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All the ideas for 'Theory of Knowledge (2nd edn)', 'Foundations of Geometry' and 'Truth'

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9 ideas

1. Philosophy / C. History of Philosophy / 4. Later European Philosophy / b. Seventeenth century philosophy
Most philosophers start with reality and then examine knowledge; Descartes put the study of knowledge first [Lehrer]
     Full Idea: Some philosophers (e.g Plato) begin with an account of reality, and then appended an account of how we can know it, ..but Descartes turned the tables, insisting that we must first decide what we can know.
     From: Keith Lehrer (Theory of Knowledge (2nd edn) [2000], I p.2)
1. Philosophy / F. Analytic Philosophy / 4. Conceptual Analysis
To explain a concept, we need its purpose, not just its rules of usage [Dummett]
     Full Idea: We cannot in general suppose that we give a proper account of a concept by describing those circumstance in which we do, and those in which we do not, make use of the relevant word. We explain the point of the concept, what we use the word for.
     From: Michael Dummett (Truth [1959], p.231)
     A reaction: Well said. I am beginning to develop a campaign to make sure that analytical philosophy focuses on understanding concepts (in a full 'logos' sort of way), and doesn't just settle for logical form or definition or rules of usage.
You cannot demand an analysis of a concept without knowing the purpose of the analysis [Lehrer]
     Full Idea: An analysis is always relative to some objective. It makes no sense to simply demand an analysis of goodness, knowledge, beauty or truth, without some indication of the purpose of the analysis.
     From: Keith Lehrer (Theory of Knowledge (2nd edn) [2000], I p.7)
     A reaction: Your dismantling of a car will go better if you know what a car is for, but you can still take it apart in ignorance.
3. Truth / A. Truth Problems / 1. Truth
It is part of the concept of truth that we aim at making true statements [Dummett]
     Full Idea: It is part of the concept of truth that we aim at making true statements.
     From: Michael Dummett (Truth [1959], p.231)
     A reaction: This strikes me as a rather contentious but very interesting claim. An even stronger claim might be that its value (its normative force) is ALL that the concept of truth contributes to speech, other aspects being analysed into something else.
3. Truth / A. Truth Problems / 2. Defining Truth
We must be able to specify truths in a precise language, like winning moves in a game [Dummett]
     Full Idea: For a particular bounded language, if it is free of ambiguity and inconsistency, it must be possible to characterize the true sentences of the language; somewhat as, for a given game, we can say which moves are winning moves.
     From: Michael Dummett (Truth [1959], p.237)
     A reaction: The background of this sounds rather like Tarski, with truth just being a baton passed from one part of the language to another, though Dummett adds the very un-Tarskian notion that truth has a value.
3. Truth / F. Semantic Truth / 2. Semantic Truth
Tarski's truth is like rules for winning games, without saying what 'winning' means [Dummett, by Davidson]
     Full Idea: Tarski's definition of truth is like giving a definition of what it is to win in various games, without giving a hint as to what winning is (e.g. that it is what one tries to do when playing).
     From: report of Michael Dummett (Truth [1959]) by Donald Davidson - Truth and Predication 7
     A reaction: This led Dummett to his 'normative' account of truth. Formally, the fact that speakers usually aim at truth seems irrelevant, but in life you certainly wouldn't have grasped truth if you thought falsehood was just as satisfactory. The world is involved.
5. Theory of Logic / C. Ontology of Logic / 3. If-Thenism
Geometrical axioms imply the propositions, but the former may not be true [Russell]
     Full Idea: We must only assert of various geometries that the axioms imply the propositions, not that the axioms are true and therefore that the propositions are true.
     From: Bertrand Russell (Foundations of Geometry [1897], Intro vii), quoted by Alan Musgrave - Logicism Revisited §4
     A reaction: Clearly the truth of the axioms can remain a separate issue from whether they actually imply the theorems. The truth of the axioms might be as much a metaphysical as an empirical question. Musgrave sees this as the birth of if-thenism.
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
Geometry is united by the intuitive axioms of projective geometry [Russell, by Musgrave]
     Full Idea: Russell sought what was common to Euclidean and non-Euclidean systems, found it in the axioms of projective geometry, and took a Kantian view of them.
     From: report of Bertrand Russell (Foundations of Geometry [1897]) by Alan Musgrave - Logicism Revisited §4
     A reaction: Russell's work just preceded Hilbert's famous book. Tarski later produced some logical axioms for geometry.
18. Thought / E. Abstraction / 1. Abstract Thought
You can't infer a dog's abstract concepts from its behaviour [Dummett]
     Full Idea: One could train a dog to bark only when a bell rang and a light shone without presupposing that it possessed the concept of conjunction.
     From: Michael Dummett (Truth [1959], p.235)