60 ideas
| 15169 | Metaphysics is clarifying how we speak and think (and possibly improving it) [Sidelle] |
| 9123 | Someone standing in a doorway seems to be both in and not-in the room [Priest,G, by Sorensen] |
| 15164 | We seem to base necessities on thought experiments and imagination [Sidelle] |
| 8720 | A logic is 'relevant' if premise and conclusion are connected, and 'paraconsistent' allows contradictions [Priest,G, by Friend] |
| 9672 | Free logic is one of the few first-order non-classical logics [Priest,G] |
| 9697 | X1 x X2 x X3... x Xn indicates the 'cartesian product' of those sets [Priest,G] |
| 9685 | <a,b&62; is a set whose members occur in the order shown [Priest,G] |
| 9675 | a ∈ X says a is an object in set X; a ∉ X says a is not in X [Priest,G] |
| 9674 | {x; A(x)} is a set of objects satisfying the condition A(x) [Priest,G] |
| 9673 | {a1, a2, ...an} indicates that a set comprising just those objects [Priest,G] |
| 9677 | Φ indicates the empty set, which has no members [Priest,G] |
| 9676 | {a} is the 'singleton' set of a (not the object a itself) [Priest,G] |
| 9679 | X⊂Y means set X is a 'proper subset' of set Y [Priest,G] |
| 9678 | X⊆Y means set X is a 'subset' of set Y [Priest,G] |
| 9681 | X = Y means the set X equals the set Y [Priest,G] |
| 9683 | X ∩ Y indicates the 'intersection' of sets X and Y, the objects which are in both sets [Priest,G] |
| 9682 | X∪Y indicates the 'union' of all the things in sets X and Y [Priest,G] |
| 9684 | Y - X is the 'relative complement' of X with respect to Y; the things in Y that are not in X [Priest,G] |
| 9694 | The 'relative complement' is things in the second set not in the first [Priest,G] |
| 9693 | The 'intersection' of two sets is a set of the things that are in both sets [Priest,G] |
| 9692 | The 'union' of two sets is a set containing all the things in either of the sets [Priest,G] |
| 9698 | The 'induction clause' says complex formulas retain the properties of their basic formulas [Priest,G] |
| 9695 | An 'ordered pair' (or ordered n-tuple) is a set with its members in a particular order [Priest,G] |
| 9696 | A 'cartesian product' of sets is the set of all the n-tuples with one member in each of the sets [Priest,G] |
| 9686 | A 'set' is a collection of objects [Priest,G] |
| 9689 | The 'empty set' or 'null set' has no members [Priest,G] |
| 9690 | A set is a 'subset' of another set if all of its members are in that set [Priest,G] |
| 9691 | A 'proper subset' is smaller than the containing set [Priest,G] |
| 9688 | A 'singleton' is a set with only one member [Priest,G] |
| 9687 | A 'member' of a set is one of the objects in the set [Priest,G] |
| 9680 | The empty set Φ is a subset of every set (including itself) [Priest,G] |
| 13373 | Typically, paradoxes are dealt with by dividing them into two groups, but the division is wrong [Priest,G] |
| 13368 | The 'least indefinable ordinal' is defined by that very phrase [Priest,G] |
| 13370 | 'x is a natural number definable in less than 19 words' leads to contradiction [Priest,G] |
| 13369 | By diagonalization we can define a real number that isn't in the definable set of reals [Priest,G] |
| 13366 | The least ordinal greater than the set of all ordinals is both one of them and not one of them [Priest,G] |
| 13367 | The next set up in the hierarchy of sets seems to be both a member and not a member of it [Priest,G] |
| 13371 | If you know that a sentence is not one of the known sentences, you know its truth [Priest,G] |
| 13372 | There are Liar Pairs, and Liar Chains, which fit the same pattern as the basic Liar [Priest,G] |
| 15180 | There doesn't seem to be anything in the actual world that can determine modal facts [Sidelle] |
| 15184 | Causal reference presupposes essentialism if it refers to modally extended entities [Sidelle] |
| 15172 | Clearly, essential predications express necessary properties [Sidelle] |
| 15181 | Being a deepest explanatory feature is an actual, not a modal property [Sidelle] |
| 15173 | That the essence of water is its microstructure is a convention, not a discovery [Sidelle] |
| 15185 | We aren't clear about 'same stuff as this', so a principle of individuation is needed to identify it [Sidelle] |
| 15175 | Evaluation of de dicto modalities does not depend on the identity of its objects [Sidelle] |
| 15032 | Necessary a posteriori is conventional for necessity and nonmodal for a posteriority [Sidelle, by Sider] |
| 15179 | To know empirical necessities, we need empirical facts, plus conventions about which are necessary [Sidelle] |
| 15171 | The necessary a posteriori is statements either of identity or of essence [Sidelle] |
| 15167 | Empiricism explores necessities and concept-limits by imagining negations of truths [Sidelle] |
| 15177 | Contradictoriness limits what is possible and what is imaginable [Sidelle] |
| 15176 | The individuals and kinds involved in modality are also a matter of convention [Sidelle] |
| 15174 | A thing doesn't need transworld identity prior to rigid reference - that could be a convention of the reference [Sidelle] |
| 15183 | 'Dthat' operates to make a singular term into a rigid term [Sidelle] |
| 15165 | A priori knowledge is entirely of analytic truths [Sidelle] |
| 20653 | Six reduction levels: groups, lives, cells, molecules, atoms, particles [Putnam/Oppenheim, by Watson] |
| 15168 | That water is essentially H2O in some way concerns how we use 'water' [Sidelle] |
| 15166 | Causal reference seems to get directly at the object, thus leaving its nature open [Sidelle] |
| 15182 | Because some entities overlap, reference must have analytic individuation principles [Sidelle] |
| 15178 | Can anything in science reveal the necessity of what it discovers? [Sidelle] |