15413 | With four tense operators, all complex tenses reduce to fourteen basic cases |

15415 | The temporal Barcan formulas fix what exists, which seems absurd |

15430 | Is classical logic a part of intuitionist logic, or vice versa? |

15431 | It is still unsettled whether standard intuitionist logic is complete |

15429 | Relevance logic's → is perhaps expressible by 'if A, then B, for that reason' |

15404 | Technical people see logic as any formal system that can be studied, not a study of argument validity |

15405 | Classical logic neglects the non-mathematical, such as temporality or modality |

15427 | The Cut Rule expresses the classical idea that entailment is transitive |

15421 | Classical logic neglects counterfactuals, temporality and modality, because maths doesn't use them |

15403 | Philosophical logic is a branch of logic, and is now centred in computer science |

15407 | Formalising arguments favours lots of connectives; proving things favours having very few |

15424 | Asserting a disjunction from one disjunct seems odd, but can be sensible, and needed in maths |

15409 | All occurrences of variables in atomic formulas are free |

15414 | The denotation of a definite description is flexible, rather than rigid |

15406 | 'Induction' and 'recursion' on complexity prove by connecting a formula to its atomic components |

15426 | We can build one expanding sequence, instead of a chain of deductions |

15425 | The sequent calculus makes it possible to have proof without transitivity of entailment |

15408 | 'Tautologies' are valid formulas of classical sentential logic - or substitution instances in other logics |

15418 | Validity (for truth) and demonstrability (for proof) have correlates in satisfiability and consistency |

15412 | Models leave out meaning, and just focus on truth values |

15411 | We only need to study mathematical models, since all other models are isomorphic to these |

15416 | We aim to get the technical notion of truth in all models matching intuitive truth in all instances |

15428 | The Liar seems like a truth-value 'gap', but dialethists see it as a 'glut' |

10185 | Set theory is the standard background for modern mathematics |

10184 | Structuralists take the name 'R' of the reals to be a variable ranging over structures, not a structure |

10189 | There is no one relation for the real number 2, as relations differ in different models |

10186 | If set theory is used to define 'structure', we can't define set theory structurally |

10187 | Abstract algebra concerns relations between models, not common features of all the models |

10188 | How can mathematical relations be either internal, or external, or intrinsic? |

15420 | De re modality seems to apply to objects a concept intended for sentences |

15419 | General consensus is S5 for logical modality of validity, and S4 for proof |

15417 | Logical necessity has two sides - validity and demonstrability - which coincide in classical logic |

15423 | It is doubtful whether the negation of a conditional has any clear meaning |

15422 | Three conditionals theories: Materialism (material conditional), Idealism (true=assertable), Nihilism (no truth) |