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8625 | What physical facts could underlie 0 or 1, or very large numbers? |

17895 | Combining two distinct assertions does not necessarily lead to a single 'complex proposition' |

10427 | All names are names of something, real or imaginary |

4944 | Mill says names have denotation but not connotation |

7762 | Proper names are just labels for persons or objects, and the meaning is the object |

9801 | Numbers must be assumed to have identical units, as horses are equalised in 'horse-power' |

8742 | The only axioms needed are for equality, addition, and successive numbers |

9800 | Arithmetic is based on definitions, and Sums of equals are equal, and Differences of equals are equal |

9799 | 3=2+1 presupposes collections of objects ('Threes'), which may be divided thus |

9803 | We can't easily distinguish 102 horses from 103, but we could arrange them to make it obvious |

9802 | Numbers denote physical properties of physical phenomena |

9804 | Arithmetical results give a mode of formation of a given number |

9805 | 12 is the cube of 1728 means pebbles can be aggregated a certain way |

8741 | Numbers must be of something; they don't exist as abstractions |

5201 | Mill says logic and maths is induction based on a very large number of instances |

9360 | If two black and two white objects in practice produced five, what colour is the fifth one? |

9888 | Mill mistakes particular applications as integral to arithmetic, instead of general patterns |

9796 | Things possess the properties of numbers, as quantity, and as countable parts |

9794 | There are no such things as numbers in the abstract |

9795 | Numbers have generalised application to entities (such as bodies or sounds) |

9797 | '2 pebbles and 1 pebble' and '3 pebbles' name the same aggregation, but different facts |

9798 | Different parcels made from three pebbles produce different actual sensations |

12411 | Mill is too imprecise, and is restricted to simple arithmetic |

5656 | Empirical theories of arithmetic ignore zero, limit our maths, and need probability to get started |

9624 | Numbers are a very general property of objects |

9806 | Whatever is made up of parts is made up of parts of those parts |

11156 | The essence is that without which a thing can neither be, nor be conceived to be |

12190 | Necessity is what will be, despite any alternative suppositions whatever |

16859 | Most perception is one-tenth observation and nine-tenths inference |

9082 | Clear concepts result from good observation, extensive experience, and accurate memory |

16860 | Inductive generalisation is more reliable than one of its instances; they can't all be wrong |

16845 | The whole theory of induction rests on causes |

16843 | Mill's methods (Difference,Agreement,Residues,Concomitance,Hypothesis) don't nail induction |

17086 | Surprisingly, empiricists before Mill ignore explanation, which seems to transcend experience |

17091 | Explanation is fitting of facts into ever more general patterns of regularity |

16805 | Causal inference is by spotting either Agreements or Differences |

16835 | The Methods of Difference and of Agreement are forms of inference to the best explanation |

9079 | We can focus our minds on what is common to a whole class, neglecting other aspects |

9081 | We don't recognise comparisons by something in our minds; the concepts result from the comparisons |

9080 | General conceptions are a necessary preliminary to Induction |

9078 | The study of the nature of Abstract Ideas does not belong to logic, but to a different science |

8345 | A cause is the total of all the conditions which inevitably produce the result |

10391 | Causes and conditions are not distinct, because we select capriciously from among them |

14547 | The strict cause is the total positive and negative conditions which ensure the consequent |

8377 | Causation is just invariability of succession between every natural fact and a preceding fact |

14545 | A cause is an antecedent which invariably and unconditionally leads to a phenomenon |

4773 | Mill's regularity theory of causation is based on an effect preceded by a conjunction of causes |

4775 | In Mill's 'Method of Agreement' cause is the common factor in a range of different cases |

4776 | In Mill's 'Method of Difference' the cause is what stops the effect when it is removed |

9417 | What are the fewest propositions from which all natural uniformities could be inferred? |