POLSC 135 1st Edition Lecture 3 Outline of Last Lecture Introduction Logic Outline of Current Lecture Logic cont examples Current Lecture I Categorical Syllogism cont from previous lecture The minor premise consists of a claim about either the antecedent or the consequent of the conditional statement Example The country is poor The conclusion is a claim that is thought to be supported by the premises Four types of conditional arguments can be represented by a syllogism 1 Arguments that affirm the antecedent 2 Arguments that deny the antecedent 3 Arguments that affirm the consequent 4 Arguments that deny the consequent Which of these arguments are valid Answer 1 4 Case 1 Affirming the antecedent This is a valid argument If P then Q P therefore Q For example if it rains then it s wet on the ground It rained therefore the ground is wet Case 2 Denying the antecedent This is an invalid argument If not P then Q Not P therefore not Q this second half is the invalid argument Example If a country is wealthy then it is a democracy The country is not wealthy thus it is not a democracy Case 3 Affirming the consequent This is an invalid argument If P then Q Q therefore P this second half is the invalid argument Example If a person is republican then they will be religious A person is religious therefore they are a republican Case 4 Denying the consequent This is a valid argument If P then Q Not Q therefore not P Example If a bag is filled of items then it is full The bag is not filled with items therefore it is not full II Testing theories 1 Imagine that we have some theory that rich countries tend to be democracies One implication is that rich democracies last longer than poor democracies Can we conclude that this theory is correct These notes represent a detailed interpretation of the professor s lecture It is best used as a supplement to your own notes not as a substitute III No this theory affirms the consequent and therefore is invalid 2 Imagine we had a theory that implied rich democracies live longer than poor democracies Say that we observe that they do not Can we conclude this theory is correct Yes this theory denies the consequent and therefore is a valid argument Note There is an asymmetry in the logical claims that can be made on the basis of confirming and disconfirming cases When an implication of our theory is confirmed the most we can say is that the theory may be correct When an implication of our theory is disconfirmed we are compelled to conclude that our theory is wrong Additional Terms to know Deductive learning formulates expectations based on a theory then finds observations Inductive learning start with observations find patterns then can be used to generate explanations End Lecture
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