62 ideas
| 3067 | A philosopher should have principles ready for understanding, like a surgeon with instruments [Aurelius] |
| 9786 | Philosophers working like teams of scientists is absurd, yet isolation is hard [Cartwright,R] |
| 9784 | A false proposition isn't truer because it is part of a coherent system [Cartwright,R] |
| 9123 | Someone standing in a doorway seems to be both in and not-in the room [Priest,G, by Sorensen] |
| 13941 | Are the truth-bearers sentences, utterances, ideas, beliefs, judgements, propositions or statements? [Cartwright,R] |
| 13942 | Logicians take sentences to be truth-bearers for rigour, rather than for philosophical reasons [Cartwright,R] |
| 8720 | A logic is 'relevant' if premise and conclusion are connected, and 'paraconsistent' allows contradictions [Priest,G, by Friend] |
| 9672 | Free logic is one of the few first-order non-classical logics [Priest,G] |
| 9697 | X1 x X2 x X3... x Xn indicates the 'cartesian product' of those sets [Priest,G] |
| 9685 | <a,b&62; is a set whose members occur in the order shown [Priest,G] |
| 9675 | a ∈ X says a is an object in set X; a ∉ X says a is not in X [Priest,G] |
| 9674 | {x; A(x)} is a set of objects satisfying the condition A(x) [Priest,G] |
| 9673 | {a1, a2, ...an} indicates that a set comprising just those objects [Priest,G] |
| 9677 | Φ indicates the empty set, which has no members [Priest,G] |
| 9676 | {a} is the 'singleton' set of a (not the object a itself) [Priest,G] |
| 9679 | X⊂Y means set X is a 'proper subset' of set Y [Priest,G] |
| 9678 | X⊆Y means set X is a 'subset' of set Y [Priest,G] |
| 9681 | X = Y means the set X equals the set Y [Priest,G] |
| 9683 | X ∩ Y indicates the 'intersection' of sets X and Y, the objects which are in both sets [Priest,G] |
| 9682 | X∪Y indicates the 'union' of all the things in sets X and Y [Priest,G] |
| 9684 | Y - X is the 'relative complement' of X with respect to Y; the things in Y that are not in X [Priest,G] |
| 9694 | The 'relative complement' is things in the second set not in the first [Priest,G] |
| 9693 | The 'intersection' of two sets is a set of the things that are in both sets [Priest,G] |
| 9692 | The 'union' of two sets is a set containing all the things in either of the sets [Priest,G] |
| 9698 | The 'induction clause' says complex formulas retain the properties of their basic formulas [Priest,G] |
| 9695 | An 'ordered pair' (or ordered n-tuple) is a set with its members in a particular order [Priest,G] |
| 9696 | A 'cartesian product' of sets is the set of all the n-tuples with one member in each of the sets [Priest,G] |
| 9686 | A 'set' is a collection of objects [Priest,G] |
| 9689 | The 'empty set' or 'null set' has no members [Priest,G] |
| 9690 | A set is a 'subset' of another set if all of its members are in that set [Priest,G] |
| 9691 | A 'proper subset' is smaller than the containing set [Priest,G] |
| 9688 | A 'singleton' is a set with only one member [Priest,G] |
| 9687 | A 'member' of a set is one of the objects in the set [Priest,G] |
| 9680 | The empty set Φ is a subset of every set (including itself) [Priest,G] |
| 13373 | Typically, paradoxes are dealt with by dividing them into two groups, but the division is wrong [Priest,G] |
| 13368 | The 'least indefinable ordinal' is defined by that very phrase [Priest,G] |
| 13370 | 'x is a natural number definable in less than 19 words' leads to contradiction [Priest,G] |
| 13369 | By diagonalization we can define a real number that isn't in the definable set of reals [Priest,G] |
| 13366 | The least ordinal greater than the set of all ordinals is both one of them and not one of them [Priest,G] |
| 13367 | The next set up in the hierarchy of sets seems to be both a member and not a member of it [Priest,G] |
| 13371 | If you know that a sentence is not one of the known sentences, you know its truth [Priest,G] |
| 13372 | There are Liar Pairs, and Liar Chains, which fit the same pattern as the basic Liar [Priest,G] |
| 3072 | Everything is changing, including yourself and the whole universe [Aurelius] |
| 9783 | While no two classes coincide in membership, there are distinct but coextensive attributes [Cartwright,R] |
| 14961 | Clearly a pipe can survive being taken apart [Cartwright,R] |
| 14962 | Bodies don't becomes scattered by losing small or minor parts [Cartwright,R] |
| 13952 | Essentialism says some of a thing's properties are necessary, and could not be absent [Cartwright,R] |
| 13954 | The difficulty in essentialism is deciding the grounds for rating an attribute as essential [Cartwright,R] |
| 13955 | Essentialism is said to be unintelligible, because relative, if necessary truths are all analytic [Cartwright,R] |
| 13953 | An act of ostension doesn't seem to need a 'sort' of thing, even of a very broad kind [Cartwright,R] |
| 13945 | A token isn't a unique occurrence, as the case of a word or a number shows [Cartwright,R] |
| 13948 | For any statement, there is no one meaning which any sentence asserting it must have [Cartwright,R] |
| 13950 | People don't assert the meaning of the words they utter [Cartwright,R] |
| 13944 | We can pull apart assertion from utterance, and the action, the event and the subject-matter for each [Cartwright,R] |
| 13947 | 'It's raining' makes a different assertion on different occasions, but its meaning remains the same [Cartwright,R] |
| 13943 | We can attribute 'true' and 'false' to whatever it was that was said [Cartwright,R] |
| 13946 | To assert that p, it is neither necessary nor sufficient to utter some particular words [Cartwright,R] |
| 13951 | Assertions, unlike sentence meanings, can be accurate, probable, exaggerated, false.... [Cartwright,R] |
| 3066 | Nothing is evil which is according to nature [Aurelius] |
| 3071 | Justice has no virtue opposed to it, but pleasure has temperance opposed to it [Aurelius] |
| 3069 | The art of life is more like the wrestler's than the dancer's [Aurelius] |
| 3065 | Humans are naturally made for co-operation [Aurelius] |