250A Lecture 2 - FORM AND VALIDITY QUESTION WHAT MAKES AN...

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7 FORM AND VALIDITY QUESTION : WHAT MAKES AN ARGUMENT LOGICALLY GOOD ( VALID )? ITS FORM (ITS STRUCTURE) FROM NOW ON, WHEN WE WANT TO CHARACTERIZE AN ARGUMENT AS “LOGICALLY GOOD,” WE WILL CALL IT A VALID ARGUMENT. BUT BEFORE WE GET TO A MORE FORMAL DEFINITION OF VALIDITY, LET’S COVER THE PRELIMINARIES. QUESTION : WHAT IS THE FORM OF AN ARGUMENT? ROUGHLY, WHAT YOU GET WHEN YOU ABSTRACT ALL NON- LOGICAL WORDS (CONTENT) LEAVING ONLY BLANKS AND LOGICAL WORDS . QUESTION : WHAT ARE LOGICAL WORDS !? EXAMPLES: NOT; AND; OR; IF…, THEN…; …IF AND ONLY IF…; ALL…, SOME…, …IS… NOW, LET’S LOOK AT SOME EXAMPLES OF ARGUMENTS AND ABSTRACT AWAY TO THEIR RESPECTIVE FORMS:
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8 EX 1) P1. EITHER THE 5 OR THE 10 GOES TO SAN BERNARDINO P2. THE 5 DOES NOT GO TO SAN BERNARDINO C. THEREFORE, THE 10 GOES TO SAN BERNARDINO EX 2) P1. CLINTON IS EITHER A REPUBLICAN OR A LIBERTARIAN P2. CLINTON IS NOT A REPUBLICAN C. THEREFORE, CLINTON IS A LIBERTARIAN THE RELEVANT FORM FOR EXAMPLES 1 AND 2: P1. EITHER p OR q P2. NOT p C. THEREFORE, q EXAMPLE 3) P1. ALL MEN ARE MAMMALS P2. JOHN IS A MAN C. THEREFORE, JOHN IS A MAMMAL EXAMPLE 4) P1. ALL FISH SWIM P2. MOBY DICK IS A FISH C. THEREFORE, MOBY DICK SWIMS THE RELEVANT FORM FOR EXAMPLES 3 AND 4: P1. ALL A’s ARE B’s P2. x IS A C. THERFORE, x IS B OTHER VALID FORMS:
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9 P1. IF p THEN q P2. p C. q P1. p IF AND ONLY IF q P2. NOT q C. NOT p P1. p AND q C. p P1. p AND q C. q P1. p C. p DEFINITION OF A VALID ARGUMENT: A PARTICULAR INSTANCE OF AN ARGUMENT IS VALID IF IT IS AN INSTANCE OF A VALID FORM. AN ARGUMENT FORM IS VALID IF AND ONLY IF THERE ARE NO INSTANCES OF THAT FORM WITH ALL TRUE PREMISES AND A FALSE CONCLUSION.
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  • Summer '07
  • Powell
  • Logic, Valid argument, San Bernardino, true premises

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