13 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) |
| 12177 | Human artefacts may have essences, in their purposes [Popper] |
| Full Idea: One might adopt the view that certain things of our own making, such as clocks, may well be said to have 'essences', viz. their 'purposes', and what makes them serve these purposes. | |
| From: Karl Popper (Conjectures and Refutations [1963], 3.3 n17) | |
| A reaction: This is from one of the arch-opponents of essentialism. Could we take him on a slippery slope into essences for evolved creatures, or their organs? His argument says admitting an essence for a clock prevents using it for another purpose. |
| 12176 | Science does not aim at ultimate explanations [Popper] |
| Full Idea: I contest the essentialist doctrine that science aims at ultimate explanations, one which cannot be further explained, and which is in no need of any further explanation. | |
| From: Karl Popper (Conjectures and Refutations [1963], 3.3) | |
| A reaction: If explanations are causal, this seems to a plea for an infinite regress of causes, which is an odd thing to espouse. Are the explanations verbal descriptions or things in the world. There can be no perfect descriptions, but there may be ultimate things. |
| 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. |
| 12175 | Galilean science aimed at true essences, as the ultimate explanations [Popper] |
| Full Idea: The third of the Galilean doctrines of science is that the best, the truly scientific theories, describe the 'essences' or the 'essential natures' of things - the realities which lie behind the appearances. They are ultimate explanations. | |
| From: Karl Popper (Conjectures and Refutations [1963], 3.3) | |
| A reaction: This seems to be the seventeenth century doctrine which was undermined by Humeanism, and hence despised by Popper, but is now making a comeback, with a new account of essence and necessity. |
| 12179 | Essentialist views of science prevent further questions from being raised [Popper] |
| Full Idea: The essentialist view of Newton (due to Roger Cotes) ...prevented fruitful questions from being raised, such as, 'What is the cause of gravity?' or 'Can we deduce Newton's theory from a more general independent theory?' | |
| From: Karl Popper (Conjectures and Refutations [1963], 3.3) | |
| A reaction: This is Popper's main (and only) objection to essentialism - that it is committed to ultimate explanations, and smugly terminates science when it thinks it has found them. This does not strike me as a problem with scientific essentialism. |