Combining Texts

All the ideas for 'Lectures on the History of Philosophy', 'Set Theory and the Continuum Hypothesis' and 'Review of Aron 'Our Knowledge of Universals''

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5 ideas

1. Philosophy / D. Nature of Philosophy / 3. Philosophy Defined
Philosophy is the conceptual essence of the shape of history [Hegel]
     Full Idea: Philosophy is the supreme blossom - the concept - of the entire shape of history, the consciousness and the spiritual essence of the whole situation, the spirit of the age as the spirit present and aware of itself in thought.
     From: Georg W.F.Hegel (Lectures on the History of Philosophy [1830], p.25), quoted by Stephen Houlgate - An Introduction to Hegel 01
     A reaction: This sees philosophy as intrinsically historical, which is a founding idea for 'continental' philosophy. Analysis is tied to science, in which the history of the subject is seen as irrelevant to its truth. Does this mean we can't go back to Aristotle?
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism
We could accept the integers as primitive, then use sets to construct the rest [Cohen]
     Full Idea: A very reasonable position would be to accept the integers as primitive entities and then use sets to form higher entities.
     From: Paul J. Cohen (Set Theory and the Continuum Hypothesis [1966], 5.4), quoted by Oliver,A/Smiley,T - What are Sets and What are they For?
     A reaction: I find this very appealing, and the authority of this major mathematician adds support. I would say, though, that the integers are not 'primitive', but pick out (in abstraction) consistent features of the natural world.
18. Thought / D. Concepts / 2. Origin of Concepts / a. Origin of concepts
We reach concepts by clarification, or by definition, or by habitual experience [Price,HH]
     Full Idea: We have three different ways in which we arrive at concepts or universals: there is a clarification, where we have a ready-made concept and define it; we have a combination (where a definition creates a concept); and an experience can lead to a habit.
     From: H.H. Price (Review of Aron 'Our Knowledge of Universals' [1946], p.190)
     A reaction: [very compressed] He cites Russell as calling the third one a 'condensed induction'. There seems to an intellectualist and non-intellectualist strand in the abstractionist tradition.
18. Thought / E. Abstraction / 2. Abstracta by Selection
A 'felt familiarity' with universals is more primitive than abstraction [Price,HH]
     Full Idea: A 'felt familiarity' with universals seems to be more primitive than explicit abstraction.
     From: H.H. Price (Review of Aron 'Our Knowledge of Universals' [1946], p.188)
     A reaction: This I take to be part of the 'given' of the abstractionist view, which is quite well described in the first instance by Aristotle. Price says that it is 'pre-verbal'.
Our understanding of 'dog' or 'house' arises from a repeated experience of concomitances [Price,HH]
     Full Idea: Whether you call it inductive or not, our understanding of such a word as 'dog' or 'house' does arise from a repeated experience of concomitances.
     From: H.H. Price (Review of Aron 'Our Knowledge of Universals' [1946], p.191)
     A reaction: Philosophers don't use phrases like that last one any more. How else could we form the concept of 'dog' - if we are actually allowed to discuss the question of concept-formation, instead of just the logic of concepts.