40 ideas
| 19275 | You cannot understand what exists without understanding possibility and necessity [Hale] |
| 19291 | A canonical defintion specifies the type of thing, and what distinguish this specimen [Hale] |
| 19297 | The two Barcan principles are easily proved in fairly basic modal logic [Hale] |
| 19301 | With a negative free logic, we can dispense with the Barcan formulae [Hale] |
| 17610 | The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy] |
| 19296 | If second-order variables range over sets, those are just objects; properties and relations aren't sets [Hale] |
| 17620 | Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy] |
| 19289 | Maybe conventionalism applies to meaning, but not to the truth of propositions expressed [Hale] |
| 19298 | Unlike axiom proofs, natural deduction proofs needn't focus on logical truths and theorems [Hale] |
| 17605 | Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy] |
| 17625 | If two mathematical themes coincide, that suggest a single deep truth [Maddy] |
| 17615 | Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy] |
| 17618 | Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy] |
| 17614 | The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy] |
| 19295 | Add Hume's principle to logic, to get numbers; arithmetic truths rest on the nature of the numbers [Hale] |
| 19281 | Interesting supervenience must characterise the base quite differently from what supervenes on it [Hale] |
| 19278 | There is no gap between a fact that p, and it is true that p; so we only have the truth-condtions for p [Hale] |
| 19302 | If a chair could be made of slightly different material, that could lead to big changes [Hale] |
| 19290 | Absolute necessities are necessarily necessary [Hale] |
| 19286 | 'Absolute necessity' is when there is no restriction on the things which necessitate p [Hale] |
| 19288 | Logical and metaphysical necessities differ in their vocabulary, and their underlying entities [Hale] |
| 19285 | Logical necessity is something which is true, no matter what else is the case [Hale] |
| 19287 | Maybe each type of logic has its own necessity, gradually becoming broader [Hale] |
| 19282 | It seems that we cannot show that modal facts depend on non-modal facts [Hale] |
| 19276 | The big challenge for essentialist views of modality is things having necessary existence [Hale] |
| 19293 | Essentialism doesn't explain necessity reductively; it explains all necessities in terms of a few basic natures [Hale] |
| 19294 | If necessity derives from essences, how do we explain the necessary existence of essences? [Hale] |
| 19279 | What are these worlds, that being true in all of them makes something necessary? [Hale] |
| 19299 | Possible worlds make every proposition true or false, which endorses classical logic [Hale] |
| 2181 | It is an absurd Kantian idea that at the limit rationality and freedom coincide [Williams,B] |
| 2176 | There is only a problem of free will if you think the notion of 'voluntary' can be metaphysically deepened [Williams,B] |
| 19300 | The molecules may explain the water, but they are not what 'water' means [Hale] |
| 4317 | We judge weakness of will by an assessment after the event is concluded [Williams,B, by Cottingham] |
| 2174 | Responsibility involves cause, intention, state of mind, and response after the event [Williams,B] |
| 2178 | In bad actions, guilt points towards victims, and shame to the agent [Williams,B] |
| 2169 | Greek moral progress came when 'virtue' was freed from social status [Williams,B] |
| 2172 | The modern idea of duty is unknown in archaic Greece [Williams,B] |
| 2179 | If the moral self is seen as characterless, then other people have a very limited role in our moral lives [Williams,B] |
| 2180 | If reason cannot lead people to good, we must hope they have an internal voice [Williams,B] |
| 2175 | There is a problem of evil only if you expect the world to be good [Williams,B] |