13 ideas
| 13831 | Logic is based on transitions between sentences [Prawitz] |
| Full Idea: I agree entirely with Dummett that the right way to answer the question 'what is logic?' is to consider transitions between sentences. | |
| From: Dag Prawitz (Gentzen's Analysis of First-Order Proofs [1974], §04) | |
| A reaction: I always protest at this point that reliance on sentences is speciesism against animals, who are thereby debarred from reasoning. See the wonderful Idea 1875 of Chrysippus. Hacking's basic suggestion seems right. Transition between thoughts. |
| 13827 | Logical consequence isn't a black box (Tarski's approach); we should explain how arguments work [Prawitz] |
| Full Idea: Defining logical consequence in the way Tarski does is a rather meagre result, treating an argument as a black box, observing input and output, while disregarding inner structure. We should define logical consequence on the basis of valid arguments. | |
| From: Dag Prawitz (On the General Idea of Proof Theory [1974], §2) |
| 13825 | Natural deduction introduction rules may represent 'definitions' of logical connectives [Prawitz] |
| Full Idea: With Gentzen's natural deduction, we may say that the introductions represent, as it were, the 'definitions' of the logical constants. The introductions are not literally understood as 'definitions'. | |
| From: Dag Prawitz (Gentzen's Analysis of First-Order Proofs [1974], 2.2.2) | |
| A reaction: [Hacking, in 'What is Logic? §9' says Gentzen had the idea that his rules actually define the constants; not sure if Prawitz and Hacking are disagreeing] |
| 13823 | In natural deduction, inferences are atomic steps involving just one logical constant [Prawitz] |
| Full Idea: In Gentzen's natural deduction, the inferences are broken down into atomic steps in such a way that each step involves only one logical constant. The steps are the introduction or elimination of the logical constants. | |
| From: Dag Prawitz (Gentzen's Analysis of First-Order Proofs [1974], 1.1) |
| 13826 | Model theory looks at valid sentences and consequence, but not how we know these things [Prawitz] |
| Full Idea: In model theory, which has dominated the last decades, one concentrates on logically valid sentences, and what follows logically from what, but one disregards questions concerning how we know these things. | |
| From: Dag Prawitz (On the General Idea of Proof Theory [1974], §1) |
| 24162 | Planck introduced the idea that energy can be quantized [Baggott] |
| Full Idea: By deriving his radiation law, Planck had inadvertently introduced the idea that energy itself could be 'quantized'. | |
| From: Jim Baggott (The Quantum Story: 40 moments [2011], 01) | |
| A reaction: He earlier assumed energy is continuously variable. I presume this means that the older idea of energy is now subsumed into the concept of fields, which are quantized into particles. The powers of nature are found in the fields. |
| 21731 | Fields can be 'scalar', or 'vector', or 'tensor', or 'spinor' [Baggott] |
| Full Idea: Fields can be 'scalar', with no particular direction (pointing, but not pushing or pulling); or 'vector', with a direction (like magnetism, or Newtonian gravity); or 'tensor' (needing further parameters); or 'spinor' (depending on spin orientation). | |
| From: Jim Baggott (Farewell to Reality: fairytale physics [2013], 2 'Quantum') | |
| A reaction: [compressed] So the question is, why do they differ? What is it in the nature of each field the result in a distinctive directional feature? |
| 21730 | A 'field' is a property with a magnitude, distributed across all of space and time [Baggott] |
| Full Idea: A 'field' is defined in terms of the magnitude of some physical property distributed over every point in time and space. | |
| From: Jim Baggott (Farewell to Reality: fairytale physics [2013], 2 'Quantum') | |
| A reaction: If it involves a 'property', normal usage entails that there is some entity which possesses the property. So what's the entity? Eh? Eh? You don't know! Disappointed... |
| 24163 | Free electrons have clouds of virtual particles, arising from field interaction [Baggott] |
| Full Idea: A free electron doesn't simply persist as a point particle travelling along a predetermined, classical path; it is surrounded by a swarm of virtual particles arsising from self-interactions with its own magnetic field. | |
| From: Jim Baggott (The Quantum Story: 40 moments [2011], 19) | |
| A reaction: It seems to me important for amateurs and mere philosophers to hang on to this idea of virtual particles, because they undermine any attempt to impose a macro picture on sub-atomic events. |
| 24161 | Thermodynamics sees nature as a continuous flow of energy, as radiation and as substance [Baggott] |
| Full Idea: Thermodynamics reinforced a vision of nature as one of harmonious flow. Energy, which could be neither created nor destroyed, flowed continuously between radiation and material substance, in themselves unbroken continua. | |
| From: Jim Baggott (The Quantum Story: 40 moments [2011], 01) | |
| A reaction: Interestingly, Einstein's Special Relativity e = mc2 seems to endorse this view, by equation energy and mass. I've always wanted to know what energy is, but no one seems to know. |
| 21732 | The current standard model requires 61 particles [Baggott] |
| Full Idea: The current model requires 61 particles: three generations of two leptons and two flavours of quark, in three different colours (making 24); the anti-particles of all of these (48); 12 force particles (photon, W1, Z0, 8 gluons), and a Higgs boson. | |
| From: Jim Baggott (Farewell to Reality: fairytale physics [2013], 6 n) |
| 24160 | Particle measurements don't seem to reflect their reality [Baggott] |
| Full Idea: It seems that we can no longer assume that the particle properties we measure necessarily reflect or represent the properties of the particles as they really are. | |
| From: Jim Baggott (The Quantum Story: 40 moments [2011], Pref) | |
| A reaction: [He cites a 2006 experiment] This gives an interesting response to the Copenhagen Interpretation - that observers appear to be creating the reality they observe, because they only have 'observations', with no reality to correspond to them. I like it. |
| 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) |