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) |
| 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. |
| 22868 | The value and truth of knowledge are measured by success in activity [Dewey] |
| Full Idea: What measures knowledge's value, its correctness and truth, is the degree of its availability for conducting to a successful issue the activities of living beings. | |
| From: John Dewey (The Middle Works (15 vols, ed Boydston) [1910], 4:180), quoted by David Hildebrand - Dewey 2 'Critique' | |
| A reaction: Note that this is the measure of truth, not the nature of truth (which James seemed to believe). Dewey gives us a clear and perfect statement of the pragmatic view of knowledge. I don't agree with it. |
| 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. |
| 22865 | Habits constitute the self [Dewey] |
| Full Idea: All habits are demands for certain kinds of activity; and they constitute the self. | |
| From: John Dewey (The Middle Works (15 vols, ed Boydston) [1910], 14:22), quoted by David Hildebrand - Dewey 1 'Acts' | |
| A reaction: Not an idea I have encountered elsewhere. He emphasises that habits are not repeated actions, but are dispositions. I'm not clear whether these habits must be conscious. |
| 22871 | The good people are those who improve; the bad are those who deteriorate [Dewey] |
| Full Idea: The bad man is the man who no matter how good he has been is beginning to deteriorate, to grow less good. The good man is the man who no matter how morally unworthy he has been is moving to become better. | |
| From: John Dewey (The Middle Works (15 vols, ed Boydston) [1910], 12:181), quoted by David Hildebrand - Dewey 3 'Reconstruct' | |
| A reaction: Although a slightly improving rat doesn't sound as good as a slightly deteriorating saint, I have some sympathy with this thought. The desire to improve seems to be right at the heart of what makes good character. |
| 22876 | Democracy is the development of human nature when it shares in the running of communal activities [Dewey] |
| Full Idea: Democracy is but a name for the fact that human nature is developed only when its elements take part in directing things which are common, things for the sake of which men and women form groups. | |
| From: John Dewey (The Middle Works (15 vols, ed Boydston) [1910], 12:199), quoted by David Hildebrand - Dewey 4 'Democracy' | |
| A reaction: It is hard to prove that human nature develops when it particpates in groups. If people are excluded from power, their loyalty tends to switch to sub-groups, such as friends in a pub, or a football team. Powerless nationalists baffle me. |
| 22875 | Democracy is not just a form of government; it is a mode of shared living [Dewey] |
| Full Idea: A democracy is more than a form of government; it is primarily a mode of associated living, of conjoint communicated experience | |
| From: John Dewey (The Middle Works (15 vols, ed Boydston) [1910], 9:93), quoted by David Hildebrand - Dewey 4 'Democracy' | |
| A reaction: This precisely pinpoints the heart of the culture wars in 2021. A huge swathe of western populations believe in Dewey's idea, but a core of wealthy right-wingers and their servants only see democracy as the mechanism for obtaining power. |
| 22874 | Individuality is only developed within groups [Dewey] |
| Full Idea: Only in social groups does a person have a chance to develop individuality. | |
| From: John Dewey (The Middle Works (15 vols, ed Boydston) [1910], 15:176), quoted by David Hildebrand - Dewey 4 'Individuals' | |
| A reaction: This is a criticism of both Rawls and Nozick. Rawls's initial choosers don't consult, or have much social background. Nozick's property owners ignore everything except contracts. |