12 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) |
| 22419 | 'I' is a subject in 'I am in pain' and an object in 'I am bleeding' [Wittgenstein, by McGinn] |
| Full Idea: 'I' is used as a subject in 'I am in pain', ....and used as an object in 'I am bleeding'. | |
| From: report of Ludwig Wittgenstein (The Blue and Brown Notebooks [1936], pp. 66-7) by Colin McGinn - Subjective View: sec qualities and indexicals 4 | |
| A reaction: How about 'my wound is painful'? Does that have the logical form of a conversation? This idea is incorrect. Shoemaker (1968) suggests that the subjective use is immune to error, unlike the object use. |
| 6318 | The doctrine of indeterminacy of translation seems implied by the later Wittgenstein [Wittgenstein, by Quine] |
| Full Idea: Perhaps the doctrine of indeterminacy of translation will have little air of paradox for readers familiar with Wittgenstein's latter-day remarks on meaning. | |
| From: report of Ludwig Wittgenstein (The Blue and Brown Notebooks [1936], II.§16 n) by Willard Quine - Word and Object II.§16 n | |
| A reaction: This may be right, and I am inclined to link the names of Wittgenstein and Quine among those who led philosophy up a relativistic and sceptical cul-de-sac for many years. You can think too hard, you know. |
| 16006 | Either Abraham rises higher than universal ethics, or he is a mere murderer [Kierkegaard] |
| Full Idea: Either Abraham was a murderer, or we confront a paradox higher than all mediation. His story therefore contains the teleological suspension of the ethical, and he becomes higher than the universal. If not, he is not a tragic hero or the father of faith. | |
| From: Søren Kierkegaard (Fear and Trembling [1843], p.49) | |
| A reaction: A nice dilemma for Christian thinkers who want to reconcile reason and morality with religion. [SY] |
| 7577 | Abraham was willing to suspend ethics, for a higher idea [Kierkegaard] |
| Full Idea: The story of Abraham (and Isaac) contains a teleological suspension of the ethical. ...In his action he overstepped the ethical altogether, and had a higher idea outside it, in relation to which he suspended it. | |
| From: Søren Kierkegaard (Fear and Trembling [1843], Prob I) | |
| A reaction: My immediate response is to find this proposal very sinister. I can't remotely understand what Abraham's (or God's) 'higher' idea could be that could justify this crime. Maybe ethics is suspended if you are on the beach and a tidal wave arrives? |