3 ideas
| 18491 | The idea of 'making' can be mere conceptual explanation (like 'because') [Künne] |
| Full Idea: If we say 'being a child of our parent's sibling makes him your first cousin', that can be paraphrased using 'because', and this is the 'because' of conceptual explanation: the second part elucidates the sense of the first part. | |
| From: Wolfgang Künne (Conceptions of Truth [2003], 3.5.2) | |
| A reaction: Fans of truth-making are certainly made uncomfortable by talk of 'what makes this a good painting' or 'this made my day'. They need a bit more sharpness to the concept of 'making' a truth. |
| 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. |
| 18170 | The Axiom of Reducibility is self-effacing: if true, it isn't needed [Quine] |
| Full Idea: The Axiom of Reducibility is self-effacing: if it is true, the ramification it is meant to cope with was pointless to begin with. | |
| From: Willard Quine (Introduction to Russell's Theory of Types [1967], p.152), quoted by Penelope Maddy - Naturalism in Mathematics I.1 | |
| A reaction: Maddy says the rejection of Reducibility collapsed the ramified theory of types into the simple theory. |