The Problem of Induction
REVIEW
Topics
So far in class we’ve discussed the following
philosophical questions:
• What is (the essence of) knowledge?
• Is knowledge possible?
• Is knowledge of other minds possible?
Other Minds
Last time we considered the problem of other
minds: how can we know that other people/
animals have minds and mental states, and how
can we even conceive of the minds and mental
states of others?
Solutions to the Problem of Other
Minds
We considered 3 potential solutions:
1. We know that other people have minds by
reasoning from analogy with our own mind.
2. We know that other people have minds,
because mental states are a kind of behavior,
and we can observe behavior.
3. We know that other people have minds in
the same way we know electrons exist: it’s
the best explanation for what we observe.
Analogy
The biggest issue facing the analogy solution to
the problem of other minds was that it tries to
argue from what is true in one case (our own
mind) to what is true in every case (everybody
else’s mind). This isn’t usually a good inference
(what is true at my house, or in my country is
not necessarily true in every house or every
country), and there’s no reason to think the
mind is unusual in this regard.
Behaviorism
Behaviorism has a truly unimpeachable solution
to the problem of other minds. Unless we are
global skeptics and don’t believe we can even
know about others’ behaviors, then of course (if
behaviorism is true) we can know about other
minds. The biggest problem for behaviorism was
that it is so radically implausible: one and the
same belief can lead to radically different
behaviors, and identical behaviors can be
produced by radically different beliefs.
Abduction
On the abductive strategy, we don’t take
behaviors as being identical to mental states, we
take behaviors as evidence for people’s mental
states. The best explanation for people’s
behaviors is that they have a complex array of
mental states that cause them to act in certain
ways (i.e. functionalism or computationalism is
true). The biggest problem here is that it doesn’t
suggest how we can know that others have
conscious inner mental lives.
Today
Today we’ll be considering another variety of
local skepticism: induction skepticism. The basic
problem is that we are only directly aware of
things we have observed. If we want to know
about things we haven’t observed (for example,
future things), we must infer how they are from
how the observed things are. But how do the
observed things tell us anything at all about the
unobserved ones?
INDUCTION
Kinds of Inference
C.S. Pierce (1839-1914), an American pragmatist
philosopher (in fact, the founder of
pragmatism), was the first to divide inferences
into three types:
• Deductive
• Abductive
• Inductive
Jars of Balls
Jars of Balls
Imagine that we are reasoning about a jar full of
a mix of red and black balls. For any ball it can
have one of three features (or their opposites):
• J = it is in the jar
• S = it is part of a random sample of balls taken
from the jar
• R = it is red
Deductive Arguments
A deductive argument (also known as a logically
valid argument) is an argument such that if the
premises are true, then the conclusion must be
true; the premises can’t all be true while the
conclusion is false; if the conclusion is false, at
least one of the premises must also be false.
Deduction Example
Everything in the jar is red; this sample is taken
from the jar; so everything in this sample is red.
[Rule] All J’s are R’s.
[Case] All S’s are J’s.
Therefore,
[Result] All S’s are R’s.
Abductive Arguments
An abductive argument, unlike a deductive
argument, is ‘ampliative’: the conclusion goes
beyond what is contained in the premises.
Abductive arguments are also called ‘inferences
to the best explanation.’ We observe some
phenomenon, think about all the different ways
it could have been produced, and conclude that
it was produced in the way that is most
plausible, best fits with our other theories, etc.
Abduction Example
Everything in the jar is red; everything in the
sample is red; so the sample came from the jar.
[Rule] All J’s are R’s.
[Result] All S’s are R’s.
Therefore,
[Case] All S’s are J’s.
Generalized Abduction
X% of what’s in the jar is red; Y% of what’s in the
sample is red; so the sample came from the jar.
[Rule] X% of J’s are R’s.
[Result] Y% of S’s are R’s.
Therefore,
[Case] All S’s are J’s.
Inductive Arguments
Inductive arguments are also ‘ampliative’ in that
the truth of their premises does not guarantee
the truth of their conclusions. Inductive
arguments reason from what’s true of a sample,
to what’s true of the population as a whole.
