11 ideas
| 17611 | We want the essence of continuity, by showing its origin in arithmetic [Dedekind] |
| Full Idea: It then only remained to discover its true origin in the elements of arithmetic and thus at the same time to secure a real definition of the essence of continuity. | |
| From: Richard Dedekind (Continuity and Irrational Numbers [1872], Intro) | |
| A reaction: [He seeks the origin of the theorem that differential calculus deals with continuous magnitude, and he wants an arithmetical rather than geometrical demonstration; the result is his famous 'cut']. |
| 10572 | A cut between rational numbers creates and defines an irrational number [Dedekind] |
| Full Idea: Whenever we have to do a cut produced by no rational number, we create a new, an irrational number, which we regard as completely defined by this cut. | |
| From: Richard Dedekind (Continuity and Irrational Numbers [1872], §4) | |
| A reaction: Fine quotes this to show that the Dedekind Cut creates the irrational numbers, rather than hitting them. A consequence is that the irrational numbers depend on the rational numbers, and so can never be identical with any of them. See Idea 10573. |
| 17612 | Arithmetic is just the consequence of counting, which is the successor operation [Dedekind] |
| Full Idea: I regard the whole of arithmetic as a necessary, or at least natural, consequence of the simplest arithmetic act, that of counting, and counting itself is nothing else than the successive creation of the infinite series of positive integers. | |
| From: Richard Dedekind (Continuity and Irrational Numbers [1872], §1) | |
| A reaction: Thus counting roots arithmetic in the world, the successor operation is the essence of counting, and the Dedekind-Peano axioms are built around successors, and give the essence of arithmetic. Unfashionable now, but I love it. Intransitive counting? |
| 18087 | If x changes by less and less, it must approach a limit [Dedekind] |
| Full Idea: If in the variation of a magnitude x we can for every positive magnitude δ assign a corresponding position from and after which x changes by less than δ then x approaches a limiting value. | |
| From: Richard Dedekind (Continuity and Irrational Numbers [1872], p.27), quoted by Philip Kitcher - The Nature of Mathematical Knowledge 10.7 | |
| A reaction: [Kitcher says he 'showed' this, rather than just stating it] |
| 10369 | How fine-grained Kim's events are depends on how finely properties are individuated [Kim, by Schaffer,J] |
| Full Idea: How fine-grained Kim's events are depends on how finely properties are individuated. | |
| From: report of Jaegwon Kim (Events as property exemplifications [1976]) by Jonathan Schaffer - The Metaphysics of Causation 1.2 | |
| A reaction: I don't actually buy the idea that an event could just be an 'exemplification'. Change seems to be required, and processes, or something like them, must be mentioned. Degrees of fine-graining sound good, though, for processes too. |
| 8976 | If events are ordered triples of items, such things seem to be sets, and hence abstract [Simons on Kim] |
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Full Idea:
If Kim's events are just the ordered triple of |
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| From: comment on Jaegwon Kim (Events as property exemplifications [1976]) by Peter Simons - Events 2.1 | |
| A reaction: You might reply that the object, and maybe the attribute, are concrete, and the time is natural, but the combination really is an abstraction, even though it is located (like the equator). Where is the set of my books located? |
| 8975 | Events cannot be merely ordered triples, but must specify the link between the elements [Kim, by Simons] |
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Full Idea:
Kim's events cannot just be the ordered triple of |
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| From: report of Jaegwon Kim (Events as property exemplifications [1976]) by Peter Simons - Events 2.1 | |
| A reaction: Why should they even be in that particular order? This requirement rather messes up Kim's plan for a very streamlined, Ockhamised ontology. Circles have symmetry at all times. Is 'near Trafalgar Square' a property? |
| 8974 | Events are composed of an object with an attribute at a time [Kim, by Simons] |
| Full Idea: Kim's events are exemplifications by an object of an attribute at a time...It does not make events basic entities, as the three constituents are more basic, but it gives identity conditions (two events are the same if object, attribute and time the same). | |
| From: report of Jaegwon Kim (Events as property exemplifications [1976]) by Peter Simons - Events 2.1 | |
| A reaction: [Aristotle is said to be behind this] I am more sympathetic to this view than the claim that events are primitive. If a pebble is ellipsoid for a million years, is that an event? I think the concept of a 'process' is the most fruitful one to investigate. |
| 8977 | Since properties like self-identity and being 2+2=4 are timeless, Kim must restrict his properties [Simons on Kim] |
| Full Idea: Since some tautologously universal properties such as self-identity or being such that 2+2=4 apply to all things at all times, that is stretching Kim's events too far. Candidate properties need to be realistically restricted, and it is unclear how. | |
| From: comment on Jaegwon Kim (Events as property exemplifications [1976]) by Peter Simons - Events 2.1 | |
| A reaction: You could deploy Schoemaker's concept of natural properties in terms of the source of causal powers, but the problem would be that you were probably hoping to then use Kim's events to define causation. Answer: treat causation as the primitive. |
| 8980 | Kim's theory results in too many events [Simons on Kim] |
| Full Idea: The criticism most frequently levelled against Kim's theory is that it results in an unacceptable plurality of finely differentiated events, because of the requirement for identity of the constituent property. | |
| From: comment on Jaegwon Kim (Events as property exemplifications [1976]) by Peter Simons - Events 4.4 | |
| A reaction: This may mean that the Battle of Waterloo was several trillion events, which seems daft to the historian, but it doesn't to the physicist. A cannon firing is indeed an accumulation of lots of little events. |
| 21906 | Political theory should not focus on the state or economy, but on the small scale of power [Deleuze/Guattari, by May] |
| Full Idea: Liberals who focus on the state and Marxists who focus on the economy are macropolitical theorists. They overlook the small elements that comprise our political lives. To understand how we are constructed and power works we must turn to the smaller scale. | |
| From: report of G Deleuze / F Guattari (A Thousand Plateaus [1980]) by Todd May - Gilles Deleuze 4.04 | |
| A reaction: This seems to be precisely in tune with the ideas of Foucault. I'm not sure that a study of power within the family or the office throws much light on macropolitics. How the micro intrudes into the micro seems more interesting. |