Who has actually read Godel's theorems?

Thread starter gravenewworld
Start date Feb 17, 2005

In summary, the conversation is about Godel's theorems and the speaker's experience with reading and understanding them in their math logic class. They discuss the common misinterpretations of Godel's theorems and clarify that the theorems do not state that there are true statements that cannot be proven. They also mention the independence of certain propositions and give examples of this concept in different mathematical theories. They also mention Godel's completeness theorem and its relationship to the incompleteness theorems. The conversation ends with a question about the truth value of statements without corresponding models.

Mar 2, 2005

honestrosewater

Gold Member

jennycraig10 said:

I'm a high school student and am doing a report on Kurt Godel... Can anyone help me out by telling me what career there is out there that uses Godel's theory? I would really appreciate it.

Teaching or doing research in logic, math, computer science or, less likely, philosophy. Minor point: it's theorem; see here.

<h2>1. What are Godel's theorems?</h2><p>Godel's theorems, also known as Godel's incompleteness theorems, are two theorems in mathematical logic that demonstrate the inherent limitations of formal systems.</p><h2>2. Who is Godel and why are his theorems important?</h2><p>Kurt Godel was an Austrian mathematician and logician who is best known for his contributions to mathematical logic, specifically his incompleteness theorems. These theorems have had a major impact on the fields of mathematics, computer science, and philosophy.</p><h2>3. What do Godel's theorems say?</h2><p>Godel's first theorem states that within any formal system of arithmetic, there will always be statements that are true but cannot be proven within the system. His second theorem states that no consistent formal system can prove its own consistency.</p><h2>4. Who has actually read Godel's theorems?</h2><p>Many mathematicians, logicians, and philosophers have read and studied Godel's theorems. They are considered to be fundamental and influential results in the field of mathematical logic, so they are often studied by those in related fields.</p><h2>5. How do Godel's theorems impact our understanding of mathematics and logic?</h2><p>Godel's theorems have had a significant impact on our understanding of mathematics and logic. They have shown that there are inherent limitations to formal systems and that there will always be statements that are true but cannot be proven. This has led to further exploration and development of alternative systems and approaches to mathematics and logic.</p>

1. What are Godel's theorems?

Godel's theorems, also known as Godel's incompleteness theorems, are two theorems in mathematical logic that demonstrate the inherent limitations of formal systems.

2. Who is Godel and why are his theorems important?

Kurt Godel was an Austrian mathematician and logician who is best known for his contributions to mathematical logic, specifically his incompleteness theorems. These theorems have had a major impact on the fields of mathematics, computer science, and philosophy.

3. What do Godel's theorems say?

Godel's first theorem states that within any formal system of arithmetic, there will always be statements that are true but cannot be proven within the system. His second theorem states that no consistent formal system can prove its own consistency.

4. Who has actually read Godel's theorems?

Many mathematicians, logicians, and philosophers have read and studied Godel's theorems. They are considered to be fundamental and influential results in the field of mathematical logic, so they are often studied by those in related fields.

5. How do Godel's theorems impact our understanding of mathematics and logic?

Godel's theorems have had a significant impact on our understanding of mathematics and logic. They have shown that there are inherent limitations to formal systems and that there will always be statements that are true but cannot be proven. This has led to further exploration and development of alternative systems and approaches to mathematics and logic.