Logic

I was recently having a discussion with someone about the argument from ignorance fallacy, or "absence of evidence is not evidence of absence." We think that the following is a fallacy: 1. Alien spaceships orbiting the earth are observable through a telescope. 2. No one has observed alien spaceships orbiting the earth. 3. Therefore, there are no alien spaceships orbiting the earth. However, what if you changed the premises slightly to this: 1. Alien spaceships orbiting the earth would PROBABLY be observable through a telescope. 2. No one has observed alien spaceships orbiting the earth. 3. Therefore, there are PROBABLY no alien spaceships orbiting the earth. Even though I agree with the conclusion, I think this argument is also a fallacy since it follows the same form as the first one. But then I seemed to remember some kind of rule that the premises of an argument must be absolutes. You can't introduce probabilities, otherwise the laws of logic do not even apply and all bets are off. Or does it not matter what the actual statement is, as long as it evaluates to true or false? On the other hand, if the form of the argument is messed up, then does it really matter whether or not the content of the propositions are true or false? So I guess my question is, do premises have to be absolutes, or not?

Comments

Arguments can have probabilistic premises. Some such arguments are inductive -- merely be intended to show that their conclusions are likely. Others can be deductive. For example: here's a deductively valid argument with probabilistic premises:

1. It's likely that X
2. If it's likely that X, then it's likely that Y.
3. Therefore, it's likely that Y

But this doesn't have a lot to do with your worry. Let's start with the first argument. The problem here, intuitively, is that just because something is observable with a telescope, we can't conclude that it would have been or even likely would have been observed. Put another way: if alien spaceship visitations are rare events, then even if they could be observed, it would be no surprise if they weren't. And so from the mere fact that they could be observed by someone lucky enough to point a telescope in the right direction at the right time, it doesn't follow that they would have been observed, nor even that they probably would have been observed.

So let's move to version 2. And here we encounter an ambiguity. The first premise says

Alien spaceships orbiting the earth would PROBABLY be observable through a telescope.

On a straightforward reading, this means it's probably that they are the sort of things that could be observed by someone who had a telescope aimed the right way at the right time. If that's what the premise means, then the argument inherits the difficulties of the original: "observable" doesn't imply "would have been observed," not even "likely would have been observed."

So perhaps the premise means something else -- something like

If alien spaceships have orbited the earth, someone probably would have observed them through a telescope.

In that case, the argument doesn't contain any glaring errors in reasoning, though we'd want to make a few things more explicit. Of course, errors in reasoning wouldn't be the problem. The problem would be that the premise isn't obvious; it's not clear why we'd expect to have seen alien spaceships if there are any. But if the issue is whether an argument of this general sort could be acceptable, the answer is yes. After all, this seems reasonable: I don't see a moose in my office. (true) If there were a moose in my office, then probably I would see it. (Hope so) Therefore, there probably isn't a moose in my office. (Thank goodness!)

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