Some of my favorite "paradoxes" have to do with induction. Below I describe the Raven's Paradox and the Tacking Paradox.
The Raven's Paradox
Let's first make two very reasonable assumptions about the concepts of evidence and theory and how they relate to one another.
First we assume that if we have a generalization T (e.g., a theory that says "all lawyers are greedy"), and we observe an instance E of this generalization (i.e., we observe a greedy lawyer), then this instance E serves as some positive evidence for T.
Second we assume that if E serves as evidence for T, and T is logically equivalent to another theory S, then E serves as evidence for S.
As I said, both of these assumptions seem entirely reasonable.
Now consider the theory T that "all ravens are black." Note that this theory is logically equivalent to the theory S that "all nonblack things are nonravens." Now imagine that I have just seen a green apple. Since this apple is a nonblack thing which is also a nonraven, then by the first assumption we made above, this serves as evidence for S. But since S is logically equivalent to T, then by our second assumption, this also serves as evidence for T. So my observation of a green apple is evidence that all ravens are black. But this seems absurd.
The Tacking Paradox
We start with two more assumptions.
First we assume that if E is a logically necessary consequence of T, then E serves as evidence for T. For example, say we have a T which says "my roommate was out drinking last night." We combine this with the proposition "if T, then my roommate will sleep through his alarm clock's ringing." Now I observe the event E that my roommate has slept through his alarm. So on this assumption, E serves as evidence that my roommate was out drinking last night.
Second we assume that if E serves as evidence for T, and S is some other logically necessary consequence of T, then E serves as evidence for S. Continuing with the roommate example, suppose we add a second proposition that "if T, then my roommate will sleep with his shoes still on." So on this assumption, observing that my roommate has slept through his alarm clock's ringing serves as evidence that he has also slept with his shoes still on, by virtue of the fact that the former serves as evidence that my roommate was out drinking last night.
Again, these are reasonable assumptions.
But now let's take any other proposition P, such as "the moon is made of green cheese." Since T from above entails E, then by hypothesis, T & P (that is, my roommate was out drinking last night AND the moon is made of green cheese) also entails E (that my roommate will sleep through his alarm clock's ringing). So by our third assumption, E serves as evidence for T & P. Now, it is obvious that T & P entails P (trivially). But then, by our fourth assumption, it follows that E serves as evidence for P  that is, my observation that my roommate has slept through his alarm clock's ringing is evidence that the moon is made of green cheese. But again, this seems absurd.


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