Combining Texts

All the ideas for 'Truth (frags)', 'Elements of Intuitionism' and 'Giordano Bruno and Hermetic Tradition'

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4 ideas

1. Philosophy / B. History of Ideas / 4. Early European Thought

9288	The magic of Asclepius enters Renaissance thought mixed into Ficino's neo-platonism [Yates]
	Full Idea: The magic of Asclepius, reinterpreted through Plotinus, enters with Ficino's De Vita into the neo-platonic philosophy of the Renaissance, and, moreover, into Ficino's Christian Platonism.
	From: Frances A. Yates (Giordano Bruno and Hermetic Tradition [1964], Ch.4)
	A reaction: Asclepius is the source of 'Hermetic' philosophy. This move seems to be what gives the Renaissance period its rather quirky and distinctive character. Montaigne was not a typical figure. Most of them wanted to become gods and control the stars!

9291	The dating, in 1614, of the Hermetic writings as post-Christian is the end of the Renaissance [Yates]
	Full Idea: The dating by Isaac Casaubon in 1614 of the Hermetic writings as not the work of a very ancient Egyptian priest but written in post-Christian times, is a watershed separating the Renaissance world from the modern world.
	From: Frances A. Yates (Giordano Bruno and Hermetic Tradition [1964], Ch.21)
	A reaction: I tend to place the end of the Renaissance with the arrival of the telescope in 1610, so the two dates coincide. Simply, magic was replaced by science. Religion ran alongside, gasping for breath. Mathematics was freed from numerology.

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / c. Potential infinite

15938	Platonists ruin infinity, which is precisely a growing structure which is never completed [Dummett]
	Full Idea: The platonist destroys the whole essence of infinity, which lies in the conception of a structure which is always in growth, precisely because the process of construction is never completed.
	From: Michael Dummett (Elements of Intuitionism [1977], p.57), quoted by Thomas J. McKay - Plural Predication
	A reaction: I don't warm to intuitionism, but I warm to this conception of infinity. Completed infinities are convenient reifications for mathematicians.

6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism

15939	For intuitionists it is constructed proofs (which take time) which make statements true [Dummett]
	Full Idea: For an intuitionist a mathematical statement is rendered true or false by a proof or disproof, that is, by a construction, and constructions are effected in time.
	From: Michael Dummett (Elements of Intuitionism [1977], p.336), quoted by Shaughan Lavine - Understanding the Infinite VI.2
	A reaction: Lavine is quoting this to draw attention to the difficulties of thinking of it as all taking place 'in time', especially when dealing with infinities.