Inductive logic

1. Inductive logic • Chapter 3 - Evaluating inductive arguments • A brief review of the differences between inductive and deductive arguments • Our approach to evaluating inductive arguments: the pattern approach • Same as deductive Inductive logic - 1

2. Inductive logic • With a difference: a inductive pattern by itself does not tell us whether the argument is strong or weak. We must look at the content of each pattern. • But knowing the pattern will tell us what content to look for. Inductive logic - 2

3. Inductive logic • E.g., Louis Pasteur’s theory that vaccination with anthrax produces immunity to anthrax disease was confirmed by an interesting experiment. Over twenty farm animals were vaccinated with the virus, and then these animals, plus a like number not so vaccinated, were given a normally fatal dose of anthrax germs. None of the vaccinated animals contracted the disease; all those not vaccinated contracted it. Inductive logic - 3

4. Inductive logic • The 4 basic patterns of inductive argumentation (there are more) • (1) simple generalization • (2) statistical generalization • (3) inductive analogy • (4) hypothetico-deductive reasoning Inductive logic - 4

5. Inductive logic • 1. Simple generalization • e.g., A.S. Pearse spent years watching fiddler crabs in many different places. On the basis of his careful observations, he concluded, among other things, that all fiddler crabs dig burrows and plug up the openings. And all fiddler crabs remain within two yards of their burrows. Inductive logic - 5

6. Inductive logic • Criteria for evaluating • (1) Must have a minimum number of data (observations, information) • (2) The greater the variety of data, the stronger the argument. Inductive logic - 6

7. Inductive logic • 2. Statistical generalization • e.g., On the basis of a survey taken by the Literary Digest in 1936, the Digest predicted that Alfred E. Landon would win the presidential election by a comfortable margin. The Digest mailed out 10 million ballots and had 2,300,000 returned. Roosevelt won by a landslide. What happened? Inductive logic - 7

8. Inductive logic • Criteria for evaluating • (1) The representativeness of the sample. How closely the sample mirrors the population • Skip the section on types of sampling Inductive logic - 8

9. Inductive logic • (2) The sample size • Some considerations • Size of the population is relatively unimportant in deciding on the size of the sample; what is important is the representativeness of the sample • The larger the number of items being sampled, the larger the required size. Inductive logic - 9

10. Inductive logic • The size of the sample required for a representative sample is relative to the size of the error one is willing to accept. • The size of the sample required for a representative sample is relative to the rarity of the variable being sample. Inductive logic - 10

11. Inductive logic • 3. Inductive analogy • E.g., The first industrial revolution, the revolution of the 'dark satanic mills,' was the devaluation of the human arm by the competition of machinery. There is not rate of pay at which a United States pick‑and‑shovel laborer can live which is low enough to compete with the work of a steam shovel as an excavator. Inductive logic - 11

12. Inductive logic • The modern industrial revolution [high speed electronic computers, so called 'thinking machines'] is similarly bound to devalue the human brain at least in its simpler and more routine decisions. Of course, just as the skilled carpenter, the skilled mechanic, the skilled dressmaker have to some degree survived the first industrial revolution, so the skilled scientist and the skilled administrator may survive the second. -- Norbert Wiener, Cybernetics (1948) Inductive logic - 12

13. Inductive logic • Criteria for evaluating • (1) The number of similarities between the two classes, things, or events being compared. • (2) The number of dissimilarities. • (3) The relevance of the similarities mentioned in the premises to the similarity stated in the conclusion. Inductive logic - 13

14. Inductive logic • 4. Hypothetico-deductive reasoning • E.g., Evangelista Torricelli (1608-47) sought to explain why a suction pump will not raise water beyond 34 feet at sea level. He proposed the hypothesis that a sea of air surrounds the surface of the earth and presses down on it, just like water presses down on the bottom of the sea. Water cannot be pumped beyond 34 feet because of this air pressure. In the 1640s, Blaise Pascal (1623-1662) performed an experiment to Inductive logic - 14

15. Inductive logic • (cont’d) test Torricelli’s sea of air hypothesis. Pascal reasoned that if this hypothesis is true, then air pressure should decrease at higher altitudes. He sent his brother-in-law up a mountain to make measurements (using a mercury barometer). The measurements confirmed Pascal’s hypothesis and also, thereby, confirmed Torricelli’s sea of air hypothesis. Inductive logic - 15

16. Inductive logic • The patterns • Pattern of confirmation H  I I  H Inductive logic - 16

17. Inductive logic • The patterns • Pattern of disconfirmation H  I ~ I  ~ H Inductive logic - 17

18. Inductive logic • Criteria for evaluating • (1) Testability • (2) Coherence • (3) Predictive or explanatory power Inductive logic - 18