57 ideas
| 18835 | Logic doesn't have a metaphysical basis, but nor can logic give rise to the metaphysics [Rumfitt] |
| 18819 | The idea that there are unrecognised truths is basic to our concept of truth [Rumfitt] |
| 18826 | 'True at a possibility' means necessarily true if what is said had obtained [Rumfitt] |
| 18803 | Semantics for propositions: 1) validity preserves truth 2) non-contradition 3) bivalence 4) truth tables [Rumfitt] |
| 18814 | 'Absolute necessity' would have to rest on S5 [Rumfitt] |
| 18798 | It is the second-order part of intuitionistic logic which actually negates some classical theorems [Rumfitt] |
| 18799 | Intuitionists can accept Double Negation Elimination for decidable propositions [Rumfitt] |
| 18830 | Most set theorists doubt bivalence for the Continuum Hypothesis, but still use classical logic [Rumfitt] |
| 18843 | The iterated conception of set requires continual increase in axiom strength [Rumfitt] |
| 18836 | A set may well not consist of its members; the empty set, for example, is a problem [Rumfitt] |
| 18837 | A set can be determinate, because of its concept, and still have vague membership [Rumfitt] |
| 18845 | If the totality of sets is not well-defined, there must be doubt about the Power Set Axiom [Rumfitt] |
| 18815 | Logic is higher-order laws which can expand the range of any sort of deduction [Rumfitt] |
| 18804 | The case for classical logic rests on its rules, much more than on the Principle of Bivalence [Rumfitt] |
| 18805 | Classical logic rules cannot be proved, but various lines of attack can be repelled [Rumfitt] |
| 18827 | If truth-tables specify the connectives, classical logic must rely on Bivalence [Rumfitt] |
| 18813 | Logical consequence is a relation that can extended into further statements [Rumfitt] |
| 18808 | Normal deduction presupposes the Cut Law [Rumfitt] |
| 18840 | When faced with vague statements, Bivalence is not a compelling principle [Rumfitt] |
| 18802 | In specifying a logical constant, use of that constant is quite unavoidable [Rumfitt] |
| 18800 | Introduction rules give deduction conditions, and Elimination says what can be deduced [Rumfitt] |
| 18809 | Logical truths are just the assumption-free by-products of logical rules [Rumfitt] |
| 18807 | Monotonicity means there is a guarantee, rather than mere inductive support [Rumfitt] |
| 18842 | Maybe an ordinal is a property of isomorphic well-ordered sets, and not itself a set [Rumfitt] |
| 18834 | Infinitesimals do not stand in a determinate order relation to zero [Rumfitt] |
| 18846 | Cantor and Dedekind aimed to give analysis a foundation in set theory (rather than geometry) [Rumfitt] |
| 18839 | An object that is not clearly red or orange can still be red-or-orange, which sweeps up problem cases [Rumfitt] |
| 18838 | The extension of a colour is decided by a concept's place in a network of contraries [Rumfitt] |
| 14703 | Superficial necessity is true in all worlds; deep necessity is thus true, no matter which world is actual [Schroeter] |
| 18816 | Metaphysical modalities respect the actual identities of things [Rumfitt] |
| 18825 | S5 is the logic of logical necessity [Rumfitt] |
| 18824 | Since possibilities are properties of the world, calling 'red' the determination of a determinable seems right [Rumfitt] |
| 18828 | If two possibilities can't share a determiner, they are incompatible [Rumfitt] |
| 14714 | Contradictory claims about a necessary god both seem apriori coherent [Schroeter] |
| 18821 | Possibilities are like possible worlds, but not fully determinate or complete [Rumfitt] |
| 18831 | Medieval logicians said understanding A also involved understanding not-A [Rumfitt] |
| 14704 | 2D semantics gives us apriori knowledge of our own meanings [Schroeter] |
| 18278 | Kant showed that our perceptions are partly constructed from our concepts [Reichenbach] |
| 18820 | In English 'evidence' is a mass term, qualified by 'little' and 'more' [Rumfitt] |
| 14706 | Your view of water depends on whether you start from the actual Earth or its counterfactual Twin [Schroeter] |
| 14711 | Rationalists say knowing an expression is identifying its extension using an internal cognitive state [Schroeter] |
| 14717 | Internalist meaning is about understanding; externalist meaning is about embedding in a situation [Schroeter] |
| 18817 | We understand conditionals, but disagree over their truth-conditions [Rumfitt] |
| 14720 | Semantic theory assigns meanings to expressions, and metasemantics explains how this works [Schroeter] |
| 14695 | Semantic theories show how truth of sentences depends on rules for interpreting and joining their parts [Schroeter] |
| 14696 | Simple semantics assigns extensions to names and to predicates [Schroeter] |
| 14697 | 'Federer' and 'best tennis player' can't mean the same, despite having the same extension [Schroeter] |
| 14698 | Possible worlds semantics uses 'intensions' - functions which assign extensions at each world [Schroeter] |
| 14699 | Possible worlds make 'I' and that person's name synonymous, but they have different meanings [Schroeter] |
| 14709 | Possible worlds semantics implies a constitutive connection between meanings and modal claims [Schroeter] |
| 14719 | In the possible worlds account all necessary truths are same (because they all map to the True) [Schroeter] |
| 14701 | Array worlds along the horizontal, and contexts (world,person,time) along the vertical [Schroeter] |
| 14702 | If we introduce 'actually' into modal talk, we need possible worlds twice to express this [Schroeter] |
| 14705 | Do we know apriori how we refer to names and natural kinds, but their modal profiles only a posteriori? [Schroeter] |
| 14715 | 2D fans defend it for conceptual analysis, for meaning, and for internalist reference [Schroeter] |
| 14716 | 2D semantics can't respond to contingent apriori claims, since there is no single proposition involved [Schroeter] |
| 18829 | The truth grounds for 'not A' are the possibilities incompatible with truth grounds for A [Rumfitt] |