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logic of atomic sentences

logic of atomic sentences - Logic of Atomic Sentences...

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9/18/2007 1 Logic of Atomic Sentences Chapter 2 Argument, Validity, Proof LING178 Arguments When we want to determine logical consequence, we want to examine the structure of the nature of our arguments. That is the structure of claim and how we prove it and whether or not they are convincing. Arguments in logic Here we are using “argument” to refer only to the structure of how we persuade someone about something. T he word “argument” has at least two other meanings: A conflict or fight we also use is as an alternative to “name” in logic. (as in, the relation Tet(c) has one argument ). Construction of an argument An argument is set up with two parts: The premises premises which support or lead to the conclusion ( because, since, after all, due to ) the conclusion conclusion or point of the argument ( hence, thus, so, consequently, therefore )
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9/18/2007 2 Validity of an argument. It is possible to evaluate an argument independently of whether its premises are true or not. This is called the validity of the argument. An argument is valid if it is necessarily the case that the conclusion follows from the premises. Example All rich actors are good actors. [premise 1] Brad Pitt is a rich actor. [premise 2] Therefore Brad Pitt is a good actor. [conclusion] Based on the premises, the conclusion is valid . Soundness If the argument is valid and we agree with the premises, we say the argument is sound . If the argument is valid and we don’t agree with the premises, the argument is unsound . An argument can be valid, but unsound. If you don’t believe that a rich actor is necessarily a good actor, then to you the conclusion is unsound. The conclusion still follows from the premises, so it is valid.
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