12 ideas
| 17950 | The logos enables us to track one particular among a network of objects [Nehamas] |
| Full Idea: The logos (the definition) is a summary statement of the path within a network of objects that one will have to follow in order to locate a particular member of that network. | |
| From: Alexander Nehamas (Episteme and Logos in later Plato [1984], p.234) | |
| A reaction: I like this because it confirms that Plato (as well as Aristotle) was interested in the particulars rather than in the kinds (which I take to be general truths about particulars). |
| 17951 | A logos may be short, but it contains reference to the whole domain of the object [Nehamas] |
| Full Idea: A thing's logos, apparently short as it may be, is implicitly a very rich statement since it ultimately involves familiarity with the whole domain to which that particular object belongs. | |
| From: Alexander Nehamas (Episteme and Logos in later Plato [1984], p.234) | |
| A reaction: He may be wrong that the logos is short, since Aristotle (Idea 12292) says a definition can contain many assertions. |
| 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) |
| 4053 | If it is desirable that a given patient die, then moral objections to killing them do not apply [Rachels] |
| Full Idea: The cause of death (injection or disease) is important from the legal point of view, but not morally. If euthanasia is desirable in a given case then the patient's death is not an evil, so the usual objections to killing do not apply. | |
| From: James Rachels (No Moral Difference [1975], p.102) | |
| A reaction: Seems reasonable, but a very consequentialist view. Is it good that small children should clean public toilets? |
| 4052 | It has become normal to consider passive euthanasia while condemning active euthanasia [Rachels] |
| Full Idea: It seems to have become accepted that passive euthanasia (by withholding treatment and allowing a patient to die) may be acceptable, whereas active euthanasia (direct action to kill the patient) is never acceptable. | |
| From: James Rachels (No Moral Difference [1975], p.97) | |
| A reaction: He goes on to attack the distinction. It is hard to distinguish the two cases, as well as being hard to judge them. |