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) |
| 8978 | Events are made of other things, and are not fundamental to ontology [Bennett] |
| Full Idea: Events are not basic items in the universe; they should not be included in any fundamental ontology...all the truths about them are entailed by and explained and made true by truths that do not involve the event concept. | |
| From: Jonathan Bennett (Events and Their Names [1988], p.12), quoted by Peter Simons - Events 3.1 | |
| A reaction: Given the variable time spans of events, their ability to coincide, their ability to contain no motion, their blatantly conventional component, and their recalcitrance to individuation, I say Bennett is right. |
| 9312 | Consciousness is reductively explained either by how it represents, or how it is represented [Kriegel/Williford] |
| Full Idea: The two main competitors for reductive theories of consciousness are the representational theory (conscious if it represents in the right way), and higher-order monitoring (conscious if it is represented in the right way). | |
| From: U Kriegel / K Williford (Intro to 'Self-Representational Consciousness' [2006], Intro) | |
| A reaction: Presumably there are also neuroscientists hunting for physical functions which might generate consciousness. The two mentioned here are rivals at one level of discourse. Both views may be simplistic, if complex teams of activities are involved. |
| 9313 | Experiences can be represented consciously or unconsciously, so representation won't explain consciousness [Kriegel/Williford] |
| Full Idea: On the assumption that any environmental feature can be represented either consciously or unconsciously, it is unclear how the mere representation of such a feature can render the representing state conscious. | |
| From: U Kriegel / K Williford (Intro to 'Self-Representational Consciousness' [2006], §1) | |
| A reaction: The authors are rejecting simple representation as the key, in favour of a distinctive sort of self-representation. I'm inclined to think that consciousness results from multiple co-ordinated layers of representation etc., which has no simple account. |
| 9315 | Red tomato experiences are conscious if the state represents the tomato and itself [Kriegel/Williford] |
| Full Idea: The self-representational theory of consciousness says that when one has a conscious experience as of a red tomato, one is in an internal state that represents both a red tomato and itself. | |
| From: U Kriegel / K Williford (Intro to 'Self-Representational Consciousness' [2006], §1) | |
| A reaction: This seems to be avoiding the concept of 'higher-order', and yet that seems the only way to describe it - thought steps outside of itself, generating a level of meta-thought. I think that's the way to go. Philosophy is about-fifth level. |
| 9316 | How is self-representation possible, does it produce a regress, and is experience like that? [Kriegel/Williford] |
| Full Idea: The difficulties with a self-representational view of consciousness are how self-representation of mental states could be possible, whether it leads to an infinite regress, and whether it can capture the actual phenomenology of experience. | |
| From: U Kriegel / K Williford (Intro to 'Self-Representational Consciousness' [2006], §3) | |
| A reaction: [compressed] All of these objections strike me as persuasive, especially the first one. I'm not sure I know what self-representation is. Mirrors externally represent, and they can't represent themselves. Two mirrors together achieve something.. |
| 9314 | Unfortunately, higher-order representations could involve error [Kriegel/Williford] |
| Full Idea: A problem for explaining consciousness by higher-order representations is that, like their first-order counterparts, they can misrepresent; there could be a subjective impression of being in a conscious state without actually being in any conscious state. | |
| From: U Kriegel / K Williford (Intro to 'Self-Representational Consciousness' [2006], §1) | |
| A reaction: It sounds plausible that this is a logical possibility, but how do you assess whether it is an actual or natural possibility? Are we saying that higher-order representations are judgments, which could be true or false? Hm. |
| 10364 | Facts are about the world, not in it, so they can't cause anything [Bennett] |
| Full Idea: Facts are not the sort of item that can cause anything. A fact is a true proposition (they say); it is not something in the world but is rather something about the world. | |
| From: Jonathan Bennett (Events and Their Names [1988], p.22), quoted by Jonathan Schaffer - The Metaphysics of Causation 1.1 | |
| A reaction: Compare 10361. Good argument, but maybe 'fact' is ambiguous. See Idea 10365. Events are said to be more concrete, and so can do the job, but their individuation also seems to depend on a description (as Davidson has pointed out). |