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Full Idea
The arrow paradox starts with the assumption that space and time are atomic; the tortoise starts with the opposite assumption that space and time are infinitely divisible.
Gist of Idea
Space and time are atomic in the arrow, and divisible in the tortoise
Source
Keith Devlin (Goodbye Descartes [1997], Ch. 2)
Book Ref
Devlin,Keith: 'Goodbye Descartes: the end of logic' [Wiley 1997], p.24
A Reaction
Aquinas similarly covers all options (the cosmos has a beginning, or no beginning). The nature of movement in a space which involves quantum leaps remains metaphysically puzzling. Where is a particle at half of the Planck time?
| 8072 | Sentences of apparent identical form can have different contextual meanings [Devlin] |
| 8073 | How do we parse 'time flies like an arrow' and 'fruit flies like an apple'? [Devlin] |
| 8076 | The distinction between sentences and abstract propositions is crucial in logic [Devlin] |
| 8075 | Space and time are atomic in the arrow, and divisible in the tortoise [Devlin] |
| 8081 | 'No councillors are bankers' and 'All bankers are athletes' implies 'Some athletes are not councillors' [Devlin] |
| 8082 | Where a conditional is purely formal, an implication implies a link between premise and conclusion [Devlin] |
| 8087 | Golden ages: 1900-1960 for pure logic, and 1950-1985 for applied logic [Devlin] |
| 8085 | Modern propositional inference replaces Aristotle's 19 syllogisms with modus ponens [Devlin] |
| 8086 | Predicate logic retains the axioms of propositional logic [Devlin] |
| 8088 | People still say the Hopi have no time concepts, despite Whorf's later denial [Devlin] |
| 8091 | Situation theory is logic that takes account of context [Devlin] |
| 8089 | Montague's intensional logic incorporated the notion of meaning [Devlin] |
| 8092 | Logic was merely a branch of rhetoric until the scientific 17th century [Devlin] |