53 ideas
| 18450 | Philosophy has its own mode of death, by separating soul from body [Porphyry] |
| 17749 | Post proved the consistency of propositional logic in 1921 [Walicki] |
| 17765 | Propositional language can only relate statements as the same or as different [Walicki] |
| 17764 | Boolean connectives are interpreted as functions on the set {1,0} [Walicki] |
| 17752 | The empty set is useful for defining sets by properties, when the members are not yet known [Walicki] |
| 17753 | The empty set avoids having to take special precautions in case members vanish [Walicki] |
| 17759 | Ordinals play the central role in set theory, providing the model of well-ordering [Walicki] |
| 17741 | To determine the patterns in logic, one must identify its 'building blocks' [Walicki] |
| 17747 | A 'model' of a theory specifies interpreting a language in a domain to make all theorems true [Walicki] |
| 17748 | The L-S Theorem says no theory (even of reals) says more than a natural number theory [Walicki] |
| 17763 | Axiomatic systems are purely syntactic, and do not presuppose any interpretation [Walicki] |
| 17761 | A compact axiomatisation makes it possible to understand a field as a whole [Walicki] |
| 17757 | Members of ordinals are ordinals, and also subsets of ordinals [Walicki] |
| 17758 | Ordinals are transitive sets of transitive sets; or transitive sets totally ordered by inclusion [Walicki] |
| 17755 | Ordinals are the empty set, union with the singleton, and any arbitrary union of ordinals [Walicki] |
| 17756 | The union of finite ordinals is the first 'limit ordinal'; 2ω is the second... [Walicki] |
| 17760 | Two infinite ordinals can represent a single infinite cardinal [Walicki] |
| 17762 | In non-Euclidean geometry, all Euclidean theorems are valid that avoid the fifth postulate [Walicki] |
| 17754 | Inductive proof depends on the choice of the ordering [Walicki] |
| 13076 | Scholastics treat relations as two separate predicates of the relata [Cover/O'Leary-Hawthorne] |
| 18451 | The presence of the incorporeal is only known by certain kinds of disposition [Porphyry] |
| 15034 | Are genera and species real or conceptual? bodies or incorporeal? in sensibles or separate from them? [Porphyry] |
| 13102 | If you individuate things by their origin, you still have to individuate the origins themselves [Cover/O'Leary-Hawthorne] |
| 13103 | Numerical difference is a symmetrical notion, unlike proper individuation [Cover/O'Leary-Hawthorne] |
| 13104 | Haecceity as property, or as colourless thisness, or as singleton set [Cover/O'Leary-Hawthorne] |
| 18459 | Diversity arises from the power of unity [Porphyry] |
| 13100 | Maybe 'substance' is more of a mass-noun than a count-noun [Cover/O'Leary-Hawthorne] |
| 13068 | We can ask for the nature of substance, about type of substance, and about individual substances [Cover/O'Leary-Hawthorne] |
| 13069 | The general assumption is that substances cannot possibly be non-substances [Cover/O'Leary-Hawthorne] |
| 13072 | Modern essences are sets of essential predicate-functions [Cover/O'Leary-Hawthorne] |
| 17080 | Modern essentialists express essence as functions from worlds to extensions for predicates [Cover/O'Leary-Hawthorne] |
| 13101 | Necessity-of-origin won't distinguish ex nihilo creations, or things sharing an origin [Cover/O'Leary-Hawthorne] |
| 17742 | Scotus based modality on semantic consistency, instead of on what the future could allow [Walicki] |
| 13081 | Even extreme modal realists might allow transworld identity for abstract objects [Cover/O'Leary-Hawthorne] |
| 18452 | Memory is not conserved images, but reproduction of previous thought [Porphyry] |
| 13071 | We can go beyond mere causal explanations if we believe in an 'order of being' [Cover/O'Leary-Hawthorne] |
| 18453 | Intelligence is aware of itself, so the intelligence is both the thinker and the thought [Porphyry] |
| 18462 | The soul is everywhere and nowhere in the body, and must be its cause [Porphyry] |
| 18463 | Successful introspection reveals the substrate along with the object of thought [Porphyry] |
| 18458 | The soul is bound to matter by the force of its own disposition [Porphyry] |
| 18464 | Justice is each person fulfilling his function [Porphyry] |
| 18448 | We should avoid the pleasures of love, or at least, should not enact our dreams [Porphyry] |
| 18444 | Civil virtues make us behave benevolently, and thereby unite citizens [Porphyry] |
| 18445 | Civil virtues control the passions, and make us conform to our nature [Porphyry] |
| 18446 | Purificatory virtues detach the soul completely from the passions [Porphyry] |
| 18447 | There are practical, purificatory, contemplative, and exemplary virtues [Porphyry] |
| 18456 | Unified real existence is neither great nor small, though greatness and smallness participate in it [Porphyry] |
| 18454 | Time is the circular movement of the soul [Porphyry] |
| 18455 | Some think time is seen at rest, as well as in movement [Porphyry] |
| 18460 | God is nowhere, and hence everywhere [Porphyry] |
| 18461 | Everything existing proceeds from divinity, and is within divinity [Porphyry] |
| 18449 | Nature binds or detaches body to soul, but soul itself joins and detaches soul from body [Porphyry] |
| 18457 | Individual souls are all connected, though distinct, and without dividing universal Soul [Porphyry] |