1

Introduction/Hume’s Problem of Induction

Seminar 1: Philosophy of the Sciences

6 September 2011

2

What is this course about?

This course will address some of the fundamental questions in the philosophy of science.

Question 1: Can we know (or have justify beliefs) about what will happen in the future on the basis of past experiences?

Example: Can we know that the sun will rise tomorrow on the basis that it has risen in the past?

3

Question 2

Question 2: When does some putative evidence support or confirm a hypothesis and when does it disconfirm it?

Example: Do observations of Fs being Gs always support the hypothesis that all Fs are Gs?

4

Question 3

Question 3: What is a good explanation?

Example: What makes the drinking of contaminated water a good explanation of certain instances of disease, or the big bang theory a good explanation of the current state of the universe?

Question 4

Question 4: Can we know about the unobserved world on the basis of what we know about the observed world? Relatedly, can we know that our best scientific theories are true, or at least approximately true? Example: Can the observed results of experiments and measurements give us good reason to think that there are electrons, or that global warming is occurring?

5

6

Topics of the course

There will be 10 2hr seminars covering five topics:i) Hume’s problem of inductionii) The Ravens paradoxiii) The Grue paradoxiv) Explanationv) Scientific realism Each topic will be have required and optional readingsFor further administration information, see the course guide

7

Topic 1: Hume’s problem of Induction

Required reading: ‘The Problem of Induction’, Section I, Chapter 7 of Richard Feldman’s book Epistemology pp 130-141 (on course website)

Optional reading: ‘Popper: Conjectures and Refutation’, Chapter 4 of Peter Godfrey Smith’s book Theory and Reality (which can be downloaded from HKU library)

8

Note on required reading

In a few sentences, Feldman uses the following terminology introduced in the early chapters: ‘the standard view’, ‘fallibism’, ‘high standards scepticism’, and ‘modest foundationalism’.

‘The standard view’ means roughly the commonsense view of what we know and how we know it.

The sentences containing the other terms can be ignored without loss.

9

One kind of inductive argument

Inductive pattern 1:

All As examined up till now have been Bs-------------------------------------------------------The next A to be examined will be a B

10

An instance of argument pattern 1

The sunrise argument:

All days examined up untill now have been days on which the sun has risen----------------------------------------------------------------The next examined day (tomorrow) will be a day on which the sun rises

11

A feature of inductive arguments

Inductive arguments like the sun rising argument are not deductively valid arguments

Instead, they are widely believed to be probabilistically good arguments

Def: An argument is deductively valid iff, necessarily, if its premises are true then its conclusion is true

12

What is a probabilistically good argument?

Def: An argument is probabilistically good iff, in the absence of evidence to the contrary, if we know its premises are true, then they give a good reason to believe that its conclusion is ture (that is, iff it is rational for someone who knows its premises and has no evidence to the contrary to believe to a high degree that its conclusion is true)

13

Other inductive patterns of argument

Inductive pattern 2:

All As examined up till now have been Bs-------------------------------------------------------All As are Bs

14

Other inductive patterns of argument (cont)

Inductive pattern 3:

X% of As examined up till now have been Bs-----------------------------------------------------------X% of As are Bs

15

The importance of inductive arguments

If inductive arguments were probabilistically good, then many of our beliefs would be unjustified

Examples: i) beliefs about what restaurants are good,ii) beliefs about what will happen when a light switch is pressed iii) beliefs about how to get to uniiv) the belief that the world will not end tomorrow

16

Hume’s problem

David Hume (1711-1776) asked: Do we have any good reason to accept the conclusions of inductive arguments? (That is, are inductive arguments probabilistically good?)

Hume argued that the answer is no!

17

Hume’s claim

Hume claimed that inductive arguments implicitly assume a principal such as (PF).

(PF) The future will be like the past

Hume thinks that if we add PF as a premise to inductive arguments then we get a valid argument.

But he thinks that we cannot have any justification for believing PF, and hence that we have no justification for believing the conclusion of inductive arguments.

18

Sun rising example revisited

Hume thinks that the following argument is valid, but that we have no justification for its second premise:All days examined up until now have been days on which the sun has risenThe future will be like the past----------------------------------------------------------------The next examined day (tomorrow) will be a day on which the sun rises

19

A problem with PF

It is difficult to formulate a precise and plausible version of PF. (If PF says that the future will be like the past in every respect, for example, then it is false.)

We can ignore the problem of how to precisely formulate PF since Hume thinks that nothing like PF can be justified.

20

Hume’s overall argument that PF cannot be justified

(1) If PF can be justified then either i) it can be justified by a deductively valid argument or ii) it can be justified by a probabilistically good argument

(2) PF cannot be justified by a deductively valid argument

(3) PF cannot be justified by a probabilistically good argument

---------------------------------------------------------------(4) PF cannot be justified

21

Hume’s argument for (2)

(2a) Only truths that are necessitated by our observational evidence can be justified by a deductively valid argument(2b) PF is not necessitated by our observational evidence----------------------------------------------------------------(2) PF cannot be justified by a deductively valid argument

22

Hume’s argument for (3)

(3a) Any probabilistically good argument for PF would assume the truth of PF(3b) Any argument for a principle that assumes the truth of that principle fails to justify that principle-------------------------------------------------------------(3) PF cannot be justified by a probabilistically good argument

23

Hume’s sceptical conclusion

The beliefs we form on the basis of inductive reasoning are unjustified (they are just as likely to be true as false)

We form these beliefs, not because they are rational, but as a result of our psychology.

Moreover, even if we agree with Hume that these beliefs are rational, we cannot refrain from believing them for any length of time. The forces pushing us to believe them is too strong.

24

Next week

This is a very pessimistic conclusion!

Next week we will look at some ways of trying to resist it.