The logic works regardless of what the variables are…
A random thought, from reading this article on cheating (Mike’s fault)
and bumping into this quote: “Propositional calculus is a system for deducing conclusions from true premises. It uses variables for statements because the logic works regardless of what the statements are.”
Which is standard stuff but it struck me that the whole problem of this view is the problem of definition (Plato’s problem in the Margolis and Laurence survey).
Logic works regardless of what the statements are as long as the variables mean what you wanted them to mean. “If P, then Q. P, therefore Q.” This is true so long as the entities you want to sub in for P and Q can properly take a true or false value. So we get told modus ponens as if it’s “this is a universal truth” and well, it’s more like 1+1=2, isn’t it? That *can* be one of the universals. Doesn’t have to be (dangit, I have to read up on Gödel one of these days). And even so, it rather hinges on the definition of 1 and 2. One cup of water and one cup of sugar doesn’t make two cups of anything.
Reading further (the article’s quite interesting) I see I’m not alone in this wait-a-minute reaction and now I have to look up the Wason selection task and David Buller’s critique of it.
Anyway, apparently, “meaning matters” is going to be my new hobby-horse.
Random picture test:
