6 ideas
15102 | S4 says there must be some necessary truths (the actual ones, of which there is at least one) [Cameron] |
Full Idea: S4 says there must be some necessary truths, because the actual necessary truths must be necessary. (It says if there are some actual necessary truths then that is so - but the S4 axiom is an actual necessary truth, if true). | |
From: Ross P. Cameron (On the Source of Necessity [2010], 2) |
18192 | Do the Replacement Axioms exceed the iterative conception of sets? [Boolos, by Maddy] |
Full Idea: For Boolos, the Replacement Axioms go beyond the iterative conception. | |
From: report of George Boolos (The iterative conception of Set [1971]) by Penelope Maddy - Naturalism in Mathematics I.3 |
15103 | Blackburn fails to show that the necessary cannot be grounded in the contingent [Cameron] |
Full Idea: I conclude that Blackburn has not shown that any grounding of the necessary in the contingent (the Contingency Horn of his dilemma) is doomed to failure. | |
From: Ross P. Cameron (On the Source of Necessity [2010], 2) | |
A reaction: [You must read the article for details of Cameron's argument!] He goes on to also reject the Necessity Horn (that there is a regress if necessities must rely on necessities). |
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. |
15104 | The 'moving spotlight' theory makes one time privileged, while all times are on a par ontologically [Cameron] |
Full Idea: What seems so wrong about the 'moving spotlight' theory is that here one time is privileged, but all the times are on a par ontologically. | |
From: Ross P. Cameron (On the Source of Necessity [2010], 4) | |
A reaction: The whole thing is baffling, but this looks like a good point. All our intuitions make presentism (there's only the present) look like a better theory than the moving spotlight (that the present is just 'special'). |