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. |
| 13342 | Carnap defined consequence by contradiction, but this is unintuitive and changes with substitution [Tarski on Carnap] |
| Full Idea: Carnap proposed to define consequence as 'sentence X follows from the sentences K iff the sentences K and the negation of X are contradictory', but 1) this is intuitively impossible, and 2) consequence would be changed by substituting objects. | |
| From: comment on Rudolph Carnap (The Logical Syntax of Language [1934], p.88-) by Alfred Tarski - The Concept of Logical Consequence p.414 | |
| A reaction: This seems to be the first step in the ongoing explicit discussion of the nature of logical consequence, which is now seen by many as the central concept of logic. Tarski brings his new tool of 'satisfaction' to bear. |
| 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) |
| 13251 | Each person is free to build their own logic, just by specifying a syntax [Carnap] |
| Full Idea: In logic, there are no morals. Everyone is at liberty to build his own logic, i.e. his own form of language. All that is required is that he must state his methods clearly, and give syntactical rules instead of philosophical arguments. | |
| From: Rudolph Carnap (The Logical Syntax of Language [1934], §17), quoted by JC Beall / G Restall - Logical Pluralism 7.3 | |
| A reaction: This is understandable, but strikes me as close to daft relativism. If I specify a silly logic, I presume its silliness will be obvious. By what criteria? I say the world dictates the true logic, but this is a minority view. |
| 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) |
| 22252 | Capitalism may actually be the best way to foster community [Conway,D] |
| Full Idea: Not only is there no good reason for supposing capitalism inimical to community, but there is reason to think it more conducive to community than the feasible alternatives to it. | |
| From: David Conway (Capitalism and Community [1996], I) | |
| A reaction: Conway is defending an obviously unorthodox view, while attacking the hopes of communitarians. |
| 22253 | Capitalism is just the market, with optional limited government, and perhaps democracy [Conway,D] |
| Full Idea: There are three types of capitalism: 1) the market - private ownership, labor contracts and profit, 2) limited government - the state provides goods the market cannot do, 3) limited government with democracy - with political freedom and elections. | |
| From: David Conway (Capitalism and Community [1996], II) | |
| A reaction: [compressed] I would have thought that capitalism is compatible with a fair degree of workplace democracy, which would make a fourth type. |
| 22256 | Capitalism prefers representative democracy, which avoids community decision-making [Conway,D] |
| Full Idea: By opting for representative rather than direct democracy, capitalism is said to preclude political community, for which the citizens of a state must possess a common will, which needs their direct participation in decisions. | |
| From: David Conway (Capitalism and Community [1996], V) | |
| A reaction: Conway does not accept this claim. I'm beginning to wonder whether the famous British electoral system is actually a capitalist conspiracy against the people. |
| 22255 | Capitalism breaks up extended families, and must then provide welfare for the lonely people [Conway,D] |
| Full Idea: It is said that capitalism encourages the breakup of extended families, which creates the need for extensive state welfare for those indigent members of society who can no longer rely on their own family to take care of them. | |
| From: David Conway (Capitalism and Community [1996], V) | |
| A reaction: Conway does not accept this claim. It seems to simplistic to say that capitalism is the sole culprit. Any rise of mechanisation in agriculture would break up rural extended families. |
| 22257 | Capitalism is anti-community, by only valuing individuals, and breaking up families [Conway,D] |
| Full Idea: Communitarns say capitalism is inimical to family community, because it encourages an individualistic mentality which only values self-fulfilment, and because it demands labour mobility which is disruptive of families. | |
| From: David Conway (Capitalism and Community [1996], VI) | |
| A reaction: Chicken-and-egg with the first one. Small entrepreneurs are individualists who seek their own gain. It is big capitalism that sucks in the others. Traditional community is based on labour-intensive agriculture. |