilities, either Tamino doesn't talk to me or he loves me. So, if he loves me, then he talks to me. He doesn't talk, so he doesn't love.”
The fallacy is based off a close link between or and if-then sentences, or disjunctions and conditionals. A truth table will readily illustrate this:
P | Q | P ∨ Q | ~P → Q |
T | T | T | T |
T | F | T | T |
F | T | T | T |
F | F | F | F |
~P is the negation of P, so whenever P is true ~P is false and vice versa. We see that for a conditional to be false we need the antecedent (~P) to be true, while the consequent (Q) is false. Here, this is the case when P is false and Q is false. It is important to notice that if the antecedent is false, the conditional is necessarily true. Now, a disjunction is true as long as at least one of the disjuncts (P or Q) is true. Since the truth table entries for P ∨ Q and ~P → Q are the same, we say they are (logically) equivalent.