display all the ideas for this combination of texts
13 ideas
| 13845 | The various logics are abstractions made from terms like 'if...then' in English [Hacking] |
| Full Idea: I don't believe English is by nature classical or intuitionistic etc. These are abstractions made by logicians. Logicians attend to numerous different objects that might be served by 'If...then', like material conditional, strict or relevant implication. | |
| From: Ian Hacking (What is Logic? [1979], §15) | |
| A reaction: The idea that they are 'abstractions' is close to my heart. Abstractions from what? Surely 'if...then' has a standard character when employed in normal conversation? |
| 13840 | First-order logic is the strongest complete compact theory with Löwenheim-Skolem [Hacking] |
| Full Idea: First-order logic is the strongest complete compact theory with a Löwenheim-Skolem theorem. | |
| From: Ian Hacking (What is Logic? [1979], §13) |
| 13844 | A limitation of first-order logic is that it cannot handle branching quantifiers [Hacking] |
| Full Idea: Henkin proved that there is no first-order treatment of branching quantifiers, which do not seem to involve any idea that is fundamentally different from ordinary quantification. | |
| From: Ian Hacking (What is Logic? [1979], §13) | |
| A reaction: See Hacking for an example of branching quantifiers. Hacking is impressed by this as a real limitation of the first-order logic which he generally favours. |
| 13842 | Second-order completeness seems to need intensional entities and possible worlds [Hacking] |
| Full Idea: Second-order logic has no chance of a completeness theorem unless one ventures into intensional entities and possible worlds. | |
| From: Ian Hacking (What is Logic? [1979], §13) |
| 6092 | In a logically perfect language, there will be just one word for every simple object [Russell] |
| Full Idea: In a logically perfect language, there will be one word and no more for every simple object. | |
| From: Bertrand Russell (The Philosophy of Logical Atomism [1918], §II) | |
| A reaction: In other words, there would be no universals, only names? All that matters is that a language can successfully refer (unambiguously) to anything it wishes to. There must be better ways than Russell's lexical explosion. |
| 6101 | Romulus does not occur in the proposition 'Romulus did not exist' [Russell] |
| Full Idea: Romulus does not occur in the proposition 'Romulus did not exist'. | |
| From: Bertrand Russell (The Philosophy of Logical Atomism [1918], §VI) | |
| A reaction: A very nice paradoxical assertion, which captures the problem of finding the logical form for negative existential statements. Presumably the proposition refers to the mythical founder of Rome, though. He is not, I suppose, rigidly designated. |
| 13837 | With a pure notion of truth and consequence, the meanings of connectives are fixed syntactically [Hacking] |
| Full Idea: My doctrine is that the peculiarity of the logical constants resides precisely in that given a certain pure notion of truth and consequence, all the desirable semantic properties of the constants are determined by their syntactic properties. | |
| From: Ian Hacking (What is Logic? [1979], §09) | |
| A reaction: He opposes this to Peacocke 1976, who claims that the logical connectives are essentially semantic in character, concerned with the preservation of truth. |
| 13839 | Perhaps variables could be dispensed with, by arrows joining places in the scope of quantifiers [Hacking] |
| Full Idea: For some purposes the variables of first-order logic can be regarded as prepositions and place-holders that could in principle be dispensed with, say by a system of arrows indicating what places fall in the scope of which quantifier. | |
| From: Ian Hacking (What is Logic? [1979], §11) | |
| A reaction: I tend to think of variables as either pronouns, or as definite descriptions, or as temporary names, but not as prepositions. Must address this new idea... |
| 6102 | You can understand 'author of Waverley', but to understand 'Scott' you must know who it applies to [Russell] |
| Full Idea: If you understand English you would understand the phrase 'the author of Waverley' if you had not heard it before, whereas you would not understand the meaning of 'Scott', because to know the meaning of a name is to know who it is applied to. | |
| From: Bertrand Russell (The Philosophy of Logical Atomism [1918], §VI) | |
| A reaction: Actually, you would find 'Waverley' a bit baffling too. Would you understand "he was the author of his own destruction"? You can understand "Homer was the author of this" without knowing quite who 'Homer' applies to. All very tricky. |
| 10423 | There are a set of criteria for pinning down a logically proper name [Russell, by Sainsbury] |
| Full Idea: A logically proper name must be semantically simple, have just one referent, be understood by the user, be scopeless, is not a definite description, and rigidly designates. | |
| From: report of Bertrand Russell (The Philosophy of Logical Atomism [1918], 24th pg) by Mark Sainsbury - The Essence of Reference Intro | |
| A reaction: Famously, Russell's hopes of achieving this logically desirable end got narrower and narrower, and ended with 'this' or 'that'. Maybe pure language can't do the job. |
| 7744 | Treat description using quantifiers, and treat proper names as descriptions [Russell, by McCullogh] |
| Full Idea: Having proposed that descriptions should be treated in quantificational terms, Russell then went on to introduce the subsidiary injunction that proper names should be treated as descriptions. | |
| From: report of Bertrand Russell (The Philosophy of Logical Atomism [1918]) by Gregory McCullogh - The Game of the Name 2.18 | |
| A reaction: McCulloch says Russell 'has a lot to answer for' here. It became a hot topic with Kripke. Personally I find Lewis's notion of counterparts the most promising line of enquiry. |
| 10426 | A name has got to name something or it is not a name [Russell] |
| Full Idea: A name has got to name something or it is not a name. | |
| From: Bertrand Russell (The Philosophy of Logical Atomism [1918], 66th pg), quoted by Mark Sainsbury - The Essence of Reference 18.2 | |
| A reaction: This seems to be stipulative, since most people would say that a list of potential names for a baby counted as names. It may be wrong. There are fictional names, or mistakes. |
| 13843 | If it is a logic, the Löwenheim-Skolem theorem holds for it [Hacking] |
| Full Idea: A Löwenheim-Skolem theorem holds for anything which, on my delineation, is a logic. | |
| From: Ian Hacking (What is Logic? [1979], §13) | |
| A reaction: I take this to be an unusually conservative view. Shapiro is the chap who can give you an alternative view of these things, or Boolos. |