23 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) |
| 19682 | Internalists are much more interested in evidence than externalists are [McGrew] |
| Full Idea: The notion of evidence generally plays a much more significant role in internalist epistemologies than it does in various forms of externalism. | |
| From: Timothy McGrew (Evidence [2011], 'Prop..') | |
| A reaction: I'm guessing that this is because evidence needs a certain amount of interpretation, whereas raw facts (which externalists seem to rely on) may never even enter a mind. |
| 19684 | Does spotting a new possibility count as evidence? [McGrew] |
| Full Idea: Does the sudden realization of a heretofore unrecognized possibility count as evidence? | |
| From: Timothy McGrew (Evidence [2011], 'Evid..') | |
| A reaction: [Nice use of 'heretofore'! Why say 'previously' when you can keep these wonderful old English words alive?] This means that we can imagine new evidence ('maybe the murderer was a snake'!). Wrong. The evidence is what suggests the possibility. |
| 19687 | Absence of evidence proves nothing, and weird claims need special evidence [McGrew] |
| Full Idea: Two well know slogans (popularised by Carl Sagan) are 'absence of evidence is not evidence of absence', ...and 'extraordinary claims require extraordinary evidence'. | |
| From: Timothy McGrew (Evidence [2011], 'Absence') | |
| A reaction: [Sagan was a popular science writer and broadcaster] The second one is something like Hume's argument against miracles. The old problem of the 'missing link' for human evolution embodied the first idea. |
| 19688 | Every event is highly unlikely (in detail), but may be perfectly plausible [McGrew] |
| Full Idea: At a certain level of detail, almost any claim is unprecedented. How likely is 'Matilda won at Scrabble on Thursday with a score of 438 while drinking mint tea'? But there is nothing particularly unbelievable about the claim. | |
| From: Timothy McGrew (Evidence [2011], 'Extraordinary') | |
| A reaction: A striking idea, which rules out the simplistic idea that we can just assess evidence by its isolated likelihood. Context is crucial. How good is 438? What if she smoked opium? What if there is no Scrabble set on her island? |
| 19686 | Criminal law needs two separate witnesses, but historians will accept one witness [McGrew] |
| Full Idea: An ancient rule in law is that a criminal conviction needs evidence of two independent witnesses, but in history it is assumed that a document deserves the benefit of the doubt if it cannot be independently verified. | |
| From: Timothy McGrew (Evidence [2011], 'Interp..') | |
| A reaction: [compressed; McGrew's full account qualifies it a bit] A nice observation. One might even be suspicious of the two 'independent' witnesses, if there were lots of other reasons to doubt someon's guilt. A single weird document is also dubious. |
| 19680 | Maybe all evidence consists of beliefs, rather than of facts [McGrew] |
| Full Idea: Some philosophers have been attracted to the view that, strictly speaking, what counts as evidence is not a set of physical objects or even experiences, but rather a set of believed propositions. | |
| From: Timothy McGrew (Evidence [2011], 'Prop..') | |
| A reaction: This may be right. However, as always, I think animals are a key test. Do animals respond to evidence? Even if they did, they might need to 'make sense' of what they experienced, and even formulate a non-linguistic proposition. |
| 19681 | If all evidence is propositional, what is the evidence for the proposition? Do we face a regress? [McGrew] |
| Full Idea: Taking evidence as propositional may trade one problem for another. If the bloodstain isn't evidence, but 'this is a bloodstain' is evidence, then what serves as evidence for the belief about the bloodstain? Is there an infinite regress? | |
| From: Timothy McGrew (Evidence [2011], 'Prop..') | |
| A reaction: [compressed] I quite like evidence being propositional, but then find this. I'll retreat to my beloved coherence. I do not endorse Sellars's 'only a belief can justify a belief', because raw experience has to be part of what is coherent. |
| 19689 | Several unreliable witnesses can give good support, if they all say the same thing [McGrew] |
| Full Idea: The testimony of a number of independent witnesses, none of them particularly reliable, who give substantially the same account of some event, may provide a strong argument in its favor. | |
| From: Timothy McGrew (Evidence [2011], 'Testimonial') | |
| A reaction: A striking point. It obviously works well for panicking people in a crowd during an incident. Does it also apply to independent scientists who are known to cheat? They may not collaborate, but may all want the same result. |
| 19683 | Narrow evidentialism relies wholly on propositions; the wider form includes other items [McGrew] |
| Full Idea: Evidentialism comes in both narrow and wide forms depending on whether evidence is taken to consist only of propositions or of a wider range of items. | |
| From: Timothy McGrew (Evidence [2011], 'Evid..') | |
