5 ideas
| 10632 | The real numbers may be introduced by abstraction as ratios of quantities [Hale, by Hale/Wright] |
| Full Idea: The real numbers may be introduced by abstraction as ratios of quantities. ..They are not defined by Dedekind cuts; rather, the cuts constitute a domain with the properties that are a necessary precondition. | |
| From: report of Bob Hale (Reals by Abstraction [1998]) by B Hale / C Wright - Intro to 'The Reason's Proper Study' 3.3 | |
| A reaction: This is Hale's neo-logicist attempt to derive the real numbers from Hume's Principle. |
| 8840 | There are five possible responses to the problem of infinite regress in justification [Cleve] |
| Full Idea: Sceptics respond to the regress problem by denying knowledge; Foundationalists accept justifications without reasons; Positists say reasons terminate is mere posits; Coherentists say mutual support is justification; Infinitists accept the regress. | |
| From: James Van Cleve (Why coherence is not enough [2005], I) | |
| A reaction: A nice map of the territory. The doubts of Scepticism are not strong enough for anyone to embrace the view; Foundationalist destroy knowledge (?), as do Positists; Infinitism is a version of Coherentism - which is the winner. |
| 8841 | Modern foundationalists say basic beliefs are fallible, and coherence is relevant [Cleve] |
| Full Idea: Contemporary foundationalists are seldom of the strong Cartesian variety: they do not insist that basic beliefs be absolutely certain. They also tend to allow that coherence can enhance justification. | |
| From: James Van Cleve (Why coherence is not enough [2005], III) | |
| A reaction: It strikes me that they have got onto a slippery slope. How certain are the basic beliefs? How do you evaluate their certainty? Could incoherence in their implications undermine them? Skyscrapers need perfect foundations. |
| 8416 | Reductionists can't explain accidents, uninstantiated laws, probabilities, or the existence of any laws [Tooley] |
| Full Idea: Reductionist accounts of causation cannot distinguish laws from accidental uniformities, cannot allow for basic uninstantiated laws, can't explain probabilistic laws, and cannot even demonstrate the existence of laws. | |
| From: Michael Tooley (Causality: Reductionism versus Realism [1990], 2) | |
| A reaction: I am tempted to say that this is so much the worse for the idea of laws. Extensive regularities only occur for a reason. Probabilities aren't laws. Hypothetical facts will cover uninstantiated laws. Laws are just patterns. |
| 8418 | Quantum physics suggests that the basic laws of nature are probabilistic [Tooley] |
| Full Idea: Quantum physics seems to lend strong support to the idea that the basic laws of nature may well be probabilistic. | |
| From: Michael Tooley (Causality: Reductionism versus Realism [1990], 3.2.1) | |
| A reaction: Groan. Quantum physics should be outlawed from all philosophical discussions. The scientists don't understand it themselves. I'm certainly not going to build my worldview on it. I don't accept that these probabilities could count as 'laws'. |