Steven Pinker -- How the Mind Works - Hampshire High Italian ...

Good Ideas 335both"—you get only one of them free; if you want the other, you have topay for it. Farther along, we learn that John chose coffee. From thepremises "not both free beer and free coffee" and "free coffee," wederive "not free beer" by a logical inference. The answer to question (b)is also no. Our knowledge of restaurants reminds us that food and beveragesare not free unless explicitly offered as such by the menu. Wetherefore add the conditional "if not steak, then no free red wine." Johnchose the soup and salad, which suggests he did not choose steak; weconclude, using a logical inference, that he did not get a free glass ofwine.Logic is indispensable in inferring true things about the world frompiecemeal facts acquired from other people via language or from one'sown generalizations. Why, then, do people seem to flout logic in storiesabout archeologists, biologists, and chess players?One reason is that logical words in everyday languages like Englishare ambiguous, often denoting several formal logical concepts. The Englishword or can sometimes mean the logical connective OR (A or B orboth) and can sometimes mean the logical connective XOR (exclusive or:A or B but not both). The context often makes it clear which one thespeaker intended, but in bare puzzles coming out of the blue, readerscan make the wrong guess.Another reason is that logical inferences cannot be drawn out willynilly.Any true statement can spawn an infinite number of true but uselessnew ones. From "Iowa grows soybeans," we can derive "Iowa growssoybeans or the cow jumped over the moon," "Iowa grows soybeans andeither the cow jumped over the moon or it didn't," ad infinitum. (This isan example of the "frame problem" introduced in Chapter 1.) Unless ithas all the time in the world, even the best logical inferencer has to guesswhich implications to explore and which are likely to be blind alleys.Some rules have to be inhibited, so valid inferences will inevitably bemissed. The guessing can't itself come from logic; generally it comesfrom assuming that the speaker is a cooperative conversational partnerconveying relevant information and not, say, a hostile lawyer or a toughgradinglogic professor trying to trip one up.Perhaps the most important impediment is that mental logic is not ahand-held calculator ready to accept any As and B's and C's as input. Itis enmeshed with our system of knowledge about the world. A particularstep of mental logic, once set into motion, does not depend on worldknowledge, but its inputs and outputs are piped directly into that knowl-