40 ideas
| 6259 | Why can't a wise man doubt everything? [Montaigne] |
| 6263 | No wisdom could make us comfortably walk a wide beam if it was high in the air [Montaigne] |
| 23122 | Montaigne was the founding father of liberalism [Montaigne, by Gopnik] |
| 6258 | Virtue is the distinctive mark of truth, and its greatest product [Montaigne] |
| 10170 | While true-in-a-model seems relative, true-in-all-models seems not to be [Reck/Price] |
| 13913 | The four 'perfect syllogisms' are called Barbara, Celarent, Darii and Ferio [Engelbretsen/Sayward] |
| 13914 | Syllogistic logic has one rule: what is affirmed/denied of wholes is affirmed/denied of their parts [Engelbretsen/Sayward] |
| 13915 | Syllogistic can't handle sentences with singular terms, or relational terms, or compound sentences [Engelbretsen/Sayward] |
| 13916 | Term logic uses expression letters and brackets, and '-' for negative terms, and '+' for compound terms [Engelbretsen/Sayward] |
| 10166 | ZFC set theory has only 'pure' sets, without 'urelements' [Reck/Price] |
| 13850 | In modern logic all formal validity can be characterised syntactically [Engelbretsen/Sayward] |
| 13849 | Classical logic rests on truth and models, where constructivist logic rests on defence and refutation [Engelbretsen/Sayward] |
| 13851 | Unlike most other signs, = cannot be eliminated [Engelbretsen/Sayward] |
| 10175 | Three types of variable in second-order logic, for objects, functions, and predicates/sets [Reck/Price] |
| 13852 | Axioms are ω-incomplete if the instances are all derivable, but the universal quantification isn't [Engelbretsen/Sayward] |
| 10165 | 'Analysis' is the theory of the real numbers [Reck/Price] |
| 10174 | Mereological arithmetic needs infinite objects, and function definitions [Reck/Price] |
| 10164 | Peano Arithmetic can have three second-order axioms, plus '1' and 'successor' [Reck/Price] |
| 10172 | Set-theory gives a unified and an explicit basis for mathematics [Reck/Price] |
| 10167 | Structuralism emerged from abstract algebra, axioms, and set theory and its structures [Reck/Price] |
| 10169 | Relativist Structuralism just stipulates one successful model as its arithmetic [Reck/Price] |
| 10179 | There are 'particular' structures, and 'universal' structures (what the former have in common) [Reck/Price] |
| 10181 | Pattern Structuralism studies what isomorphic arithmetic models have in common [Reck/Price] |
| 10182 | There are Formalist, Relativist, Universalist and Pattern structuralism [Reck/Price] |
| 10168 | Formalist Structuralism says the ontology is vacuous, or formal, or inference relations [Reck/Price] |
| 10178 | Maybe we should talk of an infinity of 'possible' objects, to avoid arithmetic being vacuous [Reck/Price] |
| 10176 | Universalist Structuralism is based on generalised if-then claims, not one particular model [Reck/Price] |
| 10177 | Universalist Structuralism eliminates the base element, as a variable, which is then quantified out [Reck/Price] |
| 10171 | The existence of an infinite set is assumed by Relativist Structuralism [Reck/Price] |
| 6262 | We lack some sense or other, and hence objects may have hidden features [Montaigne] |
| 10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
| 6260 | Sceptics say there is truth, but no means of making or testing lasting judgements [Montaigne] |
| 6261 | The soul is in the brain, as shown by head injuries [Montaigne] |
| 7496 | Rules and duties are based on the will, as that is all we control [Montaigne] |
| 7495 | Apart from the fear, dying is an easy duty [Montaigne] |
| 22269 | We must fight fiercely to hang on to the few pleasures which survive into old age [Montaigne] |
| 20482 | Virtue inspires Stoics, but I want a good temperament [Montaigne] |
| 20480 | There is not much point in only becoming good near the end of your life [Montaigne] |
| 20481 | Nothing we say can be worse than unsaying it in the face of authority [Montaigne] |
| 20479 | People at home care far more than soldiers risking death about the outcome of wars [Montaigne] |