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K-State POLSC 135 - Logic (cont.), examples
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POLSC 135 1st Edition Lecture 3Outline of Last Lecture:Introduction, LogicOutline 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.-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.III.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


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