INDUCTIVE LOGICINDUCTIVE LOGICDEDUCTION= DRAWING OUT IMPLICIT DEDUCTION= DRAWING OUT IMPLICIT “KNOWLEDGE” OR CLAIMS FROM “KNOWLEDGE” OR CLAIMS FROM PREMISES.PREMISES.

INDUCTION= EXPANDING INDUCTION= EXPANDING “KNOWLEDGE” BY TESTING TRUTH “KNOWLEDGE” BY TESTING TRUTH OF THE PREMISESOF THE PREMISES

CONCERNED WITH WHETHER CONCERNED WITH WHETHER PREMISES ARE TRUE OR PREMISES ARE TRUE OR SUPPORTABLE.SUPPORTABLE.

INDUCTIVE LOGICINDUCTIVE LOGIC• BETTER: CONCERN WITH

STANDARDS FOR EVALUATING THE LOGICAL STRENGTH OF ANY GENERALIZATION.

• LOGICAL STRENGTH OF INDUCTION DEPENDS UPON THE WIDER CONTEXT IN WHICH ARGUMENT OR CLAIMS OCCUR. WIDER CONTEXT= EXPERIENCE, “REAL WORLD.”

INDUCTIVE LOGICINDUCTIVE LOGIC

• BASIC MODE OF INDUCTION: DRAWING A UNIVERSAL CONCLUSION ABOUT A CLASS FROM PREMISES ABOUT MEMBERS OF A CLASS.

• MOVEMENT FROM PARTICULAR TO GENERAL: GENERALIZATIONS, AND WHAT MAKES THEM SUPPORTABLE OR PLAUSIBLE.

INDUCTIVE GENERALIZATIONSINDUCTIVE GENERALIZATIONS

• WE WANT TO KNOW HOW THE GENERAL PROPOSITIONS WE ENCOUNTERED EARLIER AS PREMISES WOULD BE SUPPORTED BY EVIDENCE.

• OR BETTER, WHAT SORT OF EVIDENCE WOULD BE REQUIRED TO SUPPORT THESE GENERALIZATIONS OTHER THAN OTHER PREMISES?

INDUCTIVE GENERALIZATIONSINDUCTIVE GENERALIZATIONS

• HOW DO OTHER INSTANCES OR PARTICULAR EXAMPLES SUPPORT OR NOT THE GENERALIZATION?

• SOME GENERALIZATIONS WE HAVE ENCOUNTERED:

• NO HORNED ANIMAL IS A PREDATOR

• ALL OF SHAKESPEARE’S PLAYS ARE IN BLANK VERSE.

INDUCTIVE GENERALIZATIONSINDUCTIVE GENERALIZATIONS

• METHOD OF COMPLETE ENUMERATION:

• WHEN COMPLETE ENUMERATION IS IMPOSSIBLE OR UNREALISTIC:

• E.G.: ALL GENIUSES ARE ECCENTRIC

• BILL NEVER ADMITS HE IS WRONG.

THE NEED FOR SAMPLESTHE NEED FOR SAMPLES• SAMPLE: AN INCOMPLETE SURVEY• THE THREE “RULES” TO HELP US

DETERMINE WHETHER A SAMPLE IS REPRESENTATIVE.

• RULES DO NOT DIRECTLY ALLOW US TO CONCLUDE WHETHER A GENERALIZATION IS PLAUSIBLE OR NOT.

• SPECIFY THE CONDITIONS THAT NEED TO BE SATISFIED BEFORE WE CAN MAKE THIS JUDGMENT.

SAMPLESSAMPLES

• THEY SPECIFY A WAY OF TESTING GENERALIZATIONS WITHOUT TELLING US HOW TO APPLY THEM.

• RULE 1: THE SAMPLE SHOULD BE SUFFICIENTLY NUMBEROUS AND VARIOUS.

• THE LARGER THE S AND P, THE LARGER THE SAMPLE SIZE.

• HOW LARGE OR NUMEROUS IS SUFFICIENT?

RULES GOVERNING SAMPLESRULES GOVERNING SAMPLES

• VARIETY: OUR SAMPLE OF S SHOULD VARY IN EVERY PROPERTY THAT MIGHT BE RESPONSIBLE FOR THE S BEING A P.

• E.G. SHY PEOPLE ARE NERVOUS AT PARTIES.

