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# notes_13 - Notes for Week 13 of Confirmation Branden...

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Notes for Week 13 of Confirmation 12/05/07 Branden Fitelson 1 The Wason Selection Task 1.1 The Task Itself Here is Wason’s description of the “selection task”, in some detail: . . . given the sentence: Every card which has a D on one side has a 3 on the other side (and knowledge that each card has a letter on one side and a number on the other side), together with four cards showing respectively D , K , 3, 7, hardly any individuals make the correct choice of cards to turn over ( D and 7) in order to determine the truth of the sentence. This problem is called the “selection task” and the conditional sentence is called “the rule”. The rule has the logical form, “if p then q ” where p refers to the stimulus mentioned in the antecedent ( D ); ¯ p , i.e. not p , refers to the stimulus which negates it ( K ); q refers to the stimulus mentioned in the consequent (3); and ¯ q , i.e. not q , refers to the stimulus which negates it (7). In order to solve the problem it is necessary and sufficient to choose p and q , since if these stimuli were to occur on the same card the rule would be false but otherwise true. The combined results of four experiments . . . show that the subjects are dominated by verification rather than falsification. On the whole, they failed to select ¯ q , which could have falsified the rule (and they did select q , which could not have falsified it although this latter error is much less prevalent). Wason’s description is slightly odd. Here’s how I would describe it. Assume the subjects are told (an- tecedently) that they are going to be testing a hypothesis involving four cards. Each card has one letter on one side and one number on the other side. They will be shown the four cards (face down), and they will be asked to turn over one or more of the cards, with an eye toward determining whether the following is true (where they are to turn over the fewest cards possible for that are sufficient to make this determination): ( H ) Every card that has a “ D ” on one side has a “3” on the other side. In our terminology, the subjects will be generating some evidence ( E ) regarding H , and their goal is to generate an E which determines whether or not H is true (in such a way that E involves the fewest cards possible for this task). Wason says that the “rule” ( H ) has logical form “if p then q ”. This isn’t quite accurate. I would say that the logical form of the sentence is “ ( x)(Dx Tx) ”. Nonetheless, one could think of a conditional version of H , which might look like the following: ( H 0 ) If a card has a “ D ” on one side, then it has a “3” on the other side. My sense is that this version also has very similar response patterns. Nonetheless, I will use H rather than H 0 , since it ties in more nicely with Hempel’s raven paradox. However, I will try to be more (formally) precise about the descriptions involved. We have four cards: a , b , c , d , and I will use the following predicates: Dx x has a “ D ” on one side, Tx x has a “3” on one side, Kx x has a “ K ” on one side, and Sx x has a “7” on one side. The specific way in which the cards are shown to the agents (which is also part of their

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notes_13 - Notes for Week 13 of Confirmation Branden...

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