The Limits of Logic

Let’s examine those syllogisms I presented in the last post and find out which are valid and which are not:

Syllogism A:

No Gox box when in purple socks.
Jocks is a Gox wearing purple socks.
Therefore Jocks does not now box.

Many people struggle with this syllogism, even though its logical structure is quite simple. The difficulty arises from the confusing, unfamiliar, even silly subjects of the syllogism. If presented in terms of more familiar objects, it becomes so easy that even a child can figure it out. Take, for example, the following syllogism, which has the same structure:

No cars run when they’re out of fuel.
My car is out of fuel.
Therefore my car does not now run.

Obviously, both syllogisms are valid. But as Morton Hunt notes, “if we were truly logical thinkers, we would find the first [syllogism] just as easy to evaluate as the second one.”

Syllogism B:

Those who believe in democracy believe in free speech.
Fascists do not believe in democracy.
Therefore Fascists do not believe in free speech.

Many people assume this syllogism is valid because the premises and conclusion all seem to be true. How, then, can it not be valid? Well, consider the following syllogism, which features the same structure:

Robins have feathers.
Chickens are not robins.
Therefore chickens do not have feathers.

Obviously, we confronting an invalid syllogism. The reason so many people are fooled is because they don’t use logic when they evaluate the syllogism, they use there own experience and knowledge. This is one of the critical findings of cognitive science. People don’t think logically, they think experientially, in terms of what they know.

Syllogism C:

Whatever makes for full employment is socially beneficial.
Being in a state of war tends to make for full employment.
Therefore war is socially beneficial.

Here we are confronted by a syllogism, the premises of which appear, at least superficially, as true, yet which has a conclusion that seems false. Yet the syllogism itself is valid. What gives on this one?

People tend to think this syllogism is invalid because the conclusion is wrong. They often don’t notice that the first premise is dubious, because it seems reasonable enough at first glance. What this syllogism demonstrates is the tendency for human beings to judge arguments based solely on whether they agree (or disagree) with the conclusion. Again, logic is ignored.

Syllogism D:

If it’s raining, the streets are wet.
The streets are wet.
Therefore it’s raining.

This is another syllogism that gives people great difficulty. Why? Because it exhibits a natural form of reasoning that is useful in ordinary life—so they are inclined to regard it as valid. But it isn’t valid—not logically. Even if the streets are wet, this doesn’t necessarily mean it must be raining. The streets may be wet for some other reason, such as a broken water main or a street-washing machine. To be sure, in real life, these alternative explanations aren’t very likely and can usually be ignored. That is why such reasoning, though logically invalid, often leads to correct conclusions and is used with great effectiveness in the real world.

Syllogism E:

Disease X is known to produce various symptoms, including A, B, and C.
This patient has symptoms A, B, and C.
Therefore this patient has disease X.

This is not a syllogism that was used to test logical ability in cognitive science experiments. On the contrary, it is the form of reasoning routinely used by doctors when analyzing patients. Logically, it is an invalid form of reasoning. But, as Morton Hunt notes, “it is a highly plausible way to begin a diagnosis.”

Syllogism F:

Some of the beekeepers are artists.
None of the chemists are beekeepers.
Therefore… some of the artists are not chemists.

This is the most difficult to get right (and you don’t have a 50% chance of guessing, like you do with the others). If we make the terms a little more sensible and familiar, it’s easy at least to evaluate as to its validity:

Some birds can swim.
No fish are birds.
Therefore some animals that can swim are not fish.

So what does all this prove (or at least suggest)? Namely this: that individuals rely far more on experiential and/or plausible reasoning when they judge the validity of arguments than they do on logic. And why is experiential/plausible reasoning more important than logic? Because, as Morton Hunt puts it,

logical reasoning is in large part abnormal, unnatural, and not generally applicable to everyday experience and to the problems of survival. [Logic] consists of a set of artificial rules that we can learn and can apply—indeed, must apply—in order to solve certain kinds of problems, but it is not a means by which our minds can effectively interpret the larger part of the reality around us; our natural way of reasoning, however, is just such a means…

Logic enables us to judge the validity of our own deductive reasoning, but much of the time we need to reason nondeductively—either inductively, or in terms of likelihoods, or of causes and effects, none of which fits within the rules of formal logic. The archetype of everyday realistic [i.e., experiential] reasoning might be something like this: This object (or situation) reminds me a lot of another that I experienced before, so probably I can expect much to be true of this one that was true of that one. Such reasoning is natural and utilitarian—but logically invalid.