14 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) |
| 3291 | Emergent properties appear at high levels of complexity, but aren't explainable by the lower levels [Nagel] |
| Full Idea: The supposition that a diamond or organism should truly have emergent properties is that they appear at certain complex levels of organisation, but are not explainable (even in principle) in terms of any more fundamental properties of the system. | |
| From: Thomas Nagel (Panpsychism [1979], p.186) |
| 2534 | Mindless bodies are zombies, bodiless minds are ghosts [Sturgeon] |
| Full Idea: When bodies are conceived without mind, Zombies are the topic; when mind is conceived without bodies, Ghosts are the topic. | |
| From: Scott Sturgeon (Matters of Mind [2000], Intro) | |
| A reaction: Personally I am not too impressed by either possibility. I doubt whether either of them are even logically possible. Can you have a magnet without its magnetism? Can you have magnetism with no magnet? |
| 2537 | Types are properties, and tokens are events. Are they split between mental and physical, or not? [Sturgeon] |
| Full Idea: The question is whether mental and physical types (which are properties) are distinct, and whether mental and physical tokens (which are events) are distinct. | |
| From: Scott Sturgeon (Matters of Mind [2000], Intro) | |
| A reaction: Helpful. While the first one gives us the rather dodgy notion of 'property dualism', the second one seems to imply Cartesian dualism, if the events really are distinct. It seems to me that thought is an aspect of brain events, not a distinct event. |
| 2532 | Intentionality isn't reducible, because of its experiential aspect [Sturgeon] |
| Full Idea: The link between Aboutness and consciousness, plus the latter's theoretical recalcitrance, have prevented reduction of the former. | |
| From: Scott Sturgeon (Matters of Mind [2000], Intro) | |
| A reaction: I remain unconvinced that Aboutness (intentionality) has to be wholly (or even partly conscious). We are more interested in our conscious mental states, because those are the ones we can report to other people, and discuss. |
| 2533 | Rule-following can't be reduced to the physical [Sturgeon] |
| Full Idea: If you can't squeeze an 'ought' from an 'is', then the feature of normativity will prevent the reduction of Aboutness. | |
| From: Scott Sturgeon (Matters of Mind [2000], Intro) | |
| A reaction: A dubious argument. Hume's point is that no rational inference will get you from is to ought, but you can get there on a whim. I don't see normativity as being so intrinsically magical that it is irreducible. |
| 2535 | The main argument for physicalism is its simple account of causation [Sturgeon] |
| Full Idea: The dominant empirical argument for physicalism is the Overdetermination Argument: physics is closed and complete, mind is causally efficacious, the world isn't choc-full of overdetermination, so the mind is physical as well. | |
| From: Scott Sturgeon (Matters of Mind [2000], Intro) | |
| A reaction: I find this argument utterly convincing. The idea that there is only one thing which is outside the interconnected causal nexus which seems to constitute the rest of reality, and that is a piece of meat inside our heads, strikes me as totally ridiculous. |
| 2536 | Do facts cause thoughts, or embody them, or what? [Sturgeon] |
| Full Idea: Does a thought relate to its truth conditions like a tree to its age, a bee dance to its target, or smoke to its cause? | |
| From: Scott Sturgeon (Matters of Mind [2000], Intro) | |
| A reaction: Nice question. Is truth the purpose of thoughts, or the cause of thoughts, or the constitution(?) of thoughts? I vote for the bee….but we mustn't confuse truth with truth-conditions. |
| 3290 | Given the nature of heat and of water, it is literally impossible for water not to boil at the right heat [Nagel] |
| Full Idea: Given what heat is and what water is, it is literally impossible for water to be heated beyond a certain point at normal atmospheric pressure without boiling. | |
| From: Thomas Nagel (Panpsychism [1979], p.186) |