14 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) |
| 7535 | If all beliefs are propositional, then belief and judgement are the same thing [Monk] |
| Full Idea: Whether the words 'belief' and 'judgement' mean the same thing is a moot point. Traditionally, a judgement is the assent of mind to a proposition. If one thinks that all beliefs are propositional, then beliefs and judgements are the same thing. | |
| From: Ray Monk (Bertrand Russell: Spirit of Solitude [1996], Ch.19 n6) | |
| A reaction: If I think I have put a bit too much toothpaste on my brush, that strikes me as a non-propositional judgement, even though it could be spelled out as a proposition. But it also strikes me as a belief. |
| 22262 | Kant's moral law has no foundation - because that would undermine its priority [Sandel] |
| Full Idea: Given the stringent demands of the Kantian ethic, the moral law would seem almost to require a foundation in nothing, for any empirical precondition would undermine its priority. | |
| From: Michael J. Sandel (Procedural republic and unencumbered self [1984], 'Kantian') | |
| A reaction: The idea of a value with 'a foundation in nothing' is particular anathema to me, because my project is to find a foundation for everything (in nature, which is the Given). Kant's only foundational value seems to be rational consistency. |
| 22264 | Modern liberal rights in democracies protect individuals against the majority [Sandel] |
| Full Idea: Liberty in the modern procedural republic is defined in opposition to democracy, as an individual's guarantee against what the majority might will. | |
| From: Michael J. Sandel (Procedural republic and unencumbered self [1984], 'Present') | |
| A reaction: And so I should hope. Sandel is sort of criticising this view, but it seems obvious that rights of this sort must be basic to any civilised democracy. But how do you decide those rights, if not by a majoritarian decision? |
| 22261 | Liberals say rights always come first, and justice is neutral on social values [Sandel] |
| Full Idea: The liberal claim that the right is prior to the good means that individual rights cannot be sacrificed for the sake of the general good, and that the basic principles of justice cannot be premised on any particular vision of the good life. | |
| From: Michael J. Sandel (Procedural republic and unencumbered self [1984], 'The right') | |
| A reaction: In Rawls, the first thesis is chosen from a neutral position, and the second is all that is needed to affirm rights as basic. These two are the target of Sandel's communitarian claims. Utilitarians will make the sacrifices. No consensus on the good life! |
| 22263 | Liberal justice means the withdrawal of the self, as transcendental or as unencumbered [Sandel] |
| Full Idea: For the liberal concept of justice we must stand to our circumstances always at a certain distance, whether as transcendental subject in the case of Kant, or as unencumbered selves in the case of Rawls. | |
| From: Michael J. Sandel (Procedural republic and unencumbered self [1984], 'Transcendental') | |
| A reaction: Maybe the only way to be unencumbered is to be transcendental. There is an insecure feeling that if the self becomes immanent or encumbered it thereby loses its objective rationality. You wake up one morning and find you are a nazi? |
| 22805 | Liberalism concerns rights, and communitarianism concerns the common good [Sandel, by Avineri/De-Shalit] |
| Full Idea: Sandel argues that liberalism is the politics of rights, while communitarianism is the politics of the common good. | |
| From: report of Michael J. Sandel (Procedural republic and unencumbered self [1984]) by Avineri,S/De-Shalit,A - Intro to 'Communitarianism and Individualism' §4 | |
| A reaction: The first thing on the agenda of the common good should be to assert and protect the rights of individual citizens. How could there be a common good which trampled on individuals? I agree that the common good is prior (e.g. in a pandemic). |