51 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] |
| 9847 | A contextual definition permits the elimination of the expression by a substitution [Dummett] |
| 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] |
| 9820 | In classical logic, logical truths are valid formulas; in higher-order logics they are purely logical [Dummett] |
| 19296 | If second-order variables range over sets, those are just objects; properties and relations aren't sets [Hale] |
| 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] |
| 9896 | A prime number is one which is measured by a unit alone [Dummett] |
| 18255 | Addition of quantities is prior to ordering, as shown in cyclic domains like angles [Dummett] |
| 9895 | A number is a multitude composed of units [Dummett] |
| 9852 | We understand 'there are as many nuts as apples' as easily by pairing them as by counting them [Dummett] |
| 9829 | The identity of a number may be fixed by something outside structure - by counting [Dummett] |
| 9828 | Numbers aren't fixed by position in a structure; it won't tell you whether to start with 0 or 1 [Dummett] |
| 19295 | Add Hume's principle to logic, to get numbers; arithmetic truths rest on the nature of the numbers [Hale] |
| 9876 | Set theory isn't part of logic, and why reduce to something more complex? [Dummett] |
| 19281 | Interesting supervenience must characterise the base quite differently from what supervenes on it [Hale] |
| 9884 | The distinction of concrete/abstract, or actual/non-actual, is a scale, not a dichotomy [Dummett] |
| 9869 | Realism is just the application of two-valued semantics to sentences [Dummett] |
| 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] |
| 9880 | Nominalism assumes unmediated mental contact with objects [Dummett] |
| 9885 | The existence of abstract objects is a pseudo-problem [Dummett] |
| 9858 | Abstract objects nowadays are those which are objective but not actual [Dummett] |
| 9859 | It is absurd to deny the Equator, on the grounds that it lacks causal powers [Dummett] |
| 9860 | 'We've crossed the Equator' has truth-conditions, so accept the Equator - and it's an object [Dummett] |
| 9872 | Abstract objects need the context principle, since they can't be encountered directly [Dummett] |
| 19302 | If a chair could be made of slightly different material, that could lead to big changes [Hale] |
| 9848 | Content is replaceable if identical, so replaceability can't define identity [Dummett, by Dummett] |
| 9842 | Frege introduced criteria for identity, but thought defining identity was circular [Dummett] |
| 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] |
| 19300 | The molecules may explain the water, but they are not what 'water' means [Hale] |
| 9849 | Maybe a concept is 'prior' to another if it can be defined without the second concept [Dummett] |
| 9850 | An argument for conceptual priority is greater simplicity in explanation [Dummett] |
| 9873 | Abstract terms are acceptable as long as we know how they function linguistically [Dummett] |
| 9993 | There is no reason why abstraction by equivalence classes should be called 'logical' [Dummett, by Tait] |
| 9857 | We arrive at the concept 'suicide' by comparing 'Cato killed Cato' with 'Brutus killed Brutus' [Dummett] |
| 9833 | To abstract from spoons (to get the same number as the forks), the spoons must be indistinguishable too [Dummett] |
| 9836 | Fregean semantics assumes a domain articulated into individual objects [Dummett] |
| 7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
| 18257 | Why should the limit of measurement be points, not intervals? [Dummett] |