display all the ideas for this combination of texts
7 ideas
17286 | Logical consequence is verification by a possible world within a truth-set [Fine,K] |
Full Idea: Under the possible worlds semantics for logical consequence, each sentence of a language is associated with a truth-set of possible worlds in which it is true, and then something is a consequence if one of these worlds verifies it. | |
From: Kit Fine (Guide to Ground [2012], 1.10) | |
A reaction: [compressed, and translated into English; see Fine for more symbolic version; I'm more at home in English] |
8645 | Convert "Jupiter has four moons" into "the number of Jupiter's moons is four" [Frege] |
Full Idea: The proposition "Jupiter has four moons" can be converted into "the number of Jupiter's moons is four". | |
From: Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §57) | |
A reaction: This seems to be the beginning of the modern exploration of the whole idea of logical form. It is one thing to find a logical forms which suits your current thesis (here, that numbers are not adjectival), but another to prove that it is the right form. |
16891 | Despite Gödel, Frege's epistemic ordering of all the truths is still plausible [Frege, by Burge] |
Full Idea: Gödel undermined Frege's assumption that all but the basic truths are provable in a system, but insofar as one conceives of proof informally as an epistemic ordering among truths, one can see his vision as worth developing. | |
From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Tyler Burge - Frege on Apriority (with ps) 1 | |
A reaction: [compressed] This 'epistemic ordering' fits my thesis of seeing the world through our explanations of it. |
16906 | The primitive simples of arithmetic are the essence, determining the subject, and its boundaries [Frege, by Jeshion] |
Full Idea: The primitive truths contain the core of arithmetic because their constituents are simples which define the essential boundaries of the subject. …The primitive truths are the most general ones, containing the basic, essence determining elements. | |
From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Robin Jeshion - Frege's Notion of Self-Evidence 2 | |
A reaction: This presents Frege as explicable in essentialist terms, as identifying the core of an abstract discipline, from which the rest of it is generated. Jeshion says 'simples are the essence'. |
14236 | Each horse doesn't fall under the concept 'horse that draws the carriage', because all four are needed [Oliver/Smiley on Frege] |
Full Idea: Frege says the number four is assigned to the concept 'horse that draws the Kaiser's carriage', but the four horses that drew the carriage did so together, not separately. No horses, not four, fall under the Fregean concept. | |
From: comment on Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §46) by Oliver,A/Smiley,T - What are Sets and What are they For? Intro | |
A reaction: They say that Frege stumbles because he is blind to irreducibly plural predicates. |
22294 | We can show that a concept is consistent by producing something which falls under it [Frege] |
Full Idea: We can only establish that a concept is free from contradiction by first producing something that falls under it. | |
From: Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §095), quoted by Michael Potter - The Rise of Analytic Philosophy 1879-1930 19 'Exist' | |
A reaction: Potter quotes this as an example of proof by modelling. If it has one model then it must be consistent. Then we ask whether all the models are or are not consistent with one another. Circular squares fail the test. |
17624 | To understand axioms you must grasp their logical power and priority [Frege, by Burge] |
Full Idea: Understanding the axioms depends not only on understanding Frege's elucidatory remarks about the interpretation of his symbols, but also on understanding their logical structure - their power to entail other truths, and their reason-giving priority. | |
From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], 4) by Tyler Burge - Frege on Knowing the Foundations 4 | |
A reaction: This is a distinctively Burgean spin put on what Frege has to say about axioms, but I like it, and it seems well enough supported in Frege's writings (e.g. 1914). |