11 ideas
| 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) |
| 7880 | If a blind persons suddenly sees a kestrel, that doesn't make visual and theoretical kestrels different [Papineau on Jackson] |
| Full Idea: An ornithological Mary might know everything theoretical about kestrels, but be blind from birth, then have her sight restored. She now knows "That bird eats mice", so visual kestrels must be ontologically distinct from theoretical ones. | |
| From: comment on Frank Jackson (Epiphenomenal Qualia [1982]) by David Papineau - Thinking about Consciousness 6.3 | |
| A reaction: A nice reductio, and I think this pinpoints best what is wrong with the knowledge argument. Knowledge, and the means of acquiring it, are two distinct things. When I see x, I don't acquire knowledge of x, AND knowledge of my seeing x. |
| 7378 | No one bothers to imagine what it would really be like to have ALL the physical information [Dennett on Jackson] |
| Full Idea: That Mary "has all the physical information" is not readily imaginable, so no one bothers. They just imagine she knows lots and lots - perhaps everything known today - but that is just a drop in the bucket. | |
| From: comment on Frank Jackson (Epiphenomenal Qualia [1982]) by Daniel C. Dennett - Consciousness Explained 12.5 | |
| A reaction: I certainly don't see how we can rule out a priori the possibility that someone who really had all the physical knowledge might be able to infer the phenomenal properties of colour. |
| 7377 | Mary learns when she sees colour, so her complete physical information had missed something [Jackson] |
| Full Idea: It seems obvious that Mary will learn something about the world when she is released from her black-and-white room; but then it is inescapable that her previous knowledge was incomplete; she had all the physical information, so there is more to have. | |
| From: Frank Jackson (Epiphenomenal Qualia [1982], §1) | |
| A reaction: This is Jackson's famous 'knowledge argument', which seems to me misconceived. Since I don't think phenomenal colours are properties of objects (Idea 5456), Mary learns more about herself, and about her means of acquiring knowledge. |
| 21094 | There are two kinds of right - to power, and to property [Hume] |
| Full Idea: Right is of two kinds: right to power and right to property. | |
| From: David Hume (Of the First Principles of Government [1750], p.25) | |
| A reaction: These seem to be positive rights. No mention of the right not be to unjustly abused. It is hard to find any sort of radical political thinking in Hume. His empirical scepticism extends to his politics. He approves of modern consitutional monarchy. |
| 21095 | It is an exaggeration to say that property is the foundation of all government [Hume] |
| Full Idea: A noted author has made property the foundation of all government; and most of our political writers seem inclined to follow him in that particular. This is carrying the matter too far. | |
| From: David Hume (Of the First Principles of Government [1750], p.25) | |
| A reaction: This obviously refers to John Locke. Locke's idea strikes me as hideous. It says the foundation of government is the right of property owners to protect what they have against non-owners. It implies social exclusion in the constitution. |