49 ideas
| 5988 | Anaximander produced the first philosophy book (and maybe the first book) [Anaximander, by Bodnár] |
| 23770 | Reductive analysis makes a concept clearer, by giving an alternative simpler set [Williams,NE] |
| 1496 | The earth is stationary, because it is in the centre, and has no more reason to move one way than another [Anaximander, by Aristotle] |
| 23769 | Promoting an ontology by its implied good metaphysic is an 'argument-by-display' [Williams,NE] |
| 10888 | Sets can be defined by 'enumeration', or by 'abstraction' (based on a property) [Zalabardo] |
| 10889 | The 'Cartesian Product' of two sets relates them by pairing every element with every element [Zalabardo] |
| 10890 | A 'partial ordering' is reflexive, antisymmetric and transitive [Zalabardo] |
| 10886 | Determinacy: an object is either in a set, or it isn't [Zalabardo] |
| 10887 | Specification: Determinate totals of objects always make a set [Zalabardo] |
| 10897 | A first-order 'sentence' is a formula with no free variables [Zalabardo] |
| 10893 | Γ |= φ for sentences if φ is true when all of Γ is true [Zalabardo] |
| 10899 | Γ |= φ if φ is true when all of Γ is true, for all structures and interpretations [Zalabardo] |
| 10896 | Propositional logic just needs ¬, and one of ∧, ∨ and → [Zalabardo] |
| 10898 | The semantics shows how truth values depend on instantiations of properties and relations [Zalabardo] |
| 10902 | We can do semantics by looking at given propositions, or by building new ones [Zalabardo] |
| 10892 | We make a truth assignment to T and F, which may be true and false, but merely differ from one another [Zalabardo] |
| 10895 | 'Logically true' (|= φ) is true for every truth-assignment [Zalabardo] |
| 10900 | Logically true sentences are true in all structures [Zalabardo] |
| 10894 | A sentence-set is 'satisfiable' if at least one truth-assignment makes them all true [Zalabardo] |
| 10901 | Some formulas are 'satisfiable' if there is a structure and interpretation that makes them true [Zalabardo] |
| 10903 | A structure models a sentence if it is true in the model, and a set of sentences if they are all true in the model [Zalabardo] |
| 10891 | If a set is defined by induction, then proof by induction can be applied to it [Zalabardo] |
| 14874 | Anaximander saw the contradiction in the world - that its own qualities destroy it [Anaximander, by Nietzsche] |
| 23783 | Change exists, it is causal, and it needs an explanation [Williams,NE] |
| 23784 | Processes don't begin or end; they just change direction unexpectedly [Williams,NE] |
| 23790 | Processes are either strings of short unchanging states, or continuous and unreducible events [Williams,NE] |
| 23786 | The status quo is part of what exists, and so needs metaphysical explanation [Williams,NE] |
| 23768 | A metaphysic is a set of wider explanations derived from a basic ontology [Williams,NE] |
| 23773 | Humeans say properties are passive, possibility is vast, laws are descriptions, causation is weak [Williams,NE] |
| 23779 | We shouldn't posit the existence of anything we have a word for [Williams,NE] |
| 23775 | Powers are 'multi-track' if they can produce a variety of manifestations [Williams,NE] |
| 23780 | Every possible state of affairs is written into its originating powers [Williams,NE] |
| 23789 | Naming powers is unwise, because that it usually done by a single manifestation [Williams,NE] |
| 23771 | Fundamental physics describes everything in terms of powers [Williams,NE] |
| 23776 | Rather than pure powers or pure categoricals, I favour basics which are both at once [Williams,NE] |
| 23777 | Powers are more complicated than properties which are always on display [Williams,NE] |
| 23774 | There are basic powers, which underlie dispositions, potentialities, capacities etc [Williams,NE] |
| 23791 | Dispositions are just useful descriptions, which are explained by underlying powers [Williams,NE] |
| 23772 | If objects are property bundles, the properties need combining powers [Williams,NE] |
| 23788 | Four-Dimensional is Perdurantism (temporal parts), plus Eternalism [Williams,NE] |
| 1495 | Anaximander introduced the idea that the first principle and element of things was the Boundless [Anaximander, by Simplicius] |
| 405 | The essential nature, whatever it is, of the non-limited is everlasting and ageless [Anaximander] |
| 13222 | The Boundless cannot exist on its own, and must have something contrary to it [Aristotle on Anaximander] |
| 404 | Things begin and end in the Unlimited, and are balanced over time according to justice [Anaximander] |
| 23785 | Causation needs to explain stasis, as well as change [Williams,NE] |
| 23782 | Causation is the exercise of powers [Williams,NE] |
| 23787 | If causes and effects overlap, that makes changes impossible [Williams,NE] |
| 23778 | Powers contain lawlike features, pointing to possible future states [Williams,NE] |
| 1746 | The parts of all things are susceptible to change, but the whole is unchangeable [Anaximander, by Diog. Laertius] |