Polling is an example of induction, as are
inferences from past experience to future
experience (since what’s past is only a sample of
what happens).
Induction Example
This sample is taken from the jar; everything in
the sample is red; so everything in the jar is red.
[Case] All S’s are J’s.
[Result] All S’s are R’s.
Therefore,
[Rule] All J’s are R’s.
Generalized Induction
This sample is taken from the jar; Y% of what’s
in the sample is red; so X% of what’s in the jar is
red.
[Case] All S’s are J’s.
[Result] Y% of S’s are R’s.
Therefore,
[Rule] X% of J’s are R’s.
Enumerative Induction
A common form induction takes is what is
known as enumerative induction:
a1 is F and G
a2 is F and G
…
an is F and G
Therefore, everything that is F is G
Example of Enumerative Induction
Fruit #1 is a durian that smells bad.
Fruit #2 is a durian that smells bad.
…
Fruit #563 is a durian that smells bad.
Fruit #564 is a durian that smells bad.
Therefore,
All durians smell bad.
Need Not Infer to a Rule
Fruit #1 is a durian that smells bad.
Fruit #2 is a durian that smells bad.
…
Fruit #563 is a durian that smells bad.
Fruit #564 is a durian that smells bad.
Therefore,
Fruit #565, if it’s a durian, will smell bad.
“Generalized Deduction”
Another form that induction can take is not
often discussed by philosophers: it’s the
‘generalized’ form of the deductive argument:
[Rule] X% of J’s are R’s.
[Case] All S’s are J’s.
Therefore,
[Result] Y% of S’s are R’s.
Example
90% of French people like to eat snails.
Pierre is a French person.
Therefore, Pierre likes to eat snails.
Maybe this isn’t induction? It’s definitely neither
deduction nor abduction.
HUME’S PROBLEM OF INDUCTION
David Hume (1711-1776)
Hume
David Hume was a Scottish Enlightenment
thinker (other notables include the economist
Adam Smith, the poet Robert Burns, and the
philosopher Thomas Reid). He is widely
regarded as one of the two greatest Western
philosophers after Plato and Aristotle (the other
is Kant). He wrote his most important work, the
Treatise on Human Understanding, when he was
only 26 years old.
British Empiricism
Hume is often grouped with John Locke (16321704) and George Berkeley as a British
Empiricist. The empiricists believed that all ideas
came from experience, and that all knowledge
came from experience. Empiricism is thus a sort
of local skepticism: it’s the view that knowledge
about things that cannot be experienced is
impossible– and, additionally, it is impossible to
even think of things that can’t be experienced.
Impressions vs. Ideas
Hume begins Section II of the Enquiry by
observing that remembering or imagining a
sensation is like perceiving that sensation, but
never so like as to be confused with actually
perceiving that sensation. Hume calls the mental
state one is in when one is actually perceiving
some sensation an ‘impression’. He calls the
mental state one is in when one remembers or
imagines a sensation an ‘idea’.
Humean Empiricism
Hume’s version of empiricism says that all
simple ideas are copies of simple impressions.
(The restriction to simple ideas and simple
impressions is a nod to the fact that we can have
a complex idea, like an idea of a golden
mountain, without ever having had an
impression of a golden mountain.)
Arguments for Humean Empiricism
1. By introspection we can see that all our ideas
are either simple, and always attended by a
prior impression of which they are copied; or
complex, and analyzable into such simple
ideas.
2. People who are blind or deaf have no ideas
of colors or sounds, respectively, and that
people who have never tasted wine or felt
anger have no ideas of such sensations or
emotions.
Hume’s Challenge
If there is a counterexample to Humean
empiricism (a simple idea that is not derived
from a prior sense impression), Hume
challenges his reader to produce it.
The Missing Shade of Blue
Infamously, Hume then goes on to produce a
counterexample himself: the missing shade of
blue.
Hume wants you to imagine that you have never
seen one particular shade of blue (no
impression of it). But then you are presented
with a sequence of all the other shades, with
the missing shade removed.
The Missing Shade
Missing Shade Counterexample
Now you still have not ever had an impression of
the missing shade. However, Hume thinks that
when you see the sequence of other shades
converging on the missing one, you will be able
to come to an idea of it. So you can have an idea
that is not copied from any impression.
