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The Science of Good Reasons http://www.harryhiker.com/logic.htm

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Reflects on the nature of thinking itself; The most fundamental branch of Philosophy; Is the study of HOW we reason; Is prescriptive: ◦ i.e., develops rules for correct reasoning ◦ Applying logic: enables us to make clear and powerful arguments (or to be able to analyze another’s and avoid being “sold” a bill of goods)

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What is an ARGUMENT? ◦ http://www.youtube.com/watch?v=kQFKtI6gn9Y http://www.youtube.com/watch?v=kQFKtI6gn9Y “An argument is a connected series of statements to establish a definite proposition” The use of one or more reasons to support an idea or action.

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Premise (a proposition/statement) Premise (a statement) Conclusion (another statement) NOT always in that order

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Which statement is supported by the other statements? ◦ Conclusion ◦ Key words identifying the conclusion: “So…” “Therefore…” “Ergo…” “Consequently…” “Hence” ◦ “Hint Words” are not always included in the statement, sometimes they are implied

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Since… Because…

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The mental process that occurs when we move from premises (reasons) to a conclusions. Using existing information to develop new information.

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From general to particular (specific) Is conclusive, NECESSARY inferences IF the reasons are true, the conclusion MUST be true Focuses on rules for determining VALIDITY of an argument From particular to general Conclusions are only PROBABLE IF the reasons are true, the conclusion is PROBABLY true (i.e., it might be false)

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Formal: ◦ Rules concerning the “form” i.e. structure of arguments ◦ Dealing with VALID inferences (are the premises linked in such a way that the conclusion follows from them) Informal (a.k.a., Critical Thinking) ◦ Day-to-day situations ◦ Rhetoric ◦ Emotional appeal ◦ Relevance / ambiguity

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Deal with declarative statements, ◦ i.e., sentences used to assert something about something else Declarative statements are the only ways that we can say something about the world. Declarative sentences can be either true or false.

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IF the premises are true –in a VALID argument - it will be impossible for the conclusion to be false. A SOUND argument is a VALID argument that uses TRUE premises.

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Does NOT guarantee that the conclusion is NECESSARILY TRUE! Determined by the FORM of the argument: ◦ Are the premises organized in such a way that they can indeed lead to the conclusion? ◦ Validity is NOT concerned with the truth of the premises, ◦ Validity is concerned with possibility or reliability of the INFERENCE.

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An argument with two premises that lead to a conclusion. A Syllogism can be made with premises (statements) that are: ◦ Categorical ◦ Hypothetical / Conditional (If a, then c.) ◦ Disjunctive (A or B)

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Use Categorical statements: ◦ All S are P. ◦ No S are P. ◦ Some S are P. ◦ Some S are not P. 2 premises (categorical statements) Leading to a conclusion (also a categorical)

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A SUBJECT: that about which something is said. All giraffes are animals. ◦ (giraffes = subject) A PREDICATE: that which is said about something. All giraffes are animals. ◦ (animals = predicate) The COPULA: connects together or separates the S and the P. All giraffes are animals. ◦ (is/is not)

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By QUALITY, ◦ Are we AFFIRMING the predicate of the subject? ◦ Are we NEGATING (i.e., denying) the predicate of the subject? (Ex. 2) By QUANTITY, ◦ Are we saying the predicate applies to ALL of the subject, i.e., is UNIVERSAL? ◦ Are we saying the predicate applies to only SOME of the subject, i.e., is PARTICULAR? ◦ ALL & SOME are QUANTIFIERS (Ex. 1)

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QUALITY Affirmative (+) Negative (-) Universal Particular All S is (are) P. ANo S is P. E Some S is P. ISome S is not P. O All women are human.No cats are dogs. Some men are bald.Some students are not athletes.

