The Raven Paradox
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 a long time -- in fact, one of my first entries in the blog's early days was about Popper. And even though I don't see anything wrong with what I said in that early blog post, my understanding of philosophy has come a long way and I now have a very different way of approaching it.
Popper says that we can never prove that all ravens are black; all we can do is disprove that all ravens are black by finding one that isn't. Seeing millions of black ravens does not advance the argument that all ravens are black one iota, and therefore finding non-white non-ravens is equally useless.
If one takes the collection of objects that we call "ravens" as a platonic group, Popper is at least correct in the technical sense that we can never demonstrate empirically that all ravens are black. The problem with this is that, in the material world, there are no platonic objects. "Raven" is a word we use to describe a bird of a particular type. There is no ideal raven type that captures the essence of raven-ness, that we could be sure was absolutely a raven and nothing else.
I've spent considerable effort elsewhere (here and here) showing that material things are not absolutes. They exist, to be sure, but any form they exist in is temporary, and any name we use to categorize that form is arbitrary on the margins. If I say a square is a figure with four equal sides and four equal angles, I have defined that square, and what I say will always be true of every square. If you find something that seems to be a square but doesn't fit one of those criteria, you have found something that is -- by definition -- not a square. No observations are necessary to know this.
If I say that a raven is a bird of certain features, one of which is that its colour is always black, I have described a type of bird that I have observed. I can't prove that all ravens are black through any amount of observations, but I could solve the problem simply enough by saying that ravens are, by definition, black. Then if you observe an albino raven (for example), you have no disproved my argument, which is not an argument but a definition. You have found something that is, by definition, not a raven.
Now, a definition of "raven" that simply defined away all birds that don't match the colour I say they are would not be a very useful definition. The reason is that I'm not trying to come up with an absolute definition of raven, I'm trying to describe what exists in the world. My point is that any argument based on material objects is a description rather than a definition, and therefore it is not suitable to absolute statements.
Let's take the classic syllogism:
All men are mortal;
Socrates is a man;
Therefore, Socrates is mortal.
Few would disagree with the major or minor premises or the conclusion of this syllogism. But let's suppose that we somehow discovered that Socrates was not mortal. Would we conclude that he isn't a man? I don't think so. I think we would be more likely to conclude that we have found an exception and that some men are not necessarily mortal. What if we discovered an orange raven? We would say that, indeed, some ravens may not be black. We would say that even if no other raven had ever been orange and no other raven ever will be orange again.
Now, what if there actually has not been an orange raven ever to appear on the earth? If we could actually witness every raven ever to have lived, and confirm that they are all black, could we then safely state that "all ravens are black"? Well, yes, in practice; but no, we can't make that statement as a definition of ravens, because there may someday be an orange raven and it will refute our definition. All we can say is that, so far, there haven't been any non-black ravens; but that doesn't mean you won't see an orange raven the next time you're outside.
Therefore, I don't think it's meaningful to try to prove, in a logical sense, whether "all ravens are black" or "all men are mortal" or any other statement that makes reference to the physical world. Those are not logical statements, but rather descriptions, and the descriptions are subject to change at any time. On the other hand, gathering more observations of ravens does give us more evidence that ravens are normally black, and that is the most that we can hope for.
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 a long time -- in fact, one of my first entries in the blog's early days was about Popper. And even though I don't see anything wrong with what I said in that early blog post, my understanding of philosophy has come a long way and I now have a very different way of approaching it.
Popper says that we can never prove that all ravens are black; all we can do is disprove that all ravens are black by finding one that isn't. Seeing millions of black ravens does not advance the argument that all ravens are black one iota, and therefore finding non-white non-ravens is equally useless.
If one takes the collection of objects that we call "ravens" as a platonic group, Popper is at least correct in the technical sense that we can never demonstrate empirically that all ravens are black. The problem with this is that, in the material world, there are no platonic objects. "Raven" is a word we use to describe a bird of a particular type. There is no ideal raven type that captures the essence of raven-ness, that we could be sure was absolutely a raven and nothing else.
I've spent considerable effort elsewhere (here and here) showing that material things are not absolutes. They exist, to be sure, but any form they exist in is temporary, and any name we use to categorize that form is arbitrary on the margins. If I say a square is a figure with four equal sides and four equal angles, I have defined that square, and what I say will always be true of every square. If you find something that seems to be a square but doesn't fit one of those criteria, you have found something that is -- by definition -- not a square. No observations are necessary to know this.
If I say that a raven is a bird of certain features, one of which is that its colour is always black, I have described a type of bird that I have observed. I can't prove that all ravens are black through any amount of observations, but I could solve the problem simply enough by saying that ravens are, by definition, black. Then if you observe an albino raven (for example), you have no disproved my argument, which is not an argument but a definition. You have found something that is, by definition, not a raven.
Now, a definition of "raven" that simply defined away all birds that don't match the colour I say they are would not be a very useful definition. The reason is that I'm not trying to come up with an absolute definition of raven, I'm trying to describe what exists in the world. My point is that any argument based on material objects is a description rather than a definition, and therefore it is not suitable to absolute statements.
Let's take the classic syllogism:
All men are mortal;
Socrates is a man;
Therefore, Socrates is mortal.
Few would disagree with the major or minor premises or the conclusion of this syllogism. But let's suppose that we somehow discovered that Socrates was not mortal. Would we conclude that he isn't a man? I don't think so. I think we would be more likely to conclude that we have found an exception and that some men are not necessarily mortal. What if we discovered an orange raven? We would say that, indeed, some ravens may not be black. We would say that even if no other raven had ever been orange and no other raven ever will be orange again.
Now, what if there actually has not been an orange raven ever to appear on the earth? If we could actually witness every raven ever to have lived, and confirm that they are all black, could we then safely state that "all ravens are black"? Well, yes, in practice; but no, we can't make that statement as a definition of ravens, because there may someday be an orange raven and it will refute our definition. All we can say is that, so far, there haven't been any non-black ravens; but that doesn't mean you won't see an orange raven the next time you're outside.
Therefore, I don't think it's meaningful to try to prove, in a logical sense, whether "all ravens are black" or "all men are mortal" or any other statement that makes reference to the physical world. Those are not logical statements, but rather descriptions, and the descriptions are subject to change at any time. On the other hand, gathering more observations of ravens does give us more evidence that ravens are normally black, and that is the most that we can hope for.
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