The Tribunal of Experience
At the end of Section II, Hume proposes what
Reid later derisively called the “tribunal of
experience.” Whenever someone purports to
talk about something (say, justice) we ask a
series of questions:
Is the idea of justice simple or complex?
The Tribunal of Experience
If it is simple, what impression is it copied from?
[If there’s no impression, there’s no such thing
as justice.]
If it is complex, what are its simple constituents?
What impressions are those simple constituents
copied from? [If we can’t find the impressions,
then there’s no such thing as justice.]
Division of Types of Knowledge
Hume divides all human knowledge into two
types: knowledge of logical truths (relations of
ideas) and knowledge of matters of fact.
Knowledge of relations of ideas is logical or
mathematical. It is certain, and it is a
contradiction to deny any true relation of ideas.
Logical Truths
The way Hume is thinking, a logical truth is
something that you cannot even imagine is
false.
You can’t, for example, imagine a case where
you have two cats on the left, 10 cats on the
right, yet more cats on the left than there are on
the right. There’s no problem with knowing how
they’re true, because you can never even
suppose them to be false.
Matters of Fact
Knowledge of matters of fact divides into two
further subcategories: (a) the immediate
testimony of the senses, and of memory; and (b)
knowledge inferred from such testimony.
I’ll reserve the expression ‘knowledge of matters
of fact’ for the second type, that is, not the
immediate deliverances of the senses or
memory. This is how Hume uses the expression.
Matters of Fact = Unobserved Facts
Thus “matters of fact” are the unobserved
things that we ordinarily think we know about.
We know that people are now living in Australia,
though we can’t see them, we know that
tomorrow, the sun will come up, even though
we haven’t yet experienced what happens
tomorrow.
The Problem of Induction
The problem of induction is thus the problem of
justifying our beliefs in matters of fact.
It’s clear that our sense experience justifies us in
our beliefs regarding observed phenomena. But
what about our sense experience (or logic and
mathematics) justifies us in believing matters of
fact?
Not Justified by Logic Alone
No matter of fact is a logical truth (this is
definitional). That is, it is possible to imagine
that there are no people in Australia, or that the
sun will not come up tomorrow.
However, maybe matters of fact are the
deductive consequences of our sense
experience (plus maybe some logical truths as
well).
Not Justified Deductively
Matters of fact are not arrived at by logical
deduction. If we could reason deductively from
all our past sense experience + all our
knowledge of logical and mathematical truths to
conclude a certain matter of fact, then it should
be contradictory to imagine our past experience
being the same, but the matter of fact coming
out differently.
Not Justified Deductively
For example, there’s no contradiction in
supposing that the sun has risen every day of
our past experience, but the sun won’t rise
tomorrow. This is a possible course of events.
This means that there is no deductive argument
from our past experience to the conclusion that
the sun will rise tomorrow. Because in a
deductive argument, it’s impossible that the
premises are true, and the conclusion is false.
Justified by Cause-Effect Reasoning
Hume therefore concludes, “All reasonings
concerning matter of fact seem to be founded
on the relation of cause and effect.”
Example
Whenever we’re asked ‘Why do you believe
that?’ about some matter of fact, we cite our
knowledge of its cause, or some effect it has had
on us. For example, when asked ‘Why do you
believe there’s a person in this dark room?’ I
might reply ‘Because I heard his voice, and
people are the causes of human voices.’
How Do We Know Causal Relations?
Now the question arises: how do we know
causal relations? What justifies our belief in
them?
For example, how do we come to know that
humans are the causes of human voices, or that
one billiard ball striking another causes the
other to move?
Not Justified by Logic Alone
We don’t know causal relations merely by
inspecting our ideas. Adam and Eve couldn’t just
look at water, for example, and know from its
appearance of transparence and liquidity that it
would cause them to suffocate and drown if
they tried to breathe it.
Similarly, you can’t just tell by looking that a
particular piece of stone is magnetic. You need
experience to know these things.
Not Justified by Logic Alone
We cannot infer causal relations on the basis of
logic alone, because any cause may be
consistently supposed to have different effects.
