34 ideas
6947 | Metaphysics does not rest on facts, but on what we are inclined to believe [Peirce] |
6937 | Reason aims to discover the unknown by thinking about the known [Peirce] |
16951 | It was realised that possible worlds covered all modal logics, if they had a structure [Dummett] |
16953 | Relative possibility one way may be impossible coming back, so it isn't symmetrical [Dummett] |
16952 | If something is only possible relative to another possibility, the possibility relation is not transitive [Dummett] |
16960 | If possibilitiy is relative, that might make accessibility non-transitive, and T the correct system [Dummett] |
16958 | In S4 the actual world has a special place [Dummett] |
14239 | The empty set is usually derived from Separation, but it also seems to need Infinity [Oliver/Smiley] |
14240 | The empty set is something, not nothing! [Oliver/Smiley] |
14241 | We don't need the empty set to express non-existence, as there are other ways to do that [Oliver/Smiley] |
14242 | Maybe we can treat the empty set symbol as just meaning an empty term [Oliver/Smiley] |
14243 | The unit set may be needed to express intersections that leave a single member [Oliver/Smiley] |
14234 | If you only refer to objects one at a time, you need sets in order to refer to a plurality [Oliver/Smiley] |
14237 | We can use plural language to refer to the set theory domain, to avoid calling it a 'set' [Oliver/Smiley] |
14245 | Logical truths are true no matter what exists - but predicate calculus insists that something exists [Oliver/Smiley] |
14246 | If mathematics purely concerned mathematical objects, there would be no applied mathematics [Oliver/Smiley] |
14247 | Sets might either represent the numbers, or be the numbers, or replace the numbers [Oliver/Smiley] |
21492 | Realism is basic to the scientific method [Peirce] |
6949 | If someone doubted reality, they would not actually feel dissatisfaction [Peirce] |
16957 | Possible worlds aren't how the world might be, but how a world might be, given some possibility [Dummett] |
16959 | If possible worlds have no structure (S5) they are equal, and it is hard to deny them reality [Dummett] |
6941 | We are entirely satisfied with a firm belief, even if it is false [Peirce] |
6940 | The feeling of belief shows a habit which will determine our actions [Peirce] |
6942 | We want true beliefs, but obviously we think our beliefs are true [Peirce] |
6943 | A mere question does not stimulate a struggle for belief; there must be a real doubt [Peirce] |
6598 | We need our beliefs to be determined by some external inhuman permanency [Peirce] |
6944 | Demonstration does not rest on first principles of reason or sensation, but on freedom from actual doubt [Peirce] |
6948 | Doubts should be satisfied by some external permanency upon which thinking has no effect [Peirce] |
6945 | Once doubt ceases, there is no point in continuing to argue [Peirce] |
16956 | To explain generosity in a person, you must understand a generous action [Dummett] |
6939 | What is true of one piece of copper is true of another (unlike brass) [Peirce] |
16954 | Generalised talk of 'natural kinds' is unfortunate, as they vary too much [Dummett] |
6938 | Natural selection might well fill an animal's mind with pleasing thoughts rather than true ones [Peirce] |
6946 | If death is annihilation, belief in heaven is a cheap pleasure with no disappointment [Peirce] |