• HOW MANY SHY PEOPLE AT PARTIES?

RULES GOVERNING SAMPLESRULES GOVERNING SAMPLES

• WHAT IS SUFFICIENT VARIATION?

• NEED TO VARY ACROSS GENDER, AGE, INTELLIGENCE, TEMPERAMENT, RACE, SOCIAL BACKGROUND, SOCIO-ECONOMIC CONDITION.

• LOOK FOR FACTORS!

• WHAT ABOUT HEIGHT? WEIGHT? POLITICAL VIEWS?

RULES GOVERNING SAMPLESRULES GOVERNING SAMPLES

• WHAT ARE REVELEVANT FACTORS? THIS IS A MATTER OF JUDGMENT!!

• RULE OF THUMB: THE MORE ABSTRACT THE SUBJECT TERM, THE MORE NUMBEROUS AND VARIED THE SAMPLE MUST BE.

RULES GOVERNING SAMPLESRULES GOVERNING SAMPLES• RULE 2: LOOK FOR DISCONFIRMING AS

WELL AS CONFIRMING INSTANCES OF THE GENERALIZATION.

• DISCONFIRMING ONES: EMPHASIS PLACED ON LOOKING HARD FOR DISCONFIRMING INSTANCES.

• REMEMBER: IT IS EASY TO NEGATE OR DISPROVE A UNIVERSAL PROPOSITION. ONLY ONE EXAMPLE OF THE CONTRADICTION IS NEEDED.

RULES GOVERNING SAMPLESRULES GOVERNING SAMPLES• WHAT IF THIS IS DEPENDENT ON PRIOR

KNOWLEDGE?• USE OF IMAGINATION.• HOW WE LOOK FOR DISCONFIRMING

INSTANCES• 1. LOOK FOR CLEAR-CUT CASES;

REGULAR EXAMPLES• 2. LOOK FOR CASES OR EXAMPLES CLOSE

TO THE BORDERLINE.• I.E. “ALL BIRDS CAN FLY.”

RULES GOVERNING SAMPLESRULES GOVERNING SAMPLES• RULE 3: CONSIDER WHETHER THE

LINK BETWEEN S AND P IS PLAUSIBLE IN LIGHT OF OTHER KNOWLEDGE WE POSSESS.

• THE STUDENT MIGHT HAVE SOME SPECIALIZED KNOWLEDGE ABOUT SOMETHING THAT COULD HAVE AN IMPACT ON THEIR JUDGMENT.

• WHAT DO YOU DO WHEN YOU DO NOT HAVE ANY?

RULES GOVERNING SAMPLESRULES GOVERNING SAMPLES• THE NEED FOR EXPERIENCE TO

DETERMINE PLAUSIBILITY?• THOUGHT EXPERIMENT. THE ABILITY TO

IMAGINE AND CONCEPTUALIZE THE KIND OF KNOWLEDGE THAT WOULD BE NEEDED TO TEST FOR PLAUSIBILITY.

• WE THINK ABOUT WHAT KNOWLEDGE WE MIGHT NEED OR COULD ACQUIRE TO HELP US IN OUR JUDGMENT.

• THE OPEN-ENDED CHARACTER OF INDUCTION AND PAGE 460 OF THE TEXT.

• P. QUIZ 15.1.

CAUSALITYCAUSALITY

• WHAT CONNECTIONS BETWEEN S AND P ARE WE LOOKING FOR?

• CAUSAL RELATIONSHIPS

• NEED FOR A GENERAL PURPOSE TECHNIQUE TO HELP US ANALYZE ALL CAUSAL RELATIONSHIPS.

• NECESSARY CONDITIONS:

• SUFFICENT CONDITION:

CAUSALITY: NECESSARY AND CAUSALITY: NECESSARY AND SUFFICIENT CONDITIONSSUFFICIENT CONDITIONS

• E.G. IF I DROP AN EGG IT WILL BREAK. • WHAT ARE THE NECESSARY CONDITIONS

THAT BRING ABOUT THIS? • WHAT IS THE SUFFICIENT CONDITION FOR

THE EGG BREAKING? ALL THE NECESSARY CONDITIONS.

• AVOIDING THE POST HOC FALLACY. DO NOT ASSUME THAT BECAUSE A OCCURRED BEFORE B THAT A CAUSED B.

