4 ideas
| 18192 | Do the Replacement Axioms exceed the iterative conception of sets? [Boolos, by Maddy] |
| Full Idea: For Boolos, the Replacement Axioms go beyond the iterative conception. | |
| From: report of George Boolos (The iterative conception of Set [1971]) by Penelope Maddy - Naturalism in Mathematics I.3 |
| 13827 | Logical consequence isn't a black box (Tarski's approach); we should explain how arguments work [Prawitz] |
| Full Idea: Defining logical consequence in the way Tarski does is a rather meagre result, treating an argument as a black box, observing input and output, while disregarding inner structure. We should define logical consequence on the basis of valid arguments. | |
| From: Dag Prawitz (On the General Idea of Proof Theory [1974], §2) |
| 13826 | Model theory looks at valid sentences and consequence, but not how we know these things [Prawitz] |
| Full Idea: In model theory, which has dominated the last decades, one concentrates on logically valid sentences, and what follows logically from what, but one disregards questions concerning how we know these things. | |
| From: Dag Prawitz (On the General Idea of Proof Theory [1974], §1) |
| 6581 | Hume thought (unlike Locke) that property is a merely conventional relationship [Hume, by Fogelin] |
| Full Idea: Hume thought (in contrast to Locke) that property reflects a conventional (rather than natural) relationship determined by the laws that protect people from having things taken from them. | |
| From: report of David Hume (Nine political essays [1741]) by Robert Fogelin - Walking the Tightrope of Reason Ch.3 | |
| A reaction: It seems pretty obvious that the idea of property was invented by the powerful, to protect their gains against the weak. I suspect that you might till a piece of land simply in order to assert ownership of it, just as you might bring in colonists. |