RI Critical Thinking Unit F (Evaluating Inductive Arguments) 2023

UNIT F Evaluating Inductive Arguments

STRENGTH AND COGENCY ▪ Inductive arguments are evaluated on two grounds: truth of premises and strength ▪ Strength: an inductive argument is strong if the premises are true and it is improbable for the conclusion to be false ▪ i.e. the conclusion is highly likely to be true if the premises are true ▪ Upshot: regardless of the content of the premises, inductive arguments can be evaluated for their strength ▪ A cogent inductive argument is one which is both strong and has true premises

TEST FOR STRENGTH ▪ Assume that the premises are true, ▪ Is the conclusion likely to be true? ▪ If yes, then the argument is strong ▪ If no, then the argument is weak

WHICH IS STRONG? ▪ Eg 1 P1: All dinosaur bones discovered to this day have been at least 20 million years old. C: The next dinosaur bone to be found will be at least 20 million years old. (P1) ▪ Eg 2 P1: All meteorites found to this day contain bananas. C: the next meteorite to be found will contain bananas. (P1) ▪ Eg 3 P1: When a lighted match is immersed in water, the flame will be extinguished. P2: kerosene is a liquid, just like water. C: when a lighted match is immersed in kerosene, the flame will be extinguished. (P1-2)

STRENGTH ▪ Unlike deductive arguments, the strength of inductive arguments consists of degrees ▪ If the conclusion follows with 50% or more probability , it is strong ▪ Otherwise, it is weak

WHICH IS STRONG? ▪ Eg 1 P1: This drawer contains 100 pens. P2: Three pens selected at random were found to be blue. C: All the pens are blue. (P1-2) ▪ Eg 2 P1: This drawer contains 100 pens. P2: Eighty pens selected at random were found to be blue. C: All the pens are blue. (P1-2)

TEST FOR COGENCY ▪ Is the inductive argument strong? ▪ Are the premises true? ▪ If any of the answers is a “no”, then the argument is not cogent. ▪ i.e. an argument needs to be both strong and possesses true premises for it to be cogent ▪ Upshot: possible for an argument to be strong and still not cogent because of false premises.

SOME PERMUTATIONS Strong Weak True premise Probably true conclusion All previous American Presidents were men. Therefore, probably the next American President will be a man. [cogent] A few American Presidents were Christians. Therefore, probably the next American President will be a man. [not cogent] True premise Probably false conclusion None exist A few American Presidents were Christians. Therefore, probably the next American President will be a Christian. [not cogent] False premise Probably true conclusion All previous American Presidents were television debaters. Therefore, probably the next American President will be a television debater. [not cogent] A few American Presidents were Libertarians. Therefore, probably the next American President will be a television debater. [not cogent] False premise Probably false conclusion All previous American Presidents were women. Therefore, probably the next American President will be a woman. [not cogent] A few American Presidents were Libertarians. Therefore, probably the next American President will be a Libertarian. [not cogent]

TEST FOR RELIABILITY ▪ On top of cogency , inductive arguments can be further tested for reliability. ▪ A reliable argument is cogent and: ▪ 1) contains all known relevant information, ▪ 2) and it would be impossible to insert additional premises that would change the probability of the conclusion ▪ Upshot: a cogent inductive argument might not be reliable because of some ‘missing’ information

IS THIS RELIABLE? ▪ Example P1: Swimming in the sea is usually lots of fun. P2: Today, the water is warm, the waves are gentle and there are no dangerous jellyfish lurking around. C: it would be fun to go swimming now. (P1-2)