It’s no contradiction to think that if ball A strikes
ball B, ball B doesn’t move; it goes up; it goes
down; it is annihilated; it turns into Bozo the
Clown, etc.
Justified by the Laws of Nature
Maybe, we might respond, we know the causal
relations because we deduce them from laws.
For example, a logical consequence of Newton’s
Second Law, F = ma, is that if I apply a force of
1N to a billiard ball with mass 1kg, it will
accelerate at 1 meter per second squared. I
know which causes have which effects because I
know the laws.
How Do We Know the Laws?
But this only pushes the problem back. How do
we know the laws of nature?
Even though with, say, Newton’s laws we can
deduce the motion of the ball, still Newton’s
laws are not known by logic alone, but rather
discovered by experience. (In fact, subsequent
experimentation has shown these laws to be
false).
We Must Learn Them from Experience
OK, so we know that we discover causal
relations/ laws of nature by experience. But how
exactly does our experience justify our beliefs
about causal relations?
Hume is going to argue that nothing about our
experience justifies our conclusions about causal
relations/ laws of nature.
Inferring the Future from the Past
We should like to reason as follows:
Premise 1. In the past, water has always
quenched my thirst.
… [insert other premises we know] …
Conclusion: Therefore, in the future, water will
continue to quench my thirst.
Assuming What’s at Issue
To simply take arguments of this form (without
the missing premises filled in) is to assume that
induction is justified. But that is what is at issue:
we want to know why induction is justified (why
we are justified in believing unobserved matters
of fact), and it is no help to be told ‘well, I’m
assuming it is, that’s why.’
The Uniformity of Nature
If I can’t reason in this way, all my knowledge of
matters of fact will be unjustified. For I took the
voice in the dark room to indicate the presence
of a person, only because in the past, words
have always been spoken by people.
The needed premise seems to be, that the
future will resemble the past. But again, how do
we know this?
Again, Not By Logic Alone
We certainly don’t know it by logic alone, for it is
no contradiction to suppose the past was one
way, and the future will be entirely different.
Furthermore, it can’t be a logical truth, because
sometimes it’s false: As Hume says, “Nothing so
like as eggs; yet no one, on account of this
appearing similarity, expects the same taste and
relish in all of them.”
Can’t Reason from Experience
Second, we can’t learn that the future will
resemble the past from experience. Consider:
Premise 1. In the past, later events always
resembled earlier, similar events.
… [insert other known premises] …
Conclusion: Therefore, at present and in the
future, later events will resemble earlier, similar
ones.
Circular Inductive Argument
Again, to simply take arguments of this form
(without the missing premises filled in) is to
assume that induction is justified. But that is
what is at issue: we want to know why induction
is justified, and it is no help to be told ‘well, I’m
assuming it is, that’s why.’
Circular Deductive Argument
We could add in a premise to make the
argument deductive. The needed premise seems
to be the conclusion, that the future will
resemble the past.
No Deductive Argument at All
And we cannot find a non-circular premise among
the things we believe about observables + logic that
would make the argument deductive.
Given what we believe about observables + logic, it
is always possible to deny the conclusion of an
inductive argument (“the sun won’t rise
tomorrow”). But if the conclusion followed
deductively from what we believed about
observables + logic, this would be impossible.
Do Laws Help?
Would it help if we moved to a formulation
regarding laws? Maybe our past experiences
justify us in believing in a certain law of nature,
and that law then justifies our causal claims
(water quenches thirst) and our predictions
about the future (water will quench thirst)
Inferring the Future from the Past
Premise 1. In the past, water has always
quenched my thirst.
… [insert other premises we know] …
Conclusion 1: Therefore, it is a law that water
drinking is followed by thirst quenching.
Conclusion 2: Therefore, in the future, water will
continue to quench my thirst.
Abductive Argument?
Here it’s possible to deny that the inference
from Premise 1 to Conclusion 1 is inductive and
to deny that it’s deductive. The inference is
abductive: the best explanation for the
regularity of the past was that it is a law of
nature that water quenches thirst. Since it is a
law of nature, we can conclude (Conclusion 2)
that in the future water will quench thirst (laws
are true always and everywhere).
Does It Work?
