A break from proofs and rules for a note about counterexamples. I’ve talked about them before briefly, but before we go any further, it’s important to talk a bit more about soundness, validity, and counterexamples. Counterexample is one of the most elegant ways to demonstrate an argument’s invalidity, but it rests on a solid understanding of what constitutes validity, and what constitutes soundness.
“Whether you think you can, or you think you can’t–you’re right.”
- Henry Ford
A friend of mine mentioned that I should do some posts on words I use differently or don’t use at all, the kinds of things I put in my linguistic garbage can. That’s one of the fun things about language, we can remodel it for our own use, and use it in the ways we want. “Can’t” is the first of these, and represents a whole class of words, like “Impossible”, “Insurmountable”, and “Unattainable”, etc. You know the ones. I want to talk about what they mean to me, how I deal with them, and why they belong in the garbage.