41 ideas
8092 | Logic was merely a branch of rhetoric until the scientific 17th century [Devlin] |
5750 | Consistency is modal, saying propositions are consistent if they could be true together [Melia] |
8081 | 'No councillors are bankers' and 'All bankers are athletes' implies 'Some athletes are not councillors' [Devlin] |
8085 | Modern propositional inference replaces Aristotle's 19 syllogisms with modus ponens [Devlin] |
8086 | Predicate logic retains the axioms of propositional logic [Devlin] |
5737 | Predicate logic has connectives, quantifiers, variables, predicates, equality, names and brackets [Melia] |
5744 | First-order predicate calculus is extensional logic, but quantified modal logic is intensional (hence dubious) [Melia] |
13011 | New axioms are being sought, to determine the size of the continuum [Maddy] |
13013 | The Axiom of Extensionality seems to be analytic [Maddy] |
13014 | Extensional sets are clearer, simpler, unique and expressive [Maddy] |
13021 | The Axiom of Infinity states Cantor's breakthrough that launched modern mathematics [Maddy] |
13022 | Infinite sets are essential for giving an account of the real numbers [Maddy] |
13023 | The Power Set Axiom is needed for, and supported by, accounts of the continuum [Maddy] |
13024 | Efforts to prove the Axiom of Choice have failed [Maddy] |
13025 | Modern views say the Choice set exists, even if it can't be constructed [Maddy] |
13026 | A large array of theorems depend on the Axiom of Choice [Maddy] |
13019 | The Iterative Conception says everything appears at a stage, derived from the preceding appearances [Maddy] |
13018 | Limitation of Size is a vague intuition that over-large sets may generate paradoxes [Maddy] |
8091 | Situation theory is logic that takes account of context [Devlin] |
8087 | Golden ages: 1900-1960 for pure logic, and 1950-1985 for applied logic [Devlin] |
8089 | Montague's intensional logic incorporated the notion of meaning [Devlin] |
8082 | Where a conditional is purely formal, an implication implies a link between premise and conclusion [Devlin] |
8072 | Sentences of apparent identical form can have different contextual meanings [Devlin] |
5740 | Second-order logic needs second-order variables and quantification into predicate position [Melia] |
5741 | If every model that makes premises true also makes conclusion true, the argument is valid [Melia] |
8075 | Space and time are atomic in the arrow, and divisible in the tortoise [Devlin] |
5735 | Maybe names and predicates can capture any fact [Melia] |
5736 | No sort of plain language or levels of logic can express modal facts properly [Melia] |
5746 | The Identity of Indiscernibles is contentious for qualities, and trivial for non-qualities [Melia] |
5738 | We may be sure that P is necessary, but is it necessarily necessary? [Melia] |
5732 | 'De re' modality is about things themselves, 'de dicto' modality is about propositions [Melia] |
5739 | Sometimes we want to specify in what ways a thing is possible [Melia] |
5734 | Possible worlds make it possible to define necessity and counterfactuals without new primitives [Melia] |
5742 | In possible worlds semantics the modal operators are treated as quantifiers [Melia] |
5743 | If possible worlds semantics is not realist about possible worlds, logic becomes merely formal [Melia] |
5749 | Possible worlds could be real as mathematics, propositions, properties, or like books [Melia] |
5751 | The truth of propositions at possible worlds are implied by the world, just as in books [Melia] |
8088 | People still say the Hopi have no time concepts, despite Whorf's later denial [Devlin] |
5748 | We accept unverifiable propositions because of simplicity, utility, explanation and plausibility [Melia] |
8073 | How do we parse 'time flies like an arrow' and 'fruit flies like an apple'? [Devlin] |
8076 | The distinction between sentences and abstract propositions is crucial in logic [Devlin] |