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Results tagged with incompleteness
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user 683
5
votes
Analogy between Gödel's incompleteness proof and Richard's argument
Both examples are instances of diagonalization, a technique also used to prove Cantor's theorem ($\kappa < 2^\kappa$ for all cardinals $\kappa$) and Turing's theorem that the halting problem is undeci …
- 279k
2
votes
Why does soundness imply consistency?
Your proof system is neither sound nor consistent, since $A$ is not a true proposition unless $A \equiv \top$, In which case $\lnot A \equiv \bot$ is not a true proposition. This argument shows that e …
- 279k
5
votes
Accepted
Understanding of Turing's Answer to the Entscheidungsproblem
For example, it won't be able to prove its own consistency (this is Gödel's second incompleteness theorem). (A proof system is consistent if it doesn't prove a statement and its converse.) …
- 279k