Induction

1. Induction

2. The growth of our knowledge • We go on with these questions: • What are the sources of our knowledge? • What is the basis of our knowledge? • Sources: Perception, memory, inference, (testimony)‏ • How can we acquire knowledge? • How can we extend our knowledge? • Inference: The things we already know provide reasons in favour of other beliefs. • We have beliefs about the future events or unobserved events, facts.

3. Inferences in everyday life • Steve forgot his keys again. He will have a hard time getting into the house. • We had seen that some foreign tourists were ripped off in restaurants in Budapest, so we concluded that the foreign tourists would be ripped off in Budapest. • We saw three swans. All of these swans were white, so we conclude that all swans are white. • Joan didn’t come to our date yesterday. She didn’t call or text. I am sure she is breaking up with me.

4. Inductive inferences • The premises are claimed to support the conclusion in a such way that it is improbable that the premises are true and conclusion is false. • All dinosaur bones discovered until this day have been at least 65 million years old. • Therefore: (it is probable that) The dinosaurs became extinct 65 million years ago.

5. Inductive generalisation • (Enumerative inductive generalisation)‏ • The 1. observed individual with property A had a property B. • The 2. observed individual with property A had a property B. • …. • Therefore: The individuals with property A haveproperty B. (All of A’s are B’s.) • Or: All A’s are B’s. • Other form: • All observed A’s were B’s. • So all of A’s are B’s. (inductive generalization) • Or: The next A will also be B.

6. Overgeneralization • It is a common mistake • We conclude a too general conclusion based on a few observed cases and we ignore the differences between the individuals. • Many people have stereotypes. Based on a few experiences they conclude that … • Joan didn’t come to our date yesterday. She didn’t call or text. I am sure she is breaking up with me. How typical!

7. Statistical inferences • In everyday life and in science we encounter statistical inferences. • Commercial: 80 % of the Hungarian dentists recommend Snow White toothpaste. • Science: Statistical evidence gives justification that a certain medicine is probably effective. • These statistical inferences are reliable (strong inductive reasoning), when the sample is representative.

8. Strong and weak inferences • The Sun has risen every day. • Therefore the Sun will rise tomorrow. • -strong • In the past I have never been to Bratislava. • Therefore, I won't be to Bratislava tomorrow. • -weak • How can we set criteria to set dffierent criteria to differentiate between weak and strong inferences? • What presuppositions do you need for your empirical research to yield knowledge? What are the premises that you need for your inquiry?

9. Problems concerning induction

10. Epsitemological problem • How can we differentiate between processes that yield knowledge from those that don’t? • How can we prove that inductive processes yielding knowledge are indeed plausible? (plausible and sound inferences) • Hume reasoned that induction is a habit that is part of the imagination and not of the reasoning capacities of humans. • So if we see a brick moving towards a window, we are right to assume that they will collide and the window will be crashed. However this is purely based on imagination and similarly other possibilities are also imaginable.

11. Hume’s problem of induction • We infer to general rules from particular instances. • Induction as a process yielding knowledge cannot be justified. OR • Whatever induction yields cannot be granted the role of knowledge. (Justified True Beliefs) • We have seen previously that induction can indeed lead to knowledge. • But I only have reason to believe that my experiences make the conclusion of inductive inference probable, if I have reason to believe that events which I have not observed are similar to events which I have observed. • But this cannot be justified unless we presuppose inductive inferences yield knowledge.

12. Goodman’s new riddle of induction • Let’s define the predicate ‘grue’ as: emeralds observed are green before t and blue after t. • How can we know whether we should use the predicate ‘green’ or ‘grue’ to describe emeralds? • Although no one is willing to commit to the existence of the predicate ‘grue’, the paradox clearly shows the asymmetry of inductive inferences concerning the past and the future.

13. Inductive inferences are based on the claim: „The unobserved things are /will be similar to the observed cases.” • We believe (presuppose) that nature is uniform. (Example: The mass of the electron is the same independently from the time and location of the electron.),  inductive inferences can be justified. • But how do we know that? When I appeal to the uniformity of past experience, it begs the question. Experience itself has not given to me reason the unobserved will resemble the observed, because when we argue for this claim we appeal to an inductive inference.

14. Begging the question (Petitio principii)‏ • Ford Motor Company clearly produces the finest cars in the United States. We know they produce the finest cars because they have the best design engineers. • This is true because they can afford to pay them more than other manufacturers. Obviously they can afford to pay them more because they produce the finest cars in the United States. • This argument is clearly fallacious.

