This continues the series that I started at
Today’s post distinguishes between conventions of word usage, and conventions of other kinds of behavior. Word use is, of course, a kind of behavior.
I’ll give an example of each.
A word use convention
In his “Truth by convention,” Quine writes:
A contextual definition sets up indefinitely many mutually analogous pairs of definienda and definientia according to some general scheme; an example is the definition whereby expressions of the form ‘sin —/cos —‘ are abbreviated as ‘tan —‘.
That’s a word use definition. It allows us to abbreviate some expressions that use trigonometric functions. We can agree that it is a useful convention, because it allows us to write more concisely. If you are familiar with that convention, you are able to read more of the mathematical literature than if you are not familiar. However, it does not really add any mathematical value. The convention does not allow us to solve any problems that could not previously be solved.
This example fits the criticism that John Wilkins had of conventions, namely that it does not express any fact of the matter. It fails to express anything we would consider a mathematical fact. It expresses only a notational fact.
In the introduction to this series, I mentioned that there appears to be suspicion of conventions. It is entirely proper to be suspicious of this kind of convention which has to do purely with word usage. The convention might be useful, but it is hardly important.
A behavioral convention
For an example of a behavioral convention, we can look to the convention in Australia, that one should drive on the left side of the road. John accepts that as a convention, and mentioned it as an example in our discussion in comments on his post. In North America, there is a corresponding convention of driving on the right side of the road.
Driving on the left is not a word use convention. It isn’t that when one talks of driving in Australia, one is supposed to add “on the left side of the road” to such talk. Rather, it is a behavioral convention. The expression “they drive on the left side of the road in Australia” does express a matter of fact. You can visit Australia, watch how people drive and see for yourself.
John did say:
Yes, if we all did the same things we’d all be driving on the left, but there is no fact of the matter which is best, left or right.
Well, that’s true. That’s precisely why we need a convention. There is great benefit in everyone driving on the one side (left or right, relative to the direction of travel), as that significantly reduces the risk of traffic accidents (of head-on collisions). And since there is no fact of the matter on which to choose, we need a convention to settle that issue. However, there is a fact of the matter presented in the description “they drive on the left side of the road in Australia.”
Suspicion of convention might be appropriate for conventions that are purely conventions of word use. But that suspicion is not warranted for all conventions. In particular, there are some behavioral conventions for which the suspicion is clearly unwarranted.