0:00:00.040,0:00:05.920
(intro music)

0:00:05.920,0:00:07.499
My name is Marc Lange.

0:00:07.499,0:00:10.969
I teach at the University of[br]North Carolina at Chapel Hill,

0:00:10.969,0:00:14.469
and today I want to talk to you about[br]the paradox of confirmation.

0:00:14.469,0:00:16.830
It's also known as the[br]"paradox of the ravens,"

0:00:16.830,0:00:20.600
because the philosopher Karl Hempel,[br]who discovered the paradox,

0:00:20.600,0:00:24.340
first presented it in terms of[br]an example involving ravens.

0:00:24.340,0:00:29.949
The paradox concerns confirmation, that[br]is, the way that hypotheses in science

0:00:29.949,0:00:33.180
and in everyday life are supported[br]by our observations.

0:00:33.180,0:00:38.200
As we all know from detective stories,[br]a detective gathers evidence for or

0:00:38.200,0:00:42.729
against various hypotheses about who[br]committed some dastardly crime.

0:00:42.729,0:00:45.379
Typically, none of the individual pieces

0:00:45.379,0:00:47.500
of evidence available to the detective

0:00:47.500,0:00:51.379
is enough all by itself[br]to prove which suspect

0:00:51.379,0:00:53.140
did or did not commit the crime.

0:00:53.140,0:00:57.340
Instead, a piece of evidence[br]might count to some degree in

0:00:57.340,0:01:00.690
favor of the hypothesis[br]that the butler is guilty.

0:01:00.690,0:01:04.229
The evidence is then said[br]to confirm the hypothesis.

0:01:04.229,0:01:08.240
It might confirm the hypothesis[br]strongly or only to a slight degree.

0:01:08.240,0:01:11.270
On the other hand, the[br]piece of evidence might,

0:01:11.270,0:01:14.460
to some degree, count against[br]the truth of the hypothesis.

0:01:14.460,0:01:18.470
In that case, the evidence is said[br]to disconfirm the hypothesis.

0:01:18.470,0:01:21.770
Again, the disconfirmation[br]might be strong or weak.

0:01:21.770,0:01:25.369
The final possibility is that[br]the evidence is neutral,

0:01:25.369,0:01:29.360
neither confirming nor disconfirming[br]the hypothesis to any degree.

0:01:29.360,0:01:33.290
The paradox of confirmation[br]is concerned with the question

0:01:33.290,0:01:37.710
"what does it take for some piece of[br]evidence to confirm a hypothesis,

0:01:37.710,0:01:41.059
"rather than to disconfirm it[br]or to be neutral regarding it?"

0:01:41.059,0:01:44.200
The paradox of confirmation begins with

0:01:44.200,0:01:48.030
three very plausible ideas,[br]and derives from them

0:01:48.030,0:01:51.500
a very implausible-looking[br]conclusion about confirmation.

0:01:51.500,0:01:55.649
Let's start with the first of these[br]three plausible-looking ideas,

0:01:55.649,0:01:58.120
which I'll call "instance confirmation."

0:01:58.120,0:02:01.000
Suppose that we're testing a hypothesis like

0:02:01.000,0:02:04.079
"all lightning bolts are[br]electrical discharges,"

0:02:04.079,0:02:08.360
or "all human beings have[br]forty-six chromosomes," or

0:02:08.360,0:02:09.860
"all ravens are black."

0:02:09.860,0:02:12.989
Each of these hypotheses is general,

0:02:12.989,0:02:16.349
in that each takes the[br]form "all Fs are G,"

0:02:16.349,0:02:18.769
for some F and some G.

0:02:18.769,0:02:23.680
Instance confirmation says that if we're[br]testing a hypothesis of this form,

0:02:23.680,0:02:26.399
and we discover a[br]particular F to be a G,

0:02:26.399,0:02:29.430
then this evidence counts,[br]at least to some degree,

0:02:29.430,0:02:32.040
in favor of the hypothesis.

0:02:32.040,0:02:35.269
I told you this was going to be[br]a plausible-sounding idea.

0:02:35.269,0:02:36.780
Isn't it plausible?

0:02:36.780,0:02:40.840
The second idea is called[br]the "equivalence condition."

0:02:40.840,0:02:45.990
Suppose we have two hypotheses that say[br]exactly the same thing about the world.

0:02:45.990,0:02:48.550
in other words, they are equivalent, in

0:02:48.550,0:02:52.370
the sense that they must either[br]both be true or both be false.

0:02:52.370,0:02:56.280
For one of them to be true and the[br]other false would be a contradiction

0:02:56.280,0:02:59.459
For instance, suppose that one hypothesis

0:02:59.459,0:03:03.629
is that all diamonds are made entirely[br]of carbon, and the other hypothesis

0:03:03.629,0:03:07.370
is that carbon is what all diamonds[br]are made entirely out of.

0:03:07.370,0:03:10.170
These two hypotheses are equivalent.

