INCOMPLETENESS THEOREM AND A SYSTEM WITHIN WHICH THE CONSTRUCTION OF A NAME OF A SENTENCE IS POSSIBLE
| Project/Area Number |
06801001
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
Philosophy
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| Research Institution | TOKYO INSTITUTE OF TECHNOLOGY |
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Principal Investigator |
WARAGAI Toshiharu TOKYO INSTITUTE OF TECHNOLOGY FACULTY OF ENGINEERING PROFESSOR, 工学部, 教授 (80136209)
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| Project Period (FY) |
1994 – 1995
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| Project Status |
Completed (Fiscal Year 1995)
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| Budget Amount *help |
¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 1995: ¥400,000 (Direct Cost: ¥400,000)
Fiscal Year 1994: ¥600,000 (Direct Cost: ¥600,000)
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| Keywords | Incompleteness / Set theory / Definition / Event / Name of Events / General sentence / Knowledge Representation / Ontology / 命題の名前 / ライプンッツの法則 / 「もの」と「こと」 / 命題における個別と普遍 / Incomoleteness Theorems / Undefinability / Truth Predicate / Godel / Tarski / General Sentence / Singular Sentence / Non-Fregean Logic |
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| Research Abstract |
The main results of the present reserach are following :
1 We constructed a logical system within which we can construct a name of a sentence by a proper extention of the standard logical system. We thus enriched the expressive power of the logical system.
2 A remarkable feature if the system is that it contains as a theorem a formula that expresses the principle of comprehension. This fact implies that the notions considered to be peculiar to set theory belong to this enriched system. This suggests the inadequacy of the standard logical system the representative means of natural language.
3 In the system thus obtained, we can develop a method by means of which we can distinguish singular sentences from general ones. This method leads us to a solution of [the problem of the unique correspondence between the form and the content of a sentence].
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Report
(3 results)
Research Products
(11 results)
