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| 8859 | The main modal logics disagree over three key formulae |
| Full Idea: Lewis's different systems of modal logic differed about such formulae as □P implies □□P; ◊□P implies □P; and ◊S implies □◊S | |||
| From: Stephen Yablo (Apriority and Existence [2000], §06) | |||
| A reaction: Yablo's point is that the various version don't seem to make much difference to our practices in logic, mathematics and science. The problem, says Yablo, is deciding exactly what you mean by 'necessarily' and 'possibly'. |
| 8865 | If 'the number of Democrats is on the rise', does that mean that 50 million is on the rise? |
| Full Idea: If someone says 'the number of Democrats is on the rise', he or she wants to focus on Democrats, not numbers. If the number is 50 million, is 50 million really on the rise? | |||
| From: Stephen Yablo (Apriority and Existence [2000], §14) | |||
| A reaction: This is a very nice warning from Yablo, against easy platonism, or any sort of platonism at all. We routinely say that numbers are 'increasing', but the real meaning needs entangling. Here it refers to people joining a party. |
| 8863 | We must treat numbers as existing in order to express ourselves about the arrangement of planets |
| Full Idea: It is only by making as if to countenance numbers that one can give expression in English to a fact having nothing to do with numbers, a fact about stars and planets and how they are numerically proportioned. | |||
| From: Stephen Yablo (Apriority and Existence [2000], §13) | |||
| A reaction: To avoid the phrase 'numerically proportioned', he might have alluded to the 'pattern' of the stars and planets. I'm not sure which -ism this is, but it seems to me a good approach. The application is likely to precede the theory. |
| 8862 | Platonic objects are really created as existential metaphors |
| Full Idea: The means by which platonic objects are simulated is existential metaphor. Numbers are conjured up as metaphorical measures of cardinality. | |||
| From: Stephen Yablo (Apriority and Existence [2000], §12) | |||
| A reaction: 'Fictional' might be a better word than 'metaphorical', since the latter usually implies some sort of comparison. |
| 8864 | We quantify over events, worlds, etc. in order to make logical possibilities clearer |
| Full Idea: It is not that the contents of sentences are inexpressible without quantifying over events, worlds, etc. (they aren't). But the logical relations become much more tractable if we represent them quantificationally. | |||
| From: Stephen Yablo (Apriority and Existence [2000], §13) | |||
| A reaction: Yablo is explaining why we find ourselves committed to abstract objects. It is essentially, as I am beginning to suspect, a conspiracy of logicians. What on earth is 'the empty set' when it is at home? What's it made of? |
| 8858 | Philosophers keep finding unexpected objects, like models, worlds, functions, numbers, events, sets, properties |
| Full Idea: There's a tradition in philosophy of finding 'unexpected objects' in truth-conditions, such as countermodels, possible worlds, functions, numbers, events, sets and properties. | |||
| From: Stephen Yablo (Apriority and Existence [2000], §02) | |||
| A reaction: This is a very nice perspective on the whole matter of abstract objects. If we find ourselves reluctantly committed to the existence of something which is ontologically peculiar, we should go back to the philosophical drawing-board. |
| 8861 | Hardly a word in the language is devoid of metaphorical potential |
| Full Idea: There is hardly a word in the language - be it an adverb, preposition, conjunction, or what have you - that is devoid of metaphorical potential. | |||
| From: Stephen Yablo (Apriority and Existence [2000], §12) | |||
| A reaction: Yablo goes on to claim that metaphor is at the heart of all of our abstract thinking. 'Dead metaphors' (like the "mouth" of a river) sink totally into literal language. I think Yablo is on the right lines. |