27 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. |
| 4761 | The 'error theory' of morals says there is no moral knowledge, because there are no moral facts [Mackie, by Engel] |
| Full Idea: Mackie's 'error theory' of ethics says that if a fact is something that corresponds to a true proposition, there are actually no moral facts, hence no knowledge of what moral statements are about. | |
| From: report of J.L. Mackie (Ethics: Inventing Right and Wrong [1977]) by Pascal Engel - Truth §4.2 | |
| A reaction: Personally I am inclined to think that there are moral facts (about what nature shows us constitutes a good human being), based on virtue theory. Mackie is a good warning, though, against making excessive claims. You end up like a bad scientist. |
| 1868 | The world was made as much for animals as for man [Celsus] |
| Full Idea: The world was made as much for the irrational animals as for men. | |
| From: Celsus (On the True Doctrine (Against Christians) [c.178], §V) | |
| A reaction: A good remark. It seems to be a classic distortion of European Christianity that the world is made for us, and that animals only exist to fill our sandwiches. |
| 8337 | Some says mental causation is distinct because we can recognise single occurrences [Mackie] |
| Full Idea: It is sometimes suggested that our ability to recognise a single occurrence as an instance of mental causation is a feature which distinguishes mental causation from physical or 'Humean' causation. | |
| From: J.L. Mackie (Causes and Conditions [1965], §9) | |
| A reaction: Hume says regularities are needed for mental causation too. Concentrate hard on causing a lightning flash - 'did I do that?' Gradually recovering from paralysis; you wouldn't just move your leg once, and know it was all right! |
| 8342 | Mackie tries to analyse singular causal statements, but his entities are too vague for events [Kim on Mackie] |
| Full Idea: In spite of Mackie's announced aim of analysing singular causal statements, it is doubtful that the entities that he is concerned with can be consistently interpreted as spatio-temporally bounded individual events. | |
| From: comment on J.L. Mackie (Causes and Conditions [1965]) by Jaegwon Kim - Causes and Events: Mackie on causation §3 | |
| A reaction: This is because Mackie mainly talks about 'conditions'. Nearly every theory I encounter in modern philosophy gets accused of either circular definitions, or inadequate individuation conditions for key components. A tough world for theory-makers. |
| 8343 | Necessity and sufficiency are best suited to properties and generic events, not individual events [Kim on Mackie] |
| Full Idea: Relations of necessity and sufficiency seem best suited for properties and for property-like entities such as generic states and events; their application to individual events and states is best explained as derivative from properties and generic events. | |
| From: comment on J.L. Mackie (Causes and Conditions [1965]) by Jaegwon Kim - Causes and Events: Mackie on causation §4 | |
| A reaction: This seems to suggest that necessity must either derive from laws, or from powers. It is certainly hard to see how you could do Mackie's assessment of necessary and sufficient components, without comparing similar events. |
| 8385 | A cause is part of a wider set of conditions which suffices for its effect [Mackie, by Crane] |
| Full Idea: The details of Mackie's analysis are complex, but the general idea is that the cause is part of a wider set of conditions which suffices for its effect. | |
| From: report of J.L. Mackie (Causes and Conditions [1965]) by Tim Crane - Causation 1.3.3 | |
| A reaction: Helpful. Why does something have to be 'the' cause? Immediacy is a vital part of it. A house could be a 'fire waiting to happen'. Oxygen is an INUS condition for a fire. |
| 8335 | Necessary conditions are like counterfactuals, and sufficient conditions are like factual conditionals [Mackie] |
| Full Idea: A necessary causal condition is closely related to a counterfactual conditional: if no-cause then no-effect, and a sufficient causal condition is closely related to a factual conditional (Goodman's phrase): since cause-here then effect. | |
| From: J.L. Mackie (Causes and Conditions [1965], §4) | |
| A reaction: The 'factual conditional' just seems to be an assertion that causation occurred (dressed up with the logical-sounding 'since'). An important distinction for Lewis. Sufficiency doesn't seem to need possible-worlds talk. |
| 8336 | The INUS account interprets single events, and sequences, causally, without laws being known [Mackie] |
| Full Idea: My account shows how a singular causal statement can be interpreted, and how the corresponding sequence can be shown to be causal, even if the corresponding complete laws are not known. | |
| From: J.L. Mackie (Causes and Conditions [1965], §9) | |
| A reaction: Since the 'complete' laws are virtually never known, it would be a bit much to require that to assert causation. His theory is the 'INUS' account of causal conditions - see Idea 8333. |
| 8333 | A cause is an Insufficient but Necessary part of an Unnecessary but Sufficient condition [Mackie] |
| Full Idea: If a short-circuit causes a fire, the so-called cause is, and is known to be, an Insufficient but Necessary part of a condition which is itself Unnecessary but Sufficient for the result. Let us call this an INUS condition. | |
| From: J.L. Mackie (Causes and Conditions [1965], §1) | |
| A reaction: I'm not clear why it is necessary, given that the fire could have started without the short-circuit. The final situation must certainly be sufficient. If only one situation can cause an effect, then the whole situation is necessary. |
| 8395 | Mackie has a nomological account of general causes, and a subjunctive conditional account of single ones [Mackie, by Tooley] |
| Full Idea: For general causal statements Mackie favours a nomological account, but for singular causal statements he argued for an analysis in terms of subjunctive conditionals. | |
| From: report of J.L. Mackie (Causes and Conditions [1965]) by Michael Tooley - Causation and Supervenience 5.2 | |
| A reaction: These seem to be consistent, by explaining each by placing it within a broader account of reality. Personally I think Ducasse gives the best account of how you get from the particular to the general (via similarity and utility). |
| 8334 | The virus causes yellow fever, and is 'the' cause; sweets cause tooth decay, but they are not 'the' cause [Mackie] |
| Full Idea: We may say not merely that this virus causes yellow fever, but also that it is 'the' cause of yellow fever; but we could only say that sweet-eating causes dental decay, not that it is the cause of dental decay (except in an individual case). | |
| From: J.L. Mackie (Causes and Conditions [1965], §3) | |
| A reaction: A bit confusing, but there seems to be something important here, concerning the relation between singular causation and law-governed causation. 'The' cause may not be sufficient (I'm immune to yellow fever). So 'the' cause is the only necessary one? |
| 1867 | Christians presented Jesus as a new kind of logos to oppose that of the philosophers [Celsus] |
| Full Idea: Christians put forth this Jesus not only as the son of God, but as the very Logos - not the pure and holy Logos known to the philosophers, but a new kind of Logos. | |
| From: Celsus (On the True Doctrine (Against Christians) [c.178], III) |
| 1473 | Is evil an illusion, or a necessary contrast, or uncontrollable, or necessary for human free will? [Mackie, by PG] |
| Full Idea: Perhaps evil is an illusion, or it is necessary for good to exist, or in humans it is required because we have free will, or God lacks the full power to control it, but none of these looks convincing. | |
| From: report of J.L. Mackie (Evil and Omnipotence [1955], §B) by PG - Db (ideas) |
| 1472 | The propositions that God is good and omnipotent, and that evil exists, are logically contradictory [Mackie, by PG] |
| Full Idea: There is a contradiction between the propositions that God is wholly good, God is omnipotent, and evil exists, and one of them has got to give way (assuming good eliminates evil, and omnipotence has no limit). | |
| From: report of J.L. Mackie (Evil and Omnipotence [1955], Pref.) by PG - Db (ideas) |