11 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) |
| 8499 | Nominalists cannot translate 'red resembles pink more than blue' into particulars [Jackson] |
| Full Idea: It is not always possible for nominalists to translate all statements putatively about universals as statements about particulars. It is not possible for 'red is a colour' and 'red resembles pink more than blue' | |
| From: Frank Jackson (Statements about Universals [1977], p.89) | |
| A reaction: His second example strikes me as the biggest challenge facing nominalism. I wish they wouldn't use secondary qualities as examples. I am unconvinced that the existence of universals will improve the explanation. It's a mystery. |
| 8500 | Colour resemblance isn't just resemblance between things; 'colour' must be mentioned [Jackson] |
| Full Idea: Some red things resemble some blue things more than some pink things because of factors other than colour. Nominalists must offer 'anything red colour-resembles anything pink', but that may contain a universal in disguise. | |
| From: Frank Jackson (Statements about Universals [1977], p.90) | |
| A reaction: Hume and Quine are probably right that we spot resemblances instantly, and only articulate the respect of the resemblance at a later stage. |
| 20769 | Sphaerus he was not assenting to the presence of pomegranates, but that it was 'reasonable' [Sphaerus, by Diog. Laertius] |
| Full Idea: When Sphaerus accepted pomegranates from the king, he was accused of assenting to a false presentation, to which Sphaerus replied that what he had assented to was not that they were pomegranates, but that it was reasonable that they were pomegranates. | |
| From: report of Sphaerus (fragments/reports [c.240 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 07.177 | |
| A reaction: He then cited the stoic distinction between a 'graspable' presentation and a 'reasonable' one. This seems a rather helpful response to Dretske's zebra problem. I like the word 'sensible' in epistemology, because animals can be sensible. |