Bivalence and determinacy
The principle that every statement is bivalent (i.e. either true or false) has been a bone of philosophical contention for centuries, for an apparently powerful argument for it (due to Aristotle) sits alongside apparently convincing counterexamples to it. This chapter analyzes Aristotle’s argument,...
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| Format: | Book section |
| Language: | English |
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Oxford University Press
2018
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| _version_ | 1797111569556963328 |
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| author | Rumfitt, I |
| author2 | Glanzberg, M |
| author_facet | Glanzberg, M Rumfitt, I |
| author_sort | Rumfitt, I |
| collection | OXFORD |
| description | The principle that every statement is bivalent (i.e. either true or false) has been a bone of philosophical contention for centuries, for an apparently powerful argument for it (due to Aristotle) sits alongside apparently convincing counterexamples to it. This chapter analyzes Aristotle’s argument, then, in the light of this analysis, examines three sorts of problem case for bivalence. Future contingents, it is contended, are bivalent. Certain statements of higher set theory, by contrast, are not. Pace the intuitionists, though, this is not because excluded middle does not apply to such statements, but because they are not determinate. Vague statements too are not bivalent, in this case because the law of proof by cases does not apply. The chapter goes on to show how this opens the way to a solution to the ancient paradox of the heap (or Sorites) that draws on quantum logic. |
| first_indexed | 2024-03-07T08:12:12Z |
| format | Book section |
| id | oxford-uuid:23fad716-3737-43cb-9add-69473a030f47 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T08:12:12Z |
| publishDate | 2018 |
| publisher | Oxford University Press |
| record_format | dspace |
| spelling | oxford-uuid:23fad716-3737-43cb-9add-69473a030f472023-12-04T09:18:40ZBivalence and determinacyBook sectionhttp://purl.org/coar/resource_type/c_3248uuid:23fad716-3737-43cb-9add-69473a030f47EnglishSymplectic Elements at OxfordOxford University Press2018Rumfitt, IGlanzberg, MThe principle that every statement is bivalent (i.e. either true or false) has been a bone of philosophical contention for centuries, for an apparently powerful argument for it (due to Aristotle) sits alongside apparently convincing counterexamples to it. This chapter analyzes Aristotle’s argument, then, in the light of this analysis, examines three sorts of problem case for bivalence. Future contingents, it is contended, are bivalent. Certain statements of higher set theory, by contrast, are not. Pace the intuitionists, though, this is not because excluded middle does not apply to such statements, but because they are not determinate. Vague statements too are not bivalent, in this case because the law of proof by cases does not apply. The chapter goes on to show how this opens the way to a solution to the ancient paradox of the heap (or Sorites) that draws on quantum logic. |
| spellingShingle | Rumfitt, I Bivalence and determinacy |
| title | Bivalence and determinacy |
| title_full | Bivalence and determinacy |
| title_fullStr | Bivalence and determinacy |
| title_full_unstemmed | Bivalence and determinacy |
| title_short | Bivalence and determinacy |
| title_sort | bivalence and determinacy |
| work_keys_str_mv | AT rumfitti bivalenceanddeterminacy |