The antecendent always a expresses a sufficient condition for the consequent


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1 Critical Thinking Lecture Four October 5, 2012 Chapter 3 Deductive Argument Patterns Diagramming Arguments Deductive Argument Patterns  There are some common patterns shared by many deductive arguments  They form a frame that is common to many arguments  Understanding some basic argument patterns help to determine (a) whether an argument is deductive (b) whether is it valid or invalid  Many of these patterns involve two kids of statements Conditionals (if) & Disjunctions (either or) Conditional Statements A conditional statement is a statement of the form If p, then q Examples:  If it rains, then the picnic will be cancelled  If Jones didn t commit the murder, the butler did Conditionals are compound statements composed of two parts: The antecendent what follows the word if The consequent what follows the word then The antecendent always a expresses a sufficient condition for the consequent The consequent expresses a necessary condition (not on quiz two) Disjunctive Statement A disjunctive statement is a statement of the form Either p or q.
2 Examples Either the picnic was cancelled or it rained Either Jones commited the murder or the butler didi Disjunctions are compound statements composed of two parts called the disjuncts. Some valid conditional argument patterns 1. Affirming the antecedent (Modus Ponens): If p, then q p. Therefore q. (1) If the conservatives won the election, then Stepehen Harper is the new Prime Minister (antecedent) (2) The Conservatives won the election (3) Stepehen Harper is the new Prime Minister (from premise (1) and premise (2) by Modus Ponens) 2. Denying the consequent (Modus Tallens) If p, then q. Not q. not p. (1) If the liberals won the election, then Paul Martin is the new Prime Minister (2) Paul Martin is not the new Prime Minister (3) The liberals did not win the election (From Premise (1) and premise (2) by Modus Tallens) 3. Hypothetical Syllogism If p, then q. If q, then r. if p, then r (1) If the conservatives won the election, then Stephen Harper is the new Prime Minister (2) If Stephen Harper is the new Prime Minister, then someone from Alberta is the new Prime Minister.
3 (3) If the conservatives won the election, then someone from Alberta is the new Prime Minister (from Premise 1 and Premise 2 by Hypothetical Syllogism) Some Invalid Conditional Argument Patterns 4. Denying the Antecedent If p, then q Not P. Therefore not q. Example (1) If Einstein invented the computer, then he s a genius (2) Einstein did not invent the computer (3) He s not a genius (From premise (1) and premise (2) by???) 5. Affirming the Consequent If p, then q. q. Therefore p. Example (1) If Einstein invented the computer then he s a genius (2) Einstein is a genius (3) He invented the computer. (From Premise (1) and Premise (2) by?? A valid disjunctive argument pattern 6. Disjunctive Syllogisms (i) Either p or q Not p. Therefore q. (ii) Either p or q Not q. p. (1) Either the liberals won or the Conservatives did (2) The liberals did not win. (3) The conservatives won. (From Premise (1) and Premise (2) by Disjunctive Syllogism)
4 (4) Chapter 4: Diagramming Arguments Before Evaluating an argument, therefore, it often helps to reconstruct it in a more perspicuous manner. One way to do this is to make a diagram of the argument Method for Diagramming Arguments: (*Please see Study Guide for Quiz 2 I will post this later.) Step 1: Underline all premise and indicator words. Then number the statements. Step 2: Find the conclusion and draw a wavy line under it. Step 3: Locate the premises and draw a line under them. Step 4: Cross out extraneous statements redundancies, irrelevant sentences, questions, exclamations, etc. Step 5: Draw the diagram, connecting premises and conclusions with arrows showing the logical connections. Include both dependent and independent premises. Dependent Premises: Depend on each other to provide support for the conclusion Independent Premises: These offer support for the conclusion without the help of any premises. Exercise 3.9 #4 If an individual in a coma is no longer a person, then giving him a drug to kill him is not murder. Such an individual is not in fact a person. So, giving him the drug is not murder. (1) If an individual in a coma is no longer a person, then giving him a drug to kill him is not murder. (2) Such an individual is not in fact a person. (3) So, giving him the drug is not murder. (1) + (2)
5 (3) (Pr. 1) If an individual in a coma is no longer a person, then giving him a drug to kill him is not murder. (Pr. 2) An individual in a coma is no longer a person. (Conc.) Giving an individual in a coma a drug to kill him is not murder. (from (1) and (2) ) If the dog bit the mail carrier, there would be a scar on her leg(1). And some witnesses said they saw the scar(2). But in any case, the mail carrier didn t deny having a scar(3). So the dog probably bit the mail carrier.(4) And if that s the case, the carrier has ground for a lawsuit(5). So, she has grounds for a lawsuit.(6) (6) (1)A causeandeffect relationship is often drawn between men viewing pornography and men attacking women, especially in the form of rape.not RELEVENT TO ARGUMENT (2) But studies and experts disagree as to whether any relationship exists between pornography and violence. (3) Even the procensorship government report admitted that the data connecting pornography to rape was unreliable.(4) the alleged causeandeffect relationship is dubious (1) You should not give Edward an allowance because (2) he never does any work around the house, (3) and he will probably just waste it since (4) he has no conception of the value of anything. 2 4
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