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) |
| 7346 | Jeremiah implied a link between weakness and goodness, and the evil of the state [Jeremiah, by Johnson,P] |
| Full Idea: Jeremiah was the first to perceive the possibility that powerlessness and goodness were somehow linked; ...he comes close to the notion that the state itself was inherently evil. | |
| From: report of Jeremiah (24: Book of Jeremiah [c.570 BCE]) by Paul Johnson - The History of the Jews Pt II | |
| A reaction: This looks like the first seeds of the anarchist idea. You abandon the state for something 'higher'. 'Perceive' rather begs the question of whether he is right. This is the full 'inversion of values' of Nietzsche. |
| 22920 | Do I not fill heaven and earth? saith the Lord [Jeremiah] |
| Full Idea: Can any hide himself in secret places that I shall not see him? saith the Lord. Do I not fill heaven and earth? | |
| From: Jeremiah (24: Book of Jeremiah [c.570 BCE], 23:24), quoted by Robin Le Poidevin - Travels in Four Dimensions 03 'Where' | |
| A reaction: If the Lord is omnipresent, then He must be present in each one of us. But does the Lord interact with each of us? |
| 7902 | The Buddha made flowers float in the air, to impress people, and make them listen [Mahavastu] |
| Full Idea: When the young Brahmin threw her two lotuses, they stood suspended in the air. This was one of the miracles by which the Buddhas impress people, to make them listen to the truth. | |
| From: Mahavastu (The Great Event [c.200], I.231-9) | |
| A reaction: Presumably this is the reason that Jesus did miracles. It is hard to spot the truth among the myriad of lies, if there is no supporting miracle to give authority to the speaker. |
| 22089 | Am I a God afar off, and not a God close at hand? [Jeremiah] |
| Full Idea: Am I a God afar off, and not a God close at hand? Do I not fill heaven and earth? | |
| From: Jeremiah (24: Book of Jeremiah [c.570 BCE], 23:23), quoted by Clare Carlisle - Kierkegaard: a guide for the perplexed 3 | |
| A reaction: I assume this was often quoted by eighteenth century divines, against the rise of deism. |