First, it’s not clear that this sort of abductive
argument is a good one. Something like a law
that enforced this regularity in the past may in
fact be the best explanation for the regularity in
the past. But we haven’t observed any regularity
in the future.
Does It Work?
For example, suppose everyone you observe in
Hong Kong drives on the left side of the road. It
might make sense to infer that there is a law of
the road in HK that everyone should drive on the
left. But it wouldn’t make sense to infer that
there is a law of the road everywhere that
everyone should drive on the left.
Wouldn’t It Overgeneralize?
Suppose in the past that no one has ever made
a stinky tofu pizza. Surely it doesn’t follow that
there is a law of nature: stinky tofu pizzas
cannot be made.
Regularities in the past don’t always suggest
laws. So if we’re going to maintain the abductive
inference from Premise 1 to Conclusion 1, we
have to say why this case is special.
Conclusion
Hume denies that any species of inductive
inference (from the observed to the
unobserved), such as causal inference, can be
justified. It can’t be justified inductively on pain
of circularity. It can’t be justified deductively,
because we can always deny the conclusion of
such an inference. And it can’t be justified by an
appeal to laws, because the evidence only
supports laws concerning the observed entities,
not laws concerning the unobserved ones.
HUME’S SOLUTION
The Association of Ideas
Hume proposes that there is a universal, innate
mechanism in the mind that connects ideas
together.
He calls this a ‘principle of connection,’ but don’t
be misled: it is a mechanism, not an abstract
principle.
Arguments for the Mechanism
1. If you pick up a serious book, say a philosophy
book, any particular sentence will be related to
the sentence before it, and related to the
sentence afterward.
2. The same thing is true even in more free-form
conversations, and in dreams.
Arguments for the Mechanism
3. Even when it seems not to be true in
conversation, if you stop and ask someone who has
just brought up a new topic, he will be able to
provide you with the connection to the old topic
that led him to think of the new one.
4. Unrelated languages tend to have words for the
same complex ideas. So there is probably some
universal, innate mechanism that connects the
same simple ideas into complex ideas among all
people.
Three Ways to Get Connected
There are, says Hume, only three ways ideas get
connected to one another by the mind:
• 1. Resemblance
• 2. Contiguity in place or time
• 3. Cause/ effect
There could be more, but Hume can’t think of any.
Proof that the Mind Connects These
1. Resemblance: if we see a picture, we think of
the person it is a picture of, because the picture
resembles her.
2. Contiguity in place or time: if we’re talking
about one apartment in a building, we naturally
think of the others.
3. Cause/ effect: if we think of a wound, we’re
likely to also think of the pain it causes.
Brute Inductive Mechanism
We may now wonder why the mind connects
two events A and B causally, when (if Hume is
right) there is no rational basis for belief in
causal relations.
Hume’s solution to this problem is that there is
no rational reason why the mind behaves this
way, that’s simply the way it’s built.
Not All Behavior is Rational
Sometimes there is no good reason to behave in
a certain way, and we still do it. Sometimes we
even know that there is no good reason, but we
still do it. For example, we might take
methamphetamines, despite our knowledge
that our habit is killing us– not because we have
a good reason to, but because that is how we
are built– we are addicted and cannot stop.
Induction is Brute, Not Rational
Hume’s view of inductive inference is like this.
He thinks that we do it out of “habit” or
“custom” (though he might better say
“compulsion”).
Even if we recognize that inductive inferences
are never justified, we cannot help but continue
to reason as though they were justified.
Hume’s Model: Belief
Hume is going to present a model of the mind on
which this picture is true and plausible. He begins
by asking, what is it to believe something?
Belief is not a further idea that, when we add it to
another idea, makes the latter into a belief. For the
mind is free to combine any of its ideas in any way
it chooses, but it is not free to believe whatsoever it
wishes.
Belief = Vivid Idea
Therefore, belief is a sentiment or attitude towards
an idea. Hume says that this sentiment cannot be
described to anyone who doesn’t have it (just as
red can’t be described to a blind man), but we can
analogize it to a “more vivid, lively, forcible, firm,
steady conception of an object.”
These are the aspects of belief, says Hume, that
make it more influential than imagination; of more
apparent importance; and able to govern our
actions.
