If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Main content

Epistemology: The Paradox of the Ravens

In this video, Marc Lange (UNC) introduces the paradox of confirmation, one that arises from instance confirmation, the equivalence condition, and common inference rules of logic.

Speaker: Dr. Marc Lange, Professor of Philosophy, University of North Carolina at Chapel Hill.

Want to join the conversation?

  • aqualine ultimate style avatar for user lilifehertoi
    I don't understand how the instance confirmation works. If I see a black raven how does that in any way confirm that ALL ravens are black? That would be like seeing a Chinese person and concluding that all humans are Chinese.
    (8 votes)
    Default Khan Academy avatar avatar for user
  • aqualine sapling style avatar for user Busterwithprotons
    At , But what if the chair is black?
    (6 votes)
    Default Khan Academy avatar avatar for user
  • duskpin ultimate style avatar for user nayfat2001
    What about black things which are non-ravens ?
    (3 votes)
    Default Khan Academy avatar avatar for user
  • leaf green style avatar for user jose.rueda
    At , Dr. Lange says that finding a particular F to be a G would tip the balance in favor of the hypothesis. At the end, the red chair example paradoxically "makes sense" and suggests that the strangely phrased hypothesis is indeed true: "All non-black things are non-ravens". However, using the red chair observation with the first hypothesis in mind ("All ravens are black") seems quite strange and nonsensical. The red chair has nothing to do with ravens or the hypothesis that they may all be black. So, doesn't it seem that an observation, in order to really support two equal hypotheses, must be logically attached to both statements?

    In other words, in order to claim that an observation really does make two equal statements truer, does it not have to apply to both?
    (2 votes)
    Default Khan Academy avatar avatar for user
    • ohnoes default style avatar for user Tejas
      Not really. If one hypothesis is true, then the other must be true, so supporting one hypothesis also supports the other. Looking for confirmation has more to do with relative population sizes of things to look at. For example, in a world with a trillion ravens and only three non-black things, then showing that one of the non-black things is a red chair, not a raven, does more to confirm that all ravens are black than showing that one of the trillion ravens in the world is black.
      (4 votes)
  • blobby green style avatar for user jrey2010
    Instance confirmation requires every instance to be observed before you can really make a conclusion right? So if you observe a non-black thing that's not a raven, you've partly confirms that all raven are black. Now all you have to do is observe the rest of the non-black things in the universe and notice that none of them are ravens to fully confirm that all ravens are black.
    (3 votes)
    Default Khan Academy avatar avatar for user
    • duskpin ultimate style avatar for user Chara S.
      True. You'd also have to observe every raven in the universe to confirm that they are, in fact, all black. This is not true, however, because not all ravens are black. If you could go back in time to see every raven that has ever existed, you would come across an extinct species, the Pied Raven. Quite a lot of the Pied Raven is not black. Also, this doesn't take into account albinism and things like that.
      (2 votes)
  • orange juice squid orange style avatar for user Daniel Rigal
    I am not sure that equivalence is the weakest link in the chain of argument but I can see two arguments against it.

    1. The claim that "all ravens are black" seems to assert the existence of ravens in a way that claiming that "everything non-black is non-raven" doesn't. So I can say that "anything non-pink and non-fluffy is non-unicorn" and you can't really complain about that but if I try to assert equivalence to the claim that "all unicorns are pink and fluffy" then you might well think that I am either deceiving you or that I have lost my mind.

    Maybe that only works for things that don't exist, like unicorns. My second idea doesn't rely on this.

    2. The two claims are not wholly equivalent because by flipping the subject from ravens to non-black items we change the subject from a class were we can gather a sample which is representative of the whole (say a few dozen ravens, which is good enough to make a reasonable guess as to whether they are all the same colour) to a subject where you cannot get a representative sample of the whole. The non-black things you have to hand are going to differ wildly from other non-black things elsewhere and you can't have any confidence that the lack of ravens in your sample means anything, even if it is very large. How large a sample of items would you need for it to be likely that it would contain at least one raven if ravens were eligible for inclusion? The universe is approximately 0% composed of ravens.

    Do either of these objections hold water?
    (2 votes)
    Default Khan Academy avatar avatar for user
  • blobby green style avatar for user Ayan
    I don't understand... how is All F's are G's the same as All Non-F's are Non-G's? It doesn't confirm anything except the statement that was made. I'm not certain, but I feel like either there is something missing in the explanation or we're missing the sense that this is supposed to DISPROVE the truth of the statement, instead proving Confirmation Bias?
    (2 votes)
    Default Khan Academy avatar avatar for user
  • blobby green style avatar for user goku v
    at the end of the video like so which one is the problem he says I will leave it to you
    (1 vote)
    Default Khan Academy avatar avatar for user

Video transcript

(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