Exercise · ZW-GODELS-INCOMPLETENESS-005 · ★☆☆ Basic
Gödel's incompleteness does not claim that...
Choose one option.
Show answer
- D. Every proposition is unprovable
Explanation
The theorem shows that some propositions are unprovable, but not that all of them are. So the claim that every proposition is unprovable is not what it asserts.
Review the concept: Gödel’s incompleteness
A consistent system \(\mathcal{S}\) that represents enough arithmetic is incomplete: there is a formula \(\varphi\) that it can neither prove nor refute.
\[\\exists\\varphi\\,(\\mathcal{S}\\nvdash\\varphi\\land\\mathcal{S}\\nvdash\\neg\\varphi)\]
More practice problems: gödel’s incompleteness
- ZW-GODELS-INCOMPLETENESS-001 Gödel's incompleteness refers to systems that are...
- ZW-GODELS-INCOMPLETENESS-002 A result of Gödel is that certain systems contain propositions...
- ZW-GODELS-INCOMPLETENESS-003 Gödel's coding relates formulas to...
- ZW-GODELS-INCOMPLETENESS-004 To apply the idea of incompleteness, the system must be able to express at least...
- ZW-GODELS-INCOMPLETENESS-006 The incompleteness theorems require systems that can express...
- ZW-GODELS-INCOMPLETENESS-007 An undecidable sentence is one that...
- ZW-GODELS-INCOMPLETENESS-008 The first incompleteness theorem states that there is a formula the system cannot...
- ZW-GODELS-INCOMPLETENESS-009 Select the feature associated with Gödel's result.
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