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```Hume’s Problem of Induction 2
Seminar 2: Philosophy of the
Sciences
Wednesday, 14 September 2011
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Required reading: ‘The Problem of Induction’,
Section I, Chapter 7 of Richard Feldman’s book
Epistemology pp 130-141 (on course website)
Refutation’, Chapter 4 of Peter Godfrey Smith’s
book Theory and Reality (which can be
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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 September
Class 1: 1 PM - 2 PM seminar room 305
Class 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
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 discussion
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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
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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
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
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