WEBVTT

00:00:00.040 --> 00:00:05.920
(intro music)

00:00:05.920 --> 00:00:07.499
My name is Marc Lange.

00:00:07.499 --> 00:00:10.969
I teach at the University of
North Carolina at Chapel Hill,

00:00:10.969 --> 00:00:14.469
and today I want to talk to you about
the paradox of confirmation.

00:00:14.469 --> 00:00:16.830
It's also known as the
"paradox of the ravens,"

00:00:16.830 --> 00:00:20.600
because the philosopher Karl Hempel,
who discovered the paradox,

00:00:20.600 --> 00:00:24.340
first presented it in terms of
an example involving ravens.

00:00:24.340 --> 00:00:29.949
The paradox concerns confirmation, that
is, the way that hypotheses in science

00:00:29.949 --> 00:00:33.180
and in everyday life are supported
by our observations.

00:00:33.180 --> 00:00:38.200
As we all know from detective stories,
a detective gathers evidence for or

00:00:38.200 --> 00:00:42.729
against various hypotheses about who
committed some dastardly crime.

00:00:42.729 --> 00:00:45.379
Typically, none of the individual pieces

00:00:45.379 --> 00:00:47.500
of evidence available to the detective

00:00:47.500 --> 00:00:51.379
is enough all by itself
to prove which suspect

00:00:51.379 --> 00:00:53.140
did or did not commit the crime.

00:00:53.140 --> 00:00:57.340
Instead, a piece of evidence
might count to some degree in

00:00:57.340 --> 00:01:00.690
favor of the hypothesis
that the butler is guilty.

00:01:00.690 --> 00:01:04.229
The evidence is then said
to confirm the hypothesis.

00:01:04.229 --> 00:01:08.240
It might confirm the hypothesis
strongly or only to a slight degree.

00:01:08.240 --> 00:01:11.270
On the other hand, the
piece of evidence might,

00:01:11.270 --> 00:01:14.460
to some degree, count against
the truth of the hypothesis.

00:01:14.460 --> 00:01:18.470
In that case, the evidence is said
to disconfirm the hypothesis.

00:01:18.470 --> 00:01:21.770
Again, the disconfirmation
might be strong or weak.

00:01:21.770 --> 00:01:25.369
The final possibility is that
the evidence is neutral,

00:01:25.369 --> 00:01:29.360
neither confirming nor disconfirming
the hypothesis to any degree.

00:01:29.360 --> 00:01:33.290
The paradox of confirmation
is concerned with the question

00:01:33.290 --> 00:01:37.710
"what does it take for some piece of
evidence to confirm a hypothesis,

00:01:37.710 --> 00:01:41.059
"rather than to disconfirm it
or to be neutral regarding it?"

00:01:41.059 --> 00:01:44.200
The paradox of confirmation begins with

00:01:44.200 --> 00:01:48.030
three very plausible ideas,
and derives from them

00:01:48.030 --> 00:01:51.500
a very implausible-looking
conclusion about confirmation.

00:01:51.500 --> 00:01:55.649
Let's start with the first of these
three plausible-looking ideas,

00:01:55.649 --> 00:01:58.120
which I'll call "instance confirmation."

00:01:58.120 --> 00:02:01.000
Suppose that we're testing a hypothesis like

00:02:01.000 --> 00:02:04.079
"all lightning bolts are
electrical discharges,"

00:02:04.079 --> 00:02:08.360
or "all human beings have
forty-six chromosomes," or

00:02:08.360 --> 00:02:09.860
"all ravens are black."

00:02:09.860 --> 00:02:12.989
Each of these hypotheses is general,

00:02:12.989 --> 00:02:16.349
in that each takes the
form "all Fs are G,"

00:02:16.349 --> 00:02:18.769
for some F and some G.

00:02:18.769 --> 00:02:23.680
Instance confirmation says that if we're
testing a hypothesis of this form,

00:02:23.680 --> 00:02:26.399
and we discover a
particular F to be a G,

00:02:26.399 --> 00:02:29.430
then this evidence counts,
at least to some degree,

00:02:29.430 --> 00:02:32.040
in favor of the hypothesis.

00:02:32.040 --> 00:02:35.269
I told you this was going to be
a plausible-sounding idea.

00:02:35.269 --> 00:02:36.780
Isn't it plausible?

00:02:36.780 --> 00:02:40.840
The second idea is called
the "equivalence condition."

00:02:40.840 --> 00:02:45.990
Suppose we have two hypotheses that say
exactly the same thing about the world.

00:02:45.990 --> 00:02:48.550
in other words, they are equivalent, in

00:02:48.550 --> 00:02:52.370
the sense that they must either
both be true or both be false.

00:02:52.370 --> 00:02:56.280
For one of them to be true and the
other false would be a contradiction

00:02:56.280 --> 00:02:59.459
For instance, suppose that one hypothesis

00:02:59.459 --> 00:03:03.629
is that all diamonds are made entirely
of carbon, and the other hypothesis

00:03:03.629 --> 00:03:07.370
is that carbon is what all diamonds
are made entirely out of.

00:03:07.370 --> 00:03:10.170
These two hypotheses are equivalent.

