8 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. |
| 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) |
| 8511 | Stout first explicitly proposed that properties and relations are particulars [Stout,GF, by Campbell,K] |
| Full Idea: In modern times, it was G.F. Stout who first explicitly made the proposal that properties and relations are as particular as the substances that they qualify. | |
| From: report of G.F. Stout (The Nature of Universals and Propositions [1923]) by Keith Campbell - The Metaphysic of Abstract Particulars §1 | |
| A reaction: Note that relations will have to be tropes, as well as properties. Williams wants tropes to be parts of objects, but that will be tricky with relations. If you place two objects on a table, how does the 'to the left of' trope come into existence? |