(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.
Subtitles by the Amara.org community