71 ideas
5831 | The new view is that "water" is a name, and has no definition [Schwartz,SP] |
6052 | Definitions identify two concepts, so they presuppose identity [McGinn] |
6064 | Regresses are only vicious in the context of an explanation [McGinn] |
6088 | Truth is a method of deducing facts from propositions [McGinn] |
6084 | 'Snow does not fall' corresponds to snow does fall [McGinn] |
6085 | The idea of truth is built into the idea of correspondence [McGinn] |
6083 | The coherence theory of truth implies idealism, because facts are just coherent beliefs [McGinn] |
6086 | Truth is the property of propositions that makes it possible to deduce facts [McGinn] |
6087 | Without the disquotation device for truth, you could never form beliefs from others' testimony [McGinn] |
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] |
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] |
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] |
9680 | The empty set Φ is a subset of every set (including itself) [Priest,G] |
6051 | In 'x is F and x is G' we must assume the identity of x in the two statements [McGinn] |
6055 | Both non-contradiction and excluded middle need identity in their formulation [McGinn] |
6059 | Identity is unitary, indefinable, fundamental and a genuine relation [McGinn] |
5829 | We refer to Thales successfully by name, even if all descriptions of him are false [Schwartz,SP] |
5830 | The traditional theory of names says some of the descriptions must be correct [Schwartz,SP] |
6067 | Existential quantifiers just express the quantity of things, leaving existence to the predicate 'exists' [McGinn] |
6042 | The quantifier is overrated as an analytical tool [McGinn] |
6069 | 'Partial quantifier' would be a better name than 'existential quantifier', as no existence would be implied [McGinn] |
6068 | We need an Intentional Quantifier ("some of the things we talk about.."), so existence goes into the proposition [McGinn] |
6070 | Existence is a primary quality, non-existence a secondary quality [McGinn] |
6062 | Existence can't be analysed as instantiating a property, as instantiation requires existence [McGinn] |
6065 | We can't analyse the sentence 'something exists' in terms of instantiated properties [McGinn] |
6082 | If causal power is the test for reality, that will exclude necessities and possibilities [McGinn] |
6075 | Facts are object-plus-extension, or property-plus-set-of-properties, or object-plus-property [McGinn] |
6058 | Identity propositions are not always tautological, and have a key epistemic role [McGinn] |
6053 | Identity is as basic as any concept could ever be [McGinn] |
6043 | Type-identity is close similarity in qualities [McGinn] |
6044 | Qualitative identity is really numerical identity of properties [McGinn] |
6046 | Qualitative identity can be analysed into numerical identity of the type involved [McGinn] |
6045 | It is best to drop types of identity, and speak of 'identity' or 'resemblance' [McGinn] |
6066 | Existence is a property of all objects, but less universal than self-identity, which covers even conceivable objects [McGinn] |
6054 | Sherlock Holmes does not exist, but he is self-identical [McGinn] |
6047 | All identity is necessary, though identity statements can be contingently true [McGinn] |
6049 | Leibniz's Law says 'x = y iff for all P, Px iff Py' [McGinn] |
6048 | Leibniz's Law is so fundamental that it almost defines the concept of identity [McGinn] |
6050 | Leibniz's Law presupposes the notion of property identity [McGinn] |
6080 | Modality is not objects or properties, but the type of binding of objects to properties [McGinn] |
6079 | If 'possible' is explained as quantification across worlds, there must be possible worlds [McGinn] |
6081 | Necessity and possibility are big threats to the empiricist view of knowledge [McGinn] |
6071 | Scepticism about reality is possible because existence isn't part of appearances [McGinn] |
5826 | The intension of "lemon" is the conjunction of properties associated with it [Schwartz,SP] |
6077 | Semantics should not be based on set-membership, but on instantiation of properties in objects [McGinn] |
6074 | Clearly predicates have extensions (applicable objects), but are the extensions part of their meaning? [McGinn] |
6072 | If Satan is the most imperfect conceivable being, he must have non-existence [McGinn] |
6073 | I think the fault of the Ontological Argument is taking the original idea to be well-defined [McGinn] |