A Curious Little Blog

I feel like the arguments I advanced against the Raven Paradox yesterday are valid, and yet not completely satisfying, because they do not address its strictly logical sense.  In other words, I think statements like "all ravens are black" are not categorical and thus can't be proven in the sense that mathematical theorems are proven; nevertheless, I feel that there is a deeper logical inadequacy in the raven paradox that would invalidate it even if it did not have this deficiency. The basis of the raven paradox is that the statement "all ravens are black" should be logically equivalent to its " contrapositive ," "all non-black objects are not ravens."  Nevertheless, there seems to be a difference between the two, because the first statement asserts something about ravens and the second does not.  To illustrate, let's consider unicorns.  Suppose I say that "all unicorns are white."  The contrapositive is that "all non-whi...

I have been enjoying the "Up and Atom" videos on YouTube, which discuss various logical questions.  I particularly found the Raven Paradox interesting.  The principle is pretty simple:  if we think that all ravens are black, then seeing more black ravens helps confirm our hypothesis.  However, saying "all ravens are black" is logically the same as saying "all non-black objects are not ravens," and therefore, seeing non-black objects that are not ravens would also seem to confirm our hypothesis.  Which seems weird, since it means that seeing, for example, a white shoe would help confirm that all ravens are black! There are actually several different ways of approaching this question, but I want to address Karl Popper's argument (raised in the video) that we can never positively prove anything, we can only disprove things.  As the approximately, um, zero people who follow my blog are sure to know, I have been interested in Popper's assertions for ...