display all the ideas for this combination of texts
6 ideas
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. |
8453 | If we had to name objects to make existence claims, we couldn't discuss all the real numbers [Quine] |
Full Idea: Since one wants to say that real numbers exist and yet one cannot name each of them, it is not unreasonable to relinquish the connection between naming an object and making an existence claim about it. | |
From: Willard Quine (works [1961]), quoted by Alex Orenstein - W.V. Quine Ch.2 | |
A reaction: One could say that same about people, such as 'the most recent citizen of Brazil'. Some sort of successful reference seems to be needed, such as 'the next prime beyond the biggest so far found'. Depends what your predicate is going to be. |
10311 | No sense can be made of quantification into opaque contexts [Quine, by Hale] |
Full Idea: Quine says that no good sense can be made of quantification into opaque contexts. | |
From: report of Willard Quine (works [1961]) by Bob Hale - Abstract Objects Ch.2 | |
A reaction: This is because poor old Quine was trapped in a world of language, and had lost touch with reality. I can quantify over the things you are thinking about, as long as you are thinking about things that can be quantified over. |
10538 | Finite quantification can be eliminated in favour of disjunction and conjunction [Quine, by Dummett] |
Full Idea: Quine even asserts that where we have no infinite domains, quantification can be eliminated in favour of finite disjunction and conjunction. | |
From: report of Willard Quine (works [1961]) by Michael Dummett - Frege Philosophy of Language (2nd ed) Ch.14 | |
A reaction: Thus ∃x is expressed as 'this or this or this...', and ∀ is expressed as 'this and this and this...' Dummett raises an eyebrow, but it sounds OK to me. |
10793 | Quine thought substitutional quantification confused use and mention, but then saw its nominalist appeal [Quine, by Marcus (Barcan)] |
Full Idea: Quine at first regarded substitutional quantification as incoherent, behind which there lurked use-mention confusions, but has over the years, given his nominalist dispositions, come to notice its appeal. | |
From: report of Willard Quine (works [1961]) by Ruth Barcan Marcus - Nominalism and Substitutional Quantifiers p.166 |