What Logic Is v 1.3

What Logic Is v 1.3 - What is Logic? 1. Logic, Truth, and...

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1 What is Logic? 1. Logic, Truth, and Entailment In general, logic is the study of forms and tools of good reasoning. Logicians are especially interested in questions about how the truth of some sentences or claims might depend on or affect the truth of other claims. For example, we might think of the sentence: (1) Jack and Jill went up the hill. If that sentence is true, then this one has to be true too: (2) Jack went up the hill. Also, if sentence (1) is true, then this sentence can’t be true: (3) Jill did not go up the hill. A logician would say that sentence (2) “ follows from ” sentence (1) or that sentence (1) entails ” sentence 2. All that means is that sentence (2) has to be true if sentence (1) is true. There is no way for sentence (1) to be true while sentence (2) is false. Sometimes a claim follows from a collection of other claims. For example, we might consider these three claims: (4) Socrates is mortal. (5) All mortals are men. (6) Socrates is a man. Neither (4) nor (5) entails ‘Socrates is a man’. It is logically possible for Socrates to be mortal but not a man. It is also logically possible for all mortals to be men but for Socrates not to be a man. But it is not logically possible for (4) and (5) to both be true without (6) being true. If Socrates is mortal and all mortals are men, then it must be true that Socrates is a man. So, we would say that (6) follows from (4) and (5) together, and we would say that (4) and (5) together entail (6). 2. Arguments: Premises and Conclusions The concept of entailment becomes important when we ask one of the central questions in logic: What is the difference between good arguments and bad ones? To answer that question, we need to get clear about what arguments are in the first place. A popular Monty Python skit involves two people having an argument about arguments. One of them, played by Eric Idle, has paid the other, John Cleese, to have an argument.
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2 But Cleese’s character is a lazy debater: he simply contradicts whatever Idle’s character happens to say. Idle’s character quickly grows impatient: IDLE: An argument’s not the same thing as a contradiction. CLEESE: It can be. IDLE: No, it can’t. An argument is a connected series of statements intended to establish a definite proposition. CLEESE: No it isn’t. IDLE: Yes, it is! It isn’t just a contradiction. CLEESE: Look, if I am to argue with you, I must take up a contrary position. IDLE: But it isn’t just saying, “No, it isn’t.” CLEESE: Yes, it is. IDLE: No, it isn’t! In logic, the word ‘argument’ does not mean “debate” or “disagreement.” Instead, it means pretty much what Idle’s character says: ARGUMENT: An argument is a set of sentences meant to establish something. Arguments express chains of reasoning.
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This note was uploaded on 01/29/2011 for the course PHL 100 taught by Professor Sharp during the Spring '07 term at Alabama.

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What Logic Is v 1.3 - What is Logic? 1. Logic, Truth, and...

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