16 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) |
| 9455 | Maybe proper names have the content of fixing a thing's category [Bealer] |
| Full Idea: Some say that proper names have no descriptive content, but others think that although a name does not have the right sort of descriptive content which fixes a unique referent, it has a content which fixes the sort or category to which it belongs. | |
| From: George Bealer (Propositions [1998], §7) | |
| A reaction: Presumably 'Mary', and 'Felix', and 'Rover', and 'Smallville' are cases in point. There is a well known journalist called 'Manchester', a famous man called 'Hilary', a village in Hertfordshire called 'Matching Tie'... Interesting, though. |
| 9454 | The four leading theories of definite descriptions are Frege's, Russell's, Evans's, and Prior's [Bealer] |
| Full Idea: The four leading theories of definite descriptions are Frege's, Russell's, Evans's, and Prior's, ...of which to many Frege's is the most intuitive of the four. Frege says they refer to the unique item (if it exists) which satisfies the predicate. | |
| From: George Bealer (Propositions [1998], §5) | |
| A reaction: He doesn't expound the other three, but I record this a corrective to the view that Russell has the only game in town. |
| 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) |
| 7751 | Meaning needs an intention to induce a belief, and a recognition that this is the speaker's intention [Grice] |
| Full Idea: For a statement to have (non-naturally) meant something, not merely must it have been 'uttered' with the intention of inducing a certain belief, but also the utterer must have intended an 'audience' to recognise the intention behind the utterance. | |
| From: H. Paul Grice (Meaning [1957], p.43) | |
| A reaction: This is Grice's famous and distinctive theory of meaning. I am struck by the problem of a password, which seems to have a quite different intention from its literal meaning. Also a speaker with two different audiences and opposite intentions. |
| 7752 | Only the utterer's primary intention is relevant to the meaning [Grice] |
| Full Idea: Only what I may call the primary intention of an utterer is relevant to the (non-natural) meaning of an utterance. | |
| From: H. Paul Grice (Meaning [1957], p.47) | |
| A reaction: This sounds okay for simple statements, but gets really tricky with complex statements, such as very ironic remarks delivered to an audience of diverse people. |
| 7753 | We judge linguistic intentions rather as we judge non-linguistic intentions, so they are alike [Grice] |
| Full Idea: To show that the criteria for judging linguistic intentions are very like the criteria for judging non-linguistic intentions is to show that linguistic intentions are very like non-linguistic intentions. | |
| From: H. Paul Grice (Meaning [1957], p.48) | |
| A reaction: This hint at the end of his paper is one of the key attractions of Grice's view. It offers an account of language that fits it into the world of animal communication and evolution. It never seems to quite capture the way meaning goes beyond intentions. |
| 9453 | Sentences saying the same with the same rigid designators may still express different propositions [Bealer] |
| Full Idea: The propositions behind 'Cicero is emulated more than Tully' seems to differ somehow from 'Tully is emulated more than Cicero', despite the proper names being rigid designators. | |
| From: George Bealer (Propositions [1998], §1) | |
| A reaction: Interesting, because this isn't a directly propositional attitude situation like 'believes', though it depends on such things. Bealer says this is a key modern difficulty with propositions. |
| 9452 | Propositions might be reduced to functions (worlds to truth values), or ordered sets of properties and relations [Bealer] |
| Full Idea: The reductionist view of propositions sees them as either extensional functions from possible worlds to truth values, or as ordered sets of properties, relations, and perhaps particulars. | |
| From: George Bealer (Propositions [1998], §1) | |
| A reaction: The usual problem of all functional accounts is 'what is it about x that enables it to have that function?' And if they are sets, where does the ordering come in? A proposition isn't just a list of items in some particular order. Both wrong. |
| 9451 | Modal logic and brain science have reaffirmed traditional belief in propositions [Bealer] |
| Full Idea: Philosophers have been skeptical about abstract objects, and so have been skeptical about propositions,..but with the rise of modal logic and metaphysics, and cognitive science's realism about intentional states, traditional propositions are now dominant. | |
| From: George Bealer (Propositions [1998], §1) | |
| A reaction: I personally strongly favour belief in propositions as brain states, which don't need a bizarre ontological status, but are essential to explain language, reasoning and communication. |