I think there are two things described as "generalisation":
1) Noting properties shared by disparate objects, articulating the properties, interacting with or reasoning about the objects in terms of those properties.
2) Noting groups of objects which are likely to have certain properties, or which express a particular property in differing degrees. Interacting with or reasoning about the objects in terms of those properties.
The former is analytical, has formal correctness as a rule of inference, and (empirically) works unless you make a mistake in your analysis. The latter leads to "categorical" statements with exceptions, relies on intuition for whether the exceptions "matter", and is logically unsound in that it can lead you to reason about an object in terms of a property which it does not actually have.
They're both pretty useful in daily life, depending how you prefer to think about different things. Language seems to be mostly built of type 2 generalisations. Mathematics attempts to be built exclusively of type 1 generalisations. Reasoning with type 2 generalisations is prone to arguments about the meaning of "socialism", or "fruitcake", or "dangerous dog", or whatever. Reasoning with type 1 generalisation is prone to not having the full information needed to get anywhere with certainty.
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Date: 2007-06-14 01:32 pm (UTC)1) Noting properties shared by disparate objects, articulating the properties, interacting with or reasoning about the objects in terms of those properties.
2) Noting groups of objects which are likely to have certain properties, or which express a particular property in differing degrees. Interacting with or reasoning about the objects in terms of those properties.
The former is analytical, has formal correctness as a rule of inference, and (empirically) works unless you make a mistake in your analysis. The latter leads to "categorical" statements with exceptions, relies on intuition for whether the exceptions "matter", and is logically unsound in that it can lead you to reason about an object in terms of a property which it does not actually have.
They're both pretty useful in daily life, depending how you prefer to think about different things. Language seems to be mostly built of type 2 generalisations. Mathematics attempts to be built exclusively of type 1 generalisations. Reasoning with type 2 generalisations is prone to arguments about the meaning of "socialism", or "fruitcake", or "dangerous dog", or whatever. Reasoning with type 1 generalisation is prone to not having the full information needed to get anywhere with certainty.