55 ideas
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] |
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] |
9675 | a ∈ X says a is an object in set X; a ∉ X says a is not in X [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] |
9678 | X⊆Y means set X is a 'subset' of set Y [Priest,G] |
9679 | X⊂Y means set X is a 'proper 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] |
9684 | Y - X is the 'relative complement' of X with respect to Y; the things in Y that are not in X [Priest,G] |
9682 | X∪Y indicates the 'union' of all the things in sets X and Y [Priest,G] |
9692 | The 'union' of two sets is a set containing all the things in either of the sets [Priest,G] |
9693 | The 'intersection' of two sets is a set of the things that are in both sets [Priest,G] |
9694 | The 'relative complement' is things in the second set not in the first [Priest,G] |
9698 | The 'induction clause' says complex formulas retain the properties of their basic formulas [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] |
9687 | A 'member' of a set is one of the objects in the set [Priest,G] |
9695 | An 'ordered pair' (or ordered n-tuple) is a set with its members in a particular order [Priest,G] |
9688 | A 'singleton' is a set with only one member [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] |
9680 | The empty set Φ is a subset of every set (including itself) [Priest,G] |
2730 | Because 'gold is malleable' is necessary does not mean that it is analytic [Audi,R] |
2715 | Beliefs are based on perception, memory, introspection or reason [Audi,R] |
2735 | Could you have a single belief on its own? [Audi,R] |
2736 | We can make certain of what we know, so knowing does not entail certainty [Audi,R] |
2722 | Sense-data theory is indirect realism, but phenomenalism is direct irrealism [Audi,R] |
2721 | If you gradually remove a book's sensory properties, what is left at the end? [Audi,R] |
2727 | Red and green being exclusive colours seems to be rationally graspable but not analytic [Audi,R] |
2728 | The concepts needed for a priori thought may come from experience [Audi,R] |
2716 | To see something as a field, I obviously need the concept of a field [Audi,R] |
2717 | How could I see a field and believe nothing regarding it? [Audi,R] |
2719 | Sense data imply representative realism, possibly only representing primary qualities [Audi,R] |
2720 | Sense-data (and the rival 'adverbial' theory) are to explain illusions and hallucinations [Audi,R] |
2718 | Perception is first simple, then objectual (with concepts) and then propositional [Audi,R] |
2729 | Virtually all rationalists assert that we can have knowledge of synthetic a priori truths [Audi,R] |
2741 | The principles of justification have to be a priori [Audi,R] |
2725 | To remember something is to know it [Audi,R] |
2724 | I might remember someone I can't recall or image, by recognising them on meeting [Audi,R] |
2731 | Justification is either unanchored (infinite or circular), or anchored (in knowledge or non-knowledge) [Audi,R] |
2739 | Internalism about justification implies that there is a right to believe something [Audi,R] |
2732 | Maths may be consistent with observations, but not coherent [Audi,R] |
2733 | It is very hard to show how much coherence is needed for justification [Audi,R] |
2734 | A consistent madman could have a very coherent belief system [Audi,R] |
2738 | Consistent accurate prediction looks like knowledge without justified belief [Audi,R] |
2740 | A reliability theory of knowledge seems to involve truth as correspondence [Audi,R] |
2737 | 'Reliable' is a very imprecise term, and may even mean 'justified' [Audi,R] |
2726 | We can be ignorant about ourselves, for example, our desires and motives [Audi,R] |
13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |