PHILOSOPHY!

1. PHILOSOPHY! *** SCORNS: Arrogance. VALUES: Humility. IS HAPPIEST: When your cheeks are wet with tears. ***

2. FROM: Observed Cases TO: Unobserved Case or Generalization Induction Induction is an inference:

3. Examples I’ve observed numerous zebras and all have had stripes. Therefore, all zebras have stripes. I’ve observed numerous zebras and all have had stripes. Therefore, the next zebra I observe will have stripes.

4. More examples. The sun came up today. The sun came up yesterday. The sun came up the day before that. … Therefore, the sun will come up tomorrow.

5. Induction vs. Deduction • Notice that none of these inductive arguments are deductively valid. • It’s possible that the premises are true, but the conclusion false. • (That is, it’s possible that the sun won’t rise tomorrow, or that we’ll discover a zebra without stripes, or fire that is cold, or a bottle that doesn’t fall when dropped.)

6. Hume on Induction • Because inductive arguments are not deductively valid, the premises never guarantee that the conclusion is true. • However, we think that in a good inductive argument the premises show that the conclusion is likely to be true. • Hume’s “Problem of Induction” questions this. Hume argues that we can never even show that the conclusion of an inductive argument is likely to be true.

7. Hume’s problem of induction: The intuitive idea. • What could we say in support of induction? What could we say that would show that induction is a good way of forming beliefs? • It seems like the only thing we can say is: Induction works so well! • But notice the circularity of that reasoning.

8. Hume’s problem of induction: A more rigorous argument. • As we saw, inductive arguments are not valid as they stand. • However, we can make them valid if we specify a key implicit premise. • Let’s call this premise the “Principle of the Uniformity of Nature”.

9. Uniformity of Nature We can put the “Principle of the Uniformity of Nature” (PUN) in a few different, but related, ways: • Nature is uniform. • The future resembles the past • The world admits of representative sampling.

10. Is (PUN) justified? • Hume argues that in order to be justified in believing the conclusion of an inductive argument, we need to be justified in believing (PUN). • But how could we be justified in believing this principle?

11. Is (PUN) justified? • Notice that we can’t give any deductive argument for (PUN). (As we’ve pointed out, there’s nothing that guarantees that the future will be like the past. • So it seems the only way to show that (PUN) is justified is to give an inductive argument.

12. Circularity! • But we can’t give a good inductive argument for (PUN) because, as we saw, all inductive arguments rely on (PUN). • Hume’s conclusion is that there is no way to justify (PUN) and thus we can never be justified in believing anything on the basis of induction.