What is the Raven Paradox?

Hello, I'm glad to discuss this very interesting topic with you – the Raven Paradox. Also known as Hempel's Paradox, it might sound a bit convoluted, but its core idea is actually fascinating, primarily concerning how we confirm a theory through observation.

Let's break it down step by step.

Step One: A Simple Statement

Let's start with a seemingly very simple statement:

All ravens are black.

How do we prove this statement? The most straightforward way is to go outside and look for ravens. Every time we see a black raven, our confidence in the statement 'All ravens are black' increases a little. See one, confidence +1; see a hundred, confidence +100. This aligns with our intuition, doesn't it?

Step Two: A Logical Trick

Alright, now let's play a logic game.

In logic, a proposition and its 'contrapositive' are logically equivalent. It sounds technical, but it's actually quite simple:

If A, then B is equivalent to If not B, then not A.

For example: 'If it rains (A), then the ground is wet (B)' is the same as 'If the ground is not wet (not B), then it definitely didn't rain (not A).'

So, let's rephrase 'All ravens are black' into its contrapositive:

All non-black things are non-ravens.

Logically speaking, these two statements are completely equivalent. Proving the latter is equivalent to proving the former.

Step Three: The Paradox Emerges!

Since these two propositions are equivalent, evidence that supports the second proposition should also support the first, right?

So, what kind of evidence would support 'All non-black things are non-ravens'?

Look, I have a red apple on my desk.

• Is it a 'non-black thing'? Yes.
• Is it a 'non-raven'? Of course it is!

Therefore, a red apple, logically speaking, also provides a little bit of evidence for the statement 'All ravens are black'!

Similarly, a white cup, a pair of blue shoes, a green leaf... each of them, logically, contributes a small piece of evidence to prove that 'All ravens are black'.

Why Does This Feel Absurd?

This is the core of the Raven Paradox: a purely logical deduction leads to a conclusion that completely contradicts our intuition.

Our intuition tells us that to study ravens, you should observe ravens, not look at apples at home. Yet logic states that observing a red apple can also (to a very small extent) increase your confidence in the theory that 'ravens are black'.

How to Understand This Paradox?

In fact, this paradox doesn't invalidate logic. Many philosophers and logicians believe the problem lies in our intuition not accounting for the amount of 'information content'.

1. Varying Strength of Evidence

   • Imagine, how many things are there in the universe? Countless. The number of 'non-black things' is virtually infinite, while the number of 'ravens' is finite.
   • When you see a black raven, you eliminate a small part of the possibility that 'there exists a non-black raven'. This information content is significant because it directly pertains to our object of study.
   • But when you see a red apple, you are merely confirming that one item among 'countless non-black things' is 'not a raven'. This information content is so tiny it's almost negligible. So, while logically correct, the strength of the evidence it provides is so weak that our intuition simply disregards it.

2. Limitation of Scope

   • Another perspective is that when we propose the hypothesis 'All ravens are black,' we implicitly assume a scope of study: the set of 'ravens.' Under this premise, only observations about ravens are meaningful. Observing apples or shoes is completely 'off-topic' and therefore cannot be considered valid evidence.

In Summary

Overall, the Raven Paradox doesn't claim our logic is flawed; rather, it highlights the subtle relationship between logical deduction and scientific induction (how we derive general rules from observations), as well as the role our intuition plays.

It reminds us that the 'validity' of a piece of evidence is not solely about its logical consistency, but also about how much 'information content' it provides and whether it falls within the 'correct scope'.

I hope this explanation helps you understand the interesting aspects of the Raven Paradox!