phla10 12 the problem of induction - utsc.utoronto.ca

PHLA10 12

The Problem of Induction

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Knowledge versus mere justified beliefKnowledge implies truthJustified belief does not imply truthKnowledge implies the impossibility of errorJustified belief does not imply impossibility of error

Justified belief comes in grades of more or lessYou are more justified in believing you will lose the 649

lottery than in believing this coin will come up headsWe often express this ‘gradation’ in terms of probabilityThe concept of evidence can be expressed in terms of

probability tooP is evidence in favour of Q = P raises the probability

of QLearning you rolled an even number is (some)

evidence in favour of you having rolled a six

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Ordinary skepticism attacks knowledgeClaims that we have no (or almost no) knowledgeDoes not deny that some beliefs are more reasonable

than others ...Does not deny that some beliefs are evidence for others

(e.g. raises their probability)Justified belief skepticism attacks rationality

Claims that we have no reason to think that any belief is either more or less probable than any other

Denies we have any good reason to think that any belief is evidence in favour of (or against) any other possible belief

(A priori beliefs/probabilities may be an exception)

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Review: what is inductionA method of ‘amplifying’ or adding knowledge (or at least

adding to our stock of beliefs)Unlike in a valid deductive argument, the conclusion of

an inductive argument is not guaranteed to be true, even if the premises are true (analogous to justification problem in the JTB theory)

example: (1) Most dogs are pets (2) Fido is a dog (3) therefore, Fido is a pet

Recall what makes a good inductive argumentgood sample sizegood sample distribution (sample must be

representative of total)These requirements assume there are better or worse

evidential relations

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Two (closely related) forms of induction(1) Generalization (GEN)

example: All observed mammals have hair; therefore all mammals have hair.

(2) Prediction (PRED)example: All observed reptiles are cold blooded;

therefore the next reptile to be observed will be cold blooded.

Obviously (GEN) and (PRED) are not deductively valid argument forms.

But it seems intuitively obvious that the premises give us a good reason to believe the conclusion

David Hume argues that this intuition is unsupportable and wrong

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Hume’s versionHume believed that all inductive

arguments involved one crucial assumption: the Principle of the Uniformity of Nature (PUN).

PUN = nature will continue to behave in the future as it has in the past / nature will generally be similar to the way it is around here

(is this like the ‘representative-ness’ condition?)

David Hume (1711-1776)

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How does PUN fit into inductive arguments?Instead of

All thus far observed mammals have hair, so the next mammal we meet will have hair

We haveAll thus far observed mammals have hair and PUN, so

the next mammal we meet will have hairDoes PUN turn an inductive argument into a deductive

argument?Perhaps it is meant to.But what kind of proposition is PUN?

A priori (can be deductively proven)?A posteriori (can only be inductively proven)?

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Is PUN a priori?Can we give a deductive proof of PUN?Is it possible that nature should not be uniform?It seems possibleTherefore, PUN is not a priori

Therefore, PUN is a posterioriSo it must be proven either by observation or inductionWe cannot observe PUN (because it is about the future)So we must give an inductive argument for PUN

Whatever this argument might look like it will be an inductive argument.Therefore, the argument will contain an assumptionThe assumption – according to Hume – will be PUNThis is circular reasoning and cannot show PUN

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Example argument:In the past, PUN has always been trueTherefore (inductively) PUN is true

Hume notes that this argument depends on the assumption that nature will continue to obey PUN

So the argument ought to be:In the past, PUN has always been truePUNTherefore, PUN is true

This argument fails because it blatantly assumes what it wants to prove!

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Hume’s attitude towards inductionHume thought we should reason inductively even though

we have no rational reason to do soHe thought we (and many other animals) are naturally

structured to believe in and use inductionExample: Pavlov’s dogs

Hume sometimes called this ‘habit’He also noticed instincts – which are ‘built in’ by nature

and carry information about how organisms ‘expect’ the world to work

Hume wondered how instincts arose and came somewhat close to a concept of evolution

But rationality cannot support the beliefs expressed in instinct or by the habit of inductive inference

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But is PUN needed for inductive arguments or the attack on induction?

What, exactly, is the content of PUN?

