Question

What did Godel's Theorem show? What does it mean to say that a system is inconsistent? What does it mean to say that a system is incomplete?

a. Godel's Theorem demonstrated the consistency of systems.
b. An inconsistent system has no logical errors.
c. An incomplete system lacks a clear purpose.
d. Godel's Theorem revealed the limitations of formal systems.

Answer 1

Godel's Theorem revealed the limitations of formal systems and showed that they are incomplete. An inconsistent system contains logical errors or contradictions.

Step-by-step explanation:

Godel's Theorem revealed the limitations of formal systems. It showed that no consistent formal system can prove all true statements within the system. This means that there are true statements that cannot be proven within a given system, making the system incomplete.

An inconsistent system, on the other hand, is one that contains a logical error or contradiction. Inconsistency means that contradictory statements can be derived or proven within the system.