# What is the difference betwen [tag:predicate-logic] and [tag:quantifiers]?

Tag wiki for says:

Questions concerning predicate calculus, i.e. the logic of quantifiers

and for it says:

The quantifiers ∀ ("for all") and ∃ ("there exists") are what distinguishes predicate calculus from propositional logic.

These appear to be the same. I suggest that we alias one to the other.

• While in many way those two quantifiers are "what distinguishes" predicate from propositional logic (along with the rest of the term vs. predicate syntax), there are other quantifiers. Cf. provability logic for "bounded quantifiers", many other variants. – hardmath Feb 1 '15 at 19:15
• I think the problem is the wiki for (quantifiers), not the tag itself. – Git Gud Feb 1 '15 at 22:50

## 1 Answer

There is also a tag 'first-order-logic'. I would rather see 'predicate-logic' alias to that, and 'quantifiers' be a separate tag. People often encounter quantifiers in other settings, e.g. in "introduction to proofs" courses that are not really related to formal logic. When I glanced at the 'quantifiers' tagged questions just now, most of them seem to be of that sort (and many of them are incorrectly tagged as 'logic' when they are not really about mathematical logic, just about quantifiers).

• Regarding the statement in-between parentheses, you don't consider that to be logic? It's not mathematical logic in the traditional sense, but I think it's deserving of the name 'logic' anyway. I've always considered 'How to Prove It' to be a logic book, an informal logic book. – Git Gud Feb 1 '15 at 22:53
• @Git Gud: it's analogous to not considering the axioms for the ordered field of real numbers to be "real analysis" , even though these axioms may appear in Chapter 0 of undergraduate real analysis books. Basic quantifier manipulation is just part of mathematics, it's not particularly part of mathematical logic, which refers to particular disciplines of mathematics, not to the general idea that mathematicians use logical reasoning. – Carl Mummert Feb 1 '15 at 22:55
• (But the "logic" tag wiki is clear that the tag is for mathematical logic. Otherwise, it would be a meaningless meta-tag if every question that involved logical thinking could be tagged "logic") @Git Gud – Carl Mummert Feb 1 '15 at 23:03
• I do not disagree with what you say regarding 'How to Prove It' not being mathematical logic, but it is, as you say, about logical reasoning. The 'logical reasoning' part is why I think it's not a stretch to say that the book is a logic book. Regarding the tag's wiki specifically, it starts with "Questions about logic and mathematical logic", and I would include HtPI questions in the 'logic' bit. If not, how would you tag a question like "What is the truth table of $P\lor Q$" asked in the context of HtPI instead of the context of propositional calculus in mathematical logic? – Git Gud Feb 1 '15 at 23:13
• I would say truth tables could be tagged propositional logic or discrete mathematics, another area where truth tables are often studied. Truth tables are another example of a basic topic that isn't really mathematical logic. The "logic or" part of the tag wiki may be confusing - there is no other "mathematical logic" tag, and "logic" is intended to be specifically "mathematical logic". – Carl Mummert Feb 1 '15 at 23:21
• Here is an example of a kind of question that I really don't want to see tagged as "logic" (I just removed that tag): math.stackexchange.com/questions/1128643/… – Carl Mummert Feb 1 '15 at 23:27
• We actually have a tag for that: (proof-strategy). If you would tag the question I made up above as (propositional-calculus) (there isn't a propositional logic tag), given that $\text{propositional calculus}\subseteq \text{logic}$, how would that be less severe than also tagging such a question with (logic)? What about the typical questions that ask to model english statements in predicate calculus? Those aren't mathematical logic per se, they are about modelling, but you need to tag them as (predicate-calculus) anyway. Do you think there's a need for a tag to encompass HtPI-like questions? – Git Gud Feb 1 '15 at 23:39
• I am generally OK with the "logic" tag for questions that ask for modeling natural language statements in predicate logic, but I think that are at the edge. Questions that are just about how the order of quantifiers affects things are even less on-scope for that tag, I think. More generally, the trouble with certain basic topics is that they are so fundamental that they don't really "belong" in any area. These include truth tables (logic, discrete math?), the basic axioms of the real line (algebra, analysis, intro to proof?), and similar things. – Carl Mummert Feb 2 '15 at 1:14