Combining Philosophers

All the ideas for Augustin-Louis Cauchy, Aenesidemus and Hannah Arendt

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5 ideas

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / k. Infinitesimals
Values that approach zero, becoming less than any quantity, are 'infinitesimals' [Cauchy]
     Full Idea: When the successive absolute values of a variable decrease indefinitely in such a way as to become less than any given quantity, that variable becomes what is called an 'infinitesimal'. Such a variable has zero as its limit.
     From: Augustin-Louis Cauchy (Cours d'Analyse [1821], p.19), quoted by Philip Kitcher - The Nature of Mathematical Knowledge 10.4
     A reaction: The creator of the important idea of the limit still talked in terms of infinitesimals. In the next generation the limit took over completely.
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / l. Limits
When successive variable values approach a fixed value, that is its 'limit' [Cauchy]
     Full Idea: When the values successively attributed to the same variable approach indefinitely a fixed value, eventually differing from it by as little as one could wish, that fixed value is called the 'limit' of all the others.
     From: Augustin-Louis Cauchy (Cours d'Analyse [1821], p.19), quoted by Philip Kitcher - The Nature of Mathematical Knowledge 10.4
     A reaction: This seems to be a highly significan proposal, because you can now treat that limit as a number, and adds things to it. It opens the door to Cantor's infinities. Is the 'limit' just a fiction?
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / h. Against ethics
There is no universal goal to human life [Aenesidemus, by Photius]
     Full Idea: Aenesidemus does not allow either happiness or pleasure or prudence or any other goal held by anyone on the basis of philosophical doctrine as the goal of life; rather, he says that there just is no such thing as a goal which is recognised by all people.
     From: report of Aenesidemus (Pyrrhonian Arguments (frags) [c.60 BCE], Bk 8) by 'Photius Bibliotheca' - Aenesidimus (frags) 170b
     A reaction: This is probably the dominant modern (post-Darwinian, existentialist) view. Personally I am sympathetic to the Aristotelian view that (to some extent) appropriate goals for life can be inferred from a fairly stable human nature.
24. Political Theory / C. Ruling a State / 2. Leaders / c. Despotism
Modern totalitarianism results from lack of social ties or shared goals [Arendt, by Oksala]
     Full Idea: Arendt claims that modern totalitarianism's primary condition is an atomised mass society: isolated individuals who have no strong ties to communities and who are indifferent to shared political goals.
     From: report of Hannah Arendt (The Origins of Totalitarianism [1968]) by Johanna Oksala - Political Philosophy: all that matters Ch.9
     A reaction: I think the lack of ties simply describes large modern cities. Not sure about the lack of shared goals. Hitler and Stalin rode on the back of apparent shared goals. Working classes strike me as sharing more goals than middle classes.
The ideal subject for dictators is not a fanatic, but someone who can't distinguish true from false [Arendt, by Oksala]
     Full Idea: The ideal subject of totalitarianism is not the convinced Nazi or the convinced communist, but anyone who has lost the ability to make distinctions between fact and fiction and between true and false.
     From: report of Hannah Arendt (The Origins of Totalitarianism [1968]) by Johanna Oksala - Political Philosophy: all that matters Ch.9
     A reaction: We are currently living with an apparent attempt by Donald Trump to become a totalitarian President of the U.S.A., by constantly disseminating lies, and labelling all of his critics as 'fake news'.