31 ideas
| 14255 | We understand things through their dependency relations [Fine,K] |
| 17641 | Discoveries in mathematics can challenge philosophy, and offer it a new foundation [Russell] |
| 14250 | Metaphysics deals with the existence of things and with the nature of things [Fine,K] |
| 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] |
| 14259 | Maybe two objects might require simultaneous real definitions, as with two simultaneous terms [Fine,K] |
| 9193 | ZF set theory has variables which range over sets, 'equals' and 'member', and extensionality [Dummett] |
| 9194 | The main alternative to ZF is one which includes looser classes as well as sets [Dummett] |
| 9195 | Intuitionists reject excluded middle, not for a third value, but for possibility of proof [Dummett] |
| 9186 | First-order logic concerns objects; second-order adds properties, kinds, relations and functions [Dummett] |
| 9187 | Logical truths and inference are characterized either syntactically or semantically [Dummett] |
| 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] |
| 9191 | Ordinals seem more basic than cardinals, since we count objects in sequence [Dummett] |
| 17627 | It seems absurd to prove 2+2=4, where the conclusion is more certain than premises [Russell] |
| 9192 | The number 4 has different positions in the naturals and the wholes, with the same structure [Dummett] |
| 17628 | Arithmetic was probably inferred from relationships between physical objects [Russell] |
| 14253 | An object's 'being' isn't existence; there's more to an object than existence, and its nature doesn't include existence [Fine,K] |
| 14261 | There is 'weak' dependence in one definition, and 'strong' dependence in all the definitions [Fine,K] |
| 14251 | A natural modal account of dependence says x depends on y if y must exist when x does [Fine,K] |
| 14257 | An object depends on another if the second cannot be eliminated from the first's definition [Fine,K] |
| 14254 | Dependency is the real counterpart of one term defining another [Fine,K] |
| 14252 | We should understand identity in terms of the propositions it renders true [Fine,K] |
| 14256 | How do we distinguish basic from derived esssences? [Fine,K] |
| 14258 | Maybe some things have essential relationships as well as essential properties [Fine,K] |
| 14260 | An object only essentially has a property if that property follows from every definition of the object [Fine,K] |
| 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] |
| 17631 | Induction is inferring premises from consequences [Russell] |
| 17633 | The law of gravity has many consequences beyond its grounding observations [Russell] |