31 ideas
| 20320 | Truth is what unites, and the profound truths create a community [Jaspers] |
| 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] |
| 8840 | There are five possible responses to the problem of infinite regress in justification [Cleve] |
| 8841 | Modern foundationalists say basic beliefs are fallible, and coherence is relevant [Cleve] |
| 20323 | Freedom needs knowledge, the possibility of arbitrariness, and law [Jaspers] |
| 20322 | I am aware that freedom is possible, and the freedom is not in theory, but in seeking freedom [Jaspers] |
| 20324 | My freedom increases as I broaden my vision of possiblities and motives [Jaspers] |
| 20318 | My helplessness in philosophising reveals my being, and begins its upsurge [Jaspers] |
| 20321 | The struggle for Existenz is between people who are equals, and are utterly honest [Jaspers] |
| 20325 | Once we grasp freedom 'from' things, then freedom 'for' things becomes urgent [Jaspers] |
| 20317 | Mundane existence is general, falling under universals, but Existens is unique to individuals [Jaspers] |
| 20319 | We want the correct grasp on being that is neither solipsism nor absorption in the crowd [Jaspers] |
| 20315 | 'Existenz' is the potential being, which I could have, and ought to have [Jaspers] |
| 20316 | Every decision I make moves towards or away from fulfilled Existenz [Jaspers] |