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18073 | Dummett says classical logic rests on meaning as truth, while intuitionist logic rests on assertability |

18074 | Intuitionists rely on assertability instead of truth, but assertability relies on truth |

6298 | Kitcher says maths is an idealisation of the world, and our operations in dealing with it |

12392 | Mathematical a priorism is conceptualist, constructivist or realist |

18078 | The interest or beauty of mathematics is when it uses current knowledge to advance undestanding |

12426 | The 'beauty' or 'interest' of mathematics is just explanatory power |

12395 | Real numbers stand to measurement as natural numbers stand to counting |

12425 | Complex numbers were only accepted when a geometrical model for them was found |

18071 | A one-operation is the segregation of a single object |

18083 | With infinitesimals, you divide by the time, then set the time to zero |

18066 | The old view is that mathematics is useful in the world because it describes the world |

18061 | Mathematical intuition is not the type platonism needs |

12420 | If mathematics comes through intuition, that is either inexplicable, or too subjective |

12393 | Intuition is no basis for securing a priori knowledge, because it is fallible |

12421 | Kant's intuitions struggle to judge relevance, impossibility and exactness |

12387 | Mathematical knowledge arises from basic perception |

12412 | My constructivism is mathematics as an idealization of collecting and ordering objects |

18065 | We derive limited mathematics from ordinary things, and erect powerful theories on their basis |

18077 | The defenders of complex numbers had to show that they could be expressed in physical terms |

12423 | Analyticity avoids abstract entities, but can there be truth without reference? |

18068 | Arithmetic is made true by the world, but is also made true by our constructions |

18069 | Arithmetic is an idealizing theory |

18070 | We develop a language for correlations, and use it to perform higher level operations |

18072 | Constructivism is ontological (that it is the work of an agent) and epistemological (knowable a priori) |

18063 | Conceptualists say we know mathematics a priori by possessing mathematical concepts |

18064 | If meaning makes mathematics true, you still need to say what the meanings refer to |

18067 | Abstract objects were a bad way of explaining the structure in mathematics |

12390 | A priori knowledge comes from available a priori warrants that produce truth |

12418 | In long mathematical proofs we can't remember the original a priori basis |

12389 | Knowledge is a priori if the experience giving you the concepts thus gives you the knowledge |

12416 | We have some self-knowledge a priori, such as knowledge of our own existence |

12413 | A 'warrant' is a process which ensures that a true belief is knowledge |

18075 | Idealisation trades off accuracy for simplicity, in varying degrees |