(intro music)

My name is Marc Lange.

I teach at the University of
North Carolina at Chapel Hill,

and today I want to talk to you about
the paradox of confirmation.

It's also known as the
"paradox of the ravens,"

because the philosopher Karl Hempel,
who discovered the paradox,

first presented it in terms of
an example involving ravens.

The paradox concerns confirmation, that
is, the way that hypotheses in science

and in everyday life are supported
by our observations.

As we all know from detective stories,
a detective gathers evidence for or

against various hypotheses about who
committed some dastardly crime.

Typically, none of the individual pieces

of evidence available to the detective

is enough all by itself
to prove which suspect

did or did not commit the crime.

Instead, a piece of evidence
might count to some degree in

favor of the hypothesis
that the butler is guilty.

The evidence is then said
to confirm the hypothesis.

It might confirm the hypothesis
strongly or only to a slight degree.

On the other hand, the
piece of evidence might,

to some degree, count against
the truth of the hypothesis.

In that case, the evidence is said
to disconfirm the hypothesis.

Again, the disconfirmation
might be strong or weak.

The final possibility is that
the evidence is neutral,

neither confirming nor disconfirming
the hypothesis to any degree.

The paradox of confirmation
is concerned with the question

"what does it take for some piece of
evidence to confirm a hypothesis,

"rather than to disconfirm it
or to be neutral regarding it?"

The paradox of confirmation begins with

three very plausible ideas,
and derives from them

a very implausible-looking
conclusion about confirmation.

Let's start with the first of these
three plausible-looking ideas,

which I'll call "instance confirmation."

Suppose that we're testing a hypothesis like

"all lightning bolts are
electrical discharges,"

or "all human beings have
forty-six chromosomes," or

"all ravens are black."

Each of these hypotheses is general,

in that each takes the
form "all Fs are G,"

for some F and some G.

Instance confirmation says that if we're
testing a hypothesis of this form,

and we discover a
particular F to be a G,

then this evidence counts,
at least to some degree,

in favor of the hypothesis.

I told you this was going to be
a plausible-sounding idea.

Isn't it plausible?

The second idea is called
the "equivalence condition."

Suppose we have two hypotheses that say
exactly the same thing about the world.

in other words, they are equivalent, in

the sense that they must either
both be true or both be false.

For one of them to be true and the
other false would be a contradiction

For instance, suppose that one hypothesis

is that all diamonds are made entirely
of carbon, and the other hypothesis

is that carbon is what all diamonds
are made entirely out of.

These two hypotheses are equivalent.

What the equivalence condition says

is that if two hypotheses
are equivalent, then any

evidence confirming one of
them also confirms the other.

this should strike you
as a very plausible idea.

Let's focus on our favorite hypothesis:
that all ravens are black.

The third idea is that this hypothesis
is equivalent to another hypothesis.

That other hypothesis is a very clumsy
way of saying that all ravens are black.

Here it is: that anything that
is non-black is non-raven.

Let me try a different way of explaining
the equivalence of these two hypotheses,

just to make sure that
we're all together on this.

The hypothesis that all Ravens are black
amounts to a hypothesis ruling out

one possibility: a raven that isn't black.

What about the hypothesis that all
non-black things are non-ravens?

It also amounts to a hypothesis
ruling out one possibility:

a non-black thing that isn't a non-raven.

In other words, a non-black
thing that's a raven.

So both hypotheses are equivalent
to the same hypothesis:

that there are no non-black Ravens.

Since the two hypotheses are
equivalent to the same hypothesis,

they must be equivalent
to each other.

Okay, at last, we are ready for
the paradox of confirmation.

Take the hypothesis that all
non-black things are non-ravens.

That's a general hypothesis.

It takes the form "all Fs are G."

So we can apply the instance
confirmation idea to it.

it would be confirmed by the
discovery of an F that's a G.

For instance, take the red
chair that I'm sitting on.

I am very perceptive, and I've
noticed that it's a non-black thing,

and also that it's not a raven.

So the hypothesis that all
non-black things are non-ravens

is confirmed at, least a bit, by
my observation of my chair.

That's what instance confirmation says.

Now let's apply the equivalence condition.

It tells us that any observation
confirming the hypothesis that all

non-black things are non-ravens

automatically confirms any
equivalent hypothesis.

And we've got an equivalent
hypothesis in mind:

that all ravens are black.

That was our third plausible idea.

So my observation of my chair confirms
that all non-black things are non-ravens,

and thereby confirms the equivalent
hypothesis that all ravens are black.

Now that conclusion about confirmation
sounds mighty implausible,

that I could confirm a hypothesis about
ravens simply by looking around my room

and noticing that my chair, not to
mention my desk and my

coffee table, that each of them is
non-black and also not a raven.

I can do ornithology while remaining
in the comfort of my room.

So here is the challenge that you face.

either one of those three ideas must be
false, in a way that explains how we

could have arrived at are false
conclusion by using that idea,

or the conclusion must not in fact
follow from those three ideas,

or the conclusion must be true,
even though it appears to be false.

Those are your only options.

I leave it to you to think about
which of them is true.