display all the ideas for this combination of texts
3 ideas
| 14943 | Maybe mathematical logic rests on information-processing [Ladyman/Ross] |
| Full Idea: It is claimed that mathematical logic can be understood in terms of information-processing. | |
| From: J Ladyman / D Ross (Every Thing Must Go [2007], 3.7.5) | |
| A reaction: [They cite Chaitin 1987] I don't understand how this would work, but it is still worth quoting. This would presumably make logic rest on processes rather than on entities. I quite like that. |
| 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. |
| 16489 | Is it possible to state every possible truth about the whole course of nature without using 'not'? [Russell] |
| Full Idea: Imagine a person who knew everything that can be stated without using the word 'not' or some equivalent; would such a person know the whole course of nature, or would he not? | |
| From: Bertrand Russell (Human Knowledge: its scope and limits [1948], 9) | |
| A reaction: Nowadays we might express Russell's thought as 'Does God need the word 'not'?'. Russell's thesis is that such words concern psychology, and not physics. God would need 'not' to describe how human minds work. |