32 ideas
| 3123 | Science is in the business of carving nature at the joints [Segal] |
| Full Idea: Science is in the business of carving nature at the joints. | |
| From: Gabriel M.A. Segal (A Slim Book about Narrow Content [2000], 5) |
| 3125 | Psychology studies the way rationality links desires and beliefs to causality [Segal] |
| Full Idea: A person's desires and beliefs tend to cause what they tend to rationalise. This coordination of causality and rationalisation lies at the heart of psychology. | |
| From: Gabriel M.A. Segal (A Slim Book about Narrow Content [2000], 5.3) |
| 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. |
| 3105 | Is 'Hesperus = Phosphorus' metaphysically necessary, but not logically or epistemologically necessary? [Segal] |
| Full Idea: It is metaphysically necessary that Hesperus is Phosphorus, but not logically necessary, since logical deduction could not reveal its truth, and it is not epistemologically necessary, as the ancient Greeks didn't know the identity. (Natural necessity?) | |
| From: Gabriel M.A. Segal (A Slim Book about Narrow Content [2000], 1.6) |
| 3106 | If claims of metaphysical necessity are based on conceivability, we should be cautious [Segal] |
| Full Idea: Since conceivability is the chief method of assessing the claims of metaphysical necessity, I think such claims are incautious. | |
| From: Gabriel M.A. Segal (A Slim Book about Narrow Content [2000], 1.6) |
| 3061 | Anaxarchus said that he was not even sure that he knew nothing [Anaxarchus, by Diog. Laertius] |
| Full Idea: Anaxarchus said that he was not even sure that he knew nothing. | |
| From: report of Anaxarchus (fragments/reports [c.340 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 09.10.1 |
| 3113 | The success and virtue of an explanation do not guarantee its truth [Segal] |
| Full Idea: The success and virtue of an explanation do not guarantee its truth. | |
| From: Gabriel M.A. Segal (A Slim Book about Narrow Content [2000], 2.2) |
| 3112 | Folk psychology is ridiculously dualist in its assumptions [Segal] |
| Full Idea: Commonsense psychology is a powerful explanatory theory, and largely correct, but it seems to be profoundly dualist, and treats minds as immaterial spirits which can transmigrate and exist disembodied. | |
| From: Gabriel M.A. Segal (A Slim Book about Narrow Content [2000], 2.2) | |
| A reaction: Fans of folk psychology tend to focus on central normal experience, but folk psychology also seems to range from quirky to barking mad. A 'premonition' is a widely accepted mental event. |
| 3108 | If 'water' has narrow content, it refers to both H2O and XYZ [Segal] |
| Full Idea: My view is that the concepts of both the Earth person and the Twin Earth person refer to BOTH forms of diamonds or water (H2O and XYZ). | |
| From: Gabriel M.A. Segal (A Slim Book about Narrow Content [2000], 1.7) | |
| A reaction: Fair enough, though that seems to imply that my current concepts may actually refer to all sorts of items of which I am currently unaware. But that may be so. |
| 3110 | Humans are made of H2O, so 'twins' aren't actually feasible [Segal] |
| Full Idea: Humans are largely made of H2O, so there could be no twin on Twin Earth, and (as Kuhn noted) nothing with a significantly different structure from H2O could be macroscopically very like water (but topaz and citrine will do). | |
| From: Gabriel M.A. Segal (A Slim Book about Narrow Content [2000], 2.1) | |
| A reaction: A small point, but one that appeals to essentialists like me (see under Natural Theory/Laws of Nature). We can't learn much metaphysics from impossible examples. |
| 3124 | Externalists can't assume old words refer to modern natural kinds [Segal] |
| Full Idea: The question of what a pre-scientific term extends over is extremely difficult for a Putnam-style externalist to answer. …There seems no good reason to assume that they extend over natural kinds ('whale', 'cat', 'water'). | |
| From: Gabriel M.A. Segal (A Slim Book about Narrow Content [2000], 5.1) | |
| A reaction: The assumption seems to be that they used to extend over descriptions, and now they extend over essences, or expert references. This can't be right. They have never changed, but now contain fewer errors. |
| 3111 | Externalism can't explain concepts that have no reference [Segal] |
| Full Idea: Empty terms and concepts provide the largest problem for the externalist thesis of the world dependence of concepts. | |
