2. RATIONALISM OR EMPIRICISM? PURE LOGIC OR A REALLY, REALLY GOOD GUESS?

3. TWO WAYS OF OBTAINING KNOWLEDGE RATIONALISM “Deductive reasoning”— premises necessarily lead to a conclusion Pure logic leads to knowledge and truth A priori thinking—not dependent on sense observation Example: the syllogism EMPIRICISM “Inductive reasoning”— enough good premises lead to the best, most reliable conclusion Observation leads to knowledge and maybe truth A posteriori thinking— dependent on sense observation Example: scientific method

4. PART ONE: RATIONALISM AND TTHE SYLLOGISM A syllogism is an argument with exactly two premises. A standard form categorical syllogism is a syllogism entirely of standard-form categorical propositions, presented as follows: major premise first, minor premise second, conclusion last. Example: Some politicians are women. No wealthy men are women. So, some wealthy men are not politicians.

5. THE MOST SIMPLE EXAMPLE OF A DEDUCTIVE ARGUMENT IS THE SYLLOGISM. A syllogism is a statement of logical relationships. You will likely see them on Law School entrance exams

6. CLASSIC EXAMPLE 1. All men are mortal. 2. Socrates is a man. 3. Therefore, Socrates is mortal.

7. Valid ? Some politicians are women. No wealthy men are women. So, some wealthy men are not politicians.

8. WHY ARE SOME SYLLOGISMS LOGICALLY VALID, OTHERS LOGICALLY INVALID ? Valid forms have no counterexamples Invalid forms admit counterexamples..

9. CAN YOU CREATE A PLAUSIBLE* COUNTEREXAMPLE TO THIS INVALID ARGUMENT ? *One which would convince an intelligent person with no training in logic. First Argument: Some women are politicians. No men are women. So, some men are not politicians. Counterexample: ?

10. A Counterexample to Our Second Argument ? Second Argument: No working poor are wealthy bankers. Some wealthy bankers are Republicans. Some Republicans are not working poor. Counterexample: ? No counterexample possible.

11. A Counterexample to Our Third Argument ? Second Argument: All Republicans are wealthy women. No working poor are wealthy women. So, no working poor are Republicans.. Counterexample: ? No counterexample possible.

12. PARTS OF A SYLLOGISM Major premise: Broad statement of general applicability. Minor premise: Narrower statement of particular applicability. Conclusion: Logical consequence of the major and minor premises.

13. RULES FOR MAKING VALID CATEGORICAL SYLLOGISMS A valid categorical syllogism only has three terms: the major, the minor, and the middle term. MIDDLE TERM 2 Major Term 1 MinorTerm 3

14. RULES FOR MAKING VALID CATEGORICAL SYLLOGISMS  Ex. All gamblers are risk-takers. (A) Some Filipinos are gamblers. (I) Some Filipinos are risk-takers. (I) All gamblers Risk-takers Filipinos Some Filipinos who are gamblers.

15. “ALL” Animals RULES FOR MAKING VALID CATEGORICAL SYLLOGISMS Some animals are pigs. All cats are animals. Some cats are pigs. Some animals Some animals Pigs Cats There is a possibility that the middle term is not the same.

16. RULES FOR MAKING VALID CATEGORICAL SYLLOGISMS Ex. All politicians are sociable people. All councilors are politicians. Therefore, all councilors are sociable people. Politicians (Middle Term) Sociable People (Major Term) Councilors (Minor Term)

17. POWER OF SYLLOGISMS Use of Deductive Reasoning. Conclusion is compelling, based on the premises. The opponent must attack the premise, not the conclusion. Weaknesses: remember the Monty Python Witch Scene?

18. Sociable People RULES FOR MAKING VALID CATEGORICAL SYLLOGISMS Politicians Councilors

19. Corvettes EULER DIAGRAMS (PRONOUNCED “OILER”) Our example: If a car is a Corvette, then it is a Chevrolet. Since all Corvettes are Chevrolets, and Corvettes are just a piece of the Chevrolet line, here is what the Euler looks like: (it would be safe to say that the hypothesis goes ‘inside’ while the conclusion goes ‘outside’.)

20. WHAT ABOUT SUSAN? Consider this:  Susan’s car is a Corvette.  Where does it belong in the diagram? (With Chevrolets or with Corvettes?) Corvettes Susan’s car –The complete process of drawing a conclusion is called a logical argument. –This 3 part argument is called a syllogism

21. © 2008 Pearson Addison- Wesley. All rights reserved 3-5-20 EXAMPLE: USING AN EULER DIAGRAM TO DETERMINE VALIDITY (UNIVERSAL QUANTIFIER) Is the following argument valid? All cats are animals. Figgy is a cat. Figgy is an animal.