0:03:10.170,0:03:12.470
What the equivalence condition says

0:03:12.470,0:03:16.200
is that if two hypotheses[br]are equivalent, then any

0:03:16.200,0:03:19.419
evidence confirming one of[br]them also confirms the other.

0:03:19.419,0:03:22.989
this should strike you[br]as a very plausible idea.

0:03:22.989,0:03:27.910
Let's focus on our favorite hypothesis:[br]that all ravens are black.

0:03:27.920,0:03:32.540
The third idea is that this hypothesis[br]is equivalent to another hypothesis.

0:03:32.540,0:03:37.720
That other hypothesis is a very clumsy[br]way of saying that all ravens are black.

0:03:37.720,0:03:44.109
Here it is: that anything that[br]is non-black is non-raven.

0:03:44.109,0:03:49.580
Let me try a different way of explaining[br]the equivalence of these two hypotheses,

0:03:49.580,0:03:52.400
just to make sure that[br]we're all together on this.

0:03:52.400,0:03:57.510
The hypothesis that all Ravens are black[br]amounts to a hypothesis ruling out

0:03:57.510,0:04:00.900
one possibility: a raven that isn't black.

0:04:00.900,0:04:05.450
What about the hypothesis that all[br]non-black things are non-ravens?

0:04:05.450,0:04:09.920
It also amounts to a hypothesis[br]ruling out one possibility:

0:04:09.920,0:04:13.720
a non-black thing that isn't a non-raven.

0:04:13.720,0:04:16.410
In other words, a non-black[br]thing that's a raven.

0:04:16.410,0:04:20.329
So both hypotheses are equivalent[br]to the same hypothesis:

0:04:20.329,0:04:22.930
that there are no non-black Ravens.

0:04:22.930,0:04:26.300
Since the two hypotheses are[br]equivalent to the same hypothesis,

0:04:26.300,0:04:27.880
they must be equivalent[br]to each other.

0:04:27.880,0:04:34.200
Okay, at last, we are ready for[br]the paradox of confirmation.

0:04:34.200,0:04:37.699
Take the hypothesis that all[br]non-black things are non-ravens.

0:04:37.699,0:04:39.639
That's a general hypothesis.

0:04:39.639,0:04:41.889
It takes the form "all Fs are G."

0:04:41.889,0:04:45.370
So we can apply the instance[br]confirmation idea to it.

0:04:45.370,0:04:49.710
it would be confirmed by the[br]discovery of an F that's a G.

0:04:49.710,0:04:53.080
For instance, take the red[br]chair that I'm sitting on.

0:04:53.080,0:04:57.199
I am very perceptive, and I've[br]noticed that it's a non-black thing,

0:04:57.199,0:04:59.430
and also that it's not a raven.

0:04:59.430,0:05:03.190
So the hypothesis that all[br]non-black things are non-ravens

0:05:03.190,0:05:06.990
is confirmed at, least a bit, by[br]my observation of my chair.

0:05:06.990,0:05:09.179
That's what instance confirmation says.

0:05:09.179,0:05:12.380
Now let's apply the equivalence condition.

0:05:12.380,0:05:16.440
It tells us that any observation[br]confirming the hypothesis that all

0:05:16.440,0:05:18.560
non-black things are non-ravens

0:05:18.560,0:05:21.820
automatically confirms any[br]equivalent hypothesis.

0:05:21.820,0:05:25.030
And we've got an equivalent[br]hypothesis in mind:

0:05:25.030,0:05:26.449
that all ravens are black.

0:05:26.449,0:05:29.449
That was our third plausible idea.

0:05:29.449,0:05:35.000
So my observation of my chair confirms[br]that all non-black things are non-ravens,

0:05:35.000,0:05:39.020
and thereby confirms the equivalent[br]hypothesis that all ravens are black.

0:05:39.020,0:05:43.570
Now that conclusion about confirmation[br]sounds mighty implausible,

0:05:43.570,0:05:48.310
that I could confirm a hypothesis about[br]ravens simply by looking around my room

0:05:48.310,0:05:51.680
and noticing that my chair, not to[br]mention my desk and my

0:05:51.680,0:05:55.810
coffee table, that each of them is[br]non-black and also not a raven.

0:05:55.810,0:05:59.630
I can do ornithology while remaining[br]in the comfort of my room.

0:05:59.630,0:06:02.800
So here is the challenge that you face.

0:06:02.800,0:06:07.520
either one of those three ideas must be[br]false, in a way that explains how we

0:06:07.520,0:06:11.150
could have arrived at are false[br]conclusion by using that idea,

0:06:11.150,0:06:15.759
or the conclusion must not in fact[br]follow from those three ideas,

0:06:15.759,0:06:19.620
or the conclusion must be true,[br]even though it appears to be false.

0:06:19.620,0:06:21.830
Those are your only options.

0:06:21.830,0:06:24.890
I leave it to you to think about[br]which of them is true.