12 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) |
| 14919 | Empiricists deny what is unobservable, and reject objective modality [Fraassen] |
| Full Idea: To be an empiricist is to withhold belief in anything that goes beyond the actual, observable phenomena, and to recognise no objective modality in nature. | |
| From: Bas C. van Fraassen (The Scientific Image [1980], p.202), quoted by J Ladyman / D Ross - Every Thing Must Go 2.3.1 | |
| A reaction: To only believe in what is actually observable strikes me as ridiculous. It might be, though, that we observe modality, in observing dispositions. If you pull back a bowstring, you feel the possibilities. |
| 6783 | To 'accept' a theory is not to believe it, but to believe it empirically adequate [Fraassen, by Bird] |
| Full Idea: To 'accept' a theory is not to believe it, but is instead to believe it to be empirically adequate. | |
| From: report of Bas C. van Fraassen (The Scientific Image [1980]) by Alexander Bird - Philosophy of Science Ch.4 | |
| A reaction: The second half of this doesn't avoid the word 'belief'. Nevertheless the suggestion is that we never believe (i.e. commit to truth) ever again. So you avoid an on-coming bus because the threat appears to be 'empirically adequate'. Hm. |
| 14917 | To accept a scientific theory, we only need to believe that it is empirically adequate [Fraassen] |
| Full Idea: Science aims to give us theories which are empirically adequate; and acceptance of a theory involves as belief only that it is empiricially adequate. | |
| From: Bas C. van Fraassen (The Scientific Image [1980], p.12), quoted by J Ladyman / D Ross - Every Thing Must Go 2.3.1 | |
| A reaction: This won't tell us what to do if there is a tie between two theories, and we will want to know the criteria for 'adequate'. Presumably there are theories which are empirically quite good, but not yet acceptable. Theories commit beyond experience. |
| 6784 | Why should the true explanation be one of the few we have actually thought of? [Fraassen, by Bird] |
| Full Idea: Van Fraassen asks why we should think that the actual explanation of the evidence should be found among the theories we are considering, when there must be an infinity of theories which are also potential explanations of the evidence? | |
| From: report of Bas C. van Fraassen (The Scientific Image [1980]) by Alexander Bird - Philosophy of Science Ch.4 | |
| A reaction: This has become one of the leading modern anti-realist arguments. We must introduce an element of faith here; presumably evolution makes us experts on immediate puzzles, competent on intermediate ones, and hopeful on remote ones. |
| 13066 | An explanation is just descriptive information answering a particular question [Fraassen, by Salmon] |
| Full Idea: On van Fraassen's theory an explanation is simply an answer to a why-question; it is nothing other than descriptive information that, in a given context, answers a particular type of question. | |
| From: report of Bas C. van Fraassen (The Scientific Image [1980]) by Wesley Salmon - Four Decades of Scientific Explanation 4.3 | |
| A reaction: Presumably we would need some sort of criterion for a 'good' explanation, and it seems to me that a very good explanation might be given which was nevertheless beyond the grasp of the questioner. |
| 20930 | The existence of law is one thing, its merits and demerits another [Austin,J] |
| Full Idea: The existence of law is one thing; its merit and demerit another. Whether it be or be not is one enquiry; whether it be or be not conformable to an assumed standard is a different enquiry. | |
| From: John Austin (Lectures on Jurisprudence [1858], p.214), quoted by Jens Zimmermann - Hermeneutics: a very short introduction 6 'Positivism' | |
| A reaction: It is impossible to contest this point, but the issue is whether there is nothing more to law than its written existence. |