Inductive reasoning. The phrase, I am sure, sounds vaguely familiar to you. This basically means extrapolating from specific facts to general principles. You see a glove, it has fingers, so you induce that all gloves have five fingers. You can do this by way of a "statistical syllogism", whereby N% of something (A) is observed to be something else (B), therefore, if something looks like A, it's a B. Every banana you see is yellow, you see a banana, and are pretty sure it's going to be yellow. Or you have a stack of apples, and 85% of them are red and the other 15% are green, so you extrapolate that 85% of all apples are red based on your research (this, for those of you who want to sound all cool and nerdy at your next party, is called "Induction by Enumeration"). Or another way, if you have two pretty similar objects, say two banana-looking fruits, both with skins that are yellow, both about the same size and shape--with similar properties--and you know that inside the skin of one is yummy delicious banananess, so you, reasonably, assume that inside the other one is also yummy delicious banananess, given how similar they otherwise are.
Makes sense, right? Right. Sounds reasonable? Bien sûr. WRONG.
Let's think about this. How do we know stuff anyways? What does that mean to know stuff? We can know things from observation--we see it, so we know what it's like; we can be all thinking-dude-on-a-rock introspective-like, and just pretty much know things; it can be a priori, which just basically means without fact (or not dependent on fact or observation), like 2 + 2 is 4, or that nothing can be both a perfect square and a perfect circle at the same time. Or, it can be inductive, in ways we just talked about (jeez, don't you remember anything??).
Why does this not work out, then? We can know stuff from induction, right? Sure. Induction just means we accept the principle that all the stuff we haven't seen resembles what we have seen, such that if 85% of all the apples we've ever seen have been red, it's likely that about 85% of all apples are likely to be red. But you can't observe this principle, that the unobserved resembles the observed, you can't introspect it into being, and it isn't a priori--- so this principle, that everything you haven't seen is likely to resemble stuff you have seen, is something we believe because, well, that's the way it's always been. Back in the day we looked at a set of objects--birds, say, ravens--and made an observation--they're black--and made a prediction--all the other ravens are likely to be black---and, guess what? We went and observed the rest of the ravens, and they were, indeed, black. We assume the unobserved is going to be like the observed because, until now, the unobserved *did* resemble the observed. We get ourselves a good sample, make a prediction, and golly gee whiz, it turns out correct. That's how science works. But it's circular. Inductive logic works that all the future stuff out there will resemble all the currently observed stuff, and we believe this because the last time we did it, it worked, and that time we believed that because the time before that, and the time before that, and the time before the time before the time before that worked too.
So you see a raven. It's black. You see lots of ravens, they're all black. You make a generalization: all ravens are black. Which is the same thing as saying that all things that are not black are also not ravens. Consider: an object that is neither black nor a raven. An orange, for example. An orange is not black, and it ain't a raven, so it supports our theory that all non-black things are not ravens, which is the same as saying it supports our theory that all ravens are black. An orange is evidence that all ravens are black?
I don't really want to get into paradoxes, because I must confess I don't understand them (which, I guess, is why they are paradoxes). Still, consider:
The trolley Problem
It's a lovely day out, and you decide to go for a walk along the trolley tracks that crisscross your town. As you walk, you hear a trolley behind you, and you step away from the tracks. But as the trolley gets closer, you hear the sounds of panic -- the five people on board are shouting for help. The trolley's brakes have gone out, and it's gathering speed.
You find that you just happen to be standing next to a side track that veers into a sand pit, potentially providing safety for the trolley's five passengers. All you have to do is pull a hand lever to switch the tracks, and you'll save the five people. Sounds easy, right? But there's a problem. Along this offshoot of track leading to the sandpit stands a man who is totally unaware of the trolley's problem and the action you're considering. There's no time to warn him. So by pulling the lever and guiding the trolley to safety, you'll save the five passengers. But you'll kill the man. What do you do?
Consider another, similar dilemma. You're walking along the track again, you notice the trolley is out of control, although this time there is no auxiliary track. But there is a man within arm's reach, between you and the track. He's large enough to stop the runaway trolley. You can save the five people on the trolley by pushing him onto the tracks, stopping the out-of-control vehicle, but you'll kill the man by using him to stop the trolley. Again, what do you do?
Both of these grave dilemmas constitute the trolley problem, a moral paradox first posed by Phillipa Foot in her 1967 paper, "Abortion and the Doctrine of Double Effect," and later expanded by Judith Jarvis Thomson. Far from solving the dilemma, the trolley problem launched a wave of further investigation into the philosophical quandary it raises. And it's still being debated today.
Click on it, it's worth it.
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