Category talk:Classical first-order logic

Predicate logic vs. first order logic
Predicate logic is not the same as first order logic. First order logic is a subset of predicate logic where you may quantify only over individuals in your universe of discourse. For example, in set theory, where your universe of discourse is the class of all sets, you may quantify over variables of type, but not of type. Hence, it's a first order theory. Wikipedia has an example of a second-order predicate logic, with the real numbers as universe of discourse. Another predicate logic is higher-order logic where you have a hierarchy of predicates with higher-order predicates taking lower-order predicates as arguments, with the possibility of quantifying over predicates.

Maybe it's best we rename this category to Category:First-order logic or even, in accordance with the MSC naming scheme, Category:Classical first-order logic. We can then put the higher-order stuff in a different category, Category:Higher-order logic and type theory say, and place a 03B15 MSC marker on it.

--GrafZahl (talk) 18:30, 17 February 2010 (UTC)


 * Yeah, I noticed that at the end when I looked it up in MSC (my intent was a category for both first-order and higher-order logics, but MSC has no level in their hierarchy between "general logic" and the rather specific ones). I sort of like the way I was trying to categorize it, but yeah, we shouldn't have a misleading MSC tag on it. I suppose it is better to just follow the MSC system and rename this to Category:Classical first-order logic. Kingdon 01:35, 18 February 2010 (UTC)


 * Renamed.--GrafZahl (talk) 10:18, 18 February 2010 (UTC)