CAUSALITYCAUSALITY• WHAT EVIDENCE DO WE REQUIRE

TO INFER CAUSE?• JOHN STUART MILL’S METHODS OF

INDUCTION.• 1. AGREEMENT • 2. DIFFERENCE • 3. JOINT METHOD • 4. CONCOMITANT VARIATIONS • 5. RESIDUES.

AGREEMENTAGREEMENT

• IDEA IS TO LOOK FOR A COMMON FACTOR ACROSS DIFFERENT INSTANCES.

• FOR SEVERAL CASES, OR ACROSS SEVERAL CASES, IS THERE ANY FACTOR IN WHICH EACH CASE AGREES?

DIFFERENCEDIFFERENCE

• TAKING AWAY ANY GIVEN FACTOR TO SEE WHETHER THE SAME OR ANOTHER EFFECT OCCURS.

• EG. PLACEBO EFFECT. (BLIND STUDIES AND DOUBLE BLIND STUDIES)

SCHEMATIZING OR SCHEMATIZING OR FORMALIZING THESE METHODSFORMALIZING THESE METHODS

• P. 465.

• AGREEMENT:

• CASE 1: A, B, C E

• CASE 2: A, D, E E

• CASE 3: A, F, G E

THEREFORE A IS RESPONSIBLE FOR E.

SCHEMATIZING OR SCHEMATIZING OR FORMALIZING THESE METHODSFORMALIZING THESE METHODS• DIFFERENCE:• CASE 1: A, B, C E• CASE 2: --, B, C E

• JOINT METHOD: COMBINATION OF AGREEMENT AND DIFFERENCE.

• P. 466.• NEGATIVE AGREEMENT• NEGATIVE DIFFERENCE P. 468.• P. QUIZ 15.2, P. 471.

CONCOMITANT VARIATIONS CONCOMITANT VARIATIONS AND RESIDUESAND RESIDUES

• CONCOMITANT VARIATIONS• IDEA: VARYING THE AMOUNT OR

QUANTITY OF FACTOR TO SEE IF THERE IS A SIMILAR CHANGE IN EFFECT.

• IT ASSERTS THAT VARIATIONS IN QUANITITY BETWEEN CAUSE AND EFFECT SUGGEST SOME CAUSAL CONNECTION.

CONCOMITANT VARIATIONSCONCOMITANT VARIATIONS

• SCHEMATIZING:

• CASE 1: A-, B, C E-

• CASE 2: A, B, C E

• CASE 3 A+, B, C E+

• A MIGHT BE CAUSALLY RELATED TO THE GIVEN EFFECT BUT IT DOES NOT GUARANTEE THAT A IS THE SUFFICIENT CONDITION.

CONCOMITANT VARIATIONSCONCOMITANT VARIATIONS

• ADVANTAGES OF METHOD AND APPLICATION OVER AGREEMENT AND DIFFERENCE.

• THE MOON AND TIDES ON EARTH: CANNOT USE THE METHOD OF DIFFERENCE.

• TESTING FOR LEVELS OF SOMETHING AND ITS SAFETY.

RESIDUESRESIDUES

• THINK OF REMAINDER OR LEFT OVERS.

• WE ALSO QUANTIFY EFFECT• REASONING:• IF A IS A PARTIAL FACTOR IN

CAUSING E AND IF B IS A PARTIAL FACTOR IN CAUSING B, AND STILL BOTH DO NOT COMBINE TO CAUSE E, THEN THERE MUST BE ANOTHER PARTIAL CAUSE, I.E. C.

RESIDUESRESIDUES

• COMMON USES OF METHOD:• 1. WEIGHING DOG ON SCALE WITH YOU.

SUBTRACT YOUR WEIGHT AND YOU ARE LEFT WITH THE DOG’S WEIGHT (THE REMAINDER IS THE DOG’S WEIGHT) LIKE SUBSTITUTION.

• 2. DISCOVERY OF RADIUM:• MARIE AND PIERRE CURIE.

PITCHBLENDE

RESIDUESRESIDUES• POSSIBLE SCHEMA: • P= PITCHBLENDE • U= URANIUM• E= RADIOACTIVITY• CASE 1: U E• CASE 2: P E+ • HENCE, SOMETHING ELSE IS RESPONSIBLE

FOR THE HIGHER LEVELS OF RADIATION: RADIUM!

• P. QUIZ 15.3.