What does Gödel's second theorem say? (Q5890415)
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scientific article; zbMATH DE number 1694608
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | What does Gödel's second theorem say? |
scientific article; zbMATH DE number 1694608 |
Statements
7 October 2002
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Gödel's second incompleteness theorem
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derivability conditions
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What does Gödel's second theorem say? (English)
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The paper is devoted to some problems connected with Gödel's second incompleteness theorem (G2), in particular to the problem of justification of the Derivability Conditions, more accurately of the Third Derivability Condition. It is shown that the most popular justification of it (called by the author the Reflexivity Defense) has serious consequences. More accurately it is argued that, for a suitable system of generalizations of G2, use of the Reflexivity Defense induces a Fourth Derivability Condition whose justification is fraught with difficulties. The conclusion is that the Reflexivity Defense does not provide a satisfactory justification of the Third Condition.
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