5 ideas
| 14231 | We should always apply someone's theory of meaning to their own utterances [Liggins] |
| Full Idea: We should interpret philosophers as if their own theory of the meaning of their utterances were true, whether or not we agree with that theory. | |
| From: David Liggins (Nihilism without Self-Contradiction [2008], 8) | |
| A reaction: This seems to give legitimate grounds for some sorts of ad hominem objections. It would simply be an insult to a philosopher not to believe their theories, and then apply them to what they have said. This includes semantic theories. |
| 14232 | We normally formalise 'There are Fs' with singular quantification and predication, but this may be wrong [Liggins] |
| Full Idea: It is quite standard to interpret sentences of the form 'There are Fs' using a singular quantifier and a singular predicate, but this tradition may be mistaken. | |
| From: David Liggins (Nihilism without Self-Contradiction [2008], 8) | |
| A reaction: Liggins is clearly in support of the use of plural quantification, referring to 'there are some xs such that'. |
| 9992 | The 'extension of a concept' in general may be quantitatively completely indeterminate [Cantor] |
| Full Idea: The author entirely overlooks the fact that the 'extension of a concept' in general may be quantitatively completely indeterminate. Only in certain cases is the 'extension of a concept' quantitatively determinate. | |
| From: George Cantor (Review of Frege's 'Grundlagen' [1885], 1932:440), quoted by William W. Tait - Frege versus Cantor and Dedekind | |
| A reaction: Cantor presumably has in mind various infinite sets. Tait is drawing our attention to the fact that this objection long precedes Russell's paradox, which made the objection more formal (a language Frege could understand!). |
| 14233 | Nihilists needn't deny parts - they can just say that some of the xs are among the ys [Liggins] |
| Full Idea: We can interpret '..is a part of..' as '..are among..': the xs are a part of the ys just when the xs are among the ys (though if the ys are 'one' then they would not have parts). | |
| From: David Liggins (Nihilism without Self-Contradiction [2008], 9) | |
| A reaction: The trouble is that this still leaves us with gerrymandered 'parts', in the form of xs that are scattered randomly among the ys. That's not what we mean by 'part'. No account of identity works if it leaves out coherent structure. |
| 14014 | Space alone, and time alone, will fade away, and only their union has an independent reality [Minkowski] |
| Full Idea: Henceforth, space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality. | |
| From: Hermann Minkowski (Space and Time [1908], Intro) | |
| A reaction: Notice the qualification that it is a 'kind of' union. Deep confusion arises from exaggerating the analogy between space and time. Craig Bourne remarks (2006:157) that this shows independence of measurement, not of reality |