Logic as an internal organisation of language
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arXiv
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| Format: | Preprint |
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2021
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| _version_ | 1866914920912650240 |
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| author | Čulina, Boris |
| author_facet | Čulina, Boris |
| contents | Contemporary semantic description of logic is based on the ontology of all possible interpretations, an insufficiently clear metaphysical concept. In this article, logic is described as the internal organization of language. Logical concepts -- logical constants, logical truths and logical consequence -- are defined using the internal syntactic and semantic structure of language. For a first-order language, it has been shown that its logical constants are connectives and a certain type of quantifiers for which the universal and existential quantifiers form a functionally complete set of quantifiers. Neither equality nor cardinal quantifiers belong to the logical constants of a first-order language. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2105_12157 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Logic as an internal organisation of language Čulina, Boris Logic Contemporary semantic description of logic is based on the ontology of all possible interpretations, an insufficiently clear metaphysical concept. In this article, logic is described as the internal organization of language. Logical concepts -- logical constants, logical truths and logical consequence -- are defined using the internal syntactic and semantic structure of language. For a first-order language, it has been shown that its logical constants are connectives and a certain type of quantifiers for which the universal and existential quantifiers form a functionally complete set of quantifiers. Neither equality nor cardinal quantifiers belong to the logical constants of a first-order language. |
| title | Logic as an internal organisation of language |
| topic | Logic |
| url | https://arxiv.org/abs/2105.12157 |