12 ideas
| 15833 | Tell cleverness from answers, but wisdom from questions [Mahfouz] |
| Full Idea: You can tell whether a man is clever by his answers. You can tell whether a man is wise by his questions. | |
| From: Naguib Mahfouz (works [1998]) | |
| A reaction: [Popped up on Twitter. I am adjusting to the 21st century] The observation is simplistic, of course, but very nice indeed. |
| 10688 | 'Equivocation' is when terms do not mean the same thing in premises and conclusion [Beall/Restall] |
| Full Idea: 'Equivocation' is when the terms do not mean the same thing in the premises and in the conclusion. | |
| From: JC Beall / G Restall (Logical Consequence [2005], Intro) |
| 10690 | Formal logic is invariant under permutations, or devoid of content, or gives the norms for thought [Beall/Restall] |
| Full Idea: Logic is purely formal either when it is invariant under permutation of object (Tarski), or when it has totally abstracted away from all contents, or it is the constitutive norms for thought. | |
| From: JC Beall / G Restall (Logical Consequence [2005], 2) | |
| A reaction: [compressed] The third account sounds rather woolly, and the second one sounds like a tricky operation, but the first one sounds clear and decisive, so I vote for Tarski. |
| 10691 | Logical consequence needs either proofs, or absence of counterexamples [Beall/Restall] |
| Full Idea: Technical work on logical consequence has either focused on proofs, where validity is the existence of a proof of the conclusions from the premises, or on models, which focus on the absence of counterexamples. | |
| From: JC Beall / G Restall (Logical Consequence [2005], 3) |
| 10695 | Logical consequence is either necessary truth preservation, or preservation based on interpretation [Beall/Restall] |
| Full Idea: Two different views of logical consequence are necessary truth-preservation (based on modelling possible worlds; favoured by Realists), or truth-preservation based on the meanings of the logical vocabulary (differing in various models; for Anti-Realists). | |
| From: JC Beall / G Restall (Logical Consequence [2005], 2) | |
| A reaction: Thus Dummett prefers the second view, because the law of excluded middle is optional. My instincts are with the first one. |
| 10689 | A step is a 'material consequence' if we need contents as well as form [Beall/Restall] |
| Full Idea: A logical step is a 'material consequence' and not a formal one, if we need the contents as well as the structure or form. | |
| From: JC Beall / G Restall (Logical Consequence [2005], 2) |
| 10696 | A 'logical truth' (or 'tautology', or 'theorem') follows from empty premises [Beall/Restall] |
| Full Idea: If a conclusion follows from an empty collection of premises, it is true by logic alone, and is a 'logical truth' (sometimes a 'tautology'), or, in the proof-centred approach, 'theorems'. | |
| From: JC Beall / G Restall (Logical Consequence [2005], 4) | |
| A reaction: These truths are written as following from the empty set Φ. They are just implications derived from the axioms and the rules. |
| 10693 | Models are mathematical structures which interpret the non-logical primitives [Beall/Restall] |
| Full Idea: Models are abstract mathematical structures that provide possible interpretations for each of the non-logical primitives in a formal language. | |
| From: JC Beall / G Restall (Logical Consequence [2005], 3) |
| 10692 | Hilbert proofs have simple rules and complex axioms, and natural deduction is the opposite [Beall/Restall] |
| Full Idea: There are many proof-systems, the main being Hilbert proofs (with simple rules and complex axioms), or natural deduction systems (with few axioms and many rules, and the rules constitute the meaning of the connectives). | |
| From: JC Beall / G Restall (Logical Consequence [2005], 3) |
| 19701 | Fallibilism is consistent with dogmatism or scepticism, and is not alternative to them [Dougherty] |
| Full Idea: There has been a tendency to treat fallibilism as an alternative to either dogmatism or scepticism. ...But it is much better to think of fallibilism as consistent with either dogmatism or skepticism. | |
| From: Trent Dougherty (Fallibilism [2011], 'Closure') | |
| A reaction: It seems perfectly reasonably to describe oneself as a 'fallibilist dogmatist' (perhaps from the Pope?), or a 'fallibilist sceptic' (perhaps from Peter Unger?), so this idea sounds correct. |
| 19700 | It is best to see the fallibility in the reasons, rather than in the agents or the knowledge [Dougherty] |
| Full Idea: It seems best to take fallible reasons as the basic notion of fallibilism. So fallible knowers are agents who know what they know on the basis of fallible reasons. Fallible knowledge will be knowledge on basis of fallible reasons. | |
| From: Trent Dougherty (Fallibilism [2011], 'Cognates') | |
| A reaction: This is because an ideal knower would be compelled by the evidence, so if fallibilism is universal it must reside in the evidence and not in the knower (bottom p.131). |
| 19702 | We can't normally say that we know something 'but it might be false' [Dougherty] |
| Full Idea: It will ordinarily be conversationally inappropriate to say 'I know that p, but p might be false' even if it is true, since this would mislead an interlocutor to infer that that possibility was an epistemically significant one. | |
| From: Trent Dougherty (Fallibilism [2011], 'Epistemic') | |
| A reaction: This seems to imply hypocrisy when a fallibilist philosopher claims (in non-philosophical company) to know something. Fair enough. Philosophers are in a permanent state of hypocrisy about what they are really thinking. That's the fun of it. |