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The links in the text to "De Docta Ignorantia (Of Learned Ignorance)" and "De Visione Dei" as well as the link to "A biography of Nicholas of Cusado" in the "External Links" section do not appear to be working.

how does nicholas of cusa have anything to do with borda in the "borda count method"?

I do not think that Cusa proposed that the Earth revolves around the Sun. See page 34 at this website: http://cla.umn.edu/sites/jhopkins/DI-Intro12-2000.pdf.

Not good

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"and that the orbits of the planets around the sun must be elliptical. He also predated Giordano Bruno in affirming the universe is infinite and Earth has no priviledged position in the universe." - I believe the text is incorrect or at the very least sloppily written. See Koyré, A., From the Closed World to the Infinite Universe; Chapter I. There is no mention of Nicholas ever stating planets go around either Earth or the Sun, much less claiming their orbits being elliptical.

You are partially right, Cusanus simply makes a point they are not circular. Probably the editor concluded they must be elliptical, though Cusanus' text leaves room for any possible shape. Daizus 09:31, 25 February 2007 (UTC)[reply]

As far as "priviledged position" is concerned: this is somewhat of a missunderstanding: the Middle Ages conception of Earth being "in the centre" meant humans were worse off. It was not understood at the time as a privileged position. Quite the contrary: it was a despicable position, related to a heavy, material nature - the Earth was at the lowest possible position - only hell was worse (being below ground). --Lynxmb 20:50, 24 February 2007 (UTC)[reply]

Fair enough. That was my addition and I haven't valued the word "priviledged" in that context as necessarily a positive thing (I was looking for a synonym for "special", "particular"), but probably I was wrong as it gives the reader (you're one good example for that), a false impression. So what's your suggestion for rephrasing? Daizus 09:31, 25 February 2007 (UTC)[reply]
I modified the article. I dropped the "elliptic orbits" fragment and I rephrased the vision upon Earth's position in the universe. Please verify if it answers your criticism. Daizus 14:47, 26 February 2007 (UTC)[reply]

I very nearly took out Predating Kepler, Cusanus said that no perfect circle can exist in the universe (opposing the Aristotelean model, and also Copernicus' later assumption of circular orbits), thus opening the possibility for Kepler's model featuring elliptical orbits of the planets around the Sun. and will soon if no-one defends it William M. Connolley (talk) 20:40, 16 August 2012 (UTC)[reply]

Neither fininte nor infinite

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@Daizus It seems to me you are only partially acquainted with what Nicholas actually stated in his books. One of the key premises (e.g. in rejecting perfect circle orbits and finity of the cosmos) is his specific form of skepticism, formulated as "docta ignorantia" or "learned ignorance". Its importance is illustrated by the fact that he intitled his book, dealing with the shape of our world, by that exact term.

Ad. "infinity of the Universe": His explicit words: "even though not infinite, we cannot imagine it as finite, since it has no confines..."

He never said the world was infinite. He reserved that predicate for God only. So he says that God is infinitus and that the world is interminatus, very clearly indicating there is a difference between them, that we ought to respect. (There is a very good reason, why I changed "affirming the universe is infinite" to "denying the universe being finite".)

This whole article is written ignoring these fine (yet crucial!) distinctions and is therefore of little use to anyone trying to inform her-/himself about Nicholas' work. I believe it should be thoroughly revised and written properly. I only tried to point out some factual inaccuracies, but even as we corrected them, the main problem is not resolved.

