Does one need to have a strong foundation in mathematics in order to advance in the study of logic?

Question

Do logicians generally study maths also?

Answer 1

The study of introductory and mid-level logic requires little need for any mathematical knowledge.

However, advanced logic - particularly mathematical logic - is all about using logic on the language of math. Still, advanced mathematical knowledge is not absolutely required - but you'll want to have a familiarity with some simple mathematical concepts, e.g., axiom, proof, function, set, ordered pair, ordered n-tuple - before you attempt to tackle topics like Gödel's Theorems.

Mathematical logic is the most difficult course I have ever taken. The text I used was "Logic and Structure" by Dirk van Dalen. Browse this text, and if any of the math concepts seem foreign to you - you'll want to brush up on them.

Answer 2

Logic is reasoning and Mathematics is full of reasoning.

Answer 3

No, one can study these separately. In fact, with the work of Gregory Chaitin and others, some of the foundational work in mathematics is being treated quasi-empirically rather than formally.

Answer 4

No, it is the other way around. Mathematicians need to understand logic, but they learn it as part of their studies. They do not need to learn Linguistic Logic but it would help.

It would help because even in math we think linguistically. I mean, we give words to the parts of the math formulas. And math is deductive logic. And in deductive linguistic logic there are only 256 ways for the human mind to put deductions together.

And out of those 256, only 15 are valid! http://phil240.tamu.edu/LectureNotes/6.1... see page 5

So a mathematician, using words to describe his formulas, makes a deduction by saying "the square of X = yada yada." How does he know if "yada yada" is correct unless he understands which 15 forms of his deductive logic is correct?

The symbology of math is very much like that of linguistic logic ( (p  q)·(q  r) ) and also the logic of electronics schematics (which I studied in the military) because it makes mathematical sense of electricty. "And gates," "nand gates" etc, are common among the different types of logic, though they may apply a little differently.

Answer 5

NO.Only One example should do i.e. Buddha!

Answer 6

most is quite tame but when you start to get into philosophy that have weirder properties they will most likely have weird mathimatical foundations as well.

personally if you are good at making mind maps and thinking about the internal workings of the machine that is enclosed in its case then you should be good

Answer 7

I would venture and say, "no". However, a strong foundation in logic would be helpful in maths...

Answer 8

Most often philosophers are mathematicians too, but it is not a requirement.  Personally, I feel that philosophy, is more the proper use of language, and the assimilation of ideas. Put into a order of logic, so that it make sense to the receiver.  Most often you should be MORE confused after a philosophy discussion.

Peace.

Answer 9

If the Calculus is the highest level of mathematics (pure mathematics), then Philosophy is the highest level of language, so the answer is no.  Math deals with sequential logic governed by rules that yield a set answer and a set response.  Philosophy also deals with logic, but it is not necessarily neither sequential nor set, hence the reason why it is difficult for many to understand it, because unlike math philosophical logic is not neatly laid out.

See that is one of the confusing things about philosophy; it is governed by rules for the purpose that those rules be broken by other rules in a logically acceptable manner.

We needing a Tylenol yet?

I better not get deeper into it.

peace.

P.S.

You know about irrational numbers right?  The reason irrational numbers exist in the first place, is the restrictive, inflexible rules of mathematics.  Numbers have no limit, so any time you impose limits on them (like with rules governing an equation), it stands to reason, that you will get an illogical response, hence, the irrational number.

Math is not in disagreement with logic, problem is, its too simple, rigid, and rules governed to be a good enough foundation for the study of logic.  Logic, in the strictest sense, is the domain of Philosophy, which is the  highest form of language, and even the higher maths, graduate level work and research, has to borrow heavily from it, because pure Mathematics on its own isn't enough.  Story problems, are really just equations rendered into words in which you fill in the blanks, but even mathematics done with words is ultimately still mathematics governed by those rules.

Represented by words or numbers, math is math, logic on the other hand, can be represented by just about anything.

peace for real.

Answer 10

I don't know it for a fact, but math is one of the true hard sciences.  Since math is pure logic, I would assume someone interested in logic would also be interested in math.  I know a former math teacher who took the LSAT (Law School Aptitude Test) on a dare from a fellow teacher.  He aced the test and recieved a full scholarship to Harvard Law School.  The LSAT is 100% logic.

Answer 11

Not necessarily, but I think you have to have a foundation of logic to study maths.

Answer 12

I looked at Lemmon "Beginning Logic". I think it's logic, and also mathematics. I like it. But I find it hard work.