Hempel's Paradox
Posted by on Sunday, July 7, 2013 Under: Philosophy
For those who are interested in serious science news, you may want to skip today's article. It is a fascinating paradox in science, but it is more than a bit philosophical as well. This is actually a well known paradox that has been discussed and debated for a long time, but it is still worth pondering.
The experimental method in science is very straightforward. A scientist develops a hypothesis, and then goes out into the world collecting data. That data might come from observing plants or animals or weather patterns, or it may come from building a telescope to gaze at the stars, or perhaps a huge particle accelerator to probe smaller scales. But over time, data is collected which either supports the hypothesis or which contradicts it. Either way new knowledge is gained.
It seems like such a simple method, but Hempel's paradox adds the proverbial monkey wrench to the system.
Following the traditional presentation of this paradox, suppose that a scientist creates a hypothesis that all ravens/crows are black. Then following the (experimentalist's) scientific method, the next step is to go out into nature and zoos and look at ravens. Each time the raven is black, the theory gets stronger. If ever a non-black raven is observed, the hypothesis is disproved. At some point, when a large number of ravens have been found to be black, the hypothesis is considered strong enough to become a theory and is considered true.
However now consider an equivalent hypothesis. Claiming that all ravens are black, is equivalent to claiming that every object which is not black is not a raven. The reader can draw Venn diagrams and study formal set theory if they so wish, but in the end they will find that these two statements are equivalent. In order to prove that all ravens are black, it is sufficient to prove non-black things are not ravens.
And so to prove this second statement, the experimental method requires the scientist to go out and look for everything that is not a raven. And that is where the paradox enters. According to the scientific method, finding a white cow, or a yellow banana, or a bit a green mold increases the chances that all ravens are black. However these are all completely unrelated to the biology of ravens, and should have no influence at all!
There are many proposed solutions, and a decent review of them can be found here. My own personal view is that the number of data points in the second experiment would be so enormous as to be effectively useless. It is far easier to count a few millions ravens than countless trillions of non-ravens!
However it is still an interesting paradox, and reminds us all that caution must be taken even when using a simple and obvious method such as the scientific method. Question everything.
(*Throughout this article I refer to the "experimentalist's scientific method". The reason is that mathematicians and many theorists such as myself use a different method of developing theories. This alternative method is to take known facts and proven theories, and use logic alone to extrapolate new theories and models without the reliance on data and experiments.)
The experimental method in science is very straightforward. A scientist develops a hypothesis, and then goes out into the world collecting data. That data might come from observing plants or animals or weather patterns, or it may come from building a telescope to gaze at the stars, or perhaps a huge particle accelerator to probe smaller scales. But over time, data is collected which either supports the hypothesis or which contradicts it. Either way new knowledge is gained.
It seems like such a simple method, but Hempel's paradox adds the proverbial monkey wrench to the system.
Following the traditional presentation of this paradox, suppose that a scientist creates a hypothesis that all ravens/crows are black. Then following the (experimentalist's) scientific method, the next step is to go out into nature and zoos and look at ravens. Each time the raven is black, the theory gets stronger. If ever a non-black raven is observed, the hypothesis is disproved. At some point, when a large number of ravens have been found to be black, the hypothesis is considered strong enough to become a theory and is considered true.
However now consider an equivalent hypothesis. Claiming that all ravens are black, is equivalent to claiming that every object which is not black is not a raven. The reader can draw Venn diagrams and study formal set theory if they so wish, but in the end they will find that these two statements are equivalent. In order to prove that all ravens are black, it is sufficient to prove non-black things are not ravens.
And so to prove this second statement, the experimental method requires the scientist to go out and look for everything that is not a raven. And that is where the paradox enters. According to the scientific method, finding a white cow, or a yellow banana, or a bit a green mold increases the chances that all ravens are black. However these are all completely unrelated to the biology of ravens, and should have no influence at all!
There are many proposed solutions, and a decent review of them can be found here. My own personal view is that the number of data points in the second experiment would be so enormous as to be effectively useless. It is far easier to count a few millions ravens than countless trillions of non-ravens!
However it is still an interesting paradox, and reminds us all that caution must be taken even when using a simple and obvious method such as the scientific method. Question everything.
(*Throughout this article I refer to the "experimentalist's scientific method". The reason is that mathematicians and many theorists such as myself use a different method of developing theories. This alternative method is to take known facts and proven theories, and use logic alone to extrapolate new theories and models without the reliance on data and experiments.)
In : Philosophy
I am a theoretical physicist & mathematician, with training in electronics, programming, robotics, and a number of other related fields.
