1. Either 1+1=5 or 2+2=5.Obviously this is a bad argument. The second premise is true, but we'd need some reason to think that the parameters of the choice offered in the first premise was legitimate for the argument to be convincing. Of course, we know that both of the choices offered in the first premise are false.
2. It is false that 1+1=5.
3. Thus, 2+2=5.
The moral of the story is that arguments of this kind (where a dilemma is posed, and one of the disjuncts is negated in order to make the other disjunct look plausible) are tricky. They are never legitimate unless we can be convinced that the choice offered in the either/or is exhaustive of all possibilities.
Now, this isn't just a point about logic or inference. Exposing the false pull of this fallacy is a political necessity. For example, consider the following two examples.
Consider the following dilemma about budget cuts that we're hearing every day from the media:
1. Either we cut public services or the government goes into the red.This bait-and-switch operation is obviously bullshit, but one hears it all the time in the media.
2. The government can't be allowed to go into the red.
3. Thus, public services must be cut.
Notice that options presented in the first premise are not exhaustive, and the force of the conclusion trades on this deceptive feature of the premise. We must ask: why is it that we must only choose from these two options?
The "choice" presented to us in the first premise obscures the fact that there are other courses of action that could be pursued (e.g. raising taxes on the rich) in order to assuage the problems raised by budget crises. Of course, the argument above says nothing whatsoever about raising taxes, and in this way proscribes this option by omitting it from the set of possibilities at the start.
Here's the second example, a jab at Howard Zinn from the LA Times:
To a point, he helped correct mainstream popular conceptions of American history that were highly biased. But he ceased writing serious history. He had a very simplified view that everyone who was president was always a stinker and every left-winger was always great. That can't be true. A lot of people on the left spent their lives apologizing for one of the worst mass-murdering regimes of the 20th century, and Abraham Lincoln freed the slaves. You wouldn't know that from Howard Zinn.The argument here that I want to focus on is as follows.
Now this is an old Cold-War conversation-stopper. It can be deployed to cut-off any conversation in which someone wants to make a highly critical remark about capitalism: either we accept capitalism full stop, or we must accept the atrocities of Stalinism. This "argument" is deployed so frequently that it has become an unreflective truism for many people.
- Either we accept that American Presidents aren't as "bad" as Howard Zinn says or we must apologize for the atrocities committed by Stalin or Mao.
- Apologizing for Stalin is insane.
- Thus it follows that we must accept that American Presidents aren't really as bad as Howard Zinn claims that they are.
But notice that it's an invalid inference just like the 2+2=5 example above.
It says nothing about the soundness of Zinn's critique of American Presidents. The question of whether or not American presidents committed war crimes, lied, owned slaves, etc. has nothing to do with Mao or Stalin. Either Reagan did or he didn't fund murderous right-wingers in Nicaragua. Either Jimmy Carter did or he didn't have a hand in selling arms to those involved in the massacre of the East Timorese. These questions have nothing to do with Stalin or Mao.
Moreover, there's no reason in principle why we couldn't condemn both Stalin and, say, Reagan for the atrocities they're responsible for having signed off on. I think this is the position any sane person would want to take.
But this isn't what hacks like the anti-Zinn gentleman above want you to notice. They have one goal: to shield certain features of the status quo (e.g. the foreign policy of US Presidents) from radical criticism. He wants to change the subject in order to focus our attention on something other than the question of whether or not there is something radically wrong with US Foreign Policy.
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