9 ideas
| 2764 | Full coherence might involve consistency and mutual entailment of all propositions [Blanshard, by Dancy,J] |
| Full Idea: Blanshard says that in a fully coherent system there would not only be consistency, but every proposition would be entailed by the others, and no proposition would stand outside the system. | |
| From: report of Brand Blanshard (The Nature of Thought [1939], 2:265) by Jonathan Dancy - Intro to Contemporary Epistemology 8.1 | |
| A reaction: Hm. If a proposition is entailed by the others, then it is a necessary truth (given the others) which sounds deterministic. You could predict all the truths you had never encountered. See 1578:178 for quote. |
| 19080 | Coherence tests for truth without implying correspondence, so truth is not correspondence [Blanshard, by Young,JO] |
| Full Idea: Blanshard said that coherent justification leads to coherence truth. It might be said that coherence is a test for truth, but truth is correspondence. But coherence doesn't guarantee correspondence, and coherence is a test, so truth is not correspondence. | |
| From: report of Brand Blanshard (The Nature of Thought [1939], Ch.26) by James O. Young - The Coherence Theory of Truth §2.2 | |
| A reaction: [compression of Young's summary] Rescher (1973) says that Blanshard's argument depends on coherence being an infallible test for truth, which it isn't. |
| 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) |
| 1513 | The Egyptians were the first to say the soul is immortal and reincarnated [Herodotus] |
| Full Idea: The Egyptians were the first to claim that the soul of a human being is immortal, and that each time the body dies the soul enters another creature just as it is being born. | |
| From: Herodotus (The Histories [c.435 BCE], 2.123.2) |