The Ravens Paradox

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The Ravens Paradox The Paradox 1 Examining the Problem 1 Conclusion 3 Further Points 4 Mathematical proof for statement [2] 5 Mathematical proof for statements [3] and [4] 7 The Paradox Hempel first discovered the ravens paradox in 1965. It consists of five statements: 1. All ravens are black is logically equivalent to all non-ravens are non-black assuming a finite no. of things in the world. 2. Providing all the ravens I find are black, the more I find the more likely it is that all ravens are black. 3. Mimicking statement [2], the more non-black non-ravens I find the more likely it is that all non-black things are non-raven. 4. Using statement [1] we can conclude that the more non-black non-ravens I find the more likely it is that all ravens are black (statements [3] and [4] are logically equivalent). 5. Common sense dictates that we can learn nothing about the colour of ravens by looking at non-ravens. Statements [4] and [5] contradict each other and this is the root of the paradox. One of the five statements must be incorrect. Let us examine them in turn. Examining the Problem [1] This statement is one of pure logic and is correct (in the world of logic). [2] If this statement is true we should be able to mathematically calculate the probabilities. We can, and we can use them to prove that for each new raven (which must be black) that is found the probability that all ravens are black is increased. See mathematical proof below. [3] and [4] Similarly, if these statements are true, we should be able to find the probabilities. We can, and they lead us to two surprising results: 1. That the more non-black non-ravens one finds the higher the probability that all ravens are black. 2. That more black non-ravens one finds the lower the probability that all ravens are black. See

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