15 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) |
21515 | Incoherence may be more important for enquiry than coherence [Olsson] |
Full Idea: While coherence may lack the positive role many have assigned to it, ...incoherence plays an important negative role in our enquiries. | |
From: Erik J. Olsson (Against Coherence [2005], 10.1) | |
A reaction: [He cites Peirce as the main source for this idea] We can hardly by deeply impressed by incoherence if we have no sense of coherence. Incoherence is just one of many markers for theory failure. Missing the target, bad concepts... |
21514 | Coherence is the capacity to answer objections [Olsson] |
Full Idea: According to Lehrer, coherence should be understood in terms of the capacity to answer objections. | |
From: Erik J. Olsson (Against Coherence [2005], 9) | |
A reaction: [Keith Lehrer 1990] We can connect this with the Greek requirement of being able to give an account [logos], which is the hallmark of understanding. I take coherence to be the best method of achieving understanding. Any understanding meets Lehrer's test. |
21496 | Mere agreement of testimonies is not enough to make truth very likely [Olsson] |
Full Idea: Far from guaranteeing a high likelihood of truth by itself, testimonial agreement can apparently do so only if the circumstances are favourable as regards independence, prior probability, and individual credibility. | |
From: Erik J. Olsson (Against Coherence [2005], 1) | |
A reaction: This is Olson's main thesis. His targets are C.I.Lewis and Bonjour, who hoped that a mere consensus of evidence would increase verisimilitude. I don't see a problem for coherence in general, since his favourable circumstances are part of it. |
21499 | Coherence is only needed if the information sources are not fully reliable [Olsson] |
Full Idea: An enquirer who is fortunate enough to have at his or her disposal fully reliable information sources has no use for coherence, the need for which arises only in the context of less than fully reliable informations sources. | |
From: Erik J. Olsson (Against Coherence [2005], 2.6.2) | |
A reaction: I take this to be entirely false. How do you assess reliability? 'I've seen it with my own eyes'. Why trust your eyes? In what visibility conditions do you begin to doubt your eyes? Why do rational people mistrust their intuitions? |
21502 | A purely coherent theory cannot be true of the world without some contact with the world [Olsson] |
Full Idea: The Input Objection says a pure coherence theory would seem to allow that a system of beliefs be justified in spite of being utterly out of contact with the world it purports to describe, so long as it is, to a sufficient extent, coherent. | |
From: Erik J. Olsson (Against Coherence [2005], 4.1) | |
A reaction: Olson seems impressed by this objection, but I don't see how a system could be coherently about the world if it had no known contact with the world. Olson seems to ignore meta-coherence, which evaluates the status of the system being studied. |
21512 | Extending a system makes it less probable, so extending coherence can't make it more probable [Olsson] |
Full Idea: Any non-trivial extension of a belief system is less probable than the original system, but there are extensions that are more coherent than the original system. Hence more coherence does not imply a higher probability. | |
From: Erik J. Olsson (Against Coherence [2005], 6.4) | |
A reaction: [Olson cites Klein and Warfield 1994; compressed] The example rightly says the extension could have high internal coherence, but not whether the extension is coherent with the system being extended. |
21785 | We are only free, with rights, if we claim our freedom, and there are no natural rights [Hegel, by Houlgate] |
Full Idea: Hegel says we are only truly free, and so bearers of rights, in so far as we claim our freedom. ...So there are no merely natural rights, and animal's have no rights. | |
From: report of Georg W.F.Hegel (Lectures on the Philosophy of Right [1819], p.78) by Stephen Houlgate - An Introduction to Hegel 08 'Rights' | |
A reaction: If there are no natural rights, then it is hard to see how claiming a right will create it. I can't create a right to drink the best champagne. It seems particularly unjust to deny rights to people so enslaved that freedom has never occurred to them. |
22041 | Representatives by region ignores whether they care about the national interest [Hegel, by Pinkard] |
Full Idea: Selecting representatives on the basis of geography means selecting people without any regard to whether they represent the basic and important interests of the 'whole' of society. | |
From: report of Georg W.F.Hegel (Lectures on the Philosophy of Right [1819]) by Terry Pinkard - German Philosophy 1760-1860 11 | |
A reaction: Proportional representation seems to get away from this, but that can still be arranged according to large regions. Some means is needed to prevent the whole nation from exploitation a regional minority (such as Welsh speakers). |
21781 | The absolute right is the right to have rights [Hegel] |
Full Idea: The absolute right is the right to have rights. | |
From: Georg W.F.Hegel (Lectures on the Philosophy of Right [1819], p.127), quoted by Stephen Houlgate - An Introduction to Hegel 08 'Rights' | |
A reaction: What a beautifully succinct and important idea! Does a foetus, or a dog, or a person in a vegetative state, or a slave, qualify? |