I want to prove that 'All ravens are black'. An equivalent statement is 'All non-black objects are non-ravens', and if I prove the latter then I prove the former as well. I look around and see a blue sky, green grass, and an overwhelming number of things that are non-black non-ravens. I can easily prove that 'All non-black objects are non-ravens' and, by extension, I must also have proven that 'All ravens are black' because this is an equivalent statement. This is a well known paradox. Whose paradox is it?

Tabby Tom

It's Hempel's paradox, named after Professor Carl Hempel. The logic is impeccable. Of course, every time you investigate a nonblack object and find that it's not a raven, the probability that all ravens are among the black objects is slightly increased. So, as the professor says, if you find a purple cow, it helps to confirm your hypothesis that all ravens are black. If your hypothesis happened to be that all ravens are white, a purple cow would help towards confirming that theory as well. Sep 07 02, 12:33 PM

Andy

This logic is EXTREMELY faulty. You have two statements here: 'All ravens are black.' And, 'All nonblack objects are nonravens.' However, just because an object is black does not make it a raven. The only thing you can infer from the statements is that A) All ravens are black, and B) If it isn't black, then it isn't a raven. However, what about objects that ARE black, but are NOT a raven? This logic is complete bunk. Sep 07 02, 4:38 PM

Tabby Tom

But the thing that had to be proved was simply that all ravens are black, i.e. that they are included in (but do not necessarily comprise the whole of) the class of black objects. You can prove this either by examining every raven and finding it to be black, or by examining every nonblack object and finding that it isn't a raven. Either way you've proved that all ravens are black. It was never suggested that all black objects were ravens, and so any black objects that are not ravens are irrrelevant to the proof. Oopsie's (and Hempel's) statement is that 'all ravens are black' necessarily implies that 'all nonblack objects are not ravens', not that it implies 'all black objects are ravens'. Sep 07 02, 5:29 PM

sticky

Andy, 'All nonblack objects are nonravens' is the contrapositive and means the same thing. For example, if I made the statement 'all horses are black.' and you want to prove me wrong, you gather up all the horse in the universe and you find one that is purple. I will be wrong. OR. you can gather up all things in the universe that are not black and you inspect each and every one. you will find a purple item that happens to be a horse. I will be wrong. for the orig {q.;} the only logically faulty part is the 'i can easily prove...' this is flaw of induction since you cannot prove all when you inspect part. Sep 08 02, 12:10 PM