15 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) |
| 12205 | There are two families of modal notions, metaphysical and epistemic, of equal strength [Edgington] |
| Full Idea: In my view, there are two independent families of modal notions, metaphysical and epistemic, neither stronger than the other. | |
| From: Dorothy Edgington (Two Kinds of Possibility [2004], Abs) | |
| A reaction: My immediate reaction is that epistemic necessity is not necessity at all. 'For all I know' 2 plus 2 might really be 95, and squares may also be circular. |
| 12207 | Metaphysical possibility is discovered empirically, and is contrained by nature [Edgington] |
| Full Idea: Metaphysical necessity derives from distinguishing things which can happen and things which can't, in virtue of their nature, which we discover empirically: the metaphysically possible, I claim, is constrained by the laws of nature. | |
| From: Dorothy Edgington (Two Kinds of Possibility [2004], §I) | |
| A reaction: She claims that Kripke is sympathetic to this. Personally I like the idea that natural necessity is metaphysically necessary (see 'Scientific Essentialism'), but the other way round comes as a bit of a surprise. I will think about it. |
| 12206 | Broadly logical necessity (i.e. not necessarily formal logical necessity) is an epistemic notion [Edgington] |
| Full Idea: So-called broadly logical necessity (by which I mean, not necessarily formal logical necessity) is an epistemic notion. | |
| From: Dorothy Edgington (Two Kinds of Possibility [2004], §I) | |
| A reaction: This is controversial, and is criticised by McFetridge and Rumfitt. Fine argues that 'narrow' (formal) logical necessity is metaphysical. Between them they have got rid of logical necessity completely. |
| 12208 | An argument is only valid if it is epistemically (a priori) necessary [Edgington] |
| Full Idea: Validity is governed by epistemic necessity, i.e. an argument is valid if and only if there is an a priori route from premises to conclusion. | |
| From: Dorothy Edgington (Two Kinds of Possibility [2004], §V) | |
| A reaction: Controversial, and criticised by McFetridge and Rumfitt. I don't think I agree with her. I don't see validity as depending on dim little human beings. |
| 15473 | How does anything get outside itself? [Fodor, by Martin,CB] |
| Full Idea: Fodor asks the stirring and basic question 'How does anything get outside itself?' | |
| From: report of Jerry A. Fodor (works [1986]) by C.B. Martin - The Mind in Nature 03.6 | |
| A reaction: Is this one of those misconceived questions, like major issues concerning 'what's it like to be?' In what sense am I outside myself? Is a mind any more mysterious than a shadow? |
| 2981 | Is intentionality outwardly folk psychology, inwardly mentalese? [Lyons on Fodor] |
| Full Idea: For Fodor the intentionality of the propositional-attitude vocabulary of our folk psychology is the outward expression of the inward intentionality of the language of the brain. | |
| From: comment on Jerry A. Fodor (works [1986]) by William Lyons - Approaches to Intentionality p.39 | |
| A reaction: I would be very cautious about this. Folk psychology works, so it must have a genuine basis in how brains work, but it breaks down in unusual situations, and might even be a total (successful) fiction. |
| 2985 | Are beliefs brains states, but picked out at a "higher level"? [Lyons on Fodor] |
| Full Idea: Fodor holds that beliefs are brain states or processes, but picked out at a 'higher' or 'special science' level. | |
| From: comment on Jerry A. Fodor (works [1986]) by William Lyons - Approaches to Intentionality p.82 | |
| A reaction: I don't think you can argue with this. Levels of physical description exist (e.g. pure physics tells you nothing about the weather), and I think 'process' is the best word for the mind (Idea 4931). |
| 3135 | Is thought a syntactic computation using representations? [Fodor, by Rey] |
| Full Idea: The modest mentalism of the Computational/Representational Theory of Thought (CRTT), associated with Fodor, says mental processes are computational, defined over syntactically specified entities, and these entities represent the world (are also semantic). | |
| From: report of Jerry A. Fodor (works [1986]) by Georges Rey - Contemporary Philosophy of Mind Int.3 | |
| A reaction: This seems to imply that if you built a machine that did all these things, it would become conscious, which sounds unlikely. Do footprints 'represent' feet, or does representation need prior consciousness? |
| 2983 | Maybe narrow content is physical, broad content less so [Lyons on Fodor] |
| Full Idea: Fodor is concerned with producing a realist and physicalist account of 'narrow content' (i.e. wholly in-the-head content). | |
| From: comment on Jerry A. Fodor (works [1986]) by William Lyons - Approaches to Intentionality p.54 | |
| A reaction: The emergence of 'wide' content has rather shaken Fodor's game plan. We can say "Oh dear, I thought I was referring to H2O", so there must be at least some narrow aspect to reference. |