Truth tables for quantified statements

Today we had a very interesting discussion following our attempt to do problem number 10 on page 446 in Stan Baronett's Logic. In doing the proof it looked like we might have a typo in the conclusion. To check this and see if the argument was invalid (which it looked like considering the conclusion was a conjunction of Aa and not Ha with EG applied to it, but Aa would have to be entered into the proof via Addition. Only DeMorgan's would enable us to change it. But after multiple approaches none seemed to work. So we attempted to do a truth table to check it. It was at that point I realized I have never seen a truth table applied to quantified statements before - they are not truth functional? Here is one explanation I found: (from http://williamstarr.net/teaching/2310/10.20-4up.pdf) Truth tables work by explaining the truth of a complex formula in terms of the truth of its parts Example: :P is t i P is f The problem with using truth tables for quantifi ers is that the truth of quantifi ed formulas cannot be determined from the truth of its parts Example: 8x Cube(x) is t i ??? Cube(x) is t? f? Neither! Cube(x) isn't capable of truth or falsity, it's too incomplete! So, we can't use truth tables to explain what quantifi ed sentences mean But see the link and following discussion of Tarski's World. What helped was removing the quantifiers and doing the table for instances of the statements. Doing that it became obvious that the argument was invalid by that truth table.

Doing exercises in Stan Baronett's Logic I did a truth table for problem 30 page 409 and the argument is invalid - for table with P = T, and Q R S all F, the premises are true but the conclusion false.

It is that time of the logic course where we cover fallacies and I always use this time to also talk about humor. The main reason is that talking about humor means playing some hilarious videos which main class more enjoyable. But it also brings up a very interesting point - and very real point - that jokes seem to be invalid arguments. So what we can do is look at the varieties of fallacies and compare them to the varieties of jokes to see if the templates behind the fallacies are similar to those that seem to structure the jokes. Keep in mind that behind this whole exercise is making the point that the structure of fallacies / jokes might be entertaining but what makes the structure funny is at the same time what makes the structure a poor way to frame an argument.