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These codes come from the Latin words "Affirmo" and "Nego". Affirmo: I affirm. Note the A and the I ◦ A and I sentences AFFIRM a connection between subject & predicate Nego: I deny. Note the E and the O ◦ E and O sentences NEGATE (deny) link between subect & predicate Ex. 3 & 4

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a. The two premises. All A is B (first premise) Some B is C (second premise) Therefore, Some C is A b. The Conclusion. In the above syllogism, Therefore, Some C is A

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The major term: always the P (predicate) of the conclusion The minor term: always the S (subject) of the conclusion. The middle term: never in the conclusion but appears twice in the premises. (the middle term connects together or keeps apart the S and P in the conclusion). Ex. 6

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A distributed term covers 100% of the things referred to by the term. An undistributed term covers less than 100% of the things referred to by the term (few, many, almost all). For instance, All men are mortal. In this statement, "men" is distributed; for it covers 100% of the things referred by the term "men". In Some men are Italian, "men" is undistributed; for the term covers less than 100% of the things referred to by the term "men".

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Consider the example from the last slide: ◦ All men are mortal. How much of the predicate (i.e., mortal things) are we talking about in that statement? ◦ All mortal things? ◦ Only some of those things that are mortal? Since we can’t be talking about all mortal things in that statement, the predicate is UNDISTRIBUTED.

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QUALITY Affirmative (+) Negative (-) Universal Particular All S is (are) P. A No S is P. E Some S is P. I Some S is not P. O All women are human.No cats are dogs. Some men are bald.Some students are not athletes. DU DD UU U D

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Universal Affirmative statements (A statements): the subject is distributed, the predicate is undistributed. Universal Negative statements (E statements): both the subject and the predicate are distributed. Particular Affirmative statements (I statements): neither subject nor predicate is distributed (both are undistributed). Particular Negative statements (O statements): the predicate alone is distributed. Exercise 5

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FIRST, CONSIDER THE QUALITY OF THE STATEMENTS: Are BOTH premises negative? If YES, quit: it’s invalid (No conclusion follows from two negative premises) If NO, continue,

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If YES, quit: it’s invalid. (Two affirmative premises cannot lead to a negative conclusion) If NO, continue,

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If NO, quit: it’s invalid. (Conclusion MUST be negative if a premise is negative.) If YES, continue,

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Is the MIDDLE TERM distributed in AT LEAST ONE premise? If NO, quit: it’s invalid. (The middle term must be distributed AT LEAST ONCE.) If YES, continue,

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If NO, quit: it’s invalid. (A term distributed in the conclusion MUST also be distributed in the premises.) If YES, the form of the argument (the syllogism) is valid. Ex. 7

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contain hypothetical or conditional statements. e.g. If it is raining, then the ground is wet. If you study, then you’ll get a good grade. If Sue is late, then she must be sick. If we keep building bombs, then we’ll use them some day

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Antecedent: the first simple sentence, usually preceded by if. Consequent: the second simple sentence, usually preceded by then. If (the antecedent) then the (consequent)

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(AA) is a good thing!(DC) a nice place! If P, then Q. P.(AA) Therefore Q(AC) AFFIRMING the antecedent in the 2 nd premise + AFFIRMING consequent in the conclusion. If P, then Q. Not Q.(DC) Therefore not P. (DA) DENYING the consequent in the 2 nd premise + DENYING the antecedent in the conclusion.

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Would you want to be a Dumb A**? Would you like to have ACne? If P, then Q. Not P (DA) Therefore, Not Q. (DC) DENYING the antecedent in the 2 nd premise + DENYING the consequent in the conclusion If P, then Q. Q.(AC) Therefore, P.(AA) AFFIRMING the consequent in the 2 nd premise + AFFIRMING the antecedent in the conclusion.

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Either X or Y. X is true, or Y is true Either I will study or I will watch TV. Either Buddha was right or Christ was right. Either it is raining or the sprinklers are on.

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A disjunctive statement asserts that at least one disjunct is true. (there are STRICT disjuncts, where only one can be true at the same time, but most of our disjunctive statements are “weak” i.e., BOTH could be true) A disjunctive syllogism is valid if one premise denies one disjunct and the conclusion affirms the other.

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DENY 1 DISJUNCT IN PREMISE 2 AFFIRM THE OTHER DISJUNCT IN THE CONCLUSION Either A or B. Not A. Therefore B. Either A or B. Not B. Therefore A.

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ONLY IF the form of the argument is VALID, AND the premises are BOTH TRUE is the conclusion true! That is what constitutes a SOUND argument! A VALID argument DOES NOT guarantee a true conclusion (at least one of the premises could be false)

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