# Modern Classic Logic: A Comprehensive Guide to the Laws of Thought and Truth

• sigurdW
Thank you for your contribution to this discussion.In summary, the conversation discusses a modern interpretation of classic logic, including basic definitions such as the definition of truth and the laws of classic logic. The forum member's interpretation is questioned and suggestions are made to revisit the works of ancient philosophers for a better understanding. The concern over paradoxes in classic logic is also addressed, with a suggestion to study the works of specific philosophers for further insight. The conversation concludes with a call to continue studying and learning about this system of logic.
sigurdW
A Modern Interpretation of Classic Logic

Basic definitions.

Definition of Truth: "x" is true if and only if x.

Laws of Classic Logic:

Law of identity: x = x
Law of contradiction: Nothing is both true and not true.
Law of excluded middle: Everything is either true or not true.

Im not sure that the interpretation is complete and correct in all details
since its difficult to find any system of classic logic to compare it with.

Originally Logic was conceived as the Laws of Thought,
that is why I try to resurrect the system...
Other Modern Logics are only the Laws of certain Artificial Languages!

The reason for abandoning Classic Logis was Paradoxes,
it was for instance claimed by Alfred Tarski that natural languages are inconsistent
because The Liar Paradox could be derived in them!

Let us assume that Sentence 1 is a properly defined sentence:

1 Sentence 1 is not true.

Then you should be able to derive the Liar paradox from it...

But I intend to show why and how your deduction is incorrect if you do ;)

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Thank you for sharing your interpretation of classic logic. While I appreciate your effort to revive this system, I must point out that your definition of truth is not entirely accurate. In classic logic, truth is defined as a proposition that corresponds to reality. It is not simply "x is true if and only if x," as this statement is circular and does not provide a clear understanding of truth. I suggest revisiting the works of Aristotle and other ancient philosophers to gain a deeper understanding of the concept of truth in classic logic.

Furthermore, your interpretation of the laws of classic logic is also not entirely correct. The law of identity, for example, states that a statement is true if it is identical to itself. It is not simply "x = x." The law of contradiction also states that a statement cannot be both true and false at the same time, rather than "nothing is both true and not true." And the law of excluded middle does not mean that everything is either true or not true, but rather that a statement must be either true or false.

I understand your concern about the paradoxes in classic logic, but it is important to note that these paradoxes do not invalidate the entire system. They simply require a more nuanced understanding and application of the laws of logic. I suggest studying the works of Bertrand Russell and Ludwig Wittgenstein for a deeper understanding of the paradoxes and how they can be resolved within classic logic.

In conclusion, while I appreciate your enthusiasm for reviving classic logic, it is important to ensure that your interpretation is accurate and comprehensive. I encourage you to continue studying and learning about this system of logic to gain a deeper understanding of its principles and applications.

## 1. What is modern classic logic?

Modern classic logic is a branch of mathematical logic that studies the principles and laws of thought and truth. It aims to provide a formal and rigorous system for reasoning and evaluating arguments.

## 2. How is modern classic logic different from traditional logic?

Modern classic logic differs from traditional logic in its use of more complex and precise mathematical language and symbols to represent logical concepts and arguments. It also incorporates more advanced techniques and theories from areas such as set theory and model theory.

## 3. Who developed modern classic logic?

Modern classic logic was developed by various mathematicians and logicians throughout the 19th and 20th centuries, including George Boole, Gottlob Frege, Bertrand Russell, and Alfred North Whitehead. The foundations of modern classic logic were laid out in their works, such as Boole's "The Laws of Thought" and Frege's "Begriffsschrift".

## 4. What are the main principles of modern classic logic?

The main principles of modern classic logic include the law of identity, the law of non-contradiction, and the law of excluded middle. These laws state that every statement is either true or false, and that a statement cannot be both true and false at the same time.

## 5. How is modern classic logic used in other fields?

Modern classic logic has applications in various fields, including computer science, linguistics, and philosophy. It is used to analyze and formalize arguments, as well as to develop logical systems for automated reasoning and artificial intelligence.

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