The Raven Paradox and Science

“Anything that thinks logically can be fooled by something else that thinks at least as logically as it does.”
Douglas Adams, Mostly Harmless

The democratization of knowledge is a tremendous and empowering idea. The internet plays a huge role in this democratization. The growth and expansion of the Internet are almost unfathomable. The growth of online video is an example of this. In the early stages of the Internet, one small picture could slow your website to a crawl. Now we’re watching 4K YouTube videos at 60 frames per second.

You can find almost anything on YouTube. Need to paint a room in your house there’s a video for that. Want to listen to your favorite band they probably have a channel. Want to know how to build an electric guitar there is a playlist for that. There are even channels focused primarily on teaching science. Some of my favorites are Dianna Cowern’s Physics Girl, Derek Muller’s Veritasium, Michael Stevens’s Vsauce, and Brady Haran’s Numberphile.

However, there are also other channels on YouTube presenting pseudoscience or even outright falsehoods. Did you know that the Flat Earth Society has its own YouTube channel? (No, I’m not linking to it!) As much as we might like the idea of deleting them if we support an open and free Internet and the democratization of knowledge we can’t.

Fortunately, a lot of them are easy to spot. However, what about videos that make a mistake or fall into a logic trap. What about videos recommended by YouTube? Does a YouTube recommendation increase the validity of a video?

The other day a video popped up in my YouTube recommendation feed the title intrigued me “The Raven Paradox (An Issue with the Scientific Method)” the video is by a channel TritoxHD which is a channel about “science, theory, and history!” The video concludes that scientists shouldn’t make overly broad generalizations.

The video centers around the Raven Paradox, which is an argument in inductive reasoning first presented by Carl Gustav Hempel and how it impacts on the scientific method. The raven paradox is interesting from a logical standpoint. The paradox is dependent on logical equivalents from a logical point of view; all A’s are B’s is equal to if not B then not A.

The paradox uses these two statements.

  1. All ravens are black.
  2. Something is not black; then it is not a raven.

Since these two statements are logically equivalent observing one is support for the other. As an example, the flower in my front yard is pink, this flower is not black, and it is not Raven, so this pink flower supports all ravens are black. If you are like most people, your response was just “WHAT!” The idea that dissimilar things can be used to prove each other is where the paradox comes from how can an observation of a flower have anything to do with ravens. Fred Leavitt does an excellent job of explaining how this works in his article Resolving Hempel’s Raven Paradox in Philosophy Now; my interest is in the description of the scientific method.

How does The Raven Paradox relate to the scientific method? Our YouTuber and others have suggested that many if not most hypotheses are of the format all A’s are B’s. In this case, the YouTuber makes his first mistake when he takes All ravens are black as a hypothesis.  The video states that the hypothesis is the first step in the scientific method, this is not true.

I like to think of the scientific method is a cycle that we can enter from any point, so there isn’t a first step. However, if you think of the scientific method linearly the first step is to ask a question.

Two representations of the Scientific Method one circular the other liner.
Two representations of the Scientific Method one circular the other liner.

Following in the raven example the question would be “Is there a trait that all ravens share?” Then you’d go out and observe ravens. This step is necessary because a hypothesis is a prediction based on observation. So, if you need observations to make a hypothesis, the hypothesis can’t be the first step. Our YouTube author even states that a hypothesis is a prediction based on observation.

An important thing to know about the hypothesis all ravens are black is that while very rare there are white (albino) or cream (leucistic) colored ravens.

Modified from Raven by Marcin Klapczynski, licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.
Modified from Raven by Marcin Klapczynski, licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.

The argument concerning the paradox is twofold one, to “prove” the hypothesis you must observe every single raven, I’ll come back to this latter. Two, you can observe hundreds even thousands of ravens and never see a white raven and therefore conclude that all ravens are black incorrectly.

Let’s suppose you examine 50 ravens and they were all blacks you come up with the hypothesis all ravens are black. You then go out and examined 5000 ravens, and they are all black. What is the problem, while we don’t know the exact numbers there are 4 or fewer albino ravens worldwide out of a total population of 16 million. That means that your probability of seeing an albino raven is 0.000025%. 

Beyond the small chance of seeing a white raven, there is another problem with the approach. Observing Ravens to see if they are black is an experiment that is designed to prove the hypothesis.  Specifically observing 5000 black Ravens is a result that is consistent with the hypothesis, this type of research doesn’t provide any information on alternative hypotheses.

With science, supporting or consistent data is of a lower value. Experiments that focus on disproving a hypothesis always have a higher value. They have a higher value because they eliminate alternative ideas which strengthen the validity of the remaining hypothesis. Additionally, a hypothesis is only scientific if it can be disproven.  Which means if you try to disprove a hypothesis and can’t the likely hood that the hypothesis is pointing at something real is stronger.

Let’s briefly get back to the issue of testability, since all ravens are black requires an examination of all ravens something that is impossible the hypothesis is untestable and is therefore not a scientific hypothesis. 

In the end, this the video uses the Raven Paradox to say that scientists can overreach and should be careful of generalizations. However, this argument is problematic because it is dependent on the definition of a hypothesis which is not complete.  The hypothesis all ravens are black is not a valid hypothesis. The author states a hypothesis is a prediction based on observations. I would say a prediction that is consistent with observations. Additionally, a hypothesis must be testable. Lastly, a hypothesis must be falsable or able to be proven incorrect to be a scientific hypothesis.

While I would like to see the YouTube logarithm not suggest things that are incomplete or oversimplified beyond usefulness, I suspect that will not happen.  Like I have stated before we need to focus on teaching students how to evaluate information.  I suspect most of the problems with the video come from things being oversimplified. As Einstein said, “Simplify everything as much as possible but no further.” Concerning basic education, I think we’ve taken the scientific method further. We tend towards being very simplistic in how we present the scientific method. We need to do a better job of teaching the basics if our students don’t know the foundation how can we hope to teach them the specifics.

Thanks for Listening to My Musings
The Teaching Cyborg

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