Some further examples:

  • "that the earth was a near-sphere ellipse shape
  • ...that revolved around the Sun, and
  • ...that each star is itself a distant sun
  • ...with its own planets"

Again, he never said anything like the Earth being "ellipse shape". I think this is the same jumping to conlusions as the case was with orbits. As for the other three, I would like to see the source of those statements. I believe they are false. --Lynxmb 19:16, 27 February 2007 (UTC)[reply]

I have not read any full text on Cusanus except some excerpts but I have read scholarship on Cusanus. From scholars I could quote I. P. Culianu with multiple works on the mystical Renaissance or historians of medieval and Renaissant philosophy like Christian Trottmann. I have edited little in this article and I agree with many of your objections, but as far as terminology goes, the scholars I've read seem to agree Cusanus' universe is infinte, not just not finite. interminatus means ad litteram without bounds, endless, which in current English when addressed to the universe is synonymous with infinite. As long as the article does not have any detailed section about Cusanus' worldview or his terminology and concepts such nuances are useless and confusing.
On your further examples I agree with all, they seem a bit of an outstretch from what Cusanus actually seems to say (or let me more precise, from what scholars argue Cusanus would have said). I'll take your points in order:
* to my knowledge Cusanus only agree the Earth was not a perfect sphere (I'm not sure if we can translate that as near-sphere, anyway ellipse is an outstretch)
* I have no knowledge of a heliostatic solar system in Cusanus' worldview
* all celestial bodies were the same, that means the sun was a star, to call each star a sun however is a bit pushing it
* I have no knowledge of such a statement from Cusanus
Perhaps a previous editor made some confusions between Cusanus and Bruno. I'll make an edit to correct it. Please improve it if you can. Daizus 22:38, 27 February 2007 (UTC)[reply]

I've modified the text an removed the disputed-template. However, the problems I described remain. --Lynxmb 18:01, 2 March 2007 (UTC)[reply]

All the problems you signaled were removed or rephrased. So what exactly remained? Daizus 21:01, 2 March 2007 (UTC)[reply]

Influence on Copernicus?

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The article says

Nicolaus Copernicus, Galileo Galilei and Giordano Bruno were all aware of the writings of Cusanus

but also

Had Copernicus been aware of these assertions...

Exactly which of his teachings was Copernicus aware of? AxelBoldt (talk) 05:29, 25 October 2008 (UTC)[reply]

That struck me too. The latter is ref'd, so the former must go William M. Connolley (talk) 20:37, 16 August 2012 (UTC)[reply]

Cusa: Concave lenses ; infinity

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The article states: "He [Cusa] was the first to use concave lenses to correct myopia. His writings were essential for Leibniz's discovery of calculus (see Law of Continuity) as well as Cantor's later work on infinity."

The claim that Cusa was the first to use concave lenses to correct myopia rests on one very vague sentence from his book De beryllo :

"Beryllus lapis est lucidus, albus et transparent, cui datur forma concava pariter et convexa et per ipsum videns attingit prius invisibile intellectualibus occulis si intellectualis beryllus, qui formam habeat maximam pariter et minimam adaptatur per eius medium attingitur indivisibile omnium principium." (De beryllo, 1458, pages 4-5)

Translation: "The beryl is a clear, bright, transparent stone, to which is given a concave as well as a convex form, and by looking through it, one attains what was previously invisible. If the intellectual beryl, which possesses both the maximum and the minimum in the same way, is adapted to the intellectual eyes, the indivisible principle of all things is attained." (Vincent Ilardi, Renaissance Vision from Spectacles to Telescopes (Philadelphia, Pennsylvania: American Philosophical Society, 2007), page 80.)

As Ilardi points out, some readers have interpreted "the maximum" as long-range vision, so that some interpret the sentence to mean that (concave) beryls (i.e., lenses) help correct myopic (near-sighted) eyes, allowing such eyes to see objects at a distance. However, the quoted passage is far from stating something like: "I have found that concave beryls [i.e., lenses] correct myopia." Cusa's book was really about the ability of the mind to perceive and comprehend (hence the "intellectual" beryl (lens)); it was not a book about optics.

I think that the claim that Nicholas of Cusa found concave lenses correct myopia should be qualified; e.g., "Some authors claim that Nicholas of Cusa found concave lenses correct myopia."

