25 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) |
| 17963 | The facts of geometry, arithmetic or statics order themselves into theories [Hilbert] |
| Full Idea: The facts of geometry order themselves into a geometry, the facts of arithmetic into a theory of numbers, the facts of statics, electrodynamics into a theory of statics, electrodynamics, or the facts of the physics of gases into a theory of gases. | |
| From: David Hilbert (Axiomatic Thought [1918], [03]) | |
| A reaction: This is the confident (I would say 'essentialist') view of axioms, which received a bit of a setback with Gödel's Theorems. I certainly agree that the world proposes an order to us - we don't just randomly invent one that suits us. |
| 17966 | Axioms must reveal their dependence (or not), and must be consistent [Hilbert] |
| Full Idea: If a theory is to serve its purpose of orienting and ordering, it must first give us an overview of the independence and dependence of its propositions, and second give a guarantee of the consistency of all of the propositions. | |
| From: David Hilbert (Axiomatic Thought [1918], [09]) | |
| A reaction: Gödel's Second theorem showed that the theory can never prove its own consistency, which made the second Hilbert requirement more difficult. It is generally assumed that each of the axioms must be independent of the others. |
| 17967 | To decide some questions, we must study the essence of mathematical proof itself [Hilbert] |
| Full Idea: It is necessary to study the essence of mathematical proof itself if one wishes to answer such questions as the one about decidability in a finite number of operations. | |
| From: David Hilbert (Axiomatic Thought [1918], [53]) |
| 17965 | The whole of Euclidean geometry derives from a basic equation and transformations [Hilbert] |
| Full Idea: The linearity of the equation of the plane and of the orthogonal transformation of point-coordinates is completely adequate to produce the whole broad science of spatial Euclidean geometry purely by means of analysis. | |
| From: David Hilbert (Axiomatic Thought [1918], [05]) | |
| A reaction: This remark comes from the man who succeeded in producing modern axioms for geometry (in 1897), so he knows what he is talking about. We should not be wholly pessimistic about Hilbert's ambitious projects. He had to dig deeper than this idea... |
| 17964 | Number theory just needs calculation laws and rules for integers [Hilbert] |
| Full Idea: The laws of calculation and the rules of integers suffice for the construction of number theory. | |
| From: David Hilbert (Axiomatic Thought [1918], [05]) | |
| A reaction: This is the confident Hilbert view that the whole system can be fully spelled out. Gödel made this optimism more difficult. |
| 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) |
| 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. |
| 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. |
| 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? |
| 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. |
| 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. |
| 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. |
| 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. |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice. | |
| From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where? |
| 17968 | By digging deeper into the axioms we approach the essence of sciences, and unity of knowedge [Hilbert] |
| Full Idea: By pushing ahead to ever deeper layers of axioms ...we also win ever-deeper insights into the essence of scientific thought itself, and become ever more conscious of the unity of our knowledge. | |
| From: David Hilbert (Axiomatic Thought [1918], [56]) | |
| A reaction: This is the less fashionable idea that scientific essentialism can also be applicable in the mathematic sciences, centring on the project of axiomatisation for logic, arithmetic, sets etc. |