5 ideas
| 18189 | ZFC could contain a contradiction, and it can never prove its own consistency [MacLane] |
| Full Idea: We have at hand no proof that the axioms of ZFC for set theory will never yield a contradiction, while Gödel's second theorem tells us that such a consistency proof cannot be conducted within ZFC. | |
| From: Saunders MacLane (Mathematics: Form and Function [1986], p.406), quoted by Penelope Maddy - Naturalism in Mathematics | |
| A reaction: Maddy quotes this, while defending set theory as the foundation of mathematics, but it clearly isn't the most secure foundation that could be devised. She says the benefits of set theory do not need guaranteed consistency (p.30). |
| 19480 | Process philosophy places the dynamic nature of being at the centre of our theories [Seibt] |
| Full Idea: Process philosophy is based on the premise that being is dynamic and that the dynamic nature of being should be the primary focus of any comprehensive philosophical account of reality and our place within it. | |
| From: Johanna Seibt (Process Philosophy [2012], Intro) | |
| A reaction: Put like that, the chief ancestor of this approach would be Leibniz, even though his central idea concerns substances. Heraclitus is the most famous ancestor of Process Philosophy. Powers are dynamic, but powers of what? |
| 19479 | Reductionists identify processes by their 'owner', but tornadoes etc. are processes without owners [Seibt] |
| Full Idea: On the reductionist view of processes, they are all 'owned' and we identify them by their owner (such as the murder of Caesar), ...but many processes (e.g. tornadoes, lightning bolts, the NY rush hour) lack a proper 'subject' altogether. | |
| From: Johanna Seibt (Process Philosophy [2012], 2) | |
| A reaction: This seems to be a fairly conclusive refutation of the view that processes are just objects changing their properties. |
| 19481 | Traditionally small things add up to processes, but quantum mechanics reverses this [Seibt] |
| Full Idea: Instead of very small things (atoms) combining to produce standard processes (snowstorms), modern physics envisions very small processes (quantum phenomena) combining to produce standard things. | |
| From: Johanna Seibt (Process Philosophy [2012], 4 (i)) | |
| A reaction: Though electrons seem to be distinct things with a fixed set of properties, so this is not a clear point. Where do fields come into it? Beware of citing quantum mechanics in metaphysics! |
| 3061 | Anaxarchus said that he was not even sure that he knew nothing [Anaxarchus, by Diog. Laertius] |
| Full Idea: Anaxarchus said that he was not even sure that he knew nothing. | |
| From: report of Anaxarchus (fragments/reports [c.340 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 09.10.1 |