32 ideas
| 7807 | The laws of thought are true, but they are not the axioms of logic [Bolzano, by George/Van Evra] |
| 7786 | Propositional logic handles negation, disjunction, conjunction; predicate logic adds quantifiers, predicates, relations [Girle] |
| 7798 | There are three axiom schemas for propositional logic [Girle] |
| 7799 | Proposition logic has definitions for its three operators: or, and, and identical [Girle] |
| 7797 | Axiom systems of logic contain axioms, inference rules, and definitions of proof and theorems [Girle] |
| 7794 | There are seven modalities in S4, each with its negation [Girle] |
| 7793 | ◊p → □◊p is the hallmark of S5 [Girle] |
| 7795 | S5 has just six modalities, and all strings can be reduced to those [Girle] |
| 7787 | Possible worlds logics use true-in-a-world rather than true [Girle] |
| 7788 | Modal logic has four basic modal negation equivalences [Girle] |
| 7796 | Modal logics were studied in terms of axioms, but now possible worlds semantics is added [Girle] |
| 7789 | Necessary implication is called 'strict implication'; if successful, it is called 'entailment' [Girle] |
| 7790 | If an argument is invalid, a truth tree will indicate a counter-example [Girle] |
| 9618 | Bolzano wanted to reduce all of geometry to arithmetic [Bolzano, by Brown,JR] |
| 9830 | Bolzano began the elimination of intuition, by proving something which seemed obvious [Bolzano, by Dummett] |
| 17265 | Philosophical proofs in mathematics establish truths, and also show their grounds [Bolzano, by Correia/Schnieder] |
| 7800 | Analytic truths are divided into logically and conceptually necessary [Girle] |
| 7801 | Possibilities can be logical, theoretical, physical, economic or human [Girle] |
| 7792 | A world has 'access' to a world it generates, which is important in possible worlds semantics [Girle] |
| 9185 | Bolzano wanted to avoid Kantian intuitions, and prove everything that could be proved [Bolzano, by Dummett] |
| 22276 | Bolzano saw propositions as objective entities, existing independently of us [Bolzano, by Potter] |
| 17264 | Propositions are abstract structures of concepts, ready for judgement or assertion [Bolzano, by Correia/Schnieder] |
| 12232 | A 'proposition' is the sense of a linguistic expression, and can be true or false [Bolzano] |
| 12233 | The ground of a pure conceptual truth is only in other conceptual truths [Bolzano] |
| 7590 | Consequentialism emphasises value rather than obligation in morality [Scruton] |
| 7589 | Altruism is either emotional (where your interests are mine) or moral (where they are reasons for me) [Scruton] |
| 7595 | The idea of a right seems fairly basic; justice may be the disposition to accord rights to people [Scruton] |
| 7588 | Allegiance is fundamental to the conservative view of society [Scruton] |
| 7594 | Democrats are committed to a belief and to its opposite, if the majority prefer the latter [Scruton] |
| 7593 | Liberals focus on universal human freedom, natural rights, and tolerance [Scruton, by PG] |
| 7592 | For positivists law is a matter of form, for naturalists it is a matter of content [Scruton] |
| 7587 | The issue of abortion seems insoluble, because there is nothing with which to compare it [Scruton] |