| From: Gabriel M.A. Segal (A Slim Book about Narrow Content [2000], 2.2) | |
| A reaction: A speculative concept could then become a reality (e.g. an invention). The solution seems to be to say that there is an internal and an external component to most concepts. |
| 3109 | If content is external, so are beliefs and desires [Segal] |
| Full Idea: If we accept Putnam's externalist conclusion about the meaning of a word, it is a short step to a similar conclusion about the contents of the twins' beliefs, desires and so on. | |
| From: Gabriel M.A. Segal (A Slim Book about Narrow Content [2000], 2.1) | |
| A reaction: This is the key step which has launched a whole new externalist view of the nature of the mind. It is one thing to say that I don't quite know what my words mean, another that I don't know my own beliefs. |
| 3104 | Must we relate to some diamonds to understand them? [Segal] |
| Full Idea: Is a relationship with diamonds necessary for having a concept of diamonds? | |
| From: Gabriel M.A. Segal (A Slim Book about Narrow Content [2000], 1.4) | |
| A reaction: Probably not, given that I have a concept of kryptonite, and that I can invent my own concepts. Suppose I was brought up to believe that diamonds are a myth? |
| 3116 | Maybe experts fix content, not ordinary users [Segal] |
| Full Idea: Putnam and Burge claim that there could be two words that a misinformed subject uses to express different concepts, but that express just one concept of the experts. | |
| From: Gabriel M.A. Segal (A Slim Book about Narrow Content [2000], 3.2) | |
| A reaction: This pushes the concept outside the mind of the user, which leaves an ontological problem of what concepts are made of, how you individuate them, and where they are located. |
| 3117 | Concepts can survive a big change in extension [Segal] |
| Full Idea: We need to think of concepts as organic entities that can persist through changes of extension. | |
| From: Gabriel M.A. Segal (A Slim Book about Narrow Content [2000], 3.3) | |
| A reaction: This would be 'organic' in the sense of modifying and growing. This is exactly right, and the interesting problem becomes the extreme cases, where an individual stretches a concept a long way. |
| 3103 | Maybe content involves relations to a language community [Segal] |
| Full Idea: It has been argued (e.g. by Tyler Burge) that certain relations to other language users are determinants of content. | |
| From: Gabriel M.A. Segal (A Slim Book about Narrow Content [2000], 1.4) | |
| A reaction: Burge's idea (with Wittgenstein behind him) strikes me as plausible (more plausible than water and elms determining the content). Our concepts actually shift during conversations. |
| 3121 | If content is narrow, my perfect twin shares my concepts [Segal] |
| Full Idea: To say that contents of my belief are narrow is to say that they are intrinsic to me, hence that any perfect twin of mine would have beliefs with the same contents. | |
| From: Gabriel M.A. Segal (A Slim Book about Narrow Content [2000], 5) | |
| A reaction: I personally find this more congenial than externalism. If my twin and I studied chemistry, we would reach identical conclusions about water, as long as we remained perfect twins. |
| 3118 | If thoughts ARE causal, we can't explain how they cause things [Segal] |
| Full Idea: If we identify a psychological property with its causal role then we lose the obvious explanation of why the event has the causal role that it has. | |
| From: Gabriel M.A. Segal (A Slim Book about Narrow Content [2000], 4.1) | |
| A reaction: This pinpoints very nicely one of the biggest errors in modern philosophy. There are good naturalistic reasons to reduce everything to causal role, but there is a deeper layer. Essences! |
| 3119 | Even 'mass' cannot be defined in causal terms [Segal] |
| Full Idea: We can't define mass in terms of its causal powers because massive objects do different things in different physical systems. …What an object (or concept) with a given property does depends on what it interacts with. | |
| From: Gabriel M.A. Segal (A Slim Book about Narrow Content [2000], 4.1) | |
| A reaction: This leaves an epistemological problem, that we believe in mass, but can only get at it within a particular gravitational or inertial system. Don't give up on ontology at this point. |