Set Theory vs Logic: Which Should Come First?

In summary: I'll check it out.In summary, it seems that the two schools of thought are that either the basics of axiomatic set theory should be studied first, or mathematical logic should be studied first. However, there is a shift in thinking in that now it seems that it should be the opposite. The reason for this shift is that when studying logic, we use concepts introduced in set theory - numbers (&mathematical induction), sequence (definition of proof*), etc. What do you think?
  • #1
dobry_den
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It makes me wonder what should be studied first - whether the basics of axiomatic set theory or mathematical logic? Although I initially that logic should be studied first, set theory second, now something makes me think that it should be vice-versa. The reason for this shift is that - when studying logic - we use various concepts that are introduced in set theory - numbers (&mathematical induction), sequence (definition of proof*) etc. What do you think?

*formal proof is usually defined as follows: "a formal proof in propositional logic is a finite sequence of statements ..."
 
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  • #2
It's the summer vacation that causes so much confusion in my head :-) I have a lot of time to think and then I end up thinking about these obscure theories that prior to using numbers in metalanguage (used for describing our object language - first-order logic), we have to define them somehow - for example using sets.

But that is, obviously, not possible. So we take a part of mathematics - let's call it e.g. "informal mathematics" - with some basic notions (natural numbers, mathematical induction - both taken as intuitively granted) and with their help define the framework (mathematical logic, axiomatic set theory, etc.) for exact definition of them and other - more complicated - mathematical concepts.

Do you find this reasoning correct?
 
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  • #3
at least universities think like you, i.e the preliminary for logic in mathematics courses is set theory or discrete mathematics which include only an introduction to set theory.
i personally think that they are interlinked, every set theory class starts its first day in introducing basic logic connectors {v,&,->,<->,~}, with which you define the operation: union intersection and so forth.

i think the best way, is to learn mathematical logic with set theory, they complement each other, which rarely youll find an expert in set theory who doesn't have some expertise in logic, and vice versa.
 
  • #4
I personally think that one may as well learn the basics of sentential (or propositional) and predicate logic first, since it has the widest range of application. After that, further study tends to specialize, to set theory, mathematical induction, and the derivation of theorems in algebra and topology and all that good stuff in mathematics; to modal logic, deontic logic, inductive logic (which has nothing to do with mathematical induction), and counterfactuals in philosophy (and possibly in linguistics); to Boolean algebra and fuzzy logic in computer science and systems engineering.

Of course, I have no background in education to be able to say this. It stands to reason that, generalizing my opinion, we should study the basics of universal grammar and phonetics before studying any specific second languages, but that obviously is not the way languages are taught, although it is the way they used to be taught when people that thought like me were running the universities. Immersion and natural language acquisition are all the rage today, though.
 
  • #6
To be honest, I really have no knowledge of fuzzy sets/logic and no opinion on the matter, but I was under the impression it had some applications to electronic hardware problems; train switching on subways or something.
 
  • #7
There are people who study fuzzy logic as applied to engineering. Look at the AI subset of Engineering Maths at the University of Bristol.
 
  • #8

What is the difference between set theory and logic?

Set theory is a branch of mathematics that deals with the study of sets, which are collections of objects. Logic, on the other hand, is the study of reasoning and arguments. While set theory focuses on the structure and properties of sets, logic is concerned with the principles and rules of reasoning.

Which one should be learned first, set theory or logic?

This is a matter of personal preference and depends on the individual's interests and goals. Some may argue that set theory should be learned first because it provides the foundation for understanding logic. Others may argue that logic should be learned first because it is more fundamental and applicable to various fields of study.

Are set theory and logic related?

Yes, set theory and logic are closely related. In fact, logic is often used as a tool in set theory to prove theorems and establish relationships between sets. Set theory also provides a framework for understanding logical concepts such as negation, conjunction, and implication.

Can one understand set theory without learning logic?

Yes, it is possible to understand the basics of set theory without learning logic. However, having a basic understanding of logic can help in comprehending the concepts and proofs in set theory more easily.

Which one is more important, set theory or logic?

Both set theory and logic are important in mathematics and have their own applications and uses. It is difficult to say which one is more important as they complement each other and are essential for a deeper understanding of mathematics and other fields of study.

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