Today’s Outline
III.
Hume’s Problem of Induction
A. Two Kinds of Skepticism
B. Three Distinctions
1. Deduction vs. Induction
2. Relations of Ideas vs. Matters of Fact
3. A Priori Knowledge vs. A Posteriori Knowledge
C. The Problem of Induction
1. The Principle of the Uniformity of Nature
2. The Argument
D. Hume’s Anti-Rationalism
E. Some Replies to Hume’s Argument
1. Analytic Inductionism
2. Induction Justifies Induction
3. Evidential Relativism
David Hume (1711-1776)
• British philosopher and historian
• Considered the greatest philosopher to
write in the English language
• Greatest Philosophical Work: A Treatise of
Human Nature (1739)
(this was began when he was 23 years old)
• Famous doctrines: empiricism, skepticism.
• Immanuel Kant said Hume “awoke me from
my dogmatic slumber.”
III. Hume’s Problem of Induction
A. Two Kinds of Skepticism
• Skepticism about knowledge
– Perhaps after reading Descartes we
conclude we can’t be absolutely certain
about the external world.
– Perhaps we can live with this.
• Skepticism about justification
– Hume is here to tell us we have no reason
whatsoever to believe certain things we
thought obvious.
– This would be hard to live with.
B. Three Distinctions
1. Deduction vs. Induction
2. Relations of Ideas vs. Matters of Fact
3. A Priori Knowledge vs. A Posteriori
Knowledge
1. Deduction vs. Induction
“All reasonings may be divided into two kinds,
namely demonstrative reasoning, or that
concerning relations of ideas, and moral
reasoning, or that concerning matter of fact and
existence”
- from Hume’s Enquiry (1777)
1. Deduction vs. Induction
In deductive reasoning (or for deductive
arguments), it is supposed to be that:
• the premises logically entail the conclusion
• the truth of the premises guarantees the
truth of the conclusion
• it is impossible for the premises to be true
and the conclusion to be false.
1. Deduction vs. Induction
EXAMPLES of deductive arguments:
EXAMPLE 1:
1. All men are mortal.
2. Socrates is a man
--------------------------------3. Therefore, Socrates is mortal.
1. Deduction vs. Induction
EXAMPLES of deductive arguments:
EXAMPLE 2:
1. Deduction vs. Induction
EXAMPLES of deductive arguments:
EXAMPLE 2:
1. If it’s raining, then the streets are wet.
2. It’s raining.
--------------------------------3. Therefore, the streets are wet.
1. Deduction vs. Induction
EXAMPLES of deductive arguments:
EXAMPLE 3:
1. Deduction vs. Induction
EXAMPLES of deductive arguments:
EXAMPLE 3:
1. All cats are toaster ovens.
2. All toaster ovens can fly.
--------------------------------3. Therefore, all cats can fly.
1. Deduction vs. Induction
In inductive reasoning (or for inductive
arguments), it is supposed to be that:
•
the premises support (without logically
entailing) the conclusion
•
the truth of the premises makes likely the
truth of the conclusion
•
it is improbable for the premises to be true
and the conclusion to be false
1. Deduction vs. Induction
EXAMPLES of inductive arguments:
1. Deduction vs. Induction
EXAMPLES of inductive arguments:
EXAMPLE 1:
1. Every emerald that has ever been
observed is green.
--------------------------------2. Therefore, all emeralds are green.
1. Deduction vs. Induction
EXAMPLES of inductive arguments:
EXAMPLE 2:
1. Deduction vs. Induction
EXAMPLES of inductive arguments:
EXAMPLE 2:
1. The sun has risen every day in the past.
--------------------------------2. Therefore, the sun will rise tomorrow.
1. Deduction vs. Induction
EXAMPLES of inductive arguments:
EXAMPLE 3:
1. Deduction vs. Induction
EXAMPLES of inductive arguments:
EXAMPLE 3:
1. Every time I have eaten bread in the
past it has nourished me.
--------------------------------2. Therefore, the next time I eat bread it
will nourish me.
The target of Hume’s Problem of Induction is
just this sort of inductive reasoning.
Although such reasoning seems totally
legitimate and rational and justified, Hume aims
to show that it is in fact totally unjustified.
In other words, Hume aims to show that the
premises of such arguments provide no reason
at all to think that the conclusion is true.
B. Three Distinctions
1. Deduction vs. Induction
2. Relations of Ideas vs. Matters of Fact
3. A Priori Knowledge vs. A Posteriori
Knowledge
2. Relations of Ideas vs.
Matters of Fact
“All the objects of human reason or enquiry
may naturally be divided into two kinds, to wit,
Relations of Ideas, and Matters of Fact.”
2. Relations of Ideas vs.
Matters of Fact
“Propositions of this kind are
discoverable by the mere operation of
thought, without dependence on what is
anywhere existent in the universe.”
2. Relations of Ideas vs.
Matters of Fact
DEFINITION: relations of ideas are
statements that are true simply in virtue of the
concepts contained in them, and not in virtue
of the way the world is.
They are “true by definition.”
They usually seem to be fairly trivial truths.
2. Relations of Ideas vs.
Matters of Fact
EXAMPLES:
• ‘All triangles have three sides.’
• “Three times five is equal to half of thirty.”
• ‘If Bob is a bachelor, then Bob is
unmarried.’
• ‘Either it’s raining or it’s not raining.’
