34 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. |
| 6005 | Animals are dangerous and nourishing, and can't form contracts of justice [Hermarchus, by Sedley] |
| Full Idea: Hermarchus said that animal killing is justified by considerations of human safety and nourishment and by animals' inability to form contractual relations of justice with us. | |
| From: report of Hermarchus (fragments/reports [c.270 BCE]) by David A. Sedley - Hermarchus | |
| A reaction: Could the last argument be used to justify torturing animals? Or could we eat a human who was too brain-damaged to form contracts? |
| 21181 | Relativity and Quantum theory give very different accounts of forces [Hesketh] |
| Full Idea: General Relativity and quantum mechanics are the two great theories in physics today but they give two very different ideas for how forces work. | |
| From: Gavin Hesketh (The Particle Zoo [2016], 01) | |
| A reaction: Relativity says it is space curvature, and quantum theory says it is particle exchange? But is there a Relativity account of the strong nuclear force? |
| 21183 | Thermodynamics introduced work and entropy, to understand steam engine efficiency [Hesketh] |
| Full Idea: The Laws of Thermodynamics introduced the concepts of entropy and work; put simply, how much useful energy you can really get out of a steam engine. | |
| From: Gavin Hesketh (The Particle Zoo [2016], 03) | |
| A reaction: The point of science by this stage was to introduce measurable and quantifiable concepts |
| 21191 | Photons are B and W° bosons, linked by the Higgs mechanism [Hesketh] |
| Full Idea: The photon is actually a mix of two deeper things, the B and the W°, tied together by the Higgs mechanism. | |
| From: Gavin Hesketh (The Particle Zoo [2016], 06) | |
| A reaction: The B (for 'Boson') transmits a force associated with the 'winding symmetry'. (I record this without properly understanding it.) |
| 21199 | Spinning electric charge produces magnetism, so all fermions are magnets [Hesketh] |
| Full Idea: The muon, like all fermions, spins - and because a spinning electric charge generates a magnetic field all fermions act like tiny bar magnets. | |
| From: Gavin Hesketh (The Particle Zoo [2016], 11) |
| 21189 | Electrons may have smaller components, bound by a new force [Hesketh] |
| Full Idea: Quarks, leptons or bosons may actually be made up of something even smaller, bound together by a conjectural new force. | |
| From: Gavin Hesketh (The Particle Zoo [2016], 05) | |
| A reaction: Electrons are a type of lepton. Compare Idea 21180, from the same book. If electrons are not fundamental, what matters is not some 'stuff' they are made of, but a different force that would bind the ingredients. |
| 21180 | Electrons are fundamental and are not made of anything; they are properties without size [Hesketh] |
| Full Idea: As far as we can tell, electrons (and quarks) are fundamental. They are not small lumps of material, because we could always ask what the material is. The electron just ...is. They are collections of properties, with no apparent size. | |
| From: Gavin Hesketh (The Particle Zoo [2016], 01) | |
| A reaction: This idea from physics HAS to be of interest to philosophers! The bundle theory is discredited for normal objects and for minds, and so is the substrate idea for supporting properties. But rigorous physics accepts a bundle theory. |
| 21182 | Quantum mechanics is our only theory, and is very precise, and repeatedly confirmed [Hesketh] |
| Full Idea: Quantum mechanics is the only working description of the universe that we have. It is amazingly precise, and so far every experimental test has verified its predictions. | |
| From: Gavin Hesketh (The Particle Zoo [2016], 02) | |
| A reaction: I take it from this that quantum mechanics is simply TRUE. Get over it! It will never turn out to be wrong, but may be subsumed within some more fine-grained or extensive theory. |
| 21184 | Physics was rewritten to explain stable electron orbits [Hesketh] |
| Full Idea: Explaining the stable electron orbits would require a complete rewriting of the physics of subatomic particles. | |
| From: Gavin Hesketh (The Particle Zoo [2016], 03) | |
| A reaction: This really looks like a simple and major landmark moment. You can ignore a single anomaly, but not a central feature of your entire theory. |
| 21187 | Virtual particles can't be measured, and can ignore the laws of physics [Hesketh] |
| Full Idea: We can never measure these virtual (transitory) particles directly, and it turns out that they don't even have to obey the laws of physics. | |
| From: Gavin Hesketh (The Particle Zoo [2016], 05) | |
