Lecture 3_Logical Connectives and the Rules of Inference

# Lecture 3_Logical Connectives and the Rules of Inference -...

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Logical Connectives, Rules of Inference, and Fallacies of Reasoning I. Introduction: Why adhere to what is sometimes called “logical thinking”? Why reason logically? Answer : Whether as students or scholars, we are all interested in attaining truths and avoiding falsehoods. As such, we are all interested in reasoning that is “truth-preserving.” A method or pattern of reasoning is truth-preserving if it never takes one from truths to a falsehood. Basically, the study of formal logic helps develop the skills needed to present and evaluate arguments in any discipline. Now the hallmark of good deductive reasoning is that it is truth-preserving. If one starts from truths and uses good deductive reasoning, then the results one arrives at will also be true. -The primary advantage of successfully axiomatizing a body of knowledge is accordingly that it makes all the claims of that body of knowledge as certain as are the starting principles and the rules of reasoning used. II. Historical Background A. Aristotle developed a general system of logic intended to incorporate the basic principles of good reasoning. 1. These “basic principles” were to provide a way of evaluating specific cases of reasoning. 2. His system is variously known as “syllogistic logic,” “traditional logic,” or “Aristotelian logic.” a. Aristotelian logic had shortcomings (e.g., individuals; relations). B. In the nineteenth century, logicians sought alternatives to Aristotelian logic. 1. They developed systems of “sentential logic” based on the way sentences of natural language can be generated from other sentences by the use of expressions ‘or’, ‘and’, ‘if…then…’, and ‘not’. a. These expressions are typically called “logical connectives” or “sentential connectives.” III. Logical Connectives A. A few preliminaries 1. We are dealing with connectives as they appear in the realm of deductive logic. a. As such, we are concerned with factual/indicative/declarative sentences (or statements or propositions or claims). i. Such sentences make claims about what was, is, or will be the case. ii. These claims are “truth-evaluable”; they can be deemed either true or false. 2. Deductive Validity a. An argument is deductively valid if and only if it is not possible for the premises to be true and the conclusion false. i. Only arguments, but not premises, can be valid (or invalid). Validity is a property of arguments! 3. Deductive Soundness a. An argument is deductively sound if and only if it is deductively valid and its premises are true . i. Soundness is also a property of arguments. Truth (or falsity), however, is a property of a premise/statement/sentence.

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## This note was uploaded on 04/10/2012 for the course PHI 2010 taught by Professor Tacks during the Spring '12 term at Florida State College.

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Lecture 3_Logical Connectives and the Rules of Inference -...

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