3 ideas
| 13007 | Archimedes defined a straight line as the shortest distance between two points [Archimedes, by Leibniz] |
| Full Idea: Archimedes gave a sort of definition of 'straight line' when he said it is the shortest line between two points. | |
| From: report of Archimedes (fragments/reports [c.240 BCE]) by Gottfried Leibniz - New Essays on Human Understanding 4.13 | |
| A reaction: Commentators observe that this reduces the purity of the original Euclidean axioms, because it involves distance and measurement, which are absent from the purest geometry. |
| 8886 | Being a true justified belief is not a sufficient condition for knowledge [Gettier] |
| Full Idea: The claim that someone knows a proposition if it is true, it is believed, and the person is justified in their belief is false, in that the conditions do not state a sufficient condition for the claim. | |
| From: Edmund L. Gettier (Is Justified True Belief Knowledge? [1963], p.145) | |
| A reaction: This is the beginning of the famous Gettier Problem, which has motivated most epistemology for the last forty years. Gettier implies that justification is necessary, even if it is not sufficient. He gives two counterexamples. |
| 20344 | Music is not an expressive art, because it expresses no familiar emotions [Hanslick, by Wollheim] |
| Full Idea: Hanslick concluded from the fact that music doesn't express definite feelings like piety, love, joy, or sadness, that it isn't an art of expression. | |
| From: report of Eduard Hanslick (The Beautiful in Music [1854]) by Richard Wollheim - Art and Its Objects 48 | |
| A reaction: Whether music is 'expressive' (which it may not be) should not be confused with whether it is emotional, which it clearly is, even in its coolest examples. Hanslick viewed music as a code, not a language. |