15 ideas
| 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) |
| 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. |
| 20643 | Consilience is a common groundwork of explanation [Whewell] |
| Full Idea: Consilience is the jumping together of knowledge by the linking of facts and fact-based theory across disciplines to create a common groundwork of explanation. | |
| From: William Whewell (The Philosophy of the Inductive Sciences [1840]), quoted by Peter Watson - Convergence Intro 'United' | |
| A reaction: Apparently this is the first use of the word, which was popularised by E.O. Wilson in recent times. If, as I do, you dream of a final theory, in philosophy as well as in science, then you have to be a fan of consilience. |