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

2.  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)

3.  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.

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

5.  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

6.  Since…  Because…

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

8.  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)

9.  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

10.  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.

11.  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.

12.  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.

13.  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)

14.  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)

15.  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)

16.  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)

17. 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.

18.  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

19.  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

20.  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

21.  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".

22.  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.

23. 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

24.  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

25.  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,

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

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

28.  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,

29.  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

30.  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

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

32. (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.

33. 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.

34.  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.

35.  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.

36. 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.

37.  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)