11 ideas
| 13737 | The empiricist says that metaphysics is meaningless, rather than false [Schlick] |
| Full Idea: The empiricist does not say to the metaphysician 'what you say is false', but 'what you say asserts nothing at all!' He does not contradict him, but says 'I don't understand you'. | |
| From: Moritz Schlick (Positivism and Realism [1934], p.107), quoted by Jonathan Schaffer - On What Grounds What 1.1 | |
| A reaction: I take metaphysics to be meaningful, but at such a high level of abstraction that it is easy to drift into vague nonsense, and incredibly hard to assess what is meant, and whether it is correct. The truths of metaphysics are not recursive. |
| 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) |
| 23903 | When we admire a work, we see ourselves as its creator [Weil] |
| Full Idea: It is impossible to admire a work of art without thinking oneself, in a way, its creator and without, in a sense, becoming so. | |
| From: Simone Weil (Letters [1940], 1940-03c) | |
| A reaction: This rings true for me. You almost see yourself making the brush strokes, or writing the phrase, or penning the chords. It is engagment which is essential for artistic experience. So all art lovers want to be artists? |
| 23901 | Relationships depend on equality, so unequal treatment kills them [Weil] |
| Full Idea: I conceive human relations solely on the plane of equality; therefore, so soon as someone begins to treat me as an inferior, human relations between us become impossible in my eyes. | |
| From: Simone Weil (Letters [1940], 1936-03) | |
| A reaction: Love that. This is precisely where equality starts. I fear that the problem is that people who don't treat others as equals don't want relationships with them, which particularly occurs in a competitive or hierarchical culture. |
| 23904 | The cruelty of the Old Testament put me off Christianity [Weil] |
| Full Idea: I have always been kept away from Christianity by its ranking the Old Testament stories, so full of pitiless cruelty, as sacred texts. | |
| From: Simone Weil (Letters [1940], 1941-01) | |
| A reaction: After 1938 she was a devout and intense Christian, but of a highly individual and platonist kind. Her religion is dominated by love and beauty. |
| 23902 | I attach little importance to immortality, which is an undecidable fact, and irrelevant to us [Weil] |
| Full Idea: You attach great importance to the reasoning about immortality. I myself attach little. It is a factual question, which cannot be decided in advance by any reasoning. And what does it matter to us? | |
| From: Simone Weil (Letters [1940], 1937-04c) | |
| A reaction: I love 'what does it matter to us?'. The idea that our future bliss or misery depends on how we live now is an utterly wicked fiction, which derails attempts to live a proper life. |