Lecture 3 Inductive and Abductive Arguments Li Jianhui

Two Gambling Strategies The extreme conservative: This individual refuses to wager unless winning is a sure thing. –Its virtue: He will never loose a gamble; –its limitation: there are gambles he will decline that he could have won. The thoughtful risk taker: this individual at times enters into risky gambles hoping to win. –Its virtue: it can lead him to win wagers by taking risks; –its limitation: he can loose money.

Two Gambling Strategies Limiting to deductive arguments is a conservative strategy. –The virtue: you avoid the risk of reaching false conclusion from true premisses; –The limitation: you decline to say anything that goes beyond the evidence. Nodeductive arguments are riskier. –The gain: you can reach true conclusion that go beyond what the premisses say; –The risk: you may reach false conclusion from true premisses.

Science is a risky business In science as well as in everyday life, we make nondeductive inference all the time. We often are prepared to take risk. Scientists often try to reach conclusions about universal laws. When scientists conclude that a universal law is true or probably true, based on premisses that describe the observations they have made, they aren’t making a deductively valid argument.

Science is a risky business Science is a very ambitious enterprise. Science ventures beyond what strictly observed in the here and now, just as the conclusion in a nondeductive argument ventures beyond the information strictly contained in the premisses. Detective work is also taking risk. There are two sorts of nondeductive inference: indeductive and abductive.

Induction Inductive inference involves taking a description of some sample and extending that description to items outside the sample. E.g.: 60%of the county voters called are democrats.→About 60% of the county voters are democrats. Inductive strength is not a yes/no matter; arguments are either stronger or weaker. Two factors influence inductive strength –Sample size –Representativeness or unbiasedness of the sample

Abduction Inference to the best explanation. E.g.: Mendel’s theory of genetic factor. –A set of observations doesn’t deductively imply a theory; –But a theory deductively implies some observations. This corresponds more closely to what Mendel did. –So a better representation of Mendel’s inference might go like this: The theory entailed a prediction; the prediction came true; hence the theory is probably true. Note that this argument is not deductively valid (the logical form is on page 27). Successful prediction isn’t absolutely conclusive proof that the theory is true. –On the other hand, if the predictions entailed by Mendel’s theory had come out false, that would have followed him to deduce that the theory is mistaken. That is: a failed prediction is conclusve proof that the theory implying the prediction is false.

Abduction The surprise principle: –An observation O strongly supports H 1 over H 2 if both the following conditions are satisfied, but not otherwise: (1) if H 1 were true, O is to be expected; and (2) if H 2 were true, O wouldn’t have been expected. –The surprise principle explains why success of “safe” predictions provides less compelling evidence than the success of “daring” predictions. The only game in town fallacy: –If you don’t want to accept my explanation about something, you must produce a more plausible explanation of your own. If you can’t, you have to accept my explanation. Now we commit an abductively fallacy: the Only Game in Town Fallacy. –Abduction is sometimes described loosely as follows: if a theory expains some observation, and if no rival account is available that can do a better job of explain it, then you should accept the theory. Although this description of abduction is roughly correct, it makes the mistake of sanctioning the Only Game in Town Fallacy. The fact that no rival account is better than the explanation I conduct doesn’t show my explanation is even minimally plausible.