3 ideas
| 18832 | Mathematical statements and entities that result from an infinite process must lack a truth-value [Dummett] |
| Full Idea: On an intuitionistic view, neither the truth-value of a statement nor any other mathematical entity can be given as the final result of an infinite process, since an infinite process is precisely one that does not have a final result. | |
| From: Michael Dummett (Elements of Intuitionism (2nd ed) [2000], p.41), quoted by Ian Rumfitt - The Boundary Stones of Thought 7.3 | |
| A reaction: This is rather a persuasive reason to sympathise with intuitionism. Mathematical tricks about 'limits' have lured us into believing in completed infinities, but actually that idea is incoherent. |
| 19699 | A Gettier case is a belief which is true, and its fallible justification involves some luck [Hetherington] |
| Full Idea: A Gettier case contains a belief which is true and well justified without being knowledge. Its justificatory support is also fallible, ...and there is considerable luck in how the belief combnes being true with being justified. | |
| From: Stephen Hetherington (The Gettier Problem [2011], 5) | |
| A reaction: This makes luck the key factor. 'Luck' is a rather vague concept, and so the sort of luck involved must first be spelled out. Or the varieties of luck that can produce this outcome. |
| 22232 | Authenticity is taking responsibility for a situation, with all its risks and emotions [Sartre] |
| Full Idea: Authenticity consists in having a true and lucid consciousness of the situation, in assuming the responsibilities and risks that it involves, in accepting it in pride of humiliation, sometimes in horror and hate. | |
| From: Jean-Paul Sartre (Anti-Semite and Jew [1946], p.90), quoted by Christine Daigle - Jean-Paul Sartre 2.4 | |
| A reaction: [Not sure what 'pride of humiliation' is, so it may be a typo for 'or'] |