Combining Texts

All the ideas for 'The Value of Science', 'Space and Time' and 'Elements of Intuitionism'

unexpand these ideas     |    start again     |     specify just one area for these texts

---

4 ideas

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.

26. Natural Theory / D. Laws of Nature / 11. Against Laws of Nature

15877	The aim of science is just to create a comprehensive, elegant language to describe brute facts [Poincaré, by Harré]
	Full Idea: In Poincaré's view, we try to construct a language within which the brute facts of experience are expressed as comprehensively and as elegantly as possible. The job of science is the forging of a language precisely suited to that purpose.
	From: report of Henri Poincaré (The Value of Science [1906], Pt III) by Rom Harré - Laws of Nature 2
	A reaction: I'm often struck by how obscure and difficult our accounts of self-evident facts can be. Chairs are easy, and the metaphysics of chairs is hideous. Why is that? I'm a robust realist, but I like Poincaré's idea. He permits facts.

27. Natural Reality / C. Space / 6. Space-Time

14014	Space alone, and time alone, will fade away, and only their union has an independent reality [Minkowski]
	Full Idea: Henceforth, space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality.
	From: Hermann Minkowski (Space and Time [1908], Intro)
	A reaction: Notice the qualification that it is a 'kind of' union. Deep confusion arises from exaggerating the analogy between space and time. Craig Bourne remarks (2006:157) that this shows independence of measurement, not of reality