Combining Philosophers

All the ideas for Metrodorus (Lamp), Henri Poincar and Alexander Baumgarten

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10 ideas

6. Mathematics / A. Nature of Mathematics / 2. Geometry

10245	One geometry cannot be more true than another [Poincaré]
	Full Idea: One geometry cannot be more true than another; it can only be more convenient.
	From: Henri Poincaré (Science and Method [1908], p.65), quoted by Stewart Shapiro - Philosophy of Mathematics
	A reaction: This is the culminating view after new geometries were developed by tinkering with Euclid's parallels postulate.

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / d. Actual infinite

15923	Poincaré rejected the actual infinite, claiming definitions gave apparent infinity to finite objects [Poincaré, by Lavine]
	Full Idea: Poincaré rejected the actual infinite. He viewed mathematics that is apparently concerned with the actual infinite as actually concerning the finite linguistic definitions the putatively describe actually infinite objects.
	From: report of Henri Poincaré (On the Nature of Mathematical Reasoning [1894]) by Shaughan Lavine - Understanding the Infinite

6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism

10180	Mathematicians do not study objects, but relations between objects [Poincaré]
	Full Idea: Mathematicians do not study objects, but relations between objects; it is a matter of indifference if the objects are replaced by others, provided the relations do not change. They are interested in form alone, not matter.
	From: Henri Poincaré (Science and Hypothesis [1902], p.20), quoted by E Reck / M Price - Structures and Structuralism in Phil of Maths §6
	A reaction: This connects modern structuralism with Aritotle's interest in the 'form' of things. Contrary to the views of the likes of Frege, it is hard to see that the number '7' has any properties at all, apart from its relations. A daffodil would do just as well.

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

9916	Convention, yes! Arbitrary, no! [Poincaré, by Putnam]
	Full Idea: Poincaré once exclaimed, 'Convention, yes! Arbitrary, no!'.
	From: report of Henri Poincaré (talk [1901]) by Hilary Putnam - Models and Reality
	A reaction: An interesting view. It mustn't be assumed that conventions are not rooted in something. Maybe a sort of pragmatism is implied.

6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism

18203	Avoid non-predicative classifications and definitions [Poincaré]
	Full Idea: Never consider any objects but those capable of being defined in a finite number of word ...Avoid non-predicative classifications and definitions.
	From: Henri Poincaré (The Logic of Infinity [1909], p.63), quoted by Penelope Maddy - Naturalism in Mathematics II.4

21. Aesthetics / A. Aesthetic Experience / 1. Aesthetics

8063	Baumgarten founded aesthetics in 1750 [Baumgarten, by Tolstoy]
	Full Idea: Baumgarten founded aesthetics in the year 1750.
	From: report of Alexander Baumgarten (Aesthetica [1739]) by Leo Tolstoy - What is Art? Ch.2
	A reaction: He gave it a label, separated it off from the rest of philosophy, and made taste the main focus. The philosophy of art goes back to at least Plato's 'Republic' and 'Symposium'.

21. Aesthetics / B. Nature of Art / 2. Art as Form

8118	Beauty is an order between parts, and in relation to the whole [Baumgarten, by Tolstoy]
	Full Idea: Beauty is defined by Baumgarten as a correspondence, that is, an order of parts in their mutual relations to each other and in their relation to the whole.
	From: report of Alexander Baumgarten (Aesthetica [1739]) by Leo Tolstoy - What is Art? Ch.3
	A reaction: This may be one aspect of what is beautiful, but rather more than a nice arrangement is probably needed for art. We must distinguish flower arranging from poetic drama. Some masterpieces are rather messily arranged.

22. Metaethics / C. The Good / 1. Goodness / b. Types of good

8117	Perfection comes through the senses (Beauty), through reason (Truth), and through moral will (Good) [Baumgarten, by Tolstoy]
	Full Idea: For Baumgarten, Beauty is the Perfect (the Absolute), recognised through the senses; Truth is the Perfect perceived through reason; Goodness is the Perfect reached by moral will.
	From: report of Alexander Baumgarten (Aesthetica [1739]) by Leo Tolstoy - What is Art? Ch.3
	A reaction: At last, after many years of searching, I have found the origin of that great trio of ideals: Beauty, Goodness and Truth. Tolstoy sneers at them, but a person could do a lot worse than spending their lives trying to promote them.

23. Ethics / A. Egoism / 2. Hedonism

5954	All inventions of the mind aim at pleasure, and those that don't are worthless [Metrodorus of Lamp., by Plutarch]
	Full Idea: Metrodorus says that all the wonderful, ingenious and brilliant inventions of the mind have been contrived for the sake of pleasure of the flesh or for the sake of looking forward to it, and any accomplishment not leading to this end is worthless.
	From: report of Metrodorus (Lamp) (fragments/reports [c.291 BCE], Fr 6) by Plutarch - 74: Reply to Colotes §1125
	A reaction: It is very hard to think of counterexamples! Would anyone bother to work out the theorems of number theory if they didn't enjoy doing it? Would any sensible person make great sacrifices if they didn't think that increased happiness would result?

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.