Regarding the claim that "His [Cusa's] writings were essential for Leibniz's discovery of calculus (see Law of Continuity) as well as Cantor's later work on infinity," Carl Boyer says: "The cardinal … did not contribute any work of lasting importance in mathematics." (Carl B. Boyer, The History of the Calculus and its Conceptual Development (Mineola, N.Y.: Dover, 1959), pages 89 - 94, especially page 92.)

Cwkmail (talk) 20:29, 29 June 2012 (UTC)[reply]

Over enthusiastic

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This page seemed to me far too enthusiastic (slight disclaimer: I came here via the risible http://www.schillerinstitute.org/fid_91-96/961_fascist_hobbes.html). I removed the "influence" header - I don't see why his philosophy should be discussed under that header, rather than just being about itself. I also took out the science header, and much of the section: it was largely unref'd and (as several comments above say) probably incorrect or too hypothetical. Here it is:

Nicholas is also considered by many to be a genius ahead of his time in the field of science. Galileo Galilei [citation needed] and Giordano Bruno [citation needed] were aware of the writings of Cusanus as was Johannes Kepler (who called Cusanus 'divinely inspired' in the first paragraph of his first published work). He also influenced Giordano Bruno by denying the finiteness of the universe and the Earth's exceptional position in it (being not the center of the universe, and in that regard equal in rank with the other stars). He was not, however, describing a scientifically verifiable theory of the universe: his beliefs (which proved uncannily accurate) were based almost entirely on his own personal numerological calculations and metaphysics.[1]
Cusanus made important contributions to the field of mathematics by developing the concepts of the infinitesimal and of relative motion. He was the first to use concave lenses to correct myopia [dubious – discuss].

William M. Connolley (talk) 17:35, 17 August 2012 (UTC)[reply]

References

  1. ^ Tamara Albertini, "Mathematics and Astronomy," in Introducing Nicholas of Cusa, pp. 373-406.

His views on what we now call extra terrestrials

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Shouldn't this article mention that Nicolas de Cusa is noted for his views on what we now call extra terrestrials?

“Life, as it exists on Earth in the form of men, animals and plants, is to be found, let us suppose in a high form in the solar and stellar regions. Rather than think that so many stars and parts of the heavens are uninhabited and that this earth of ours alone is peopled – and that with beings perhaps of an inferior type – we will suppose that in every region there are inhabitants, differing in nature by rank and all owing their origin to God, who is the center and circumference of all stellar regions.”

Those are just a few pages I found just now, but it's widely mentioned in discussions on extra terrestrials and theology. I thought I'd come to the wikipedia article to find out more about the background to this but there seems to be nothing which is why I'm suggesting it. Robert Walker (talk) 18:05, 29 May 2015 (UTC)[reply]

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Concave lens

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Did Nicholas of Cusa invented concave lens to treat myopia?

Possible source: "Eyeglasses made with concave lenses, for myopia, were introduced in the fifteenth century by Nikolaus von Kues Krebs (Nicholas of Cusa, 1401-1464)." Massimo Guarnieri, "An Historical Survey on Light Technologies," in IEEE Access, vol. 6, pp. 25881-25897, 2018, doi: 10.1109/ACCESS.2018.2834432 — Preceding unsigned comment added by ResIntellecta (talk • contribs) 08:28, 8 August 2024 (UTC)[reply]

We need more sources on this. This source seems to be indirectly disputing the claim: The author supplied no exact reference to Nicholas’ writings, but he probably had in mind the treatise De beryllo, written in 1450, where Nicholas described beryl as a ‘bright, clear and transparent stone, to which a concave as well as a convex form is given; by looking through it you reach what was previously invisible’ (quoted by Rosen, ‘The Invention of Eyeglasses,’ p. 206, n. 290, who rightly pointed out the difference between a piece of beryl used as a magnifying glass and spectacles). It is possible, however, that Nicholas knew of the existence of concave lenses since they were in use at Florence and Milan during his time. --Omnipaedista (talk) 13:05, 1 September 2024 (UTC)[reply]
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