What is Symbolic Logic Useful For?

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  • #1
My (soon to be) university offers a class called, "Symbolic Logic," that fulfills the GER quantitative reasoning portion of our school's requirements. I'll be an incoming freshmen next academic year and was just an average math student in high school. Honestly, I just didn't put in that many hours into it. I did OK in high school maths, but am not sure how I'd do in college.

I've thought about either going with the Symbolic Logic course or Statistics my first-year to fulfill the GER subject area. I took stats as a high school elective rather than Calculus, so am familiar with that.

Can someone maybe give their opinion of how hard Symbolic Logic is compared to Calculus?

And, additionally, can someone explain what I'd be learning in logic and where/how it's used in everyday life? I know Calculus would be very important if I were to major in a science field (which, for the moment, I'm less likely to do), but I'm not sure if a logic class would be useful in anything I would do in school or life later on.

Thanks everyone for your time and help. I greatly appreciate it!

Answers and Replies

  • #2
Stephen Tashi
Science Advisor
Introductory symbolic logic is useful if you intend to deal with fields that involve precise and legalistic use of language. (I'm not a lawyer, but I'd include law in such fields.) It's also useful in teaching how imprecise common speech is.

A knowledge of symbolic logic is useful in studying advanced math.

In the "softer" liberal arts, a knowledge of symbolic logic is useful because it makes clear the limited applicability of logic! The word "logical" , in common speech, is used to mean "true", "plausible", "realistic" etc. The actual scope of logic is only to study reliable methods of reasoning. Roughtly speaking, it shows what conclusions can be deduced from assumptions. It does not deal with whether the assumptions themselves are "true", "plausible" or "realistic". Logic itself has no results that bear on specific issues of science, politics or moral philosophy. ( When people see articles that they don't respect they often criticize them by pointing out logical fallacies in arguments. However, this is an easy game to play in the liberal arts since arguments given in common speech fail to meet the standards of mathematical logic.)
  • #3
Homework Helper
Logic, at least sentential logic, is about sentences and how we can assign a value true or false to them. Like the sentence "If it rains, I will get wet", this is a true statement whether it rains or not, unless it rains and one is indoors.

Symbolic logic can be just an algebraic version of this, so we have "if A, then B", etc. And you would learn all the rules of Boolean algebra to manipulate formulas like that, as well as learning about truth tables and possibly Karnaugh maps. The idea is to take a complex expression and find a simpler, equivalent expression. This is used when designing logic circuits as used in computers or electronic devices. If you were doing electronics, this would be important. It also helps with programming languages.

On the other hand, it can be more if it talks about deductive systems and possibly even formal semantics, which is quite a forest of talk with not whole lot of purpose to it, but I do find it fascinating.

If it is just about manipulating formulas, it probably won't be worth a whole lot to you unless you fall into those categories I mentioned. On the other hand, the deeper it goes, the better it is, for this reason: it can help one to think clearly. And I would say unless you want to take a second course in statistics in college or need the credit, retaking it wouldn't be worth much, it'd be about what you learned before.

While I say that symbolic logic, if it doesn't go very deep, may be of little use, this is not to say that non-symbolic logic is not useful. On the contrary, I very much like the verbal logic puzzles as exposed in many puzzle books by the likes of Raymond Smullyan, for example.