Limitation of logical space puts restrictions on the explication of the notions of knowledge, belief, necessity and truth
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| Year of publication | 2019 |
| Type | Conference abstract |
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| Citation | |
| Description | I demonstrate that (i) the limitation of logical space (entailed by Cantor's theorem) imposes (ii) limits to the explication of certain important 'propositional' ('intentional') notions, e.g. knowledge. A naive approach to the limitations of both types leads to a group of famous paradoxes, e.g. the Liar Paradox, the Knower paradox. I establish some theorems related to (i) and (ii), partly utilising the paradoxes. They demonstrate similarities and also dissimilarities between the notions of knowledge, necessity, truth, belief and assertion. Unlike Montague, who treated the notions as predicates applied to coding numbers of formulas, I treat them as applied to hyperintensional, fine-grained meanings of sentences. The logical framework employed is a ramified version of (a Church-like) simple theory of types. |
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