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Introduction to Logic
Truth, Validity, and Soundness

Abstract: The foundation-concepts of deductive logic are explained--truth, validity, and soundness.

 I. Truth, Validity, and Soundness: probably the three most important concepts of the course. A. First, let us briefly characterize these concepts. 1. truth: a property of statements, i.e., that they are the case. 2. validity: a property of arguments, i.e., that they have a good structure. For example, consider the structure of this argument: All B-s are Cs. All As are Bs. Therefore, All As are Cs. (The premisses and conclusion are so related that it is absolutely impossible for the premisses to be true unless the conclusion is true also.) Note that an argument can be valid even though its premisses are false. Also note that an argument is not mistaken just on account of its conclusion being false or ridiculous. 3. soundness: a property of both arguments and the statements in them, i.e., the argument is valid and all the statement are true. Sound Argument: (1) valid, (2) true premisses (obviously the conclusion is true as well by the definition of validity). B. The fact that a deductive argument is valid cannot, in itself, assure us that any of the statements in the argument are true; this fact only tells us that the conclusion must be true if the premisses are true. 1. Let's look at the variety of valid arguments that can be given as sorted by the truth of premisses and conclusion: Cases —> 1 2 3 4 Premiss(es) T F T F Conclusion T T F If it were possible to have true premisses and a false conclusion, logic would be useless to prove anything. 2. Let's look at the variety of invalid arguments that can be given as sorted by the truth of premisses and conclusion: Cases —> 1 2 3 4 Premiss(es) T F T F Conclusion T T F F That is, all possibilities can be represented; examples are given in the syllabus. II. One way to summarize these concepts is to represent the logical territory in a "tree-diagram." Arguments _________|___________ Deductive Inductive _____|_____ _____|_____ Valid Invalid correct > > > >  incorrect _______|________ Sound Unsound (all statements are true) (at  least one premiss  is false) III. Consider these examples from past quizzes A. Tell whether the following statements are true or false. 1. A sound argument is a deductive argument which is valid and has true premisses. 2. It is impossible for a deductive argument to be both valid and unsound. 3. If a deductive argument is valid, it cannot be unsound. 4. If the premisses of a deductive argument are true, then the argument must be sound. 5. If the conclusion of a deductive argument is true, then the argument might be sound or it might be unsound. 6. If the premisses of a deductive argument are true, then the conclusion must be true. 7. If a deductive argument is valid, then its conclusion might be true or it might be false. 8. A sound argument is a deductive argument that has valid premisses. 9. If a valid argument has a false conclusion, then it must have at least one false premiss. 10. If a deductive argument is valid and at least one of its premisses is false, then its conclusion is also false. B. More rules, definitions, and examples are presented in the syllabus on this topic. Also check your understanding with the quiz and test on "Truth, Validity, and Soundness.    Send corrections or suggestions to webmaster@philosophy.lander.edu  