PHI 120 Classic Logic & It's Rabbit Holes Ch. 1 Part 1
PHI 120 Classic Logic & It's Rabbit Holes Ch. 1 Part 1 PHI 120
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This 4 page Class Notes was uploaded by Maddi Caudill on Monday January 25, 2016. The Class Notes belongs to PHI 120 at University of Kentucky taught by Daniel B. Cole in Spring 2016. Since its upload, it has received 28 views.
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Date Created: 01/25/16
Classical Logic and It39s Rabbit Holes Ch1 Part 1 Propositional Logic A Formal Language Part One What is logic quotthe science of what follows from whatquot Argument a string of sentences one of the sentences is the conclusion and the others are the premises Conclusion of an argument is the sentence whose truth is to be established Premise of an argument is a sentence that is said or what is thought or that appears to play a role in establishing the truth of the conclusion Two Types of Arguments Deductive gt reasoning with Inductive gt reasoning with in premises lends to the truth of the conclusion range inductive arguments from being very weak to very strong that the truth of the either the conclusion follows the premises or it doesn t and is therefore invalid 1 Ardbeg is a prince 2 ALL princes dine daily on peas parsnips plums pita gt VALID 3 Ardbeg dines daily on peas parsnips plums and pita 1 SOME princes dine daily on peas parsnips plums and pita 2 Ardbeg is a prince gt INVALID 3 Ardbeg dines daily on peas parsnips plums and pita quotIffquot gt quotif and only ifquot Tentative Definition An argument is valid iffeither 1 Its conclusion its premises OR 1 Of necessity if its premises were true then its conclusion would also be true ie it would be An argument is invalid iffit isn39t valid ie iff either 1 Its conclusion does not follow from its premises OR 1 It would be possible for its premises to be true and for its conclusion to be false Consider quotImpossiblequot in the following statements 1 Its impossible for Ardbeg to run 208 marathon gt mpossibility Its impossible for a triangle to have four sides gt impossibility 3 Its impossible for the sentences 39AII goddesses are immortal39 and 39Coco is a goddess39 to be true and for the sentence 39Coco is immortal39 to be false gt impossibility Nor is it necessary that the conclusion actually be true 1 All even numbers are multiples of two lt true 2 Four is an even number VALID 3 Four is a multiple of two lt true 1 All logicians are magicians lt false 2 Coco is a logician INVALID 3 Coco is a magician lt false Validity is purely formal notion it is entirely about form it has nothing nothing nothing to do with the content or the subject matter of the sentences that constitute the argument Soundness An argument is sound iff 1 It is valid AND 2 Each of its premises is true Validity a proper arrangement of premises that force the truth of the conclusion to follow the truth of the premises An argument is valid if it is such that I the premises are true the conclusion must be true Aways about a not if the premises are true Not the content about the abstract relation of the premises If the premises are false WHO KNOWS P1 8 gt P If the premises are true the conclusion must be true P2 8 P Valid argument gt blender Good ingredients gt good smoothie Soundness valid to truth premises well informed inputoutput machine Deductive Logic reasoning with certainty Inductive Logic reasoning with probability True or False 1 If an argument is unsound then its invalid gt false 2 If an argument is valid then its premises are true gt false 3 If an argument is valid then its conclusion is true gt false 4 If the premises of a given argument are true and the conclusion is also true then the argument is valid gt false 5 The following is a valid argument 1 If Ardbeg is a spy for South Zedmenistan then Ardbeg is disloyal to North Zedmenistan 2 Ardbeg is disloyal to North Zedmenistan 3 Ardbeg is a spy for South Zedmenistan He COULD be disloyal in other ways 1 4 E 1 M U 7 7 M FALSE It SHOULD be D gt S Modus Ponens D S
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