10 ideas
| 10580 | Mathematics is both necessary and a priori because it really consists of logical truths [Yablo] |
| Full Idea: Mathematics seems necessary because the real contents of mathematical statements are logical truths, which are necessary, and it seems a priori because logical truths really are a priori. | |
| From: Stephen Yablo (Abstract Objects: a Case Study [2002], 10) | |
| A reaction: Yablo says his logicism has a Kantian strain, because numbers and sets 'inscribed on our spectacles', but he takes a different view (in the present Idea) from Kant about where the necessity resides. Personally I am tempted by an a posteriori necessity. |
| 10579 | Putting numbers in quantifiable position (rather than many quantifiers) makes expression easier [Yablo] |
| Full Idea: Saying 'the number of Fs is 5', instead of using five quantifiers, puts the numeral in quantifiable position, which brings expressive advantages. 'There are more sheep in the field than cows' is an infinite disjunction, expressible in finite compass. | |
| From: Stephen Yablo (Abstract Objects: a Case Study [2002], 08) | |
| A reaction: See Hofweber with similar thoughts. This idea I take to be a key one in explaining many metaphysical confusions. The human mind just has a strong tendency to objectify properties, relations, qualities, categories etc. - for expression and for reasoning. |
| 10577 | Concrete objects have few essential properties, but properties of abstractions are mostly essential [Yablo] |
| Full Idea: Objects like me have a few essential properties, and numerous accidental ones. Abstract objects are a different story. The intrinsic properties of the empty set are mostly essential. The relations of numbers are also mostly essential. | |
| From: Stephen Yablo (Abstract Objects: a Case Study [2002], 01) |
| 10578 | We are thought to know concreta a posteriori, and many abstracta a priori [Yablo] |
| Full Idea: Our knowledge of concreta is a posteriori, but our knowledge of numbers, at least, has often been considered a priori. | |
| From: Stephen Yablo (Abstract Objects: a Case Study [2002], 02) |
| 9409 | Laws are the best axiomatization of the total history of world events or facts [Lewis, by Mumford] |
| Full Idea: The Mill-Ramsey-Lewis theory takes laws to be axioms (or theorems) of the best possible systematizations of the world's total history, where such a history is a history of events or facts. | |
| From: report of David Lewis (Psychophysical and theoretical identifications [1972]) by Stephen Mumford - Laws in Nature 1.3 |
| 9423 | If simplicity and strength are criteria for laws of nature, that introduces a subjective element [Mumford on Lewis] |
| Full Idea: Lewis's simplicity and strength criteria introduce an element of subjectivity into the laws, because the best system seems to be determined by what we take to be simple and strong in a system. | |
| From: comment on David Lewis (Psychophysical and theoretical identifications [1972]) by Stephen Mumford - Laws in Nature 3.5 | |
| A reaction: [Mumford cites Armstrong 1983:67 for this] |
| 9424 | A number of systematizations might tie as the best and most coherent system [Mumford on Lewis] |
| Full Idea: Since the best system view is a coherence theory, the possibility could not be ruled out that a number of different systematizations of the same history might be tied for first place as equally best. | |
| From: comment on David Lewis (Psychophysical and theoretical identifications [1972]) by Stephen Mumford - Laws in Nature 3.5 | |
| A reaction: [Mumord cites Armstrong 1983:70] Personally I am a fan of coherence theories, and this problem doesn't bother me. |
| 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... |
| 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) |