Causal Reasoning
What it is for the mind to have the habit of
inferring B from A, as in causal reasoning, is for
the force or vivacity of A to be conferred on B.
Thus when we have an A-impression (very vivid),
we are led to a vivid B idea, and thus believe B.
Causation Preserves Vivacity
Hume thinks that the mind is led to associate
two things F and G causally when they are
“constantly conjoined”– that is, when every F in
the past has been G (for example, every durian
has been smelly, or every cup of water has
always quenched my thirst. Association (in the
causal way) preserves vivacity, so that if A and B
are causally associated, and I believe (vivid
image) A, then I will believe (vivid image) B.
Resemblance Preserves Vivacity
But is it only causal reasoning that is vivacity
preserving in this way? Hume argues that all the
principles of association operate similarly.
Resemblance. Suppose I see a picture of my friend
X. Since the picture resembles X, I am led to an idea
of X by the principle of resemblance. Is this idea
more vivid than usual? Hume says yes. We can
observe that all our X-directed emotions grow
stronger on confronting his picture.
Contiguity Preserves Vivacity
The importance here is that the transition is
vivacity-preserving. If I weren’t looking at my
friend’s picture, even if I thought of it and this led
me to think of him, I would not have a vivid idea of
my friend.
Contiguity. Suppose you’re on a train, approaching
home. Your thoughts of home get stronger and
more forceful as you approach the surrounding
areas.
Hume’s Associationist Mind
1. We have vivid impressions of what’s going on in
our immediate environment.
2. When any of these impressions are resembling,
contiguous, or constantly conjoined, our mind
associates the ideas copied from them.
3. When subsequently confronted with a vivid
impression of something, the vivacity-preserving
associative mechanisms cause us to think of
associated ideas vivaciously.
4. Since belief = vivid ideas, our impressions lead
us to beliefs about things not immediately
present to our senses.
Reasons to Think Induction is Brute
1. Conscious reasoning is slow, and our survival
requires quick causal inferences.
2. Infants aren’t rational, but they still must learn.
3. Conscious reasoning is liable to error, whereas
brute mechanisms never run astray. (Hume
doesn’t mean factual error—induction often
reaches the wrong conclusion. He means error
in function, not drawing the conclusion one is
supposed to draw from the experiences one has,
whether this conclusion is right or not).
Conclusion
There is no reason why (rationally) we should
reason inductively. However, our minds are
associative and thus there is a reason why
(causally) we reason inductively.
KANT’S SOLUTION
Immanuel Kant (1724-1804)
Immanuel Kant
Immanuel Kant was a German philosopher
whose principal concern was to surmount the
skeptical challenges offered by thinkers like
Berkeley and Hume. Kant often vies for Hume
for the title of greatest non-Ancient-Greek
Western philosopher. Kant credited Hume with
awakening him from his “dogmatic slumber.”
Phenomena vs. Things in Themselves
Kant thought that the phenomenal world (the
world that we experience) was the joint product
of “things in themselves” (external objects out
there) and principles of the mind.
The Mind Structures Reality
The mind thus imposes a certain structure on
the phenomenal world. Kant thought, for
instance, that things in themselves did not exist
in space and time, but the mind structured all
experience so that the phenomena were in
space and time.
Preconditions of Experience
We could therefore know independently of
experience that everything was located in space
and time even though this is not a logical truth.
Hume missed a third way of justifying beliefs: 1.
as logical truths, 2. inferred from experience
and, crucially, 3. as a precondition imposed by
the mind on experience itself.
Euclidean, Newtonian Structure
Kant further thought that “space-time is
Euclidean” and “Newton’s laws are true” are
preconditions the mind places on experience.
The mind orders all of its experiences so that
they conform to a Euclidean, Newtonian
structure. Thus we can know that in the future,
Newton’s laws will hold, because experience
itself is impossible without those laws.
The Problem with Kant
Kantian ideas were very popular until about the
early 20th Century, when it was discovered that
space-time was not Euclidean, and that
Newton’s laws were false at speeds approaching
the speed of light. Either Kant was wrong that
the mind imposes a certain structure on reality,
or he was wrong to think that we could find out
what aspects of the structure were contributed
by the mind.
