Friday, March 30, 2007

How to Make No Sense While Sounding Smart

Man is sentient.

Man feels fear.

The aliens feel fear.

Therefore the aliens are sentient.

And that type logic fallacy is something that absolutely plagues writing. But, unlike the other fallacies that I’ve been looking at here, this one I feel is mostly accidental; the others always strike me as shortcuts gone wrong. I think most writers don’t strive to make no sense at all, or spin a story based on an obvious fallacy. Still this type of fallacy, called the Undistributed Middle Term, comes up over and over again. I most commonly see it in character stereotypes, and in the proof of intelligence arguments. I can think of several stories in which the basis of the reason the explorers went to talk to the aliens surrounded some similar to the above logic fallacy.

The Undistributed Middle Term a.k.a How to Make No Sense While Sounding Smart

Why does this form above imply logic to us? Well, if you studied logic you know immediately why: it is the form of a syllogism, or a logical argument in which the conclusion is supported by a major and minor premise. I am pretty sure, despite being four lines and not the usual three, that this counts as a syllogism at least. All the same, syllogisms are at the foundation for deductive reasoning. Some famous examples:

Major premise: All mortal things die.

Minor premise: All men are mortal things.

Conclusion: All men die.

Major premise: No reptiles have fur.

Minor premise: All snakes are reptiles.

Conclusion: No snakes have fur.

So what is an undistributed middle term? It is when minor premise and the major premise of a syllogism may or may not be relevant to each other. I think it is easiest expressed in examples.


All dogs have fur

All cats have fur

All dogs are cats

So went wrong there? It’s obvious to all of us that it is wrong, but what is the logic problem. The middle term is “cats,” which does not fit into the category of “things that have fur” and “dogs.” One cannot base a conclusion on something that hasn't been clearly proven. We, in the case, have shown no correlation between cats and dogs, besides being warm blooded. Now, if I had said:

Only dogs have fur

Cats have fur

Therefor cats are dogs.

Can you see the difference?


All mammals are warmed blooded.

All cats are mammals.

All cats are warmed blooded.

In this case, the middle term “cats” fits into both “warm blooded” and “mammals.”

So here is the fallacy in stripped down terms:

1.All As are Bs
2.C is a B
3.Therefore, C is an A

Not too hard in these cases, but I bet we can all think of examples where the logic went wrong in writings we’ve read, or perhaps in arguments we’ve heard.


Mr. Smoot said...


1. Fabio might be good (looking)
2. Fabio is on the cover of this book.
3. Therefore, this book with Fabio on the cover might be good...

Unfortunately, this seems to sell quite a few pulp novels/novellas. Alas, logic and sales are often unrelated, hence things like Who Moved My (read: Dan's) Cheese sell well whilst others, like P.G. Wodehouse or even Nick Hornby do not.

Marketing trumps logic every time.

*ahem*..... :)

pacatrue said...

Woo-hoo! Syllogisms! I always have heard of this fallacy as "Affirming the Consequent". As you said, the proper form is:

If A then B
Therefore B

In affirming the consequent, you get:
If A then B
Therefore A.

It's amazing how correct the fallacy can seem. At least in my logic and philosophy classes a few years back, it always took the teacher a while to convince people that it really was an error.