Wisconsin Cluster[chat]

My understanding of Democracy is that if 51% of the people vote for X, then they get X.

If you don't like that, then go to Russia.

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This is an unaired Conan bit and it is amazing

The Raven Paradox or: Why Induction is Silly

Every now and then I happen upon something that reinvigorates my delight in philosophy. My latest amazing discovery is The Raven Paradox. Here is how it works:

We have a statement, "All Ravens are Black". How would we know if this statement is true? If we use induction, then we found the truth of the universal on observations of particulars. I find one black raven and count that as evidence for the universal. I find a second black raven and this is further evidence. Every black raven I find seems to increase the likelihood of the truth of the universal. However, given one problem of induction, we have to ask how many black ravens must be found in order to prove, absolutely, that all ravens are black. Every black raven is evidence for the universal, but how many ravens are required to establish the truth of the universal? Or, if we don't care about absolutes, then how do we quantify the probability that all ravens are black given, say, 300 black ravens? Short answer: One cannot establish the probability, since the attempts to do so results in an infinite inductive regress.

That's one problem with induction, but it is not the paradox. The Raven paradox occurs as a result of the logical equivalence between:

(1) All Ravens are Black
(2) All Non-Black things are Non-Ravens

If all ravens are black, then any non-black thing is not a raven. If I find a black raven, that is evidence that all ravens are black. If I find a green apple, that is evidence that all non-black things are non-ravens. But since these two statements are logically equivalent, anything that counts as evidence of (2) is also evidence for (1).

Stated plainly, this green apple is evidence that all ravens are black. I have learned about ravens by examining this apple. If the problem is not immediately apparent, then consider these examples:

(1) "All Ravens are Black" = "All Non-Black things are Non-Ravens"
(2) "All Ravens are Green" = "All Non-Green things are Non-Ravens"
(3) "All Ravens are Orange" = "All Non-Orange things are Non-Ravens"
(4) "All Ravens are Red" = "All Non-Red things are Non-Ravens"

Given the logical equivalence of the above four statements, this blue ball counts as evidence for each. Moreover, this blue ball counts as inductive evidence for a nigh-infinite number of universal statements concerning ravens, sheep, voles, and, hell, even snozberries. "All Snozberries are green" = "All Non-Green things are Non-Snozberries". This blue ball is evidence that "All Non-Green things are Non-Snozberries" since it is neither green nor a snozberry. Therefore, this blue ball is evidence that all snozberries are green!

We tend to feel like induction tells us about the world, that we can discern the truth of universals from observations of particulars. If I find a black raven, and another black raven, and a third black raven, then I feel justified in believing that all ravens are black. If I find 500 or 5,000 black ravens, then I feel even further justified. But as we have seen, the Raven Paradox indicates that inductive evidence for the claim that "All Ravens are Black" is not only ravens, but also balls, soap, and every non-black, non-raven thing. If the sight of one black raven counts as one piece of evidence for the universal "All Ravens are Black", then the sight of this blue ball also counts as one piece of evidence for that universal.

Most people think this situation is problematic and counter-intuitive because, well, it is. But let's say that in order to make your life easier, you just accept the Raven Paradox, because you can't not accept it, and so grant that my blue ball is evidence that all ravens are black. But if you do that, then you've just permitted me to philosophically phuck you. How? Well, I'm glad that you asked.

You think that "All Ravens are Black" is a true statement. Let's say that you want to prove it to me. So, you go find 5,000 black ravens. But I do not think that all ravens are black. Let's say that I think all ravens are magenta. I have never found a magenta raven, but I have found a wealth of non-magenta things that are non-ravens. So, I go find 5,000 non-magenta, non-raven things to count as inductive proof that all ravens are magenta.

Given our inductive evidence, which of us is correct? You have 5,000 black ravens, but I have 5,000 non-magenta non-ravens. You really want to say that your black ravens are better evidence than my non-magenta, non-ravens. But there is no logical basis for making that distinction. You have 5,000 evidence that all ravens are black while I have 5,000 evidence that all ravens are magenta. Since we have each offered equal quantities of evidence, and our evidence conflicts, then it must be the case that both 'All Ravens are Black' and 'All Ravens are Magenta' are false.

Isn't that fucking awesome?! Just think of the argumentative tricks afforded to us by the Raven Paradox and the folly of induction!

You think that all Blue MTG decks are control decks. To inductively prove this claim, you go find 5,000 blue control decks. Well, I shall have none of this! I contend that all blue decks are goblin decks. Now, I've never found a blue goblin deck, but I have found a wealth of non-goblin, non-blue decks. So, I go find 5,000 elf decks. We then meet on the rhetorical battle ground. You offer your 5,000 inductive evidence that all blue decks are control decks. I offer my 5,000 inductive evidence that all blue decks are goblin decks. Oh noes! We each have 5,000 inductive evidence to support our claims! Since we each have equal evidence, it can't be the case that we are both correct. Yet while I have not proven that I am correct...

I have proven that you are wrong.

And since you are wrong, I must be right.



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