POPPER’S SOLUTION
Sir Karl Popper (1902-1994)
Karl Popper
Popper was an influential philosopher of
science– perhaps the most influential of the 20th
Century.
He proposed that Hume was right, but that we
didn’t need induction anyway.
Induction Not Needed
According to Popper, no scientific theory,
hypothesis, law, or causal claim can every be
justified or shown to be probable (or more
probable than its competitors).
Induction is not a source of justification, and we
don’t need it to be.
Falsifiability
The important notion in science for Popper is
falsifiability– when it is possible to show that a
theory or hypothesis is false, by observing a
counterexample to it. For example, “all durians
are smelly” is falsifiable, because it is possible
(in theory) to observe a durian that is not false.
We should adopt the “strongest” scientific
theories, and then try hard to falsify them.
Those that survive, we keep.
Strength
A theory is strong when it is easier to falsify.
Thus “the sun will continue to rise” is stronger
than “the sun will continue to rise until 21
December 2012” because to falsify the former,
you have to observe just one day out of them all
when the sun doesn’t rise, whereas to falsify the
latter, the sun needs to not rise on one
particular day, which is obviously less likely.
Corroboration
A theory is corroborated when we have tried
many times to falsify it, but have not yet
succeeded. So the theory of general relativity is
very well corroborated, because we have spent
billions of dollars and billions of person-hours
trying to test its predictions, and so far it has
survived all the tests.
Rational to Prefer, Not Justified
We should rationally prefer the strongest (most
easily falsifiable) and most corroborated
theories we can find, according to Popper.
However, just because it is rational to prefer
them does not mean they are supported by the
evidence. According to Popper, the problem of
induction shows that such theories are never
supported by the evidence.
Problems
Popper focused on science, and his
philosophical approach just doesn’t seem right
for everyday life.
It’s not merely that we should rationally prefer
the theory “rat poison is deadly to eat,” but that
we are justified in not eating rat poison, because
of its past record in killing those who ate it.
What’s So Great about Falsifiability?
Furthermore, while Popper attacked theories he
thought weren’t falsifiable (psychoanalysis, for
example) as being unscientific, it seems as
though lots of unfalsifiable claims are within the
bounds of science: “there are durians that are
not smelly” cannot be falsified. Smelly durians
are compatible with the claim (others might not
be smelly), and non-smelly durians are also
compatible (it’s what the claim claims).
SUMMARY
Today’s Question
“Is it possible to know (non-logical facts) about
unobserved things?”
Hume against Induction
Hume famously argued that the answer was
“no”:
• All of our inferences about unobserved
instances (matters of fact) require causal
reasoning.
• Causal reasoning is a species of induction: an
inference from observed instances to
unobserved instances.
Hume against Induction
• Induction can’t be justified by induction, on
pain of circularity.
• But it can’t be justified deductively either–
otherwise we’d be certain of the conclusions
of inductive arguments, and we never are.
• We might infer laws from observed instances,
and then deduce future consequences, but it’s
difficult to elucidate why or how such
abductive arguments are suitable.
Potential Solutions
In addition to the abductive inference strategy
(laws are the best explanation for our past
observations, and they entail what we will
observe in the future), we considered three
other potential responses.
Hume’s Skeptical Solution
Hume thought that we should accept that there
is no justification for inductive inferences. He
gave arguments that people are made by nature
to reason inductively, and that what we took to
be rational inferences were simply unstoppable
brute mental mechanisms with no grounding in
reason.
Kant’s Idealist Solution
Kant thought we knew the laws because they
weren’t themselves matters of fact, but rather
preconditions of experience. Since the mind
contributed the laws to the phenomenal world,
we could inspect our minds to know they were
true. The problem with Kant’s view is its bad
track record of telling us what the preconditions
of experience are.
Popper’s Falsificationist Solution
An influential 20th Century philosopher of
science, Popper argued that we could do
without inductive inference altogether,
unjustified or not. He claimed that we should
rationally prefer strong, corroborated theories,
even though they could never be justified by the
evidence. This rings hollow in everyday life, and
is outmoded in the philosophy of science as
well.