16 ideas
| 9283 | Our ancient beliefs can never be overthrown by subtle arguments [Euripides] |
| Full Idea: Teiresias: We have no use for theological subtleties./ The beliefs we have inherited, as old as time,/ Cannot be overthrown by any argument,/ Nor by the most inventive ingenuity. | |
| From: Euripides (The Bacchae [c.407 BCE], 201) | |
| A reaction: [trans. Philip Vellacott (Penguin)] Compare Idea 8243. While very conservative societies have amazing resilience in maintaining traditional beliefs, modern culture eats into them, not directly by argument, but by arguments at fifth remove. |
| 18369 | There are at least fourteen candidates for truth-bearers [Kirkham] |
| Full Idea: Among the candidates [for truthbearers] are beliefs, propositions, judgments, assertions, statements, theories, remarks, ideas, acts of thought, utterances, sentence tokens, sentence types, sentences (unspecified), and speech acts. | |
| From: Richard L. Kirkham (Theories of Truth: a Critical Introduction [1992], 2.3) | |
| A reaction: I vote for propositions, but only in the sense of the thoughts underlying language, not the Russellian things which are supposed to exist independently from thinkers. |
| 19318 | A 'sequence' of objects is an order set of them [Kirkham] |
| Full Idea: A 'sequence' of objects is like a set of objects, except that, unlike a set, the order of the objects is important when dealing with sequences. ...An infinite sequence satisfies 'x2 is purple' if and only if the second member of the sequence is purple. | |
| From: Richard L. Kirkham (Theories of Truth: a Critical Introduction [1992], 5.4) | |
| A reaction: This explains why Tarski needed set theory in his metalanguage. |
| 19319 | If one sequence satisfies a sentence, they all do [Kirkham] |
| Full Idea: If one sequence satisfies a sentence, they all do. ...Thus it matters not whether we define truth as satisfaction by some sequence or as satisfaction by all sequences. | |
| From: Richard L. Kirkham (Theories of Truth: a Critical Introduction [1992], 5.4) | |
| A reaction: So if the striker scores a goal, the team has scored a goal. |
| 19320 | If we define truth by listing the satisfactions, the supply of predicates must be finite [Kirkham] |
| Full Idea: Because the definition of satisfaction must have a separate clause for each predicate, Tarski's method only works for languages with a finite number of predicates, ...but natural languages have an infinite number of predicates. | |
| From: Richard L. Kirkham (Theories of Truth: a Critical Introduction [1992], 5.5) | |
| A reaction: He suggest predicates containing natural numbers, as examples of infinite predicates. Davidson tried to extend the theory to natural languages, by (I think) applying it to adverbs, which could generate the infinite predicates. Maths has finite predicates. |
| 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. |
| 19315 | In quantified language the components of complex sentences may not be sentences [Kirkham] |
| Full Idea: In a quantified language it is possible to build new sentences by combining two expressions neither of which is itself a sentence. | |
| From: Richard L. Kirkham (Theories of Truth: a Critical Introduction [1992], 5.4) | |
| A reaction: In propositional logic the components are other sentences, so the truth value can be given by their separate truth-values, through truth tables. Kirkham is explaining the task which Tarski faced. Truth-values are not just compositional. |
| 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. |
| 19317 | An open sentence is satisfied if the object possess that property [Kirkham] |
| Full Idea: An object satisfies an open sentence if and only if it possesses the property expressed by the predicate of the open sentence. | |
| From: Richard L. Kirkham (Theories of Truth: a Critical Introduction [1992], 5.4) | |
| A reaction: This applies to atomic sentence, of the form Fx or Fa (that is, some variable is F, or some object is F). So strictly, only the world can decide whether some open sentence is satisfied. And it all depends on things called 'properties'. |
| 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) |
| 19322 | Why can there not be disjunctive, conditional and negative facts? [Kirkham] |
| Full Idea: It has been said that there are no disjunctive facts, conditional facts, or negative facts. ...but it is not at all clear why there cannot be facts of this sort. | |
| From: Richard L. Kirkham (Theories of Truth: a Critical Introduction [1992], 5.6) | |
| A reaction: I love these sorts of facts, and offer them as a naturalistic basis for logic. You probably need the world to have modal features, but I have those in the form of powers and dispositions. |