| A reaction: These seems to be the real significance of the Uncertainty Principle. Such particles 'borrow' huge amounts of energy for very short times. |
| 21185 | Colour charge is positive or negative, and also has red, green or blue direction [Hesketh] |
| Full Idea: Colour charge is 'three-dimensional'. As well as the charge having a positive or negative sign, it can also have a direction, and for convenience these three different directions (pointing like a weather vane) are labelled 'red', 'green' and 'blue'. | |
| From: Gavin Hesketh (The Particle Zoo [2016], 04) |
| 21194 | The Standard Model omits gravity, because there are no particles involved [Hesketh] |
| Full Idea: Gravity is not included in the Standard Model because we simply cannot study it using particles. | |
| From: Gavin Hesketh (The Particle Zoo [2016], 09) | |
| A reaction: I'm guessing that Einstein describes how gravity behaves, but not what it is. |
| 21195 | In Supersymmetry the Standard Model simplifies at high energies [Hesketh] |
| Full Idea: Supersymmetry suggest that the Standard Model becomes much simpler at high energies. | |
| From: Gavin Hesketh (The Particle Zoo [2016], 10) |
| 21197 | Standard Model forces are one- two- and three-dimensional [Hesketh] |
| Full Idea: The forces in the Standard Model are built on gauge symmetries, with a one-dimensional charge (like electromagnetism), a two-dimensional charge (the weak force), and a three dimensional charge (the strong force). | |
| From: Gavin Hesketh (The Particle Zoo [2016], 10) | |
| A reaction: See also Idea 21185. |
| 21188 | Quarks and leptons have a weak charge, for the weak force [Hesketh] |
| Full Idea: For the weak force there must be a corresponding 'weak charge', and all the fermions, all the quarks and leptons carry it. | |
| From: Gavin Hesketh (The Particle Zoo [2016], 05) | |
| A reaction: So electrons carry a weak charge, as well as an electromagnetic charge. Like owning several passports. |
| 21186 | Quarks rush wildly around in protons, restrained by the gluons [Hesketh] |
| Full Idea: Inside a proton the quarks are rushing around like caged animals, free to move until they push against the bars to try to escape, when the gluons pull them back in. | |
| From: Gavin Hesketh (The Particle Zoo [2016], 04) |
| 21192 | Neutrinos only interact with the weak force, but decays produce them in huge numbers [Hesketh] |
| Full Idea: Neutrinos only interact with the weak force, which means they barely interact at all, but because the weak force is crucial in the decays of so many other particles, neutrinos are still produced in huge numbers. | |
| From: Gavin Hesketh (The Particle Zoo [2016], 08) | |
| A reaction: They only interact with the W and Z bosons. |
| 21196 | To combine the forces, they must all be the same strength at some point [Hesketh] |
| Full Idea: If all the forces are to combine, at some point they must all be the same strength, and Supersymmetry (SuSy) makes this happen. | |
| From: Gavin Hesketh (The Particle Zoo [2016], 10) | |
| A reaction: This sounds like an impressive reason for favouring supersymmetry - as long as you have an a priori preference for everything combining. |
| 21190 | 'Space' in physics just means location [Hesketh] |
| Full Idea: 'Space' in physics really just means location. | |
| From: Gavin Hesketh (The Particle Zoo [2016], 06) | |
| A reaction: Location can, of course, only be specified relative to something else. Space is really an abstraction, but at least it means there is some sort of background to locate all the fundamental fields. |
| 21193 | The universe is 68% dark energy, 27% dark matter, 5% regular matter [Hesketh] |
| Full Idea: The most precise surveys of the stars and galaxies tell us that the universe is made up of 68% dark energy, 27% dark matter, and just 5% regular matter (the stuff of the Standard Model of particle physics). | |
| From: Gavin Hesketh (The Particle Zoo [2016], 09) | |
| A reaction: Regular matter - that's me, that is. |
| 21198 | If a cosmic theory relies a great deal on fine-tuning basic values, it is probably wrong [Hesketh] |
| Full Idea: If a theory has to rely on excessive 'fine-tuning', a series of extremely unlikely events in order to produce the universe we see around us, then it is extremely unlikely that this theory is correct. | |
| From: Gavin Hesketh (The Particle Zoo [2016], 10) | |
| A reaction: He says the Standard Model has 26 parameters which are only known by experiment, rather than by theory. So instead of saying '...so there is a God', we should say '...so our theory isn't very good'. |