Dear Matthew, (01)
We agree about the problems. I have been trying to clarify Pat's
point about using a logic that lets you relax the constraints.
In many cases, that can be helpful. But it's not magic. (02)
JFS
> With a less restricted logic, you can say anything you like.
> If it causes a contradiction, you just delete one or more axioms
> -- in this case, the axiom that a moving car shall have a driver. (03)
MW
> Sure. But there is also a problem that sometimes definitions just are
> inconsistent. So in the UK 3 wheeled cars were (at one time at least)
> classified as motorcycles with sidecars. I doubt many other countries
> defined car to exclude 3 wheelers. (04)
Any language that lets you say (P and not P) can state a contradiction. (05)
But some languages (logics) are so restrictive that they make it
impossible to express some true sentences. In some strictly typed
logics, you can't say "The number 7 is not an elephant." (06)
That's a true statement that cannot be expressed. A more subtle
example is "No object is a process." Sometimes you might want
to say that something could be either or both. (07)
John (08)
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