How do you say enough about conditionals at an introductory level, to motivate the truth-functional material conditional to beginners? On the one hand, you want to avoid telling outright fibs or entirely glossing over problems. On the other hand, you don’t want to tangle with issues about conditionals to the point where the student reader is left puzzled about why we are sticking with what has been made to seem such a dodgy rendition of the conditional. How to steer a helpful middle course?
Judging by the frequency of questions about the material conditional on math.stackexchange along the lines of “what is going on here!?”, this is a tricky issue for any entry-level lecture course or textbook. Here then is the latest version of my introductory effort for IFL2 (there’s another later chapter about rules of inference for the conditional in a Fitch-style ND system which reinforces the point made at the very end of these chapters).
Do point students to these chapters (if you think they might be helpful)! And/or send me comments (if you spot typos or can think of ways to improve them!).
Hey, I commented on your earlier post about the diagonalization lemma but it was’t in with other replies. Why not? My point was that your criticism of Carnap is unfair. The proof of the Lemma in Boolos et al is semantical and uses the completeness theorem to get the syntactic version. So all Carnap left out was the application of the completeness theorem.