Great explanation! However, I think rule 4 gets a little bit complicated due to the fact you avoid even mentioning free variables and use a "name" instead. Most of the authors I've read consider "A(u)" (being "A" a predicate function and "u" a free variable) a wff. And just from there build the other two wff by means of substituting free variable "u" for a quantified "x" variable. In that sense, the last "not-wff" in your table, where "y" is a free variable, is indeed a wff, according to this view. Is there any particular reason you go a different approach?
Yes, that is the other way of doing it. And that way is perfectly good (if not better if you plan on learning more logic!). The only downside is that when you move to the semantic side, you either (1) have to state that there are a certain class of wffs that are not interpreted (that is, they don't take a truth value) or (2) go through the complexities of explaining how you can assign truth values to wffs with free variables. Since these videos are tied to a single introductory course taught in philosophy, I use the method outlined in the video. If I were to teach a second course, I'd do it in the way you suggest. If I remember correctly (it has been a while), I think I discuss the semantics given the approach you outline in the following two videos. Part 1: ruclips.net/video/1kIao8PtWIE/видео.html and Part 2: ruclips.net/video/eN7WOdsNhjg/видео.html Best wishes!
Great explanation! However, I think rule 4 gets a little bit complicated due to the fact you avoid even mentioning free variables and use a "name" instead. Most of the authors I've read consider "A(u)" (being "A" a predicate function and "u" a free variable) a wff. And just from there build the other two wff by means of substituting free variable "u" for a quantified "x" variable. In that sense, the last "not-wff" in your table, where "y" is a free variable, is indeed a wff, according to this view. Is there any particular reason you go a different approach?
Yes, that is the other way of doing it. And that way is perfectly good (if not better if you plan on learning more logic!). The only downside is that when you move to the semantic side, you either (1) have to state that there are a certain class of wffs that are not interpreted (that is, they don't take a truth value) or (2) go through the complexities of explaining how you can assign truth values to wffs with free variables. Since these videos are tied to a single introductory course taught in philosophy, I use the method outlined in the video. If I were to teach a second course, I'd do it in the way you suggest.
If I remember correctly (it has been a while), I think I discuss the semantics given the approach you outline in the following two videos. Part 1: ruclips.net/video/1kIao8PtWIE/видео.html and Part 2: ruclips.net/video/eN7WOdsNhjg/видео.html
Best wishes!
@@LogicPhilosophy Understood. Thank you so very much. Your vids are simply fantastic!