Monday, 27 July 2015

Paradox of the Ravens

I came across this youtube video last night (below) which I thought was a real eye opener.  The argument expressed is that we can provide evidence for the proposition all ravens are black by observing things/objects which are not black and are not a raven.  So I observe a daffodil.  I note it's yellow and is not a raven.  This provides evidence that all ravens are black!  I observe grass.  I note it's green and not a raven.  This also provides evidence that all ravens are black!

This of course seems preposterous.  The video below explains why it seems we are obliged to accept such a counter-intuitive position:

Here is the argument as I see it and expressed as simply as I can put it:

Suppose we have 2 lists:

List A: Every single black object in the Universe.

List B: Every single non-black object in the Universe.

So together the 2 lists comprise all objects in the Universe.

If all ravens are indeed black, then it follows that every single raven in existence must belong in list A. Conversely no ravens whatsoever will be found in list B.

So if we look at every single object in list B, and none whatsoever is a raven, then this necessitates that all ravens are black.

But this also suggests that just looking at a single object in list B, and finding it is not a raven, constitutes an incredibly small amount of evidence that all ravens are black!

So is there a paradox here?  I've read nothing of the various arguments expressed, but it seems to me that if we observe all objects in list B and none are a raven, then this necessarily entails all ravens are black.  So the probability of each of the individual observations of the objects in list B must add up to a probability of 1.   But that doesn't mean to say that each observation provides equal evidence.  Thus it might be that the observation of manufactured non-black objects -- for example a green car -- does not add any evidence for the proposition.  But this might be made up by other observed non-black objects which are not ravens -- for example objects which nobody has ever seen -- providing a corresponding increased degree of evidence for the proposition. 

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