18 ideas
| 18776 | Contextual definitions eliminate descriptions from contexts [Linsky,B] |
| Full Idea: A 'contextual' definition shows how to eliminate a description from a context. | |
| From: Bernard Linsky (Quantification and Descriptions [2014], 2) | |
| A reaction: I'm trying to think of an example, but what I come up with are better described as 'paraphrases' than as 'definitions'. |
| 21704 | 'Impredictative' definitions fix a class in terms of the greater class to which it belongs [Linsky,B] |
| Full Idea: The ban on 'impredicative' definitions says you can't define a class in terms of a totality to which that class must be seen as belonging. | |
| From: Bernard Linsky (Russell's Metaphysical Logic [1999], 1) | |
| A reaction: So that would be defining 'citizen' in terms of the community to which the citizen belongs? If you are asked to define 'community' and 'citizen' together, where do you start? But how else can it be done? Russell's Reducibility aimed to block this. |
| 21705 | Reducibility says any impredicative function has an appropriate predicative replacement [Linsky,B] |
| Full Idea: The Axiom of Reducibility avoids impredicativity, by asserting that for any predicate of given arguments defined by quantifying over higher-order functions or classes, there is another co-extensive but predicative function of the same type of arguments. | |
| From: Bernard Linsky (Russell's Metaphysical Logic [1999], 1) | |
| A reaction: Eventually the axiom seemed too arbitrary, and was dropped. Linsky's book explores it. |
| 18774 | Definite descriptions, unlike proper names, have a logical structure [Linsky,B] |
| Full Idea: Definite descriptions seem to have a logical structure in a way that proper names do not. | |
| From: Bernard Linsky (Quantification and Descriptions [2014], 1.1.1) | |
| A reaction: Thus descriptions have implications which plain names do not. |
| 21727 | Definite descriptions theory eliminates the King of France, but not the Queen of England [Linsky,B] |
| Full Idea: The theory of definite descriptions may eliminate apparent commitment to such entities as the present King of France, but certainly not to the present Queen of England. | |
| From: Bernard Linsky (Russell's Metaphysical Logic [1999], 7.3) |
| 21719 | Extensionalism means what is true of a function is true of coextensive functions [Linsky,B] |
| Full Idea: With the principle of extensionality anything true of one propositional functions will be true of every coextensive one. | |
| From: Bernard Linsky (Russell's Metaphysical Logic [1999], 6.3) |
| 21723 | The task of logicism was to define by logic the concepts 'number', 'successor' and '0' [Linsky,B] |
| Full Idea: The problem for logicism was to find definitions of the primitive notions of Peano's theory, number, successor and 0, in terms of logical notions, so that the postulates could then be derived by logic alone. | |
| From: Bernard Linsky (Russell's Metaphysical Logic [1999], 7) | |
| A reaction: Both Frege and Russell defined numbers as equivalence classes. Successor is easily defined (in various ways) in set theory. An impossible set can exemplify zero. The trouble for logicism is this all relies on sets. |
| 21721 | Higher types are needed to distinguished intensional phenomena which are coextensive [Linsky,B] |
| Full Idea: The higher types are needed for intensional phenomena, cases where the same class is picked out by distinct propositional functions. | |
| From: Bernard Linsky (Russell's Metaphysical Logic [1999], 6.4) | |
| A reaction: I take it that in this way 'x is renate' can be distinguished from 'x is cordate', a task nowadays performed by possible worlds. |
| 21703 | Types are 'ramified' when there are further differences between the type of quantifier and its range [Linsky,B] |
| Full Idea: The types is 'ramified' because there are further differences between the type of a function defined in terms of a quantifier ranging over other functions and the type of those other functions, despite the functions applying to the same simple type. | |
| From: Bernard Linsky (Russell's Metaphysical Logic [1999], 1) | |
| A reaction: Not sure I understand this, but it evidently created difficulties for dealing with actual mathematics, and Ramsey showed how you could manage without the ramifications. |
| 21714 | The ramified theory subdivides each type, according to the range of the variables [Linsky,B] |
| Full Idea: The original ramified theory of types ...furthern subdivides each of the types of the 'simple' theory according to the range of the bound variables used in the definition of each propositional function. | |
| From: Bernard Linsky (Russell's Metaphysical Logic [1999], 6) | |
| A reaction: For a non-intiate like me it certainly sounds disappointing that such a bold and neat theory because a tangle of complications. Ramsey and Russell in the 1920s seem to have dropped the ramifications. |
| 21713 | Did logicism fail, when Russell added three nonlogical axioms, to save mathematics? [Linsky,B] |
