22 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. |
| 19855 | The purpose of society is to protect the rights of liberty, property, security and resistance [Mirabeau/committee] |
| Full Idea: The aim of all political associations is the conservation of the natural and imprescriptible rights of man. These rights are liberty, property, security, and resistance to oppression. | |
| From: Mirabeau and committee (Declaration of the Rights of Man [1789], 02) | |
| A reaction: Radical thinkers will obviously be doubtful about property being on the list, because that entrenches huge inequalities, between peasants and their landlords. Resistance to oppression will bother the likes of Edmund Burke. |
| 19856 | The law expresses the general will, and all citizens can participate [Mirabeau/committee] |
| Full Idea: The law is the expression of the general will. All citizens have the right to take part in person or through their representatives in its formulation. It must be the same for all, whether it protects or whether it punishes. | |
| From: Mirabeau and committee (Declaration of the Rights of Man [1789], 06) | |
| A reaction: Now you are wondering who qualifies as a 'citizen'. Rousseau would have been excited until he found that the citizens could send 'representatives', instead of voting themselves. Rousseau aimed at foundational laws, not all of the laws. |
| 19861 | There is only a constitution if rights are assured, and separation of powers defined [Mirabeau/committee] |
| Full Idea: Any society in which the guarantee of Rights is not assured, nor the separation of Power determined, has no Constitution. | |
| From: Mirabeau and committee (Declaration of the Rights of Man [1789], 16) | |
| A reaction: I wonder if they had Britain in mind with this one? The British latched onto Magna Carta in the early 19th century, because it offered some semblance of a constitution. |
| 19858 | No one should be molested for their opinions, if they do not disturb the established order [Mirabeau/committee] |
| Full Idea: No man is to be molested on account of his opinions, even his religious opinions, provided that their manifestation does not disturb the public order established by law. | |
| From: Mirabeau and committee (Declaration of the Rights of Man [1789], 10) | |
| A reaction: Virtually any opinion will 'disturb' the established order a little bit, so this gives the option of suppressing quite mild beliefs, on the grounds of their small disturbance. It is still a wonderful proposal, though. |
| 19859 | Free speech is very precious, and everyone may speak and write freely (but take responsibility for it) [Mirabeau/committee] |
| Full Idea: The free communication of thoughts and opinions is one of man's most precious rights. Every citizen may therefore speak, write, and publish freely; except that he shall be responsible for the abuse of that freedom in cases determined by law. | |
| From: Mirabeau and committee (Declaration of the Rights of Man [1789], 11) | |
| A reaction: Wonderful, and very nicely expressed. Tom Paine will have been a huge influence on this clause. |
| 19857 | All citizens are eligible for roles in the state, purely on the basis of merit [Mirabeau/committee] |
| Full Idea: All citizens being equal in the eyes of the law are equally eligible to all honours, offices, and public employments, according to their abilities and without other distinction than that of their virtues and talents. | |
| From: Mirabeau and committee (Declaration of the Rights of Man [1789], 06) | |
| A reaction: This proclamation of meritocracy must have rung bells around the cities of Europe, and was a reason why many people enjoyed being invaded by Napoleon. |
| 19862 | Property is a sacred right, breached only when essential, and with fair compensation [Mirabeau/committee] |
| Full Idea: Since property is an inviolable and sacred right, no man may be deprived of it except when public necessity, lawfully constituted, evidently requires it; and on condition that a just indemnity be paid in advance. | |
| From: Mirabeau and committee (Declaration of the Rights of Man [1789], 17) | |
| A reaction: This covers compulsory purchase orders. Is the ownership of slaves inviolable? Will aristocrats be compensated for the confiscation of their vast estates? |
| 19860 | Everyone must contribute to the state's power and administration, in just proportion [Mirabeau/committee] |
| Full Idea: For the maintenance of public force and the expenses of administration, a common contribution is indispensable. It must be equally apportioned among all citizens according to their abilities. | |
| From: Mirabeau and committee (Declaration of the Rights of Man [1789], 13) | |
| A reaction: Presumably this enshrines graduated income tax, an eighteenth century invention. Could you contribute just by your labour, or by fighting for the army? Those may be greater contributions than mere money. |
| 1513 | The Egyptians were the first to say the soul is immortal and reincarnated [Herodotus] |
| Full Idea: The Egyptians were the first to claim that the soul of a human being is immortal, and that each time the body dies the soul enters another creature just as it is being born. | |
| From: Herodotus (The Histories [c.435 BCE], 2.123.2) |