Hume’s Problem of Induction 2

Seminar 2: Philosophy of the Sciences

Wednesday, 14 September 2011

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Readings

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)

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Extra readings

Stroud, Barry. Hume chapter 3 (on course website)

Skyrms, Brian. Choice and Chance. Chapters 2 and 3 (On course website)

Hume, David. An enquiry concerning human understanding. Section 4. (Go to www.earlymoderntexts.com and click on Hume)

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Tutorials

Tutorials will start next Friday 23 SeptemberClass 1: 1 PM - 2 PM seminar room 305Class 2: 4 PM – 5 PM seminar room 305

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

Required reading and seminar handouts must be brought along to tutorials

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Deductively valid arguments

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

Example:P--------P or Q

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Probabilistically good arguments

Def: An argument is probabilistically good iff its premises make its conclusion probable (that is, its premises provide a good reason for believing its conclusion).

A prima facie plausible example:All examined As have been Bs----------------------------------------The next examined A will be a B

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Types of inference

Def: A deductively valid inference is an inference that occurs in a deductively valid argument

Def: A probabilistically good inference is an inference that occurs in a probabilistically good argument

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Modes of Justification

According to Hume, there are (at most) four ways we can know (or justifiably believe) a proposition p

Way 1 (A priori deductive reasoning): By either intuiting that p or by engaging in a chain of reasoning, each step of which is intuitively certain

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Modes of Justification (cont)

Note: According to Hume (and many others), if P is known on the basis of a priori deductive reasoning, then P is necessary

Way 2 (A priori probabilistic reasoning): Start with what is intuitively obvious, and then make probabilistically good inferences based on that to get a justified (and probably true) belief.

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Modes of Justification (cont)

Way 3 (A posterior deductive reasoning): Start with our experiences and what is known on the basis of intuition, and make deductively valid inferences from there.

Way 4 (A posteriori probable reasoning): Start with experiences in what is known on the basis of intuition and make probabilistically good inferences to some probably true conclusion

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Deductive justification vs probabilistic justification

Def: A belief is deductively justified (DJ) iff it is believed on the basis of either a prori deductive reasoning or a posteriori deductive reasoning

Def: A belief is probabilistically justified (PJ) iff it is believed on the basis of either a priori probabilistic reasoning or a posteriori probabilistic reasoning

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Hume’s inductive scepticism

Hume held that beliefs that are based on inductive arguments are neither deductively justified nor probabilistically justified

He therefore held that these beliefs are not justified at all

As a dramatic illustration: Imagine an inductive skeptic who uses some anti-inductive form of inference. What could we say to change their mind?

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Hume’s argument for inductive scepticism

The sunrise argument (SRA):

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

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Hume’s argument for inductive scepticism (cont)

H1 (Hume’s assumption claim): SRA (and other inductive arguments) assume PF

PF) The future is like the past

H2: Given H1, (B) can only be justifiably believed on the basis of (A) iff PF can be justifiably believed (prior to B)

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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

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Argument for (2)

(2a*) If PF can be deductively justified than either PF is necessary, or PF is a necessary consequence of our experiences (2b*) PF is neither necessary nor a necessary consequence of our experiences----------------------------------------------------------------(2) PF cannot be deductively justified

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Argument for (3)

How could we give a probabilistically good argument for PF?

Plausibly, the best we could do is give an argument like (PFA).PFA: PF has been true in the past--------------------------------------PF will be true in the future

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Argument for (3) (cont)

But by Hume’s assumption claim H1, PFA assumes PF, and hence is circular

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Response 1: The inductive defence of induction

Induction has worked in the past, so we have good reason to think it will work in the future

Objection: This defence is assumes that beliefs based on induction are justified, which is the very thesis that needs a defence.

See Feldman and Skyrms for more discussion

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Response 2: The pragmatic defence of induction

Induction is at least as good as any other method performing beliefs about the unobserved or the future

Objection: Even if this is true, it does not show that we are better off using induction rather than some other (equally good) method

See Feldman and Skyrms for more discussion20

Response 3: Popper’s response

Inductive skepticism is true, but this is okay since science doesn’t need induction. This is because science consist in falsifying theories, rather than in justifying theories.

Objection: Given inductive skepticism, in building a bridge, why should we use a well-tested theory instead of a brand new untested (and non-falsified) theory?

See Godfrey Smith Theory and Reality Sec 4.2 and 4.5 for more discussion 21

Response 4: An a priori defence of induction

In what sense does SRA assume PF?

Answer 1: SRA assumes PF in the sense that PF (or something similar) needs to be added to SRA in order to turn it into a deductively valid argument

Given answer 1, H1 is true but there is no reason to think that H2 is true

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Stroud’s charitable interpretation of Hume

To justifiably believe (B), it is not good enough to believe (A) and then believe (B). One must also believe (A) is a good reason for believing (B). Moreover, this belief must itself be justified.

Hence, in order for someone to justifiably believe (B) on the basis of (A), (C) must be justifiably believed.

(C) (A) is a good reason to believe (B)

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Hume’s new challenge

How can someone justifiably believe (C)?

The a priori answer to Hume’s challenge: We can know (C) is true by intuiting that it is true, just as we can intuit logical truths (such as D) and simple probabilistic claims (such as E).

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Hume’s new challenge (cont)

D) Knowing that snow is white is a good reason for believing that either snow is white or grass is green

E) Knowing that 999 marbles out of 1000 in a jar are black is a good reason to believe that a randomly selected marble from the jar is black

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A consequence of the a priori answer

If (C) can be known by intuition, then it must be necessarily true

Is this the case? Could (C) have been false?

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Will the a priori defence convince an inductive skeptic?

Depends on why they are an inductive skeptic.

If the defense undermines the skeptic’s reasons for being a sceptic, then possibly yes.

If the skeptic is simply crazy then presumably no.

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A new Humean inspired argument for inductive scepticism

• Suppose I am rational but haven’t had any experience.

• Then H1 and H2 have the same probability H1 = (A) and (B) H2 = (A) and not (B) • Now suppose I have all my experiences (eg I have E)• Having this happen doesn’t provide any more

support to H1 than it does to H2

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A new Humean inspired argument for inductive scepticism (cont)

Therefore: Given I have had E, H1 is no more likely than H2

Therefore: I cannot justifiably believe H1 on the basis of my experience

Therefore: The inference from (A) to (B) is not justified

Conclusion: All inductive inferences are unjustified