22. © 2008 Pearson Addison- Wesley. All rights reserved 3-5-21 EXAMPLE: USING AN EULER DIAGRAM TO DETERMINE VALIDITY (UNIVERSAL QUANTIFIER) All cats are animals. Figgy is a cat. Figgy is an animal. Animals Cats x represents Figgy. x Solution The diagram shows that Figgy is inside the region for “animals”. The argument is valid.

23. © 2008 Pearson Addison- Wesley. All rights reserved 3-5-22 EXAMPLE: USING AN EULER DIAGRAM TO DETERMINE VALIDITY (UNIVERSAL QUANTIFIER) Is the following argument valid? All cars have wheels. That vehicle has wheels. That vehicle is a car.

24. © 2008 Pearson Addison- Wesley. All rights reserved 3-5-23 EXAMPLE: USING AN EULER DIAGRAM TO DETERMINE VALIDITY (UNIVERSAL QUANTIFIER) Solution The diagram shows “that vehicle” can be inside the region for “Cars” or outside it. The argument is invalid. All cars have wheels. That vehicle has wheels. That vehicle is a car. Things that have wheels Cars x represents “that vehicle” x ?

25. © 2008 Pearson Addison- Wesley. All rights reserved 3-5-24 EXAMPLE: USING AN EULER DIAGRAM TO DETERMINE VALIDITY (EXISTENTIAL QUANTIFIER) Is the following argument valid? Some students drink coffee. I am a student. I drink coffee.

26. © 2008 Pearson Addison- Wesley. All rights reserved 3-5-25 EXAMPLE: USING AN EULER DIAGRAM TO DETERMINE VALIDITY (UNIVERSAL QUANTIFIER) Solution The diagram shows that “I” can be inside the region for “Drink coffee” or outside it. The argument is invalid. Some students drink coffee. I am a student. I drink coffee. People that drink coffee Student s I ?

27. Francis Bacon (1561 – 1626 ) A suggestion for a new way of arriving at knowledge The enemies of knowledge: The Four Idols of the Mind Idols of the Mind Idols of the Tribe Idols of the Cave Idols of the Market-Place Idols of the Theater PART II: EMPIRICISM, BACON, SOME IDOLS, AND HIS METHOD

28. IT’S (SOMETIMES) OKAY TO GENERALIZE: EMPIRICAL GENERALIZATIONS The limitation of the empirical generalization is that the premises of your argument could be true but the conclusion false. In other words, it could be true that all the students you saw were blind but the high school was not a school for the blind.

29. BACON, THE MAN! Bacon says that his method is aimed at establishing progressive stages of certainty Bacon believes that a refined method based on the senses will lead to certainty A new logic is needed that goes beyond the errors that continually result from following the older Aristotelian logic (syllogisms)

30. BACON, THE MAN Criticism of the Syllogism A true induction is the only way in which we can avoid the errors of the logic of the Syllogism The foundation of the Aristotelian syllogism is based on notions or concepts If these concepts are hastily generalized, then there will no firm foundation for K

31. As Bacon explains it, classic induction proceeds “at once from... sense and particulars up to the most general propositions” and then works backward (via deduction) to arrive at intermediate propositions. Thus, for example, from a few observations one might conclude (via induction) that “all new cars are shiny.” One would then be entitled to proceed backward from this general axiom to deduce such middle-level axioms as “all new Lexuses are shiny,” “all new Jeeps are shiny,” etc. – axioms that presumably would not need to be verified empirically since their truth would be logically guaranteed as long as the original generalization (“all new cars are shiny”) is true. Why did Bacon like inductive thinking?

32. As Bacon rightly points out, one problem with this procedure is that if the general axioms prove false, all the intermediate axioms may be false as well. All it takes is one contradictory instance (in this case one new car with a dull finish) and “the whole edifice tumbles.” For this reason Bacon prescribes a different path. His method is to proceed “regularly and gradually from one axiom to another, so that the most general are not reached till the last.” In other words, each axiom – i.e., each step up “the ladder of intellect” – is thoroughly tested by observation and experimentation before the next step is taken. In effect, each confirmed axiom becomes a foothold to a higher truth, with the most general axioms representing the last stage of the process.

33. To sum up: Bacon’s Suggestion for a new approach Senses –axioms by gradual and careful ascent –most general axioms last of all 8 Preliminary steps to True Induction Bacon warns us to be on guard of false beliefs. According to Bacon, one needs to clear away these mistakes or sources of error before we can make real progress Sources of error are called by Bacon Idols of the mind