display all the ideas for this combination of texts
7 ideas
| 9605 | If a proposition is false, then its negation is true [Brown,JR] |
| Full Idea: The law of excluded middle says if a proposition is false, then its negation is true | |
| From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 1) | |
| A reaction: Surely that is the best statement of the law? How do you write that down? ¬(P)→¬P? No, because it is a semantic claim, not a syntactic claim, so a truth table captures it. Semantic claims are bigger than syntactic claims. |
| 10316 | We should decide whether singular terms are genuine by their usage [Hale] |
| Full Idea: The criteria for a genuine singular term should pick out not the singular terms themselves but their uses, since they may be genuine in one context and not another. | |
| From: Bob Hale (Abstract Objects [1987], Ch.2.II) | |
| A reaction: [rephrased] This will certainly meet problems with vagueness (e.g. as the reference of a singular term is gradually clarified). |
| 10312 | Often the same singular term does not ensure reliable inference [Hale] |
| Full Idea: In 'the whale is increasingly scarce' and 'the whale is much improved today' (our pet whale), we cannot infer that there is something that is much improved and increasingly scarce, so this singular term fails Dummett's criterion based on inference. | |
| From: Bob Hale (Abstract Objects [1987], Ch.2) | |
| A reaction: [much rephrased] This is not just a problem for a few cunningly selected examples. With contortions almost any singular term can be undermined in this way. Singular terms are simply not a useful guide to the existence of abstracta. |
| 10313 | Plenty of clear examples have singular terms with no ontological commitment [Hale] |
| Full Idea: Some examples where a definite singular noun phrase is not 'genuine' (giving ontological commitment): 'left us in the lurch'; 'for my mother's sake'; 'given the sack'; 'in the nick of time', 'the whereabouts of the PM', 'the identity of the murderer'. | |
| From: Bob Hale (Abstract Objects [1987], Ch.2.II) | |
| A reaction: These are not just freakish examples. If I 'go on a journey', that doesn't involve extra entities called 'journeys', just because the meaning is clearer and a more commonplace part of the language. |
| 10322 | If singular terms can't be language-neutral, then we face a relativity about their objects [Hale] |
| Full Idea: If we lack any general, language-neutral characterization of singular terms, must not a parallel linguistic relativity infect the objects which are to be thought of as their non-linguistic correlates? | |
| From: Bob Hale (Abstract Objects [1987], Ch.2.III) | |
| A reaction: Hale thinks he can answer this, but I would have thought that this problem dooms the linguistic approach from the start. There needs to be more imagination about how very different a language could be, while still qualifying as a language. |
| 9649 | Axioms are either self-evident, or stipulations, or fallible attempts [Brown,JR] |
| Full Idea: The three views one could adopt concerning axioms are that they are self-evident truths, or that they are arbitrary stipulations, or that they are fallible attempts to describe how things are. | |
| From: James Robert Brown (Philosophy of Mathematics [1999], Ch.10) | |
| A reaction: Presumably modern platonists like the third version, with others choosing the second, and hardly anyone now having the confidence to embrace the first. |
| 9638 | Berry's Paradox finds a contradiction in the naming of huge numbers [Brown,JR] |
| Full Idea: Berry's Paradox refers to 'the least integer not namable in fewer than nineteen syllables' - a paradox because it has just been named in eighteen syllables. | |
| From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 5) | |
| A reaction: Apparently George Boolos used this quirky idea as a basis for a new and more streamlined proof of Gödel's Theorem. Don't tell me you don't find that impressive. |