00:03:10.170 --> 00:03:12.470
What the equivalence condition says

00:03:12.470 --> 00:03:16.200
is that if two hypotheses
are equivalent, then any

00:03:16.200 --> 00:03:19.419
evidence confirming one of
them also confirms the other.

00:03:19.419 --> 00:03:22.989
this should strike you
as a very plausible idea.

00:03:22.989 --> 00:03:27.910
Let's focus on our favorite hypothesis:
that all ravens are black.

00:03:27.920 --> 00:03:32.540
The third idea is that this hypothesis
is equivalent to another hypothesis.

00:03:32.540 --> 00:03:37.720
That other hypothesis is a very clumsy
way of saying that all ravens are black.

00:03:37.720 --> 00:03:44.109
Here it is: that anything that
is non-black is non-raven.

00:03:44.109 --> 00:03:49.580
Let me try a different way of explaining
the equivalence of these two hypotheses,

00:03:49.580 --> 00:03:52.400
just to make sure that
we're all together on this.

00:03:52.400 --> 00:03:57.510
The hypothesis that all Ravens are black
amounts to a hypothesis ruling out

00:03:57.510 --> 00:04:00.900
one possibility: a raven that isn't black.

00:04:00.900 --> 00:04:05.450
What about the hypothesis that all
non-black things are non-ravens?

00:04:05.450 --> 00:04:09.920
It also amounts to a hypothesis
ruling out one possibility:

00:04:09.920 --> 00:04:13.720
a non-black thing that isn't a non-raven.

00:04:13.720 --> 00:04:16.410
In other words, a non-black
thing that's a raven.

00:04:16.410 --> 00:04:20.329
So both hypotheses are equivalent
to the same hypothesis:

00:04:20.329 --> 00:04:22.930
that there are no non-black Ravens.

00:04:22.930 --> 00:04:26.300
Since the two hypotheses are
equivalent to the same hypothesis,

00:04:26.300 --> 00:04:27.880
they must be equivalent
to each other.

00:04:27.880 --> 00:04:34.200
Okay, at last, we are ready for
the paradox of confirmation.

00:04:34.200 --> 00:04:37.699
Take the hypothesis that all
non-black things are non-ravens.

00:04:37.699 --> 00:04:39.639
That's a general hypothesis.

00:04:39.639 --> 00:04:41.889
It takes the form "all Fs are G."

00:04:41.889 --> 00:04:45.370
So we can apply the instance
confirmation idea to it.

00:04:45.370 --> 00:04:49.710
it would be confirmed by the
discovery of an F that's a G.

00:04:49.710 --> 00:04:53.080
For instance, take the red
chair that I'm sitting on.

00:04:53.080 --> 00:04:57.199
I am very perceptive, and I've
noticed that it's a non-black thing,

00:04:57.199 --> 00:04:59.430
and also that it's not a raven.

00:04:59.430 --> 00:05:03.190
So the hypothesis that all
non-black things are non-ravens

00:05:03.190 --> 00:05:06.990
is confirmed at, least a bit, by
my observation of my chair.

00:05:06.990 --> 00:05:09.179
That's what instance confirmation says.

00:05:09.179 --> 00:05:12.380
Now let's apply the equivalence condition.

00:05:12.380 --> 00:05:16.440
It tells us that any observation
confirming the hypothesis that all

00:05:16.440 --> 00:05:18.560
non-black things are non-ravens

00:05:18.560 --> 00:05:21.820
automatically confirms any
equivalent hypothesis.

00:05:21.820 --> 00:05:25.030
And we've got an equivalent
hypothesis in mind:

00:05:25.030 --> 00:05:26.449
that all ravens are black.

00:05:26.449 --> 00:05:29.449
That was our third plausible idea.

00:05:29.449 --> 00:05:35.000
So my observation of my chair confirms
that all non-black things are non-ravens,

00:05:35.000 --> 00:05:39.020
and thereby confirms the equivalent
hypothesis that all ravens are black.

00:05:39.020 --> 00:05:43.570
Now that conclusion about confirmation
sounds mighty implausible,

00:05:43.570 --> 00:05:48.310
that I could confirm a hypothesis about
ravens simply by looking around my room

00:05:48.310 --> 00:05:51.680
and noticing that my chair, not to
mention my desk and my

00:05:51.680 --> 00:05:55.810
coffee table, that each of them is
non-black and also not a raven.

00:05:55.810 --> 00:05:59.630
I can do ornithology while remaining
in the comfort of my room.

00:05:59.630 --> 00:06:02.800
So here is the challenge that you face.

00:06:02.800 --> 00:06:07.520
either one of those three ideas must be
false, in a way that explains how we

00:06:07.520 --> 00:06:11.150
could have arrived at are false
conclusion by using that idea,

00:06:11.150 --> 00:06:15.759
or the conclusion must not in fact
follow from those three ideas,

00:06:15.759 --> 00:06:19.620
or the conclusion must be true,
even though it appears to be false.

00:06:19.620 --> 00:06:21.830
Those are your only options.

00:06:21.830 --> 00:06:24.890
I leave it to you to think about
which of them is true.