59 ideas
| 4739 | In "if and only if" (iff), "if" expresses the sufficient condition, and "only if" the necessary condition [Engel] |
| 9123 | Someone standing in a doorway seems to be both in and not-in the room [Priest,G, by Sorensen] |
| 4737 | Are truth-bearers propositions, or ideas/beliefs, or sentences/utterances? [Engel] |
| 4750 | The redundancy theory gets rid of facts, for 'it is a fact that p' just means 'p' [Engel] |
| 4744 | We can't explain the corresponding structure of the world except by referring to our thoughts [Engel] |
| 4738 | The coherence theory says truth is an internal relationship between groups of truth-bearers [Engel] |
| 4745 | Any coherent set of beliefs can be made more coherent by adding some false beliefs [Engel] |
| 4753 | Deflationism seems to block philosophers' main occupation, asking metatheoretical questions [Engel] |
| 4755 | Deflationism cannot explain why we hold beliefs for reasons [Engel] |
| 4751 | Maybe there is no more to be said about 'true' than there is about the function of 'and' in logic [Engel] |
| 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] |
| 4752 | Deflationism must reduce bivalence ('p is true or false') to excluded middle ('p or not-p') [Engel] |
| 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] |
| 15959 | If the substantial form of brass implies its stability, how can it melt and remain brass? [Alexander,P] |
| 15956 | The peripatetics treated forms and real qualities as independent of matter, and non-material [Alexander,P] |
| 4762 | The Humean theory of motivation is that beliefs may be motivators as well as desires [Engel] |
| 4754 | Our beliefs are meant to fit the world (i.e. be true), where we want the world to fit our desires [Engel] |
| 4763 | 'Evidentialists' say, and 'voluntarists' deny, that we only believe on the basis of evidence [Engel] |
| 4746 | Pragmatism is better understood as a theory of belief than as a theory of truth [Engel] |
| 4764 | We cannot directly control our beliefs, but we can control the causes of our involuntary beliefs [Engel] |
| 15975 | Can the qualities of a body be split into two groups, where the smaller explains the larger? [Alexander,P] |
| 4759 | Mental states as functions are second-order properties, realised by first-order physical properties [Engel] |
| 15963 | Science has been partly motivated by the belief that the universe is run by God's laws [Alexander,P] |
| 15951 | Alchemists tried to separate out essences, which influenced later chemistry [Alexander,P] |
| 15981 | Absolute space either provides locations, or exists but lacks 'marks' for locations [Alexander,P] |