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) |
| 14592 | Some abstract things have a beginning and end, so may exist in time (though not space) [Swoyer] |
| Full Idea: Many things that seem to be abstract also seem to have a beginning (and ending) in time, such as a language like Urdu. It may be tempting to say that such things exist in time but not in space, but where exactly? | |
| From: Chris Swoyer (Abstract Entities [2008], 1.1) | |
| A reaction: A few distinctions might be needed. Urdu-speaking is an ability of certain people. We abstract from that their 'language'. There is nothing there apart from that ability. It has no more abstract existence than the 'weather'. |
| 14594 | Ontologists seek existence and identity conditions, and modal and epistemic status for a thing [Swoyer] |
| Full Idea: Four things philosophers often want to know about a given sort of entity are: its existence conditions, its identity conditions, its modal status, and its epistemic status. | |
| From: Chris Swoyer (Abstract Entities [2008], 3) | |
| A reaction: I prefer 'modal profile' to 'modal status'. The 'existence conditions' sound rather epistemic. Why does the existence of anything require 'conditions' other than just existing? I suspect identity is irrelevant if humans aren't around. |
| 14595 | Can properties exemplify other properties? [Swoyer] |
| Full Idea: Can properties themselves exemplify properties? | |
| From: Chris Swoyer (Abstract Entities [2008], 3) | |
| A reaction: Since I espouse a rather strict causal view of true properties, and lump the rest into the category of 'predicates', I am inclined to answer 'no' to this. Most people would disagree. 'Bright red' seems to be an example. But it isn't. |
| 14593 | Quantum field theory suggests that there are, fundamentally, no individual things [Swoyer] |
| Full Idea: Quantum field theory strongly suggests that there are (at the fundamental level) no individual, particular things. | |
| From: Chris Swoyer (Abstract Entities [2008], 2.1) | |
| A reaction: When people introduce quantum theory into ontological discussions I reach for my shotgun, but it does rather look as if things turn to mush at the bottom level. |
| 19542 | It is nonsense that understanding does not involve knowledge; to understand, you must know [Dougherty/Rysiew] |
| Full Idea: The proposition that understanding does not involve knowledge is widespread (for example, in discussions of what philosophy aims at), but hardly withstands scrutiny. If you do not know how a jet engine works, you do not understand how it works. | |
| From: Dougherty,T/Rysiew,P (Experience First (and reply) [2014], p.24) | |
| A reaction: This seems a bit disingenuous. As in 'Theaetetus', knowing the million parts of a jet engine is not to understand it. More strongly - how could knowledge of an infinity of separate propositional truths amount to understanding on their own? |
| 19543 | To grasp understanding, we should be more explicit about what needs to be known [Dougherty/Rysiew] |
| Full Idea: An essential prerequisite for useful discussion of the relation between knowledge and understanding is systematic explicitness about what is to be known or understood. | |
| From: Dougherty,T/Rysiew,P (Experience First (and reply) [2014], p.25) | |
| A reaction: This is better. I say what needs to be known for understanding is the essence of the item under discussion (my PhD thesis!). Obviously understanding needs some knowledge, but I take it that epistemology should be understanding-first. That is the main aim. |
| 19541 | Rather than knowledge, our epistemic aim may be mere true belief, or else understanding and wisdom [Dougherty/Rysiew] |
| Full Idea: If we say our cognitive aim is to get knowledge, the opposing views are the naturalistic view that what matters is just true belief (or just 'getting by'), or that there are rival epistemic goods such as understanding and wisdom. | |
| From: Dougherty,T/Rysiew,P (Experience First (and reply) [2014], p.17) | |
| A reaction: [compressed summary] I'm a fan of understanding. The accumulation of propositional knowledge would relish knowing the mass of every grain of sand on a beach. If you say the propositions should be 'important', other values are invoked. |