Reversing implication: you really can't do that

One of the most common fallacies is that of reversing an implication. An implication is a statement of the form 'If A then B,' where A and B can be any statements whatsoever. Now reversing implication is an incorrect belief that 'If A then B, then if B then A.' Implication is not symmetrical, and it's easy to come up with an example that would make it clear. Suppose we have the following implication: 'If Roger Federer is the best tennis player in the world, then he is the best tennis player in Europe.' Reversing this implication you'd have 'If Roger Federer is the best tennis player in Europe, then he is the best tennis player in the world,' which is clearly not true. You just can't reverse an implication; in fact, the only valid conclusion you can get from 'If A then B' is 'If not-B then not-A' ('If Roger Federer is not the best tennis player in the world, then he is not the best tennis player in Europe').

Nonetheless, reversing implications is pretty much bread and butter of political dispute. Let me give a concrete example. On August 1, 1944, Polish anti-Nazi resistance called the Home Army (Armia Krajowa) started an open battle with Nazi troops stationed in Warsaw; the battle is known as the Warsaw Uprising (Powstanie Warszawskie). I will not get into the details of the Uprising here, as I am planning a whole series of posts on this fascinating topic in the very near future. For now I'll just talk about one fact about it: when Poland succumbed to Soviet rule soon after the war was over, the official line of communist propaganda with respect to the Uprising was that it was an insanely careless endeavor that brought more harm than good. The reason that communists were saying this was purely cynical: they hated the Uprising because it was a last-ditch effort anti-communist population of Warsaw to try to prevent the city from being taken over by the Soviets. Of course, I don't share those motivations; but I do indeed believe that the Warsaw Uprising was a tragic mistake, and that, even in its terrible post-war situation, Poland would probably have been better off if it had not happened.

I cannot count the times when, after sharing this belief of mine in a face-to-face or an online discussion, I have been called a communist for having this opinion. But it should be clear that those of my critics who were using this argument were committing the fallacy of reversing an implication. We have 'If one is a communist, then one believes that Warsaw Uprising was a mistake.' From this, my critics were concluding that 'If one believes that Warsaw Uprising was a mistake, then one is a communist.' Fallacious reasoning, clear as day. And the interesting part is those were all people smart enough that, if they were presented with the Roger Federer example given above, would no doubt understand that reversing implication is invalid reasoning. Yet in this particular context they were completely unable to realize that they were making the same silly mistake.