display all the ideas for this combination of texts
8 ideas
14980 | There is a real issue over what is the 'correct' logic [Sider] |
Full Idea: Certain debates over the 'correct' logic are genuine, and not linguistic or conceptual. | |
From: Theodore Sider (Writing the Book of the World [2011], 01.3) | |
A reaction: It is rather hard to give arguments in favour of this view, but I am pleased to have the authority of Sider with me. |
15000 | 'It is raining' and 'it is not raining' can't be legislated, so we can't legislate 'p or ¬p' [Sider] |
Full Idea: I cannot legislate-true 'It is raining' and I cannot legislate true 'It is not raining', so if I cannot legislate either true then I cannot legislate-true the disjunction 'it is raining or it is not raining'. | |
From: Theodore Sider (Writing the Book of the World [2011], 06.5) | |
A reaction: This strikes me as a very simple and very persuasive argument against the idea that logic is a mere convention. I take disjunction to be an abstract summary of how the world works. Sider seems sympathetic. |
15020 | Classical logic is good for mathematics and science, but less good for natural language [Sider] |
Full Idea: Despite its brilliant success in mathematics and fundamental science, classical logic applies uneasily to natural language. | |
From: Theodore Sider (Writing the Book of the World [2011], 10.6) | |
A reaction: He gives examples of the conditional, and debates over the meaning of 'and', 'or' and 'not', and also names and quantifiers. Many modern philosophical problems result from this conflict. |
15029 | Modal accounts of logical consequence are simple necessity, or essential use of logical words [Sider] |
Full Idea: The simplest modal account is that logical consequence is just necessary consequence; another modal account says that logical consequences are modal consequences that involve only logical words essentially. | |
From: Theodore Sider (Writing the Book of the World [2011], 12.3) | |
A reaction: [He cites Quine's 'Carnap and Logical Truth' for the second idea] Sider is asserting that Humeans like him dislike modality, and hence need a nonmodal account of logical consequence. |
8078 | Modus ponens is one of five inference rules identified by the Stoics [Chrysippus, by Devlin] |
Full Idea: Modus ponens is just one of the five different inference rules identified by the Stoics. | |
From: report of Chrysippus (fragments/reports [c.240 BCE]) by Keith Devlin - Goodbye Descartes Ch.2 | |
A reaction: Modus ponens strikes me as being more like a definition of implication than a 'rule'. Implication is what gets you from one truth to another. All the implications of a truth must also be true. |
6023 | Every proposition is either true or false [Chrysippus, by Cicero] |
Full Idea: We hold fast to the position, defended by Chrysippus, that every proposition is either true or false. | |
From: report of Chrysippus (fragments/reports [c.240 BCE]) by M. Tullius Cicero - On Fate ('De fato') 38 | |
A reaction: I am intrigued to know exactly how you defend this claim. It may depend what you mean by a proposition. A badly expressed proposition may have indeterminate truth, quite apart from the vague, the undecidable etc. |
15019 | Define logical constants by role in proofs, or as fixed in meaning, or as topic-neutral [Sider] |
Full Idea: Some say that logical constants are those expressions that are defined by their proof-theoretic roles, others that they are the expressions whose semantic values are permutation-invariant, and still others that they are the topic-neutral expressions. | |
From: Theodore Sider (Writing the Book of the World [2011], 10.3) | |
A reaction: [He cites MacFarlane 2005 as giving a survey of this] |
15001 | 'Tonk' is supposed to follow the elimination and introduction rules, but it can't be so interpreted [Sider] |
Full Idea: 'Tonk' is stipulated by Prior to stand for a meaning that obeys the elimination and introduction rules; but there simply is no such meaning; 'tonk' cannot be interpreted so as to obey the rules. | |
From: Theodore Sider (Writing the Book of the World [2011], 06.5) | |
A reaction: 'Tonk' thus seems to present a problem for so-called 'natural' deduction, if the natural deduction consists of nothing more than obey elimination and introduction rules. |