18835 | Logic doesn't have a metaphysical basis, but nor can logic give rise to the metaphysics |

18819 | The idea that there are unrecognised truths is basic to our concept of truth |

18826 | 'True at a possibility' means necessarily true if what is said had obtained |

18806 | Frege thought traditional categories had psychological and linguistic impurities |

18803 | Semantics for propositions: 1) validity preserves truth 2) non-contradition 3) bivalence 4) truth tables |

12204 | The logic of metaphysical necessity is S5 |

18814 | 'Absolute necessity' would have to rest on S5 |

18823 | To say there could have been people who don't exist, but deny those possible things, rejects Barcan |

18798 | It is the second-order part of intuitionistic logic which actually negates some classical theorems |

18799 | Intuitionists can accept Double Negation Elimination for decidable propositions |

18830 | Most set theorists doubt bivalence for the Continuum Hypothesis, but still use classical logic |

18843 | The iterated conception of set requires continual increase in axiom strength |

18836 | A set may well not consist of its members; the empty set, for example, is a problem |

18837 | A set can be determinate, because of its concept, and still have vague membership |

18845 | If the totality of sets is not well-defined, there must be doubt about the Power Set Axiom |

11211 | If a sound conclusion comes from two errors that cancel out, the path of the argument must matter |

18815 | Logic is higher-order laws which can expand the range of any sort of deduction |

9390 | Logic guides thinking, but it isn't a substitute for it |

18804 | The case for classical logic rests on its rules, much more than on the Principle of Bivalence |

18805 | Classical logic rules cannot be proved, but various lines of attack can be repelled |

18827 | If truth-tables specify the connectives, classical logic must rely on Bivalence |

12199 | There is a modal element in consequence, in assessing reasoning from suppositions |

12195 | Soundness in argument varies with context, and may be achieved very informally indeed |

12201 | We reject deductions by bad consequence, so logical consequence can't be deduction |

18813 | Logical consequence is a relation that can extended into further statements |

18808 | Normal deduction presupposes the Cut Law |

18840 | When faced with vague statements, Bivalence is not a compelling principle |

12194 | Contradictions include 'This is red and not coloured', as well as the formal 'B and not-B' |

11212 | The sense of a connective comes from primitively obvious rules of inference |

11210 | Standardly 'and' and 'but' are held to have the same sense by having the same truth table |

18802 | In specifying a logical constant, use of that constant is quite unavoidable |

12198 | Geometrical axioms in logic are nowadays replaced by inference rules (which imply the logical truths) |

18800 | Introduction rules give deduction conditions, and Elimination says what can be deduced |

18809 | Logical truths are just the assumption-free by-products of logical rules |

18807 | Monotonicity means there is a guarantee, rather than mere inductive support |

18842 | Maybe an ordinal is a property of isomorphic well-ordered sets, and not itself a set |

17462 | A single object must not be counted twice, which needs knowledge of distinctness (negative identity) |

18834 | Infinitesimals do not stand in a determinate order relation to zero |

18846 | Cantor and Dedekind aimed to give analysis a foundation in set theory (rather than geometry) |

18841 | Categoricity implies that Dedekind has characterised the numbers, because it has one domain |

17461 | Some 'how many?' answers are not predications of a concept, like 'how many gallons?' |

9389 | Vague membership of sets is possible if the set is defined by its concept, not its members |

18839 | An object that is not clearly red or orange can still be red-or-orange, which sweeps up problem cases |

18838 | The extension of a colour is decided by a concept's place in a network of contraries |

14532 | A distinctive type of necessity is found in logical consequence |

18816 | Metaphysical modalities respect the actual identities of things |

12193 | Logical necessity is when 'necessarily A' implies 'not-A is contradictory' |

12200 | A logically necessary statement need not be a priori, as it could be unknowable |

12202 | Narrow non-modal logical necessity may be metaphysical, but real logical necessity is not |

18825 | S5 is the logic of logical necessity |

18824 | Since possibilities are properties of the world, calling 'red' the determination of a determinable seems right |

18828 | If two possibilities can't share a determiner, they are incompatible |

12203 | If a world is a fully determinate way things could have been, can anyone consider such a thing? |

18821 | Possibilities are like possible worlds, but not fully determinate or complete |

18831 | Medieval logicians said understanding A also involved understanding not-A |

18820 | In English 'evidence' is a mass term, qualified by 'little' and 'more' |

18817 | We understand conditionals, but disagree over their truth-conditions |

18829 | The truth grounds for 'not A' are the possibilities incompatible with truth grounds for A |

11214 | We learn 'not' along with affirmation, by learning to either affirm or deny a sentence |