# Logic -type questions

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2 b. Old College in Edinburgh is not a new college. New College in Edinburgh is not a new college. Therefore, There are at least two colleges in Edinburgh. c. If the creature in the box has eight legs, it s a spider. The creature in the box is a spider. Therefore, The creature in the box has eight legs. d. There are at least two colleges in Oxford. There is only one college in Oxford. Therefore, There are three colleges in Edinburgh. e. The BFG believes Charles Dickens is called Darles Chickens. Charles Dickens is the author of Great Expectations. Therefore, The BFG believes the author of Great Expectations is called Darles Chickens. [END OF QUESTIONS] These notes are not intended to prescribe the only possible good answers, but to set out some lessons from having marked a number of responses to this question from the Philosophy & Theology applicants. a) The argument can be read in more than one way. A straightforward reading would take the thought that something called New College is (has the property of being) a college, regard being new as a sort of property which, if possessed by one college and not by another, must entail that there are two colleges, and affirm the validity of the argument. A second reading of the argument might note that the names could name just about anything ( a pencil was one suggestion, an hotel another). In that case, premise 1, New College is not a new college, could possibly be true because it may not be a college at all. The premises do not then entail the conclusion, and the argument is invalid. Either answer, properly explained, is fine. Many candidates simply assumed a one-name, one-thing rule and said the argument was valid whilst stating explicitly that the further information in the premises had no bearing on validity. This was a common move, and not, I think, a good one; there is no obvious reason why a person or object might not have two distinct names. b) Note the second answer to (a) discussed above; anyone taking that line will have declared this invalid for the same reason. It did provide a further check on who was using a one-name, one-thing rule; a number of candidates said this was valid for just that reason. An answer which said that two things may be known by the same name, and thus that this argument is

5 believe that Q. Some thought it valid she d not really be believing If P then Q if, believing P, she didn t then also believe Q. (Interestingly, though irrelevantly, most candidates thought Siobhan was male!) e) At the best, there were some quite sophisticated answers, on each side. A more objectivist reading agreed that this was valid, whilst agreeing that Derek may nonetheless actually believe P (he may be ignorant of the conditional). On the subjectivist side, maybe Derek falsely believes that Q s falsity entails P. There is then a clash between an obligation derived from what is in fact true, and from an internally grounded set of belief states. Those who noted this clash typically said the argument was invalid. Either answer, properly explained, was fine; the bare word valid or invalid obviously was not enough. f) Not valid. Best shown by an example. There s an issue about does not believe meaning lacks a belief that or disbelieves, but whichever approach is adopted won t make a difference. There is no assertion that If P then Q is true, of course, but in the following example it does happen to be: Strasbourg is in France. Prudence does not believe If Strasbourg is in France, Strasbourg is in Europe. Therefore, Prudence does not believe that Strasbourg is in Europe. Prudence may be a bit vague about which country Strasbourg is in, whilst being entirely confident that it s in Europe. So both premises may be true and the conclusion false.

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