17 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) |
| 3523 | Shadows are supervenient on their objects, but not reducible [Maslin] |
| Full Idea: Shadows are distinct from the physical objects casting the shadows and irreducible to them; any attempt at reduction would be incoherent, as it would entail identifying a shadow with the object of which it is a shadow. | |
| From: Keith T. Maslin (Introduction to the Philosophy of Mind [2001], 6.3) | |
| A reaction: Another failure to find a decent analogy for what is claimed in property dualism. A 'shadow' is a reification of the abstract concept of an absence of light. Objects lose their shadows at dusk, but the object itself doesn't change. |
| 3517 | 'Ontology' means 'study of things which exist' [Maslin] |
| Full Idea: The word 'ontology' is derived from the Greek word 'ontia', which means 'things which exist'. | |
| From: Keith T. Maslin (Introduction to the Philosophy of Mind [2001], 1.1) |
| 12887 | A whole must have one characteristic, an internal relation, and a structure [Rescher/Oppenheim] |
| Full Idea: A whole must possess an attribute peculiar to and characteristic of it as a whole; there must be a characteristic relation of dependence between the parts; and the whole must have some structure which gives it characteristics. | |
| From: Rescher,N/Oppenheim,P (Logical Analysis of Gestalt Concepts [1955], p.90), quoted by Peter Simons - Parts 9.2 | |
| A reaction: Simons says these are basically sensible conditions, and tries to fill them out. They seem a pretty good start, and I must resist the temptation to rush to borderline cases. |
| 3538 | Analogy to other minds is uncheckable, over-confident and chauvinistic [Maslin] |
| Full Idea: The argument from analogy makes it impossible to check my inductive inferences because of the privacy of other minds; it also seems irresponsible to generalise from a single case; and it seems like a case of human chauvinism. | |
| From: Keith T. Maslin (Introduction to the Philosophy of Mind [2001], 8.2) | |
| A reaction: Privacy of other minds need not imply scepticism about them. I'm a believer, so I have no trouble checking my theories. Solipsists can't 'check' anything. It isn't 'irresponsible' to generalise from one case if that is all you have. |
| 3540 | If we are brains then we never meet each other [Maslin] |
| Full Idea: If I am my brain this leads to the odd result that you have never met me because you have never seen my brain. | |
| From: Keith T. Maslin (Introduction to the Philosophy of Mind [2001], 10.7) | |
| A reaction: 'Star Trek' is full of aliens who appear beautiful, and turn out to be ugly grey lumps. 'I am my face' would be just as odd, particularly if I were in a coma, or dead. |
| 3518 | I'm not the final authority on my understanding of maths [Maslin] |
| Full Idea: I may be the final authority on whether my shoe pinches, but I am manifestly not the final authority on whether I understand some mathematical theorem. | |
| From: Keith T. Maslin (Introduction to the Philosophy of Mind [2001], 1.7) | |
| A reaction: However, it doesn't follow that his teachers are the final authority either, because he may get correct answers by an algorithm, and bluff his way when demonstrating his understanding. Who knows whether anyone really understands anything? |
| 3530 | Denial of purely mental causation will lead to epiphenomenalism [Maslin] |
| Full Idea: If mental events are causally efficacious only by virtue of their physical features and not their mental ones, …then anomalous monism leads straight to ephiphenomenalism. | |
| From: Keith T. Maslin (Introduction to the Philosophy of Mind [2001], 7.6) | |
| A reaction: As epiphenomenalism strikes me as being incoherent (see Idea 7379), what this amounts to is that either mental effects are causally efficacious, or they are not worth mentioning. I take them to be causally efficacious because they are brain events. |
| 3520 | Token-identity removes the explanatory role of the physical [Maslin] |
| Full Idea: In token-identity mental and physical features seem as unrelated as colour and shape, which is very weak physicalism because it does not allow physical states an explanatory role in accounting for mental states. | |
| From: Keith T. Maslin (Introduction to the Philosophy of Mind [2001], 3.8.6) | |
| A reaction: Colour and shape are not totally unrelated, as they can both be totally explained by a full knowledge of the physical substance involved. ...But maybe if we fully understood Spinoza's single substance...? See Idea 4834. |
| 3528 | Causality may require that a law is being followed [Maslin] |
| Full Idea: The principle of nomological causality says that if two events are intrinsically causally related, there must be a strict physical law under which they can be subsumed. | |
| From: Keith T. Maslin (Introduction to the Philosophy of Mind [2001], 7.5) |
| 3525 | Strict laws make causation logically necessary [Maslin] |
| Full Idea: 'Deductive-nomological' explanation consists of two premises - a strict law with no exceptions and supporting deterministic counterfactuals, and a statement of an event which falls under the law - which together logically require the effect. | |
| From: Keith T. Maslin (Introduction to the Philosophy of Mind [2001], 7.4) |
| 3527 | Strict laws allow no exceptions and are part of a closed system [Maslin] |
| Full Idea: 'Strict' laws of nature contain no ceteris paribus clauses ('all things being equal'), and are part of a closed system (so that whatever affects the system must be included within the system). | |
| From: Keith T. Maslin (Introduction to the Philosophy of Mind [2001], 7.5) |