Combining Texts

All the ideas for 'Phenomenalism', 'Oldest System Prog. of German Idealism' and 'Cours d'Analyse'

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5 ideas

2. Reason / A. Nature of Reason / 1. On Reason

7083	Highest reason is aesthetic, and truth and good are subordinate to beauty [Hegel]
	Full Idea: I am now convinced that the highest act of reason, which embraces all ideas, is an aesthetic act, and that truth and goodness are brothers only in beauty.
	From: Georg W.F.Hegel (Oldest System Prog. of German Idealism [1796]), quoted by Simon Critchley - Continental Philosophy - V. Short Intro Append
	A reaction: This seems to be the distinctive value framework of the romantic movement and the nineteenth century, where art is destined to replace religion. However, Plato in the Symposium is an interesting ally. Aim for beauty, and the rest follows?

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / k. Infinitesimals

18085	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

18084	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?

11. Knowledge Aims / C. Knowing Reality / 2. Phenomenalism

2614	Modern phenomenalism holds that objects are logical constructions out of sense-data [Ayer]
	Full Idea: Nowadays phenomenalism is held to be a theory of perception which says that physical objects are logical constructions out of sense-data.
	From: A.J. Ayer (Phenomenalism [1947], §1)

12. Knowledge Sources / B. Perception / 4. Sense Data / a. Sense-data theory

2615	The concept of sense-data allows us to discuss appearances without worrying about reality [Ayer]
	Full Idea: The introduction of the term 'sense-datum' is a means of referring to appearances without prejudging the question of what it is, if anything, that they are appearances of.
	From: A.J. Ayer (Phenomenalism [1947], §1)