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July 10th, 2017, 02:52 PM   #1
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The study of logic.

I read philosophy, but it has become very apparent that mathematical logic is going to become necessary to understand most of the modern works. Now, I haven't taken many math courses, the last of which was Algebra 2. (I've never had difficulty with maths, but the subject never jumped out at me in the way that philosophy and writing did; but after reading maths as it pertains to philosophy, it's become fairly enchanting.)

I've heard that there are no prerequisites for mathematical logic, the explanations being that logic is the foundation for all mathematics, meaning that to have a prerequisite would be oxymoronical.

I will words my questions as follows:

1). Is there any prerequisite for mathematical logic?

2). Is this something that can be self-taught? (No university anywhere near me teaches mathematical logic in a specialized way, only random bits and pieces in the form of various courses). I'm not opposed to strenuous reading of books.

3). How much reading would be involved, and how much information would there be to absorb? I know that this is extremely difficult to answer, but I would appreciate an estimate of either time-in, amount of books, comparative timing (for example, learning mathematical logic as opposed to, say, physics in all of its forms).

Thank you.

PS: Open-ended (let your mind wonder): how does mathematical logic pertain to philosophy?

Last edited by skipjack; July 10th, 2017 at 11:38 PM.
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July 10th, 2017, 11:47 PM   #2
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Read A Friendly Introduction to Mathematical Logic by Christopher C. Leary, Lars Kristiansen (ISBN 978-1942341079 or 1942341075). It has 380 pages.
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July 11th, 2017, 12:24 AM   #3
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Quote:
Originally Posted by stoic View Post
I've heard that there are no prerequisites for mathematical logic, the explanations being that logic is the foundation for all mathematics, meaning that to have a prerequisite would be oxymoronical.
It's more accurate to say that logic is necessary to do math, but not sufficient. It turns out you can't create math with just logic. You have to assume in addition some extra-logical axioms, such as the axioms for sets.

Quote:
Originally Posted by stoic View Post
1). Is there any prerequisite for mathematical logic?
There are two kinds of prerequisites: Logical and pedagogical. Logically, to study basic logic you only need a tiny bit of mathematical maturity. But the subject is self-contained. You can in theory start from nothing and learn logic.

But in practical terms, in pedagogical or learning terms, you need a certain amount of facility with symbolic manipulation. You have to be able to sling around meaningless strings of symbols and understand what they are intended to mean. That's "mathematical maturity."

So there are no actual or logical prerequisites for learning logic. The subject is self-contained. But the more math you've taken the easier it is.
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Last edited by Maschke; July 11th, 2017 at 12:37 AM.
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July 11th, 2017, 01:49 AM   #4
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My wandering mind suggests that logic is about relationships between objects.

You cannot develop a discipline without the objects

But defining or identifying these objects is not the province of logic.

It is the province of the employing Science.

In this case Mathematics, which defines mathematical objects.

In general the Science also studies the properties of the objects in isolation as well as the relationships between them.

So logic alone cannot be the entire foundation of any Science, although it is an important part of any.

One technique of great use is the splitting of objects into sub objects and applying logic to the development of relationships between the sub objects.

For example you cannot consider circles without a working definition of a circle.
But once you have one you can split the circle into radius and circumference and use logic to deduce the relationship between them and then compare with other circles.

Mathematics has a vast number of such definitions, many of which are specialist uses of common words, some even being different from the specialist uses of other Sciences such as Physics, Biology etc.

So I would reccomend getting a good Mathematics Dictionary to accompany your
studies.

In England the Collins one is better than the Oxford one (which is aimed at a more elementary audience).

Go well in your project.

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July 13th, 2017, 08:17 AM   #5
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Quote:
Originally Posted by stoic View Post
I read philosophy, but it has become very apparent that mathematical logic is going to become necessary to understand most of the modern works. Now, I haven't taken many math courses, the last of which was Algebra 2. (I've never had difficulty with maths, but the subject never jumped out at me in the way that philosophy and writing did; but after reading maths as it pertains to philosophy, it's become fairly enchanting.)

I've heard that there are no prerequisites for mathematical logic, the explanations being that logic is the foundation for all mathematics, meaning that to have a prerequisite would be oxymoronical.

I will words my questions as follows:

1). Is there any prerequisite for mathematical logic?

2). Is this something that can be self-taught? (No university anywhere near me teaches mathematical logic in a specialized way, only random bits and pieces in the form of various courses). I'm not opposed to strenuous reading of books.

3). How much reading would be involved, and how much information would there be to absorb? I know that this is extremely difficult to answer, but I would appreciate an estimate of either time-in, amount of books, comparative timing (for example, learning mathematical logic as opposed to, say, physics in all of its forms).

Thank you.

PS: Open-ended (let your mind wonder): how does mathematical logic pertain to philosophy?
Hello stoic!

Especially for people like you, Peter Smith has constructed the guide to logic. With a LOT of nice recommendations for books. Teach Yourself Logic: A Study Guide (and other Book Notes) | Logic Matters
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