Rico Vitz of the Florida Student Philosophy Blog asks, “should introductory logic satisfy a college’s or university’s general education mathematics requirement?” (here) The question appears to have been prompted by a reader who inquired about (1) whether any Florida schools permit logic to satisfy mathematics gen ed requirements and (2) how dyscalculia affects our logical reasoning skills.
To Rico’s question, I answer “absolutely not. No way. Introductory logic classes should not satisfy a college’s or university’s general educaton mathematics requirement.”
Of course I’ll give a few brief arguments for my position but first…
Weber State University is the only state college or university in Utah that allows students to satisfy a mathematics general education requirement with an introductory deductive logic class (PHIL 2200). Since I wasn’t privy to the faculty meetings, I cannot say what reasons were given in favor of satisfying a mathematics requirement with logic. One should note, however, that if a student attempts to transfer to another university within the state and s/he has taken PHIL 2200 as a means of satisfying the gen ed mathematics requirement, it is up to that institution whether they accept the PHIL 2200 credit to satisfy the mathematics requirement.
OK, now for a few brief arguments. First, introductory logic – particularly those courses covering material up through conditional proofs – is not quantitatively intensive. Sure, logic tests students reasoning abilities, but these abilities are practically unrelated to the quantitative skills mathematics courses are designed to test. Some people can be excellent reasoners but not good at mathematics, or vice versa. Given that there seems to be a disconnect between reasoning ability and quantitative skills, introductory logic shouldn’t satisfy the gen ed math requirement.
Second, if the logic courses were to cover material testing students’ quantitatively abilities, then the course would be too complex for most mathematics professors to complete successfully. The course would be impractical for students to complete because it would review non-classical logics, completeness, enumerability, etc. This course would be easy for fellow blogger Richard Zach but it wouldn’t be practical for undergraduate students attempting to satisfy a gen ed mathematics requirement.
Finally, undergraduates should have a basic understanding of topics in university-level mathematics. If they ever find themselves in a position where they meet with engineers or with scientists who presume you to be conversant in basic mathematical concepts, then not having at least a semester or two of university-level mathematics would be a problem.
So, satisfying the gen ed math requirement with an introductory logic class might be a short-term advantage for the student, but the long-term effects of doing so might be disastrous.
This seems about right. Your second point seems to me to be particularly right: most logic courses that would make a plausible math credit would have to be at a level so abstract that it usually is only studied in grad school.
I do think there are ways you could teach logic at an undergraduate level that would make it a plausible candidate for a math credit, but it couldn’t be a general logic course. It would start looking a lot like a basic abstract algebra course. I think there would be all sorts of good in having and, for majors, requiring such a course, but it’s not introductory logic.
I would have to agree with you, but I would like to argue some additional points.
1) math and logic are interrelated. The ability to do math well- especially higher math- requires well developed reasoning skill
2) the study of logic aids in the development of good reasoning skills
3) thus, logic should be studied in conjunction with math
I don’t beleve that the sanctity and value of math can be replaced by logic, and logic can not be dissmissed as unimportant. I think that institutions of higher education should addapt a system the requires an intergration of the two; I like to think of this intergration in terms of necesity. You can’t do physics without math, and math requires logic; so, you can’t do physics without logic — thus, logic is necssary for physics.
I don’t think that math and logic are unrelated. But the quantitative skills required for mathematics are not the same skills one needs to successfully complete an introductory deductive logic course.
Higher end logic courses, those incorporating alternative logics, modal logics, etc., would be decent way of satisfying an undergraduate math credit because the quantitative skills necessary for completing the course successfully would be more demanding.
But, as Brandon and I have tried to point out, introductory logic courses won’t cut it for the gen ed mathematics requirement.
I agree. I think that the gen ed math requirement should not be completed by one introductory logic course. I do, however, think that a logic course should be added to the already present math requirements.
nice post!
Ps. Joe know when you are up for a meeting.