57 ideas
9123 | Someone standing in a doorway seems to be both in and not-in the room [Priest,G, by Sorensen] |
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] |
21554 | Sets always exceed terms, so all the sets must exceed all the sets [Lackey] |
21553 | It seems that the ordinal number of all the ordinals must be bigger than itself [Lackey] |
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] |
8143 | Self is the rider, intellect the charioteer, mind the reins, and body the chariot [Anon (Upan)] |
8147 | We have an apparent and a true self; only the second one exists, and we must seek to know it [Anon (Upan)] |
8155 | Without speech we cannot know right/wrong, true/false, good/bad, or pleasant/unpleasant [Anon (Upan)] |
8142 | The wise prefer good to pleasure; the foolish are drawn to pleasure by desire [Anon (Upan)] |
8151 | Let your teacher be a god to you [Anon (Upan)] |
8153 | By knowing one piece of clay or gold, you know all of clay or gold [Anon (Upan)] |
8154 | Originally there must have been just Existence, which could not come from non-existence [Anon (Upan)] |
8148 | Brahma, supreme god and protector of the universe, arose from the ocean of existence [Anon (Upan)] |
8144 | Brahman is the Uncaused Cause [Anon (Upan)] |
8152 | Earth, food, fire, sun are all forms of Brahman [Anon (Upan)] |
8156 | The gods are not worshipped for their own sake, but for the sake of the Self [Anon (Upan)] |
8157 | A man with desires is continually reborn, until his desires are stilled [Anon (Upan)] |
8159 | Damayata - be self-controlled! Datta - be charitable! Dayadhwam - be compassionate! [Anon (Upan)] |
8145 | Those ignorant of Atman return as animals or plants, according to their merits [Anon (Upan)] |
8149 | Charity and ritual observance distract from the highest good of religion [Anon (Upan)] |
8158 | Do not seek to know Brahman by arguments, for arguments are idle and vain [Anon (Upan)] |
8146 | The immortal in us is the part that never sleeps, and shapes our dreams [Anon (Upan)] |
8150 | The immortal Self and the sad individual self are like two golden birds perched on one tree [Anon (Upan)] |