10 ideas
| 19323 | 'Snow is white' depends on meaning; whether snow is white depends on snow [Etchemendy] |
| Full Idea: The difference between (a) snow is white, and (b) 'snow is white' true is that the first makes a claim that only depends on the colour of snow, while the second depends both on the colour of snow and the meaning of the sentence 'snow is white'. | |
| From: John Etchemendy (Tarski on Truth and Logical Consequence [1988], p.61), quoted by Richard L. Kirkham - Theories of Truth: a Critical Introduction 5.7 | |
| A reaction: This is a helpful first step for those who have reached screaming point by being continually offered this apparently vacuous equivalence. This sentence works well if that stuff is a particular colour. |
| 19137 | We can get a substantive account of Tarski's truth by adding primitive 'true' to the object language [Etchemendy] |
| Full Idea: Getting from a Tarskian definition of truth to a substantive account of the semantic properties of the object language may involve as little as the reintroduction of a primitive notion of truth. | |
| From: John Etchemendy (Tarski on Truth and Logical Consequence [1988], p.60), quoted by Donald Davidson - Truth and Predication 1 | |
| A reaction: This is, I think, the first stage in modern developments of axiomatic truth theories. The first problem would be to make sure you haven't reintroduced the Liar Paradox. You need axioms to give behaviour to the 'true' predicate. |
| 13472 | Hilbert aimed to eliminate number from geometry [Hilbert, by Hart,WD] |
| Full Idea: One of Hilbert's aims in 'The Foundations of Geometry' was to eliminate number [as measure of lengths and angles] from geometry. | |
| From: report of David Hilbert (Foundations of Geometry [1899]) by William D. Hart - The Evolution of Logic 2 | |
| A reaction: Presumably this would particularly have to include the elimination of ratios (rather than actual specific lengths). |
| 9546 | Euclid axioms concerns possibilities of construction, but Hilbert's assert the existence of objects [Hilbert, by Chihara] |
| Full Idea: Hilbert's geometrical axioms were existential in character, asserting the existence of certain geometrical objects (points and lines). Euclid's postulates do not assert the existence of anything; they assert the possibility of certain constructions. | |
| From: report of David Hilbert (Foundations of Geometry [1899]) by Charles Chihara - A Structural Account of Mathematics 01.1 | |
| A reaction: Chihara says geometry was originally understood modally, but came to be understood existentially. It seems extraordinary to me that philosophers of mathematics can have become more platonist over the centuries. |
| 18742 | Hilbert's formalisation revealed implicit congruence axioms in Euclid [Hilbert, by Horsten/Pettigrew] |
| Full Idea: In his formal investigation of Euclidean geometry, Hilbert uncovered congruence axioms that implicitly played a role in Euclid's proofs but were not explicitly recognised. | |
| From: report of David Hilbert (Foundations of Geometry [1899]) by Horsten,L/Pettigrew,R - Mathematical Methods in Philosophy 2 | |
| A reaction: The writers are offering this as a good example of the benefits of a precise and formal approach to foundational questions. It's hard to disagree, but dispiriting if you need a PhD in maths before you can start doing philosophy. |
| 18217 | Hilbert's geometry is interesting because it captures Euclid without using real numbers [Hilbert, by Field,H] |
| Full Idea: Hilbert's formulation of the Euclidean theory is of special interest because (besides being rigorously axiomatised) it does not employ the real numbers in the axioms. | |
| From: report of David Hilbert (Foundations of Geometry [1899]) by Hartry Field - Science without Numbers 3 | |
| A reaction: Notice that this job was done by Hilbert, and not by the fictionalist Hartry Field. |
| 22049 | Transcendental idealism aims to explain objectivity through subjectivity [Bowie] |
| Full Idea: The aim of transcendental idealism is to give a basis for objectivity in terms of subjectivity. | |
| From: Andrew Bowie (German Philosophy: a very short introduction [2010], 1) | |
| A reaction: Hume used subjectivity to undermine the findings of objectivity. There was then no return to naive objectivity. Kant's aim then was to thwart global scepticism. Post-Kantians feared that he had failed. |
| 22055 | The Idealists saw the same unexplained spontaneity in Kant's judgements and choices [Bowie] |
| Full Idea: The Idealist saw in Kant that knowledge, which depends on the spontaneity of judgement, and self-determined spontaneous action, can be seen as sharing the same source, which is not accessible to scientific investigation. | |
| From: Andrew Bowie (German Philosophy: a very short introduction [2010]) | |
| A reaction: This is the 'spontaneity' of judgements and choices which was seen as the main idea in Kant. It inspired romantic individualism. The judgements are the rule-based application of concepts. |
| 22054 | German Idealism tried to stop oppositions of appearances/things and receptivity/spontaneity [Bowie] |
| Full Idea: A central aim of German Idealism is to overcome Kant's oppositions between appearances and thing in themselves, and between receptivity and spontaneity. | |
| From: Andrew Bowie (German Philosophy: a very short introduction [2010], 2) | |
| A reaction: I have the impression that there were two strategies: break down the opposition within the self (Fichte), or break down the opposition in the world (Spinozism). |
| 22056 | Crucial to Idealism is the idea of continuity between receptivity and spontaneous judgement [Bowie] |
| Full Idea: A crucial idea for German Idealism (from Hamann) is that apparently passive receptivity and active spontaneity are in fact different degrees of the same 'activity, and the gap between subject and world can be closed. | |
| From: Andrew Bowie (German Philosophy: a very short introduction [2010], 3) | |
| A reaction: The 'passive' bit seems to be Hume's 'impressions', which are Kant's 'intuitions', which need 'spontaneous' interpretation to become experiences. Critics of Kant said this implied a dualism. |