10 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) |
| 14534 | Shoemaker moved from properties as powers to properties bestowing powers [Shoemaker, by Mumford/Anjum] |
| Full Idea: Shoemaker ventured the theory in 1980 that properties just are clusters of powers, but he has subsequently abandoned this, and now thinks properties bestow their bearers with causal powers. | |
| From: report of Sydney Shoemaker (Self, Body and Coincidence [1999], p.297) by S.Mumford/R.Lill Anjum - Getting Causes from Powers 1.1 | |
| A reaction: Like Mumford and Anjum, I prefer the earlier theory. I think taking powers as basic is the only story that really makes sense. A power is intrinsic and primitive, whereas properties are complex, messy, partly subjective, and higher level. |
| 4894 | I say Mary does not have new knowledge, but knows an old fact in a new way [Perry on Jackson] |
| Full Idea: I say Mary knows an old fact in a new way, but I do not find a new bit of knowledge and a new fact. | |
| From: comment on Frank Jackson (What Mary Didn't Know [1986]) by John Perry - Knowledge, Possibility and Consciousness §7.3 | |
| A reaction: This seems roughly the right way to attack Jackson's 'knowledge argument', by asking exactly what he means by 'knowledge'. It is hard to see how 'qualia' can be both the means of acquiring knowledge, and the thing itself. |
| 4895 | Is it unfair that physicalist knowledge can be written down, but dualist knowledge can't be [Perry on Jackson] |
| Full Idea: Jackson seems to imply that it isn't fair that all physicalist knowledge can be written down, but not all dualist knowledge can be. | |
| From: comment on Frank Jackson (What Mary Didn't Know [1986]) by John Perry - Knowledge, Possibility and Consciousness §7.5 | |
| A reaction: This pinpoints a problem for the 'Mary' example - that Mary's new sight of colour is claimed as 'knowledge', and yet the whole point is that it cannot be expressed in propositions (which seems to leave it as 'procedural' or 'acquaintance' knowledge). |
| 4886 | Mary knows all the physical facts of seeing red, but experiencing it is new knowledge [Jackson] |
| Full Idea: Mary knows all the physical facts. ..It seems, however, that Mary does not know all there is to know. For when she is let out of the black and white room .. she will learn what it is like to see something red. | |
| From: Frank Jackson (What Mary Didn't Know [1986], §1.4) | |
| A reaction: Jackson is begging the question. A new physical event occurs when the red wavelength stimulates Mary's visual cortex for the first time. For an empiricist raw experience creates knowledge, so it can't BE knowledge. Does Mary acquire a new concept? |