display all the ideas for this combination of texts
3 ideas
| 22437 | Logical languages are rooted in ordinary language, and that connection must be kept [Quine] |
| Full Idea: A logical language is not independent of ordinary language. It has its roots in ordinary language, and these roots are not to be severed. | |
| From: Willard Quine (Mr Strawson on Logical Theory [1953], V) | |
| A reaction: Music to my ears. When you study logic, no one has to teach you what the words 'or' and 'if-then' mean, but they are disambiguated by the symbolism. The roots of logic are in ordinary talk of 'and', 'or' and 'not', which is the real world. |
| 8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
| Full Idea: Intuitionists in mathematics deny excluded middle, because it is symptomatic of faith in the transcendent existence of mathematical objects and/or the truth of mathematical statements. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 1.2) | |
| A reaction: There are other problems with excluded middle, such as vagueness, but on the whole I, as a card-carrying 'realist', am committed to the law of excluded middle. |
| 22434 | Reduction to logical forms first simplifies idioms and grammar, then finds a single reading of it [Quine] |
| Full Idea: Ordinary language is reduced to logical form in two ways: reduction of the variety of idioms and grammatical constructions, and reduction of each surviving idiom to one fixed and convenient interpretation. | |
| From: Willard Quine (Mr Strawson on Logical Theory [1953], V) | |
| A reaction: Is there a conflict between a 'fixed' and a 'convenient' result? By 'fixed' I suppose he means it is a commitment (to not waver). What is the logical form of a sentence which is deliberately ambiguous? |