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Ideas for 'Logical Pluralism', 'Number Determiners, Numbers, Arithmetic' and 'Reasoning and the Logic of Things'

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4 ideas

14. Science / C. Induction / 2. Aims of Induction
'Induction' doesn't capture Greek 'epagoge', which is singulars in a mass producing the general [Peirce]
     Full Idea: The word 'inductio' is Cicero's imitation of Aristotle's term 'epagoge'. It fails to convey the full significance of the Greek word, which implies the examples are arrayed and brought forward in a mass. 'The assault upon the generals by the singulars'.
     From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], II)
     A reaction: Interesting, thought I don't think there is enough evidence in Aristotle to get the Greek idea fully clear.
14. Science / C. Induction / 3. Limits of Induction
How does induction get started? [Peirce]
     Full Idea: Induction can never make a first suggestion.
     From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], II)
     A reaction: This seems to lead to the general modern problem of the 'theory-laden' nature of observation. You don't see anything at all without some idea of what you are looking for. How do you spot the 'next instance'. Instance of what? Nice.
Induction can never prove that laws have no exceptions [Peirce]
     Full Idea: Induction can never afford the slightest reason to think that a law is without an exception.
     From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], II)
     A reaction: Part of the general Humean doubts about induction, but very precisely stated, and undeniable. You can then give up on universal laws, or look for deeper reasons to justify your conviction that there are no exceptions. E.g. observe mass, or Higgs Boson.
The worst fallacy in induction is generalising one recondite property from a sample [Peirce]
     Full Idea: The most dangerous fallacy of inductive reasoning consists in examining a sample, finding some recondite property in it, and concluding at once that it belongs to the whole collection.
     From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], V)
     A reaction: The point, I take it, is not that you infer that the whole collection has all the properties of the sample, but that some 'recondite' or unusual property is sufficiently unusual to be treated as general.