Not All...

Originally posted on Half an Hour, March 28, 2008.

My series on homeschooling will continue. But for now, this interruption.

Dave Taylor, who is normally rational, writes: "all cars should not be black." It's part of a presentation where he's trying to encourage people to "Allow experiment & change."

Fair enough. But does it have to be expressed in the form of a basic error of logic?

The sentence "all cars should not be black" means "No cars should be black." But this is not what he meant; this is as absolute as the behaviour he is trying to discourage.

What he wants to say here, of course, is "not all cars should be black." This allows that some cars can be black, and some cars can be other colours.

There really is no excuse for such a basic error in logic, and this particular error is far too common. Every time I read another case I wonder why basic illiteracy seems to be spreading through the educational community.

And this is not simply a matter of choice of expression, or of the changing nature of language. It is a matter of logic, not language, and logic, unlike language, does not vary with usage or over time.

For the uninitiated, the rules governing universals and negations are very simple:

All N are P = No N are not P
No N are P = All N are not P

Not All N are P = Some N are not P
Not No N are P = Some N are P

That's pretty simple, hm? These rules can easily be proven using two-circle Venn Diagrams.

Want more? Here is a more complete discussion of the equivalence of two-term categorical statements (from my Guide to the Logical Fallacies).

Now.. let's keep those categoricals straight, shall we?
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