12 ideas
| 4742 | Correspondence may be one-many or many one, as when either p or q make 'p or q' true [Armstrong] |
| Full Idea: In Armstrong's version of the correspondence theory, the truth-making relation is not one-one, but one-many or many-one. Thus 'p or q' has two truth makers, p and q. | |
| From: David M. Armstrong (A World of States of Affairs [1997], p.129), quoted by Pascal Engel - Truth Ch.1 | |
| A reaction: Interesting. Armstrong deals in universals. He also cites many swans as truth-makers for 'there is a least one black swan'. Not correspondence as we know it, Jim. |
| 17884 | Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner] |
| Full Idea: There are many coherent stopping points in the hierarchy of increasingly strong mathematical systems, starting with strict finitism, and moving up through predicativism to the higher reaches of set theory. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], Intro) |
| 17893 | 'Reflection principles' say the whole truth about sets can't be captured [Koellner] |
| Full Idea: Roughly speaking, 'reflection principles' assert that anything true in V [the set hierarchy] falls short of characterising V in that it is true within some earlier level. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 2.1) |
| 17894 | We have no argument to show a statement is absolutely undecidable [Koellner] |
| Full Idea: There is at present no solid argument to the effect that a given statement is absolutely undecidable. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 5.3) |
| 17890 | There are at least eleven types of large cardinal, of increasing logical strength [Koellner] |
| Full Idea: Some of the standard large cardinals (in order of increasing (logical) strength) are: inaccessible, Mahlo, weakly compact, indescribable, Erdös, measurable, strong, Wodin, supercompact, huge etc. (...and ineffable). | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.4) | |
| A reaction: [I don't understand how cardinals can have 'logical strength', but I pass it on anyway] |
| 17887 | PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner] |
| Full Idea: To the extent that we are justified in accepting Peano Arithmetic we are justified in accepting its consistency, and so we know how to expand the axiom system so as to overcome the limitation [of Gödel's Second Theorem]. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.1) | |
| A reaction: Each expansion brings a limitation, but then you can expand again. |
| 17891 | Arithmetical undecidability is always settled at the next stage up [Koellner] |
| Full Idea: The arithmetical instances of undecidability that arise at one stage of the hierarchy are settled at the next. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.4) |
| 9497 | Without modality, Armstrong falls back on fictionalism to support counterfactual laws [Bird on Armstrong] |
| Full Idea: Armstrong has difficulty explaining how laws entail regularities. There is no real modality in the basic components of the world, but he wants to support counterfactuals. His official position is a kind of fictionalism. | |
| From: comment on David M. Armstrong (A World of States of Affairs [1997], 49-51) by Alexander Bird - Nature's Metaphysics 4.4.4 | |
| A reaction: Armstrong seems to be up against the basic problems that laws won't explain anything if they are merely regularities (assuming they are not decrees of a supernatural force). |
| 15550 | Properties are contingently existing beings with multiple locations in space and time [Armstrong, by Lewis] |
| Full Idea: Armstrong has a distinctive conception of (fundamental) properties as contingently existing beings with multiple locations in space and time. | |
| From: report of David M. Armstrong (A World of States of Affairs [1997]) by David Lewis - A world of truthmakers? p.220 | |
| A reaction: Armstrong tries to get a naturalistically founded platonism (which he claims is Aristotelian), but the idea that one thing can be multiply located strikes me as daft (especially if the number of its locations increases or decreases). |
| 4743 | The truth-maker for a truth must necessitate that truth [Armstrong] |
| Full Idea: The truth-maker for a truth must necessitate that truth. | |
| From: David M. Armstrong (A World of States of Affairs [1997], p.115), quoted by Pascal Engel - Truth Ch.1 | |
| A reaction: Armstrong's 'truth-make principle'. It seems to be a necessity which is neither natural nor analytic, making it metaphysically necessary. Or is it part of the definition of truth? |
| 22072 | Schelling always affirmed the absolute status of freedom [Schelling, by Courtine] |
| Full Idea: Throughout Schelling's work we find the affirmation of absolute freedom or of the absolute as freedom. | |
| From: report of Friedrich Schelling (Philosophy of Revelation [1843], Vol.13 p.359) by Jean-François Courtine - Schelling p.83 | |
| A reaction: Of all of the German idealists, Schelling may be the closest to modern existentialism. |
| 4798 | In recent writings, Armstrong makes a direct identification of necessitation with causation [Armstrong, by Psillos] |
| Full Idea: In recent writings, Armstrong makes a direct identification of necessitation with causation. | |
| From: report of David M. Armstrong (A World of States of Affairs [1997]) by Stathis Psillos - Causation and Explanation §6.3.3 | |
| A reaction: Obviously logical necessity is not causal, but as a proposal for simplifying accounts of necessity in nature, this is wonderfully simple and appealing. Is his proposal an elevation of causation, or a degradation of necessity? |