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) |
| 18076 | Most theories are continually falsified [Kuhn, by Kitcher] |
| Full Idea: Kuhn contends that almost all theories are falsified at almost all times. | |
| From: report of Thomas S. Kuhn (Structure of Scientific Revolutions (2nd ed) [1962]) by Philip Kitcher - The Nature of Mathematical Knowledge 07.1 | |
| A reaction: This is obviously meant to demolish Karl Popper. |
| 22191 | Kuhn's scientists don't aim to falsifying their paradigm, because that is what they rely on [Kuhn, by Gorham] |
| Full Idea: In Kuhn's view scientists are decidedly not interested in falsifying their paradigm, because without a paradigm there is no systematic inquiry at all. | |
| From: report of Thomas S. Kuhn (Structure of Scientific Revolutions (2nd ed) [1962]) by Geoffrey Gorham - Philosophy of Science 3 | |
| A reaction: This seems to be one of the stronger aspects of Kuhn's account. You'd be leaving the big house, to go out on the road with a tent. |
| 22183 | Switching scientific paradigms is a conversion experience [Kuhn] |
| Full Idea: The transfer of allegiance from paradigm to paradigm is a conversion experience which cannot be forced. | |
| From: Thomas S. Kuhn (Structure of Scientific Revolutions (2nd ed) [1962]), quoted by Samir Okasha - Philosophy of Science: Very Short Intro (2nd ed) 5 | |
| A reaction: This is the controversial part of Kuhn, which says that the most important decisions are not really rational. Anyone who thought the interpretation of a bunch of evidence is logical needed their head examined. But it IS rational. |
| 6162 | Kuhn has a description theory of reference, so the reference of 'electron' changes with the descriptions [Rowlands on Kuhn] |
| Full Idea: Kuhn and Feyerabend adopt a description theory of reference; the term 'electron' refers to whatever satisfies the descriptions associated with electrons, and since these descriptions vary between theories, so too must the reference. | |
| From: comment on Thomas S. Kuhn (Structure of Scientific Revolutions (2nd ed) [1962]) by Mark Rowlands - Externalism Ch.3 | |
| A reaction: This is a key idea in modern philosophy, showing why all of reality and science were at stake when Kripke and others introduced a causal theory of reference. All the current debates about externalism and essentialism grow from this problem. |
| 22184 | Incommensurability assumes concepts get their meaning from within the theory [Kuhn, by Okasha] |
| Full Idea: The doctrine of incommensurability stems from Kuhn's belief that scientific concepts derive their meaning from the theory in which they play a role. | |
| From: report of Thomas S. Kuhn (Structure of Scientific Revolutions (2nd ed) [1962]) by Samir Okasha - Philosophy of Science: Very Short Intro (2nd ed) 5 | |
| A reaction: Quine was the source of this. Kripke's direct reference theory was meant to be the answer. |
| 7619 | Galileo's notions can't be 'incommensurable' if we can fully describe them [Putnam on Kuhn] |
| Full Idea: To tell us that Galileo had 'incommensurable' notions and then go on to describe them at length is totally incoherent. | |
| From: comment on Thomas S. Kuhn (Structure of Scientific Revolutions (2nd ed) [1962]) by Hilary Putnam - Reason, Truth and History Ch.5 | |
| A reaction: How refreshingly sensible. Incommensurability is the sort of nonsense you slide into if you take an instrumental view of science. But scientists are continually aim to pin down what is actually there. Translation between theories is very difficult! |
| 22725 | When players don't meet again, defection is the best strategy [Axelrod] |
| Full Idea: When players will never meet again, the strategy of defection is the only stable strategy. | |
| From: Robert Axelrod (The Evolution of Co-Operation [1984], 5) | |
| A reaction: This gives good grounds for any community's mistrust of transient strangers, such as tourists. And yet any sensible tourist will want communities to trust tourists, and will therefore behave in a reliable way. |
| 22724 | Good strategies avoid conflict, respond to hostility, forgive, and are clear [Axelrod] |
| Full Idea: Successful game strategies avoid unnecessary conflict, are provoked by an uncalled for defection, forgive after a provocation, and behave clearly so the other player can adapt. | |
| From: Robert Axelrod (The Evolution of Co-Operation [1984], 1) | |
| A reaction: [compressed] Exactly what you would expect from a nice but successful school teacher. The strategies for success in these games is the same as the rules for educating a person into cooperative behaviour. TIT FOR TAT does all these. |