Introduction/Hume’s Problem of
Induction
Seminar 1: Philosophy of the
Sciences
6 September 2011
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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?
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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?
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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?
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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?
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Topics of the course
There will be 10 2hr seminars covering five topics:
i) Hume’s problem of induction
ii) The Ravens paradox
iii) The Grue paradox
iv) Explanation
v) Scientific realism
Each topic will be have required and optional
readings
For further administration information, see the
course guide
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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)
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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.
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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
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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
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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
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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)
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Other inductive patterns of argument
Inductive pattern 2:
All As examined up till now have been Bs
------------------------------------------------------All As are Bs
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Other inductive patterns of argument
(cont)
Inductive pattern 3:
X% of As examined up till now have been Bs
----------------------------------------------------------X% of As are Bs
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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 uni
iv) the belief that the world will not end tomorrow
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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!
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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.
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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 risen
The future will be like the past
---------------------------------------------------------------The next examined day (tomorrow) will be a day
on which the sun rises
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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.
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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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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
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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
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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.
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Next week
This is a very pessimistic conclusion!
Next week we will look at some ways of trying to
resist it.
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