15. Question begging argument: Arguer creates the illusion that premises provide adequate support for the conclusion by leaving out a key premise, by restating the conclusion as a premise, or by reasoning in a circle. • One of the premises depend on the truth of the conclusion. • Hume: We have no sufficient reasonsto believe in induction.

16. Back to Hume’s problem of induction • The problem is: the belief that our inductive inferences which are based on experience give us reliable knowledge about the unobserved things cannot be justified. • Because the justification of induction requires the inductive method itself. We enumerate all the previous instances of inductive processes that yielded knowledge to induce the justification of induction. • Therefore believing in induction is irrational. • But: What does 'justification' and 'rational' mean here?

17. Is the justification of induction circular? • This „circularity” is not vicious. This is not a fallacious argument (unlike the former two examples): • Inductive reasoning has proved reliable in the past. Therefore inductive reasoning is generally reliable. • It is not circular, it would be circular if the argument need the premise „(in the future) inductive reasoning is reliable”. • It is not a deductive argument. It would be circular, if it was interpreted as a deductive argument. But the argument is a good inductive argument. • The inductive inferences work, and this is enough. • We don't need a non-circular, deductively valid (sound) argument to give reasons to believe in inductive inferences. • What is wrong with this line of reasoning?

18. Justification and meta-justification • The justification of induction might be circular, but this is not a problem. • People invested in induction differentiate between premise circularity, and rule circularity • Premise circular if the proposition to be proved appears among the premises and rule circular in which the conclusion asserts something about an inferential rule that is used in the very same argument. • We can avoid the pitfalls of Petitio Principii and we don't need further justification. • If our inductive reasonings are reliable (they usually lead to true conclusions), then we can appeal to them. • We don't need to have justified beliefs about that we have justified beliefs. If our beliefs are justified, that's enough.

19. Rationality in everyday life • Hume: Because the induction cannot be justified, therefore believing claims based on induction are irrational. (We believe that because we have instincts, habits, inclinations to them.)‏ • But Hume uses the notion of rationality in a very restricted sense. But actually we use 'rational' in a different sense. • On the contrary: we think that it would be irrational to doubt about that: „the Sun will rise tomorrow.” • It is possible that the Sun won't rise, still it is rational to believe that it will. • Rational ≠ justifiable by an inference! • Why should we accept Hume's conception of rationality?

20. Inference to the best explanation or Abduction • A type of inference in which explanatory considerations are assigned special status. • In the morning you see a plate and a cup on the table surrounded by some breadcrumbs and a jar of jam. You would be correct in inferring to that one of your flatmates already had breakfast. • However, you could also infer that the Breakfast-burglar broke into your home, and had his/her usual breakfast.  however the first explanation seems more plausible

21. Abduction in the history of science • The discovery of Neptune • The orbit of Uranus was discovered to be out of sync as predicted by Newton’s theory of gravity. This might lead us to the conclusion that Newton’s theory was false. Two astronomers suggested that Newton’s theory was not false, there had to be something modifying the orbit of Uranus, and later Neptune was discovered. • The discovery of the electron (Joseph John Thomson) • „As the cathode rays carry a charge of negative electricity, are reflected by an electrostatic force as if they were negatively electrified, and are acted on by a magnetic force in just the way in which this force would act on a negatively electrified moving along the path of these rays, I can see no escape from the conclusion that they are charges of negative electricity carried by particles of matter.”

22. Induction = Inference to the best explanation • Harman: Inductions are inferences to the best explanation. • All observed A’s were B’s. • The best explanation to this fact is that all A’s are B’s. • Therefore All A's are B's • There is no circularity in here. It's an explanation why the induction is reliable. • Sceptic doesn't have an explanation why the inductive inferences work (or why they worked in the past). • There are laws in the nature, which are invariable, and the best scientific theories refer to these laws, and this is the best explanation of why the inductive inferences really work. • The induction is reliable, because in the world there are in fact universal and invariable laws.

23. Inductive inferences and coherence • Inductive principle of inference (IPI) results in increased coherence in knowledge, as long as this belief is true, we are justified in the use of IPI. • Counterexamples: • Both the theory of relativity and quantum theory are taken as justified and true by the scientific community, however the two are incompatible. • Light is described in a similar manner: in certain instances we can conclude to the existence of light-particles, in other instances we conclude that light has the properties of waves.

24. Conclusion • Induction is very common in both everyday and scientific reasoning, however it has several pitfalls. • The problems relevant to epistemology: • Hume’s problem of induction • Goodman’s new riddle of induction • Abduction as a scientific method