# Teaching Quantifiers Before Logical Connectives

In this short question, I would like to ask whether it is possibly good to teach quantifier before logical connectives in a logic introduction lecture?

I know there is a relationship between them but my question is based on my observation that students usually already get the concept of existential quantifier. Before introducing them to more complex forms of statement, maybe they can understand basic form of quantifier statements first (of course, after introducing open and closed sentence). This is just an idea. Let me know if anyone has done this because I have never seen one.

Thank you very much!

• What level is this at? Are these math majors in an upper-division course? By "logic introduction lecture" do you mean the introductory lecture in a semester-long course on formal logic, or do you mean an introductory lecture on the first day of a class on some other topic such as topology, where you want to give them some preliminary foundation in logic? You could point out to your students that they have already seen statements that have implicit quantifiers, as when they learned axioms of the real number system such as $x+y=y+x$. – Ben Crowell Feb 23 '20 at 18:40
• I think it does make sense to introduce quantifiers before complex logical expressions, because you can rely on the student's familiarity from English (or whichever is their 1st language): "All men are mortal," "Some birds do not fly," etc. – Joseph O'Rourke Feb 23 '20 at 20:41
• @JosephO'Rourke Yes. I have been thinking about that. – 10understanding Feb 24 '20 at 2:07
• @BenCrowell Undergraduate math major education. Right after they enter uni, we have an introductory set and logic course (as in highschool there is none). – 10understanding Feb 24 '20 at 2:09
• @21understanding: When someone asks you to clarify a question, it's better to edit the question rather than replying in comments. – Ben Crowell Feb 24 '20 at 2:18

## 1 Answer

A strategy I once adopted while teaching logic for philosophers at the undergraduate ( 1st year) level

(1) introducing connectives with the motivation of explaining set operations and set relations

(2) working with connectives on non explicitly quantified open sentences to prove some set theoretic basic laws ( using truth tables or natural deduction )

(3) finally introducing explicit quantification to make the proofs rigorous.

• Thanks. It is quite (maybe the most?) common too in teaching logic to math. I am indeed considering the quantification first and wondering whether it is possible. – 10understanding Feb 26 '20 at 14:09