Amount of Set Theory Required to Study Logic

In summary, a basic understanding of set theory is necessary for studying logic, as many logic books rely on this foundation. However, the amount of set theory required may vary depending on the specific topics covered in the logic book. If set theory is not of interest, one can dive into learning logic and refer back to the necessary set theory concepts as needed.
  • #1
LawdyLawdy
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Amount of Set Theory "Required" to Study Logic

Hello,
I have been self-studying set theory to try and get into logic. The book I bought is published by Dover (I love how cheap their books are) entitled Set Theory and Logic by Robert Stoll. I have gone over the basic set theory section involving union, intersection, inclusion...basically the algebra of sets...and into ordered sets and types of relations. The thing is now the book is going into what makes a number system, which I already have a basic understanding of, however the book goes into it MUCH deeper (perhaps more for the mathematician reading the book than an engineer). Any who, I flipped through to the beginning of the logic section and saw that it mainly seems to rely on the basic set theory which I already know. This may be due to my lack of knowledge on logic, but would the general population consider an understanding of basic set theory enough to dive into learning logic?
Thank you (Hopefully, I placed this in the right forum)
 
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  • #2
If set theory doesn't interest you very much, then I suggest diving into logic immediately. It might happen that they start to talk about something that you haven't learned yet, but then you can always go back in the book and study it.

If you want to know exactly how much set theory you need for logic, then you will need to tell us the topics that your logic book covers. Some logic books require quite a lot of set theory (but those books are usually not introductory).
 

1. What is the relationship between set theory and logic?

The study of logic relies heavily on set theory as it provides the foundation for understanding the concepts of sets, relations, and functions. Set theory also helps to formalize the rules of logical reasoning and provides a framework for constructing mathematical proofs.

2. How much set theory knowledge is required to study logic?

The amount of set theory knowledge required to study logic depends on the level of complexity of the logical system being studied. Generally, a basic understanding of set theory, including concepts such as sets, subsets, and operations on sets, is sufficient for most introductory courses in logic.

3. Can one study logic without any knowledge of set theory?

While it is possible to study logic without any prior knowledge of set theory, it may be more challenging to fully grasp the concepts and theories without a basic understanding of set theory. It is recommended to have at least a fundamental understanding of set theory before diving into the study of logic.

4. Is set theory a subset of logic or vice versa?

Set theory and logic are interdependent disciplines, and it is not accurate to say that one is a subset of the other. Set theory is used to formalize the rules of logical reasoning, while logic is used to study the properties and relationships of sets. Both fields complement each other and are essential for a deeper understanding of mathematics.

5. Can set theory be used to solve logical problems?

Yes, set theory can be applied to solve logical problems. Set theory provides a framework for constructing mathematical proofs and analyzing the relationships between different elements. The concepts and techniques of set theory can be used to solve problems in various branches of logic, including propositional logic, predicate logic, and modal logic.

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