| Full Idea: It is often thought that Logicism was a failure, because after Frege's contradiction, Russell required obviously nonlogical principles, in order to develop mathematics. The axioms of Reducibility, Infinity and Choice are cited. | |
| From: Bernard Linsky (Russell's Metaphysical Logic [1999], 6) | |
| A reaction: Infinity and Choice remain as axioms of the standard ZFC system of set theory, which is why set theory is always assumed to be 'up to its neck' in ontological commitments. Linsky argues that Russell saw ontology in logic. |
| 21715 | For those who abandon logicism, standard set theory is a rival option [Linsky,B] |
| Full Idea: ZF set theory is seen as a rival to logicism as a foundational scheme. Set theory is for those who have given up the project of reducing mathematics to logic. | |
| From: Bernard Linsky (Russell's Metaphysical Logic [1999], 6.1) | |
| A reaction: Presumably there are other rivals. Set theory has lots of ontological commitments. One could start at the other end, and investigate the basic ontological commitments of arithmetic. I have no idea what those might be. |
| 21729 | Construct properties as sets of objects, or say an object must be in the set to have the property [Linsky,B] |
| Full Idea: Rather than directly constructing properties as sets of objects and proving neat facts about properties by proxy, we can assert biconditionals, such as that an object has a property if and only if it is in a certain set. | |
| From: Bernard Linsky (Russell's Metaphysical Logic [1999], 7.6) | |
| A reaction: Linsky is describing Russell's method of logical construction. I'm not clear what is gained by this move, but at least it is a variant of the usual irritating expression of properties as sets of objects. |
| 20034 | Intentions must be mutually consistent, affirm appropriate means, and fit the agent's beliefs [Bratman, by Wilson/Schpall] |
| Full Idea: Bratman's three main norms of intention are 'internal consistency' (between a person's intentions), 'means-end coherence' (the means must fit the end), and 'consistency with the agent's beliefs' (especially intending to do and believing you won't do). | |
| From: report of Michael Bratman (Intention, Plans, and Practical Reason [1987]) by Wilson,G/Schpall,S - Action 4 | |
| A reaction: These are controversial, but have set the agenda for modern non-reductive discussions of intention. |
| 20033 | Intentions are normative, requiring commitment and further plans [Bratman, by Wilson/Schpall] |
| Full Idea: Intentions involve normative commitments. We settle on intended courses, if there is no reason to reconsider them, and intentions put pressure on us to form further intentions in order to more efficiently coordinate our actions. | |
| From: report of Michael Bratman (Intention, Plans, and Practical Reason [1987]) by Wilson,G/Schpall,S - Action 4 | |
| A reaction: [a compression of their summary] This distinguishes them from beliefs and desires, which contain no such normative requirements, even though they may point that way. |
| 20026 | Intention is either the aim of an action, or a long-term constraint on what we can do [Bratman, by Wilson/Schpall] |
| Full Idea: We need to distinguish intention as an aim or goal of actions, and intentions as a distinctive state of commitment to future action, a state that results from and subsequently constrains our practical endeavours as planning agents. | |
| From: report of Michael Bratman (Intention, Plans, and Practical Reason [1987]) by Wilson,G/Schpall,S - Action 2 | |
| A reaction: I'm not sure how distinct these are, given the obvious possibility of intermediate stages, and the embracing of any available short-cut. If I could mow my lawn with one blink, I'd do it. |
| 20032 | Bratman rejected reducing intentions to belief-desire, because they motivate, and have their own standards [Bratman, by Wilson/Schpall] |
| Full Idea: Bratman motivated the idea that intentions are psychologically real and not reducible to desire-belief complexes by observing that they are motivationally distinctive, and subject to their own unique standards of rational appraisal. | |
| From: report of Michael Bratman (Intention, Plans, and Practical Reason [1987]) by Wilson,G/Schpall,S - Action 4 | |
| A reaction: If I thought my belief was a bit warped, and my desire morally corrupt, my higher self might refuse to form an intention. If so, then Bratman is onto something. But maybe my higher self has its own beliefs and desires. |
| 7810 | The 'Eumenides' of Aeschylus shows blood feuds replaced by law [Aeschylus, by Grayling] |
| Full Idea: The 'Eumenides' of Aeschylus tells how the old rule of revenge and blood feud was replaced by a due process of law before a civil jury. | |
| From: report of Aeschylus (The Eumenides [c.458 BCE]) by A.C. Grayling - What is Good? Ch.2 | |
| A reaction: Compare Idea 1659, where this revolution is attributed to Protagoras (a little later than Aeschylus). I take the rule of law and of society to be above all the rule of reason, because the aim is calm objectivity instead of emotion. |