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13689 | 'Theorems' are formulas provable from no premises at all |

13705 | Truth tables assume truth functionality, and are just pictures of truth functions |

13706 | Intuitively, deontic accessibility seems not to be reflexive, but to be serial |

13710 | In D we add that 'what is necessary is possible'; then tautologies are possible, and contradictions not necessary |

13711 | System B introduces iterated modalities |

13708 | S5 is the strongest system, since it has the most valid formulas, because it is easy to be S5-valid |

13712 | Epistemic accessibility is reflexive, and allows positive and negative introspection (KK and K¬K) |

13714 | We can treat modal worlds as different times |

13718 | The Barcan Formula ∀x□Fx→□∀xFx may be a defect in modal logic |

13720 | Converse Barcan Formula: □∀αφ→∀α□φ |

13723 | System B is needed to prove the Barcan Formula |

13715 | You can employ intuitionist logic without intuitionism about mathematics |

13680 | Maybe logical consequence is a primitive notion |

13678 | The most popular account of logical consequence is the semantic or model-theoretic one |

13679 | Maybe logical consequence is more a matter of provability than of truth-preservation |

13682 | Maybe logical consequence is impossibility of the premises being true and the consequent false |

13722 | A 'theorem' is an axiom, or the last line of a legitimate proof |

13696 | When a variable is 'free' of the quantifier, the result seems incapable of truth or falsity |

13700 | A 'total' function must always produce an output for a given domain |

13703 | λ can treat 'is cold and hungry' as a single predicate |

13687 | No assumptions in axiomatic proofs, so no conditional proof or reductio |

13688 | Good axioms should be indisputable logical truths |

13690 | Proof by induction 'on the length of the formula' deconstructs a formula into its accepted atoms |

13691 | Induction has a 'base case', then an 'inductive hypothesis', and then the 'inductive step' |

13685 | Natural deduction helpfully allows reasoning with assumptions |

13686 | We can build proofs just from conclusions, rather than from plain formulae |

13697 | Valuations in PC assign truth values to formulas relative to variable assignments |

13684 | The semantical notion of a logical truth is validity, being true in all interpretations |

13704 | It is hard to say which are the logical truths in modal logic, especially for iterated modal operators |

13724 | In model theory, first define truth, then validity as truth in all models, and consequence as truth-preservation |

13698 | In a complete logic you can avoid axiomatic proofs, by using models to show consequences |

13699 | Compactness surprisingly says that no contradictions can emerge when the set goes infinite |

13701 | A single second-order sentence validates all of arithmetic - but this can't be proved axiomatically |

13692 | A 'precisification' of a trivalent interpretation reduces it to a bivalent interpretation |

13693 | A 'supervaluation' assigns further Ts and Fs, if they have been assigned in every precisification |

13694 | We can 'sharpen' vague terms, and then define truth as true-on-all-sharpenings |

13695 | Supervaluational logic is classical, except when it adds the 'Definitely' operator |

13683 | A relation is a feature of multiple objects taken together |

13702 | The identity of indiscernibles is necessarily true, if being a member of some set counts as a property |

13721 | 'Strong' necessity in all possible worlds; 'weak' necessity in the worlds where the relevant objects exist |

13707 | Maybe metaphysical accessibility is intransitive, if a world in which I am a frog is impossible |

13709 | Logical truths must be necessary if anything is |

13716 | 'If B hadn't shot L someone else would have' if false; 'If B didn't shoot L, someone else did' is true |

13717 | Transworld identity is not a problem in de dicto sentences, which needn't identify an individual |

13719 | Barcan Formula problem: there might have been a ghost, despite nothing existing which could be a ghost |