11 ideas
| 14779 | I reason in order to avoid disappointment and surprise [Peirce] |
| Full Idea: I do not reason for the sake of my delight in reasoning, but solely to avoid disappointment and surprise. | |
| From: Charles Sanders Peirce (Criterion of Validity in Reasoning [1903], I) | |
| A reaction: Hence Peirce places more emphasis on inductive and abductive reasoning than on deductive reasoning. I have to agree with him. Anyone account of why we reason must have an evolutionary framework. What advantage does reason bestow? It concerns the future. |
| 14777 | That a judgement is true and that we judge it true are quite different things [Peirce] |
| Full Idea: Either J and the judgment 'I say that J is true' are the same for all judgments or for none. But if identical, their denials are identical. These are 'J is not true' and 'I do not say that J is true', which are different. No judgment judges itself true. | |
| From: Charles Sanders Peirce (Criterion of Validity in Reasoning [1903], I) | |
| A reaction: If you are going to espouse the Ramseyan redundancy view of truth, you had better make sure you are not guilty of the error which Peirce identifies here. |
| 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) |
| 14780 | Only study logic if you think your own reasoning is deficient [Peirce] |
| Full Idea: It is foolish to study logic unless one is persuaded that one's own reasonings are more or less bad. | |
| From: Charles Sanders Peirce (Criterion of Validity in Reasoning [1903], II) |
| 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) |
| 14778 | Facts are hard unmoved things, unaffected by what people may think of them [Peirce] |
| Full Idea: Facts are hard things which do not consist in my thinking so and so, but stand unmoved by whatever you or I or any man or generations of men may opine about them. | |
| From: Charles Sanders Peirce (Criterion of Validity in Reasoning [1903], I) | |
| A reaction: This is my view of facts, with which I am perfectly happy, for all the difficulties involved in individuating facts, and in disentangling them from our own modes of thought and expression. Let us try to establish the facts. |
| 14367 | An explanation is a causal graph [Woodward,J, by Strevens] |
| Full Idea: On Woodward's manipulationist view, an explanation would take the form of a causal graph. | |
| From: report of James Woodward (Making Things Happen [2003]) by Michael Strevens - No Understanding without Explanation 1 | |
| A reaction: The idea is that causation is all to do with how nature responds when you try to manipulate it. I'm certainly in favour of tying explanation closely to causation. |