32 ideas
| 8092 | Logic was merely a branch of rhetoric until the scientific 17th century [Devlin] |
| 17641 | Discoveries in mathematics can challenge philosophy, and offer it a new foundation [Russell] |
| 2676 | Didactic argument starts from the principles of the subject, not from the opinions of the learner [Aristotle] |
| 2675 | Reasoning is a way of making statements which makes them lead on to other statements [Aristotle] |
| 17638 | If one proposition is deduced from another, they are more certain together than alone [Russell] |
| 17632 | Non-contradiction was learned from instances, and then found to be indubitable [Russell] |
| 2677 | Dialectic aims to start from generally accepted opinions, and lead to a contradiction [Aristotle] |
| 2674 | Competitive argument aims at refutation, fallacy, paradox, solecism or repetition [Aristotle] |
| 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] |
| 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] |
| 16967 | 'Are Coriscus and Callias at home?' sounds like a single question, but it isn't [Aristotle] |
| 17629 | Which premises are ultimate varies with context [Russell] |
| 17630 | The sources of a proof are the reasons why we believe its conclusion [Russell] |
| 17640 | Finding the axioms may be the only route to some new results [Russell] |
| 8075 | Space and time are atomic in the arrow, and divisible in the tortoise [Devlin] |
| 17627 | It seems absurd to prove 2+2=4, where the conclusion is more certain than premises [Russell] |
| 17628 | Arithmetic was probably inferred from relationships between physical objects [Russell] |
| 16149 | Generic terms like 'man' are not substances, but qualities, relations, modes or some such thing [Aristotle] |
| 11840 | Only if two things are identical do they have the same attributes [Aristotle] |
| 17637 | The most obvious beliefs are not infallible, as other obvious beliefs may conflict [Russell] |
| 17639 | Believing a whole science is more than believing each of its propositions [Russell] |
| 8088 | People still say the Hopi have no time concepts, despite Whorf's later denial [Devlin] |
| 17631 | Induction is inferring premises from consequences [Russell] |
| 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] |
| 17633 | The law of gravity has many consequences beyond its grounding observations [Russell] |