LOGIC: A Request for Clarification of definitions

In summary, the conversation discusses the definition of truth as a concept in mathematical logic. It is mentioned that in deductive arguments, the conclusion is true if the premises are true and an argument is valid if it follows logically from the axioms. The main question is "What is truth?" and how it is defined in the formal study of logic, specifically in terms of words like true, false, proven, provable, unprovable, and correct. It is suggested to read about language, formula, structure, and variable assignment functions to understand the definition of truth in mathematical logic. Recommendations for books in mathematical logic are also requested.
  • #1
Mathbrain
9
0
With the study of logic, lots of words get thrown around that I don't really understand their complete meaning. With a deductive argument the conclusion is true if the premises are true, and an argument is valid if all the inferences (and the conclusion) follow logically from the axioms. These are things taught in any intro to logic class, but the more important question is: "What is truth?" Not just philosophically, but in the realm of logic. If something is proven does that mean it is true? If something is provable, does that mean it is true? Which immediately asks the question, what is provable, and what is proven? This isn't an issue of picking words apart, it's a question of logic. How are these concepts defined in the formal study of logic?

Here's a list of words that I require clarification for, wiki isn't always helpful...
*True
*False
*Proven
*Provable
*Unprovable
*Correct

This is a serious query, I am not interested in getting into an argument on the nature of definitions, please do not consider "What is truth?" to be a profound philosophical question. The issue is what is true from a logical foundation.
 
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  • #2
To get an understanding of truth as a concept in mathematical logic, you should read about the definitions of language, formula in a language, structure and variable assignment functions. A definition of truth of a formula in a language uses all these terms. I suggest you get yourself a book in mathematical logic.

I suggest this thread to be moved to the math forums logic section...
 
  • #3
"get yourself a book in mathematical logic"
Any recommendations?

"Mathematical logic" sounds like a better home, but I don't know how to move the thread. Conversely if we leave the thread in logic, is the definition of truth intrinsically linked with the language of the speaker (this case English)? I'm going to assume that you meant a formal language, but I'm not aware of a logical formal language that describes True and False in a logical context. Is it a second-order logic notation?
 
  • #4
Long time ago, but I'll try and see how far I'll get. I am actually interested in how many flukes I'll make on this one.

*True, derivable either from axioms or true under all interpretations. (Philosophers may differ on the real meaning of truth.)
*False, derivably false or false under an interpretation
*Proven, a statement for which a derivation exists (or all interpretations are proven to be true)
*Provable, as in provable to be true, a statement for which it can be proven that it can be proven
*Unprovable, as in provable not to be true, a statement for which it can be proven not to be true (either since it is false, or it can't be proven true)
*Correct, dunno? As in semantic or syntactic correctness?
 
  • #5
Doesn't meet criteria for Philosophy or logic, it's not a problem.
 

What is the definition of logic?

The definition of logic is the study of reasoning and argumentation, and how we can use reason to determine what is true or false. It is a fundamental aspect of philosophy and is used to understand and evaluate arguments and beliefs.

What are the different types of logic?

There are several types of logic, including propositional logic, predicate logic, modal logic, and fuzzy logic. Each type has its own set of rules and methods for evaluating arguments and determining truth.

How is logic used in everyday life?

Logic is used in everyday life to make decisions, solve problems, and evaluate arguments. It helps us think critically, make sound judgments, and avoid logical fallacies.

What are logical fallacies?

Logical fallacies are errors in reasoning that can make an argument invalid or unsound. They are common mistakes in thinking that can lead to false conclusions and should be avoided in logical arguments.

Why is it important to have a clear understanding of logic?

A clear understanding of logic is important because it allows us to think critically, evaluate arguments and evidence, and make informed decisions. It also helps us avoid being misled by false or illogical arguments.

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