Monthly Archives: June 2013

The Raven Paradox

[Ken and Sid are sitting in the balcony of their flat near Shimla. A cool breeze blows. Sid is looking at the beautiful mountain peaks. Ken is reading a book. ]

Sid: This is a beautiful place, Dad. An ideal place to spend the summer vacation.

Ken: [Smiles.] So much cooler than Delhi. I read on the internet that it was 45 degrees Celsius there yesterday.

[ Suddenly a black coloured bird lands on the branch of a tree a little distance from where Ken and Sid are sitting.]

Sid: The crows here are completely black. The ones that we see in Delhi have grey necks.

Ken: The ones that we see here are more accurately called ravens. The ones in Delhi are Colombo crows.

Sid: So a raven is completely black.

Ken: [Smiles.] Your sentence has reminded me of something very interesting. I must tell you about it.

Sid: What?

Ken: Carl Gustav Hempel was a 20th century philosopher of science and he came up with a very interesting situation that is known as the Raven paradox.

Sid: What is this paradox about ravens?

Ken: Let’s imagine a situation: You are a scientist who has discovered this new species of birds. You call it raven.

Sid: Okay.

Ken: You are a pioneer in the field, you spend many years in the Himalayas studying the characteristics of this new species of birds. You observe hundreds of ravens from different places that you visit.

Sid: Okay.

Ken: Let’s say you see a hundred ravens and all are black, and you come up with the statement, “All ravens are black”.

Sid: Okay.

Ken: You want to collect evidence to support the statement “All ravens are black” for the paper that you are writing for “Nature” magazine.

Sid: That is simple. I need to see lots of ravens. I can also travel to different areas in the Himalayas and look at ravens. If I keep seeing only black ravens then my statement is justified.

Ken: So would it be fair to say that whenever you see a raven and the colour is black, your evidence for the statement “All ravens are black” increases? Of course, I am assuming that you never see a raven that is not black.

Sid: Yes. The more black ravens I see, the stronger my theory becomes.

Ken: [Smiles.] The interesting part begins now. Do you think your statement “All ravens are black” is logically equivalent to the statement “Anything that is not black is not a raven?”

Sid: [After thinking for a few seconds]. Yes. These are equivalent statements.

Ken: Let me repeat what I asked earlier: If you see a black raven do you think it supports your statement that “All ravens are black”?

Sid: Of course! Why do you ask again and again? It is so simple.

Ken: If I see a red apple does it support your statement, “All ravens are black”? [Smiles.]

Sid: Of course not. Why would you even ask such a silly question? How can looking at an apple tell us anything about ravens?

Ken: [ Suddenly serious.] It is not a silly question. If I see a red apple it is evidence for the statement that “Anything that is not black is not a Raven” because we have a red object, that is not a raven. But you yourself said that this statement is equivalent to the statement “All ravens are black”!

Sid: Gosh! I had not thought about that. So if I see anything that is not black and not a raven, it will add to the evidence that “All ravens are black”! I wear a blue shirt and the evidence that “all ravens are black” becomes stronger. I eat a yellow mango and it tells us that “All Ravens are black” is probably true. This is such a crazy and amazing idea!

Ken: Yes. It really is such an amazing idea. Hempel came up this paradox to illustrate the problems of inductive reasoning.

Sid: Inductive reasoning?

Ken: You see many instances of something and then come up with a general statement about the whole class of that thing. For example, we saw a hundred ravens and we came up with a statement about the colour of all ravens, even the ones that we had not seen. Inductive reasoning has always been a matter of controversy and debate in the history of science.

[ A voice from inside the house tells them that lunch is ready.]

Sid: Let’s go Dad. Mom has made biryani today.

Ken: And our tasting this biryani will add to the evidence of my statement, “all biryanis are delicious”.

Sid: But according to raven’s paradox, if you eat boiled broccoli which is not delicious, that too will add to the evidence that “all biryanis are delicious”. And this is because a dish of boiled broccoli will support the statement, “if something is not delicious, it is not biryani” and that is logically equivalent to the statement, “all biryanis are delicious”.

[Sid laughs as Ken and Sid head indoors.]


Go wondrous creature, mount where science guides
go measure earth, weigh air, state the tides,
instruct the planets in what orbs to run
correct old time, regulate the sun