PHLA10 12
The Problem of Induction
PHLA10 12
The Problem of Induction
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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The Problem of Induction
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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The Problem of Induction
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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The Problem of Induction
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
PHLA10 12
The Problem of Induction
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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The Problem of Induction
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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The Problem of Induction
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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The Problem of Induction
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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The Problem of Induction
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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The Problem of Induction
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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The Problem of Induction
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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The Problem of Induction
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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The Problem of Induction
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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The Problem of Induction
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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The Problem of Induction
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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The Problem of Induction
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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The Problem of Induction
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 Problem of Induction
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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The Problem of Induction
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”
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