Exercise · ZW-GODELS-INCOMPLETENESS-008 · ★☆☆ Basic
The first incompleteness theorem states that there is a formula the system cannot...
Choose one option.
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- A. Prove nor refute
Explanation
The first incompleteness theorem says some formulas can be neither proved nor refuted by the system. It does not say mathematics is useless or impossible to formalize.
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-005 Gödel's incompleteness does not claim that...
- 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-009 Select the feature associated with Gödel's result.
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