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All the ideas for 'Philosophy of Mathematics', 'German Philosophy 1760-1860' and 'Capital Vol. 3'

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10 ideas

1. Philosophy / C. History of Philosophy / 4. Later European Philosophy / c. Eighteenth century philosophy
Wolff's version of Leibniz dominated mid-18th C German thought [Pinkard]
     Full Idea: The dominant philosophy of mid-eighteenth century Germany was Wolffianism, a codified and almost legalistically organised form of Leibnizian thought.
     From: Terry Pinkard (German Philosophy 1760-1860 [2002], Intro)
     A reaction: Kant grew up in this intellectual climate.
Romantics explored beautiful subjectivity, and the re-enchantment of nature [Pinkard]
     Full Idea: Early Romanticism can be seen as the exploration of subjective interiority and as the re-enchantment of nature (as organic). Hegel said they had the idea of a 'beautiful soul', which (he said) either paralysed action, or made them smug.
     From: Terry Pinkard (German Philosophy 1760-1860 [2002], 06)
     A reaction: [compressed, inc Note 1] A major dilemma of life is the extent of our social engagement, because it makes life worthwhile, but pollutes the mind with continual conflicts.
The combination of Kant and the French Revolution was an excited focus for German philosophy [Pinkard]
     Full Idea: After the French Revolution, philosophy suddenly became the key rallying point for an entire generation of German intellectuals, who had been reading Kant as the harbinger of a new order.
     From: Terry Pinkard (German Philosophy 1760-1860 [2002], Pt II Intro)
     A reaction: Kant was a harbinger because he offered an autonomous status to each individual, rather than being subservient to a social order.
1. Philosophy / C. History of Philosophy / 4. Later European Philosophy / d. Nineteenth century philosophy
In Hegel's time naturalism was called 'Spinozism' [Pinkard]
     Full Idea: In Hegel's time the shorthand for the Naturalistic worldview was 'Spinozism'.
     From: Terry Pinkard (German Philosophy 1760-1860 [2002], 10)
     A reaction: Spinozism hit Germany like a bomb in 1786, when it was reported that the poet Hölderlin was a fan of Spinoza.
2. Reason / D. Definition / 8. Impredicative Definition
Predicative definitions only refer to entities outside the defined collection [Horsten]
     Full Idea: Definitions are called 'predicative', and are considered sound, if they only refer to entities which exist independently from the defined collection.
     From: Leon Horsten (Philosophy of Mathematics [2007], §2.4)
5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms
A theory is 'categorical' if it has just one model up to isomorphism [Horsten]
     Full Idea: If a theory has, up to isomorphism, exactly one model, then it is said to be 'categorical'.
     From: Leon Horsten (Philosophy of Mathematics [2007], §5.2)
6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
Computer proofs don't provide explanations [Horsten]
     Full Idea: Mathematicians are uncomfortable with computerised proofs because a 'good' proof should do more than convince us that a certain statement is true. It should also explain why the statement in question holds.
     From: Leon Horsten (Philosophy of Mathematics [2007], §5.3)
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
The concept of 'ordinal number' is set-theoretic, not arithmetical [Horsten]
     Full Idea: The notion of an ordinal number is a set-theoretic, and hence non-arithmetical, concept.
     From: Leon Horsten (Philosophy of Mathematics [2007], §2.3)
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / a. Idealism
Idealism is the link between reason and freedom [Pinkard]
     Full Idea: Idealism was conceived as a link between reason and freedom.
     From: Terry Pinkard (German Philosophy 1760-1860 [2002], 14 Conc)
     A reaction: I'm beginning to see the Romantic era as the Age of Freedom, which followed the Age of Reason. This idea fits that picture nicely. Pinkard says that paradoxes resulted from the attemptl
24. Political Theory / D. Ideologies / 9. Communism
Freedom only comes when labour is no longer necessary [Marx]
     Full Idea: The realm of freedom actually begins only where labour which is determined by necessity and mundane considerations ceases.
     From: Karl Marx (Capital Vol. 3 [1873], p.496), quoted by Peter Singer - Marx 8
     A reaction: This is a bit discouraging fo idealistic dreamers. Modern political thought needs an ecological dimension to this problem. If society always needs a fair degree of labour, there must be a way to maximise freedom in that context.