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Unformatted text preview: THE LOGIC BOOK, 4 TH EDITION: CHAPTER ONE Definitions. Truth-value: Properties of sentences. True sentences have the truth-value T , and false sentences the truth-value F . Not every sentence has a truth-value: “Where is Fredericton?”; “Please don’t throw things in class.”; “Do lots of practice questions.”; “Holy cow!”. To say the sentences we’re dealing with are those that are either true or false is not to say that for any given sentence we know which it is. Viz, “David DeDourek sneezed on July 19 th , 1985.” Argument: An argument is a set of two or more sentences, one of which is designated as the conclusion and the others as the premises. Either Ottawa won or else Toronto won. Toronto did not win. Ottawa won. But this counts as an argument, too: The moon is made of cheese. DeDourek is an orangutan. Truth-preservation: Ideally, we want arguments to be truth-preserving . That is, we want arguments where if the premises are true, the conclusion must be true. E.g., All men are mortal. Socrates is a man. Socrates is mortal. Also: All whales are pink. All pink things can fly. All whales can fly. Standard form: List the premises followed by the conclusion, with a horizontal line separating the premises from the conclusion. E.g., “Michael will not get the job, for whoever gets the job will have strong references, and Michael’s references are not strong.” In standard form: Whoever gets the job will have strong references. 1 Michael’s references are not strong. Michael will not get the job. The first step in analyzing arguments is to extract them from the discourse within which they are embedded and present them in standard form. Conclusion indicator words: Therefore; thus; it follows that; so; hence; consequently; as a result. Premise indicator words: Since; for; because; on account of; inasmuch as; for the reason that. Deductive Validity: An argument is deductively valid if and only if it is not possible for the premises to be true and the conclusion false (i.e., it is not possible consistently to both assert the premises and to deny the conclusion). An argument is deductively invalid if and only if it is not deductively valid ....
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- Winter '05