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) |
| 21982 | I only wish I had such eyes as to see Nobody! It's as much as I can do to see real people. [Carroll,L] |
| Full Idea: "I see nobody on the road," said Alice. - "I only wish I had such eyes," the King remarked. ..."To be able to see Nobody! ...Why, it's as much as I can do to see real people." | |
| From: Lewis Carroll (C.Dodgson) (Through the Looking Glass [1886], p.189), quoted by A.W. Moore - The Evolution of Modern Metaphysics 07.7 | |
| A reaction: [Moore quotes this, inevitably, in a chapter on Hegel] This may be a better candidate for the birth of philosophy of language than Frege's Groundwork. |
| 22384 | A 'double effect' is a foreseen but not desired side-effect, which may be forgivable [Foot] |
| Full Idea: 'Double effect' refers to action having an effect aimed at, and also one foreseen but in now way desired. The 'doctrine' is that it is sometimes permissible to bring about by oblique intention what one may not directly intend. | |
| From: Philippa Foot (Abortion and the Doctrine of Double Effect [1967], p.20) | |
| A reaction: Presumably this can only be justified by a trade-off. The unfortunate side effect must be rated as a price worth paying. If the side effect is not foreseen, that is presumably either understandable, or wickedly negligent. No clear rule is possible. |
| 22385 | The doctrine of double effect can excuse an outcome because it wasn't directly intended [Foot] |
| Full Idea: Supporters of double effect say that sometimes it makes a difference to the permissibility of an action involving harm to others that this harm, although foreseen, is not part of the agent's intention. | |
| From: Philippa Foot (Abortion and the Doctrine of Double Effect [1967], p.22) | |
| A reaction: The obvious major case is the direction of wartime bombing raids. Controversial, because how can someone foresee a side effect and yet claim to have no intention to cause it? Isn't it wickedly self-deluding? |
| 22386 | Double effect says foreseeing you will kill someone is not the same as intending it [Foot] |
| Full Idea: The doctrine of double effect offers us a way out [of the trolley problem], insisting that it is one thing to steer towards someone foreseeing that you will kill him, and another to aim at his death as part of your plan. | |
| From: Philippa Foot (Abortion and the Doctrine of Double Effect [1967], p.23) | |
| A reaction: [She has just created her famous Trolley Problem]. Utilitarians must constantly rely on the doctrine of double effect, as they calculate their trade-offs. |
| 22387 | Without double effect, bad men can make us do evil by threatening something worse [Foot] |
| Full Idea: Rejection of the doctrine of double effect puts us hopelessly in the power of bad men. Anyone who wants us to do something we think is wrong has only to threaten that otherwise he himself will do something we think worse. | |
| From: Philippa Foot (Abortion and the Doctrine of Double Effect [1967], p.25) | |
| A reaction: Her example is they will torture five if you don't torture one. Bernard Williams's famous Jim and the Indians is they will shoot twenty if you don't shoot one. Williams aims it at utilitarian calculations. Double effect is highly relevant. |
| 22388 | Double effect seems to rely on a distinction between what we do and what we allow [Foot] |
| Full Idea: The strength of the doctrine of double effect seems to lie in the distinction it makes between what we do (equated with direct intention) and what we allow (thought of as obliquely intended). | |
| From: Philippa Foot (Abortion and the Doctrine of Double Effect [1967], p.25) | |
| A reaction: She objects (nicely), saying her trolley driver 'does' the side-effect killing, and someone might 'allow' an obvious criminal death. There is also an intermediate class of 'brought about', where you set up a killing, but don't do it. |
| 22383 | Abortion is puzzling because we do and don't want the unborn child to have rights [Foot] |
| Full Idea: One reason why most of us feel puzzled about the problem of abortion is that we want, and do not want, to allow to the unborn child the rights that belong to adults and children. | |
| From: Philippa Foot (Abortion and the Doctrine of Double Effect [1967], p.19) | |
| A reaction: We also do and don't want children to have the same rights as adults. Rights should accrue with development and maturity, it seems. No one thinks sperm and egg have rights. Why stop at 'adult'? Superior adults deserve more rights! |