| A reaction: [He cites Conee and Feldman for the wide view, which is not restricted to beliefs] You can hardly rely on occurrent beliefs as evidence, so we often have good knowledge with forgotten justification. But such knowledge has been 'weakened'. |
| 19685 | Falsificationism would be naive if even a slight discrepancy in evidence killed a theory [McGrew] |
| Full Idea: Data do not quite speak for themselves, which speaks against a naive form of falsificationism according to which even the slightest mismatch between theory and evidence suffices to overturn a theory. | |
| From: Timothy McGrew (Evidence [2011], 'Interp..') | |
| A reaction: [He cites Robert Boyle wisely ignoring some data to get a good fit for his graph] |
| 20937 | The state should produce higher civilisations for all, in tune with the economic apparatus [Gramsci] |
| Full Idea: The role of the State is always that of creating new and higher types of civilisation; of adapting the 'civilisation' and the morality of the broades popular masses to the necessities of the continuous development of the economic apparatus of production. | |
| From: Antonio Gramsci (Selections from Prison Notebooks [1971], 2 'Collective') | |
| A reaction: This makes education virtually the prime role of the state. Reminiscent of Sir John Reith's original dream, in the 1930s, for the BBC. Many marxists feel that the economy is in direct conflict with morality and civilisation. |
| 20935 | Eventually political parties lose touch with the class they represent, which is dangerous [Gramsci] |
| Full Idea: At a certain point in their lives, social classes become detached from their traditional parties. In that particular form ...the parties are no longer recognised by their class as its exopression. ...The field is then open for violent solutions. | |
| From: Antonio Gramsci (Selections from Prison Notebooks [1971], 2 'Parties') | |
| A reaction: Left wing parties pursue ideologies that don't connect with the actual current interests of the working class, and righ wing parties are taken over by rich elites who don't value safe traditonal communities. (This thought is resonant in the 2018 UK). |
| 20936 | Caesarism emerges when two forces in society are paralysed in conflict [Gramsci] |
| Full Idea: Caesarism (as the emergence of a 'heroic' personality) expresses a situation in which the forces in conflict balance each other in a catastrophic manner ...which can only terminate in their reciprocal destruction. | |
| From: Antonio Gramsci (Selections from Prison Notebooks [1971], 2 'Caesarism') | |
| A reaction: He goes on to distinguish progressive and reactionary versions of Caesarism. Gramsci's interest is in the circumstances that throw up such people. Marx had identified 'Bonapartism'. |
| 20941 | Totalitarian parties cut their members off from other cultural organisations [Gramsci] |
| Full Idea: A totalitarian party ensures that members find in that particular party all the satisfactions that they formerly found in a multiplicity of organisations. They break the threads that bind them to extraneous cultural organisms. | |
| From: Antonio Gramsci (Selections from Prison Notebooks [1971], 2 'Organisation') | |
| A reaction: British parties traditionally had a 'club house', where you could do most of your socialising. Presumably Nazis left the church, and various interest groups. |
| 20939 | What is the function of a parliament? Does it even constitute a part of the State structure? [Gramsci] |
| Full Idea: The question has to be asked: do parliaments, even in fact constitute a part of the State structure? In other words, what is the real function? | |
| From: Antonio Gramsci (Selections from Prison Notebooks [1971], 2 'Parliament') | |
| A reaction: Nice question. In the UK it is only the cabinet which has active power. Backbench MPs are usually very frustrated, especially if their party has a comfortable majority, and their vote is not precious. They are privileged lobbyists. |
| 20938 | Liberalism's weakness is its powerful rigid bureaucracy [Gramsci] |
| Full Idea: Liberalism's weakness is the bureacracy - the crystallisation of the leading personnel - which exercises power, and at a certain point it becomes a caste. | |
| From: Antonio Gramsci (Selections from Prison Notebooks [1971], 2 'Hegemony') | |
| A reaction: This sounds more like what is called 'the Establishment' in Britain, which is the hidden controllers of power, rather than the administrators (whose role is only despised by right-wingers). |
| 20940 | Perfect political equality requires economic equality [Gramsci] |
| Full Idea: The idea that complete and perfect political equality cannot exist without economic equality ...remains correct. | |
| From: Antonio Gramsci (Selections from Prison Notebooks [1971], 2 'The State') | |
| A reaction: In the west we are living in a period (2018) when the top 0.1% of the wealthy are racing away, creating huge inequality. Their wealth controls the media, and it seems unrestrainable. The belief that we live in a 'democracy' is an illusion. |