Is nature always ‘uniform’?Do the seasons of the year show

uniformity or diversity?Is the death of animals a feature

of natural uniformity or a sudden dis-uniformity in an animal’s life

It seems impossible to state PUN in any non-trivial wayBut PUN is not needed to create the problem of induction

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Induction and reliabilityWe want our inductive knowledge to be secureLet’s say that a reliable method of inference is one that

usually leads to the truth‘usually’ can be thought of as a scale, from the not

very reliable to the highly reliableexamples: prediction of solar eclipses (highly

reliable) to weather prediction (not highly rel.)This scale can be expressed in terms of probability

The probability of an eclipse given what we know about Sun, Earth and Moon is virtually 1

The probability of snow in the next week (… I check the weather forecast … ) is less than ½

Sober’s version of the problem of inductionHow do we know that induction in general is a

reliable way to get knowledge?

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Sober’s new version of the problem of inductionHow do we know that induction in general is a reliable

way to get knowledge?Now we replay Hume’s pointEither we can deductively prove that induction is a

reliable way to get knowledge, orWe have to inductively prove it is reliableThere is no way to prove deductively that induction is

reliable (because we can consistently imagine induction failing)

But to prove that induction is reliable inductively is to argue in a circle

PUN plays no part in this argument

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Sober’s version of the problem of inductionThink about what this means (it’s a disaster!)We have zero reason to think that induction is reliableThis implies that we have no reason to believe what is

inductively reasonable versus the oppositeExample: we have zero reason to believe that the Sun

will rise tomorrow – it is exactly as reasonable to believe it will not rise as that it will ?!

How can that be right?Can we save induction?

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Strawson’s attempt to save inductionMaybe it is an analytic truth that induction is

a rational way to amplify knowledge(Recall what an analytic truth is)Strawson seems to be claiming that the idea

that induction is a good way to reason is part of the concept of rationality

Suppose that is trueWould this prove that induction is reliable?It would seem not

Sir Peter Strawson (1919-2006)

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Black’s attempt to save inductionRecall the argument in favour of induction:

Induction has been successful in the past, so it will be successful in the future

Is the argument in favour of induction really circular?

Note the difference between a premise of an argument and a rule of inference

Black argues that an argument is circular just in case the conclusion appears (maybe only implicitly) among the premises

On that understanding, the inductive argument in favour of induction is not circular

it just uses the inductive rule of inference Max Black(1909-88)

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Black’s attempt to save inductionIs Black’s notion of circularity right?

Or is there something wrong with an argument that defends a form of argument which you can accept only if you already accept that form of argument?

We could also ask Black: even if we could give this inductive proof of induction,

would that show that induction is reliable?No, because counter-induction (CI) is equally supported by

a counter-inductive argumentCI = if X has happened in the past, expect not-X

example: gambler’s fallacyThe CI argument in favour of CI

CI has failed in the past, so expect it to succeed in the future

This is a good CI argument!

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Sober’s Trip Beyond FoundationalismNote how Sober divides knowledge claims into 3 levels

Indubitable beliefs (a priori / introspectible) Present and past observations Predictions and generalizations

Descartes had problems getting from 1 to 2Hume adds problems getting from 2 to 3

Sober thinks there is just no way to Move deductively from a level to a higher level,Or even use lower level stuff as evidence for higher level

That is, IF one is restricted to the lower levelThis is because something is evidence only relative to

additional ‘background beliefs’Example: phantom limb pain ...

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The relativity of evidenceSuppose we have this evidence: we have examined

10,000 emeralds and they are all greenIs this evidence for: all emeralds are greenNot if we also believe X: There are many emeralds and

they are 99% green OR all emeralds are green but there are very, very few emeralds in the world

Notice that X is not a level 2 statementSober’s thesis: no strictly level n statements justify any

level n+1 statementsWhy? Because of the relativity of evidenceWhat if we had no level n+1 beliefs?Then we could say nothing about level n+1 based only

on level n evidence (except for trivial or a priori truths)Is that true?

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Anti-foundationalism about justificationIs ‘rational justification’ strictly about

inter-level justification?If so, Sober thinks it’s impossible to

achieveOr is there a sense of ‘rational

justification’ that takes into account our current epistemic position?

That is, could we say something likeGiven our current epistemic situation

(what we believe now) evidence E would justify belief P

This assumes an idea of ‘shared epistemic situation’

“Neurath’s Boat”

phla10 12 the problem of induction - utsc.utoronto.ca

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