8 ideas
| 17879 | Axiomatising set theory makes it all relative [Skolem] |
| Full Idea: Axiomatising set theory leads to a relativity of set-theoretic notions, and this relativity is inseparably bound up with every thoroughgoing axiomatisation. | |
| From: Thoralf Skolem (Remarks on axiomatised set theory [1922], p.296) |
| 17878 | If a 1st-order proposition is satisfied, it is satisfied in a denumerably infinite domain [Skolem] |
| Full Idea: Löwenheim's theorem reads as follows: If a first-order proposition is satisfied in any domain at all, it is already satisfied in a denumerably infinite domain. | |
| From: Thoralf Skolem (Remarks on axiomatised set theory [1922], p.293) |
| 17880 | Integers and induction are clear as foundations, but set-theory axioms certainly aren't [Skolem] |
| Full Idea: The initial foundations should be immediately clear, natural and not open to question. This is satisfied by the notion of integer and by inductive inference, by it is not satisfied by the axioms of Zermelo, or anything else of that kind. | |
| From: Thoralf Skolem (Remarks on axiomatised set theory [1922], p.299) | |
| A reaction: This is a plea (endorsed by Almog) that the integers themselves should be taken as primitive and foundational. I would say that the idea of successor is more primitive than the integers. |
| 17881 | Mathematician want performable operations, not propositions about objects [Skolem] |
| Full Idea: Most mathematicians want mathematics to deal, ultimately, with performable computing operations, and not to consist of formal propositions about objects called this or that. | |
| From: Thoralf Skolem (Remarks on axiomatised set theory [1922], p.300) |
| 14586 | Physical causation consists in transference of conserved quantities [Dowe, by Mumford/Anjum] |
| Full Idea: For Dowe physical causation consists in transference of conserved quantities. | |
| From: report of Phil Dowe (Physical Causation [2000]) by S.Mumford/R.Lill Anjum - Getting Causes from Powers 10.2 | |
| A reaction: [see Psillos 2002 on this] This is evidently a modification of the idea of physical causation as energy-transfer, but narrowing it down to exclude trivial cases. I guess. Need better physics. |
| 4787 | Causation interaction is an exchange of conserved quantities, such as mass, energy or charge [Dowe, by Psillos] |
| Full Idea: Dowe argues that a 'causal process' is a world line of an object with a conserved quantity (such as mass, energy, momentum, charge), and a 'causal interaction' is an exchange between two such objects. | |
| From: report of Phil Dowe (Physical Causation [2000]) by Stathis Psillos - Causation and Explanation §4.4 | |
| A reaction: This looks very promising. Nice distinction between causal process and causal interaction. 'Conserved quantities' is better physics than just 'energy'. We can hand causation over to the scientist? |
| 4788 | Dowe commends the Conserved Quantity theory as it avoids mention of counterfactuals [Dowe, by Psillos] |
| Full Idea: Dowe commends the Conserved Quantity theory because it avoids any mention of counterfactuals. | |
| From: report of Phil Dowe (Physical Causation [2000]) by Stathis Psillos - Causation and Explanation §4.4 | |
| A reaction: Clearly the truth of a counterfactual is quite a problem for an empiricist/scientist, but one needs to distinguish between reality and our grasp of it. We commit ourselves to counterfactuals, even if causation is transfer of conserved quantities. |
| 7482 | Resurrection developed in Judaism as a response to martyrdoms, in about 160 BCE [Anon (Dan), by Watson] |
| Full Idea: The idea of resurrection in Judaism seems to have first developed around 160 BCE, during the time of religious martyrdom, and as a response to it (the martyrs were surely not dying forever?). It is first mentioned in the book of Daniel. | |
| From: report of Anon (Dan) (27: Book of Daniel [c.165 BCE], Ch.7) by Peter Watson - Ideas | |
| A reaction: Idea 7473 suggests that Zoroaster beat them to it by 800 years. |