Relations of ideas are also called analytic
truths.
2. Relations of Ideas vs.
Matters of Fact
DEFINITION: matters of fact are statements
that are not relations of ideas.
So when they are true, they are true not in
virtue of the concepts contained in them but in
virtue of the way the world is.
They are NOT true by definition.
They tend to be substantive rather than trivial.
2. Relations of Ideas vs.
Matters of Fact
EXAMPLES:
• ‘The earth is round.’
• “The sun will rise tomorrow.”
• ‘All bachelors have messy apartments.’
• ‘Either it’s raining or it’s snowing.’
Matters of fact are also called synthetic truths.
Hume says, “The contrary of every matter of
fact is still possible.”
B. Three Distinctions
1. Deduction vs. Induction
2. Relations of Ideas vs. Matters of Fact
3. A Priori Knowledge vs. A Posteriori
Knowledge
3. A Priori Knowledge vs.
A Posteriori Knowledge
3. A Priori Knowledge vs.
A Posteriori Knowledge
DEFINITION of a priori knowledge:
S knows (or is justified in believing) p a priori
if and only if S knows (or is justified in
believing) p independent of experience.
That is: if and only if S’s reason for believing
p makes no mention of any sensory
experience.
‘a priori’ is Latin for ‘from what is before’
3. A Priori Knowledge vs.
A Posteriori Knowledge
EXAMPLES of things that can be known a priori:
• ‘All triangles have three sides.’
• ‘The internal angles of any triangle total 180º.’
• ‘If Bob is a bachelor, then Bob is unmarried.’
• ‘Either it’s raining or it’s not raining.’
RECALL: the Ontological Argument was an a
priori argument for the existence of God. If it is
sound, then ‘God exists’ is knowable a priori.
3. A Priori Knowledge vs.
A Posteriori Knowledge
TWO MORE THINGS about a priori knowledge:
• When we say you can know a priori that ‘All
triangles have three sides’, we are NOT saying
you would know this even if you never had any
experiences. We are saying the justification for
believing the proposition need not involve any
evidence from experience.
• Things that one can know a priori may also be
knowable a posteriori. (E.g., I know a
posteriori that Fermat’s Last Theorem is true,
even though it is knowable a priori.)
3. A Priori Knowledge vs.
A Posteriori Knowledge
DEFINITION of a posteriori knowledge:
S knows (or is justified in believing) p a
posteriori if and only if S knows (or is justified
in believing) p through experience.
That is: if and only if S’s reason for believing
p involves some sensory experience(s).
‘a posteriori’ is Latin for ‘from what comes
after’
B. Three Distinctions
1. Deduction vs. Induction
2. Relations of Ideas vs. Matters of Fact
3. A Priori Knowledge vs. A Posteriori
Knowledge
QUESTION:
Are there any interesting connections
between the relation of ideas / matter of
fact distinction and the a priori / a posteriori
distinction?
SOME HUMEAN ANSWERS:
• We can have a priori knowledge of a
proposition only if it is a relation of ideas.
• Matters of fact can be known only a
posteriori.
C. The Problem of Induction
• The “Problem of Induction” is an
argument (a deductive argument) for
the following conclusion:
The premises of an inductive argument
never provide any reason to think that
the conclusion is true.
Inductive Arguments:
1. Every emerald that has ever been observed is green.
--------------------------------2. Therefore, all emeralds are green.
1. Pressing the brake pedal has always stopped my car.
--------------------------------2. Therefore, pressing the brake pedal will stop my car in
the future.
1. Breathing has never killed me.
--------------------------------2. Therefore, my next breath won’t kill me.
So if Hume is right, then the next time you
want to stop your car, it would be no more
rational to press the brake pedal than to
snap your fingers!
1. The Principle of
the Uniformity of Nature
“all inferences from experience [about what will
happen in the future] suppose, as their
foundation, that the future will resemble the past
… . If there be any suspicion, that the course of
nature may change, and that the past may be no
rule for the future, all experience becomes
useless, and can give rise to no inference or
conclusion.”
PUN: The future, by and large, will
resemble the past.
2. The Argument
FIRST PART:
1. If there is any reason to believe PUN,
then our justification for PUN is either
a priori or a posteriori.
2. Our justification for PUN is not a priori.
3. Our justification is not a posteriori.
------------------------------------------4. Therefore, there is no reason to
believe PUN.
2. The Argument
SECOND PART:
4. There is no reason to believe PUN.
5. If there is no reason to believe PUN,
then the premises of an inductive
argument never provide any reason to
think that the conclusion is true.
-----------------------------------------------------6. Therefore, the premises of an inductive
argument never provide any reason to
think that the conclusion is true.
In other words:
induction is totally unjustified.
You thus have no more reason to believe
– ‘The next time I press the brake pedal in
my car, my car will stop.’
than you do this:
– ‘The next time I press the brake pedal in
my car, my car will blow up.’
You have absolutely no reason to think
your next breath won’t kill you.
D. Hume’s Anti-Rationalism
“Even after we have experience of the
operations of cause and effect, our conclusions
from that experience are not founded on
reasoning, or any process of the
understanding.”
“Men are not impelled by any reasoning or
process of the understanding, but rather from
Custom or Habit. ... Custom, then, is the great
guide of human life.”
E. Some Replies
to Hume’s Argument
1. Analytic Inductionism
2. Induction Justifies Induction
3. Evidential Relativism