lecture 7

Question 1

Fact: non-deductive (inductive) resoning

Answer 1

is the most common kind of reasoning in science and our everyday life

Question 2

Two main types of inductive reasoning

Answer 2

Generalization and Prediction

Question 3

Generalization:

Answer 3

object 01, 02, … , 0n each is observed with property P. So all 0s are P

Question 4

Prediction

Answer 4

O1, O2, … On each is observed with property P. So, the next On+1 will be P

Question 5

what is non deductive reasoning

Answer 5

A kind of risky reasoning
Unlike deductively vaid arguments, the conclusion of non-deductive reasoning only follow probabilistically from their premises

E.g. Even if I assume that it is true that each one of the meals served at UvT so far contains cheese, it does not logically follow that all meals at UvT contain Cheese. It does follow that its probably true that all meals being served at UvT contain cheese

Question 6

Possible problem (inductive reasoning)

Answer 6

No inductively strong argument - no matter how strong - guarantees the truth of its conclusion

E.g. Very strong evidence that alcohol abuse leads to liver disease. But this conclusion is “risky” (i.e. is not necessarily certain, even if we take for granted all the available evidence) e.g. it is still logically possible that people predisposed to alcohol abuse are predisposed to liver disease

Question 7

The problem of induction

Three stating observations

Answer 7

1) We (and scientists too) make generalisations and predictions based on inductive reasoning

2) A kind of reasoning is trustworthy (or reliable) if it leads to true conclusions most of the time

3) When we make generalisations and predictions, we seem to implicitly presuppose a uniformity principle: that the laws of nature do not change (the future is like the past), so that unobserved instances of a certain type of object are similar to observed instances

Question 8

How can we justify that induction (generalisations and predictions) is a trustworthy form of reasoning

Answer 8

We cannot justify that induction is trustworthy. We just follow an arational “habit” when we rely on induction

Question 9

the negation of the conclusion of a deductively valid argument

Answer 9

generates a contradiction

E.g. IF i participate in the course, then i will pass the exam

I participate in the course

I pass the exam

If we accept the premises of this argument but deny its conclusion, then we contradict ourselves: We would conclude both that I will pass the exam and that I will not pass the exam

Question 10

the negation of the conclusion of an inductive argument

Answer 10

does not generate a contradiction

E.g.

P1 All students I asked say they enjoy the course

So the next student I ask will say they enjoy the course

If we accept the premise of this argument but deny the conclusion, we are not contradicting ourselves: we could consistently accept both that all students I asked so far enjoy this course and that the next student I will ask does not enjoy this course

Question 11

A non deductive argument for Uniformity principle

Answer 11

Any non deductive argument for UP presupposes what it aims to show, viz. it involves circular reasoning

Question 12

If nature is uniform

Answer 12

use induction –> success

Question 13

If nature is not uniform

Answer 13

use induction –> failure

Use some other method –> failure