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(intro music)

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My name is Marc Lange.

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

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

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

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because the philosopher Karl Hempel,
who discovered the paradox,

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first presented it in terms of
an example involving ravens.

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

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and in everyday life are supported
by our observations.

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

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against various hypotheses about who
committed some dastardly crime.

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Typically, none of the individual pieces

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of evidence available to the detective

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is enough all by itself
to prove which suspect

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did or did not commit the crime.

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

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favor of the hypothesis
that the butler is guilty.

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The evidence is then said
to confirm the hypothesis.

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

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On the other hand, the
piece of evidence might,

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

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

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Again, the disconfirmation
might be strong or weak.

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The final possibility is that
the evidence is neutral,

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neither confirming nor disconfirming
the hypothesis to any degree.

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The paradox of confirmation
is concerned with the question

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

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

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The paradox of confirmation begins with

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three very plausible ideas,
and derives from them

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a very implausible-looking
conclusion about confirmation.

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

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which I'll call "instance confirmation."

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Suppose that we're testing a hypothesis like

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"all lightning bolts are
electrical discharges,"

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

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"all ravens are black."

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Each of these hypotheses is general,

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

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for some F and some G.

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

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and we discover a
particular F to be a G,

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then this evidence counts,
at least to some degree,

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in favor of the hypothesis.

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

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Isn't it plausible?

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The second idea is called
the "equivalence condition."

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

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in other words, they are equivalent, in

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

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

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For instance, suppose that one hypothesis

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

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

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These two hypotheses are equivalent.

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What the equivalence condition says

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is that if two hypotheses
are equivalent, then any

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evidence confirming one of
them also confirms the other.

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this should strike you
as a very plausible idea.

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

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

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

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

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

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

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

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one possibility: a raven that isn't black.

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

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It also amounts to a hypothesis
ruling out one possibility:

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

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

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So both hypotheses are equivalent
to the same hypothesis:

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that there are no non-black Ravens.

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Since the two hypotheses are
equivalent to the same hypothesis,

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they must be equivalent
to each other.

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

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

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That's a general hypothesis.

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It takes the form "all Fs are G."

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So we can apply the instance
confirmation idea to it.

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

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

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

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and also that it's not a raven.

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

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

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That's what instance confirmation says.

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Now let's apply the equivalence condition.

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It tells us that any observation
confirming the hypothesis that all

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non-black things are non-ravens

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automatically confirms any
equivalent hypothesis.

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And we've got an equivalent
hypothesis in mind:

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that all ravens are black.

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That was our third plausible idea.

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

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

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Now that conclusion about confirmation
sounds mighty implausible,

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

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

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

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

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So here is the challenge that you face.

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

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

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

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

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Those are your only options.

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