Combining Texts

Ideas for 'Structures and Structuralism in Phil of Maths', 'Philosophy of Mathematics' and 'On the Genealogy of Morals'

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3 ideas

18. Thought / A. Modes of Thought / 1. Thought
People who think in words are orators rather than thinkers, and think about facts instead of thinking facts [Nietzsche]
     Full Idea: Whoever thinks in words thinks as an orator and not as a thinker (it shows that he does not think facts, but only in relation to facts).
     From: Friedrich Nietzsche (On the Genealogy of Morals [1887], III.§08)
     A reaction: Good. It is certainly not true that we have to think in words, or else animals wouldn't think. Good thinking should focus on reality, and be too fast for words to keep up.
18. Thought / E. Abstraction / 1. Abstract Thought
'Abstract' nowadays means outside space and time, not concrete, not physical [Brown,JR]
     Full Idea: The current usage of 'abstract' simply means outside space and time, not concrete, not physical.
     From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 2)
     A reaction: This is in contrast to Idea 9609 (the older notion of being abstracted). It seems odd that our ancestors had a theory about where such ideas came from, but modern thinkers have no theory at all. Blame Frege for that.
The older sense of 'abstract' is where 'redness' or 'group' is abstracted from particulars [Brown,JR]
     Full Idea: The older sense of 'abstract' applies to universals, where a universal like 'redness' is abstracted from red particulars; it is the one associated with the many. In mathematics, the notion of 'group' or 'vector space' perhaps fits this pattern.
     From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 2)
     A reaction: I am currently investigating whether this 'older' concept is in fact dead. It seems to me that it is needed, as part of cognitive science, and as the crucial link between a materialist metaphysic and the world of ideas.