12 ideas
| 21554 | Sets always exceed terms, so all the sets must exceed all the sets [Lackey] |
| Full Idea: Cantor proved that the number of sets in a collection of terms is larger than the number of terms. Hence Cantor's Paradox says the number of sets in the collection of all sets must be larger than the number of sets in the collection of all sets. | |
| From: Douglas Lackey (Intros to Russell's 'Essays in Analysis' [1973], p.127) | |
| A reaction: The sets must count as terms in the next iteration, but that is a normal application of the Power Set axiom. |
| 21553 | It seems that the ordinal number of all the ordinals must be bigger than itself [Lackey] |
| Full Idea: The ordinal series is well-ordered and thus has an ordinal number, and a series of ordinals to a given ordinal exceeds that ordinal by 1. So the series of all ordinals has an ordinal number that exceeds its own ordinal number by 1. | |
| From: Douglas Lackey (Intros to Russell's 'Essays in Analysis' [1973], p.127) | |
| A reaction: Formulated by Burali-Forti in 1897. |
| 6900 | A prior understanding of beauty is needed to assert that the Form of the Beautiful is beautiful [Westaway] |
| Full Idea: If it were asserted that the Form of the Beautiful was itself beautiful, such a statement would require a prior understanding of the concept of beauty, so would immediately lead to an infinite regress, so the Forms can't be self-predicating. | |
| From: Luke Westaway (talk [2005]), quoted by PG - Db (ideas) | |
| A reaction: This is a nice clear statement of the mess that Plato gets himself into if he wants the Forms to be self-predicating. Clearly the Form of the Beautiful can't be beautiful, but must be that which gives other things their beauty. |
| 6956 | At what point does an object become 'whole'? [Westaway] |
| Full Idea: At what point does an object become 'whole'? | |
| From: Luke Westaway (talk [2005]), quoted by PG - Db (ideas) | |
| A reaction: This nice question strikes me as the central one in mereology. It is tempting to reply that the matter is entirely conventional, but there seems an obvious fact about something missing if one piece is absent from a jigsaw, or a cube is chipped. |
| 8361 | What is true used to be possible, but it may no longer be so [Wright,GHv] |
| Full Idea: It is not very natural to say of that which is true that it is also possible. ...What is true was possible - but whether it still is a potency of the world is not certain. | |
| From: G.H. von Wright (Logic and Epistemology of Causal Relations [1973], §5) | |
| A reaction: A simple and rather important distinction. Before encountering this, I would certainly have been happy to affirm that the actual is possible, but actually it may not be. The power to create differs from the power to sustain. Could God re-create the world? |
| 7335 | The Chinese Room should be able to ask itself questions in Mandarin [Westaway] |
| Full Idea: If the Chinese Room is functionally equivalent to a Mandarin speaker, it ought to be able to ask itself questions in Mandarin (and it can't). | |
| From: Luke Westaway (talk [2005]), quoted by PG - Db (ideas) | |
| A reaction: Searle might triumphantly say that this proves there is no understanding in the room, but the objection won't go away, because the room is presumably functionally equivalent to a speaker, and not just a mere translator (who might use mechanical tricks). |
| 8363 | p is a cause and q an effect (not vice versa) if manipulations of p change q [Wright,GHv] |
| Full Idea: What makes p a cause-factor relative to the effect-factor q (rather than vice versa) is the fact that by manipulating p, producing changes in it 'at will', we could bring about changes in q. | |
| From: G.H. von Wright (Logic and Epistemology of Causal Relations [1973], §8) | |
| A reaction: As a solution to the direction-of-causation problem, I suspect that this proposal is begging the question. Will a causal explanation be offered of the action of manipulation? If he mistook his manipulation for a cause when it is actually an effect... |
| 8364 | We can imagine controlling floods by controlling rain, but not vice versa [Wright,GHv] |
| Full Idea: Given our present knowledge of the laws of nature, we can imagine ways of controlling floods by controlling rainfall, but not the other way round. That is should be so, however, is contingent. | |
| From: G.H. von Wright (Logic and Epistemology of Causal Relations [1973], §8) | |
| A reaction: Despite my objections to Idea 8363, this is a good example. It won't establish the metaphysics of the direction of causation, though, because God might control rainfall by controlling floods. Maybe causation is more like a motorway pile-up than dominoes. |
| 8366 | The very notion of a cause depends on agency and action [Wright,GHv] |
| Full Idea: There is an implicit dependence of the very notion of a cause on a concept of agency and action. | |
| From: G.H. von Wright (Logic and Epistemology of Causal Relations [1973], §10) | |
| A reaction: This is because he thinks experimental intervention is the key to the concept of causation (see Ideas 8362 and 8363). Others go further, and say that the concept of causation arises from subjective experience of performing actions. I quite like that. |
| 8362 | We give regularities a causal character by subjecting them to experiment [Wright,GHv] |
| Full Idea: What confers on observed regularities the character of causal or nomic connections is the possibility of subjecting cause-factors to experimental test by interfering with the 'natural' course of events. | |
| From: G.H. von Wright (Logic and Epistemology of Causal Relations [1973], §7) | |
| A reaction: This is von Wright's distinctive proposal, making causation a feature of the culture of science, rather than of ordinary life. But see Idea 2461. Causation is becoming too epistemological for my taste. Either it is a feature of reality, or forget it. |
| 8360 | We must further analyse conditions for causation, into quantifiers or modal concepts [Wright,GHv] |
| Full Idea: We may be able to analyse causation into conditionship relations between events or states of affairs, ...but conditions cannot be regarded as logical primitives, ... and must be analysed into quantifiers, or modal concepts. | |
| From: G.H. von Wright (Logic and Epistemology of Causal Relations [1973], §2) | |
| A reaction: [very compressed] A nice illustration of the aim of analytical philosophy - to analyse the elements of reality down to logical primitives. This is the dream of Descartes and Leibniz, continued by Russell and co. Do we still have this aspiration? |
| 8365 | Some laws are causal (Ohm's Law), but others are conceptual principles (conservation of energy) [Wright,GHv] |
| Full Idea: Not all laws are causal 'experimentalist' laws, such as those for falling bodies, or the Gas Law, or Ohm's Law. Some are more like conceptual principles, giving a frame of reference, such as inertia, or conservation of energy, or the law of entropy. | |
| From: G.H. von Wright (Logic and Epistemology of Causal Relations [1973], §9) | |
| A reaction: An interesting and important distinction, whenever one is exploring the links between theories of causation and of laws of nature. If one wished to attack the whole concept of 'laws of nature', this might be a good place to start. |