{"id":111,"date":"2016-11-25T06:54:45","date_gmt":"2016-11-25T06:54:45","guid":{"rendered":"http:\/\/www.muslimphilosophy.com\/ma\/newsite\/?p=111"},"modified":"2016-11-25T06:54:45","modified_gmt":"2016-11-25T06:54:45","slug":"on-infinity","status":"publish","type":"post","link":"http:\/\/www.muslimphilosophy.com\/ma\/on-infinity\/","title":{"rendered":"On infinity"},"content":{"rendered":"

<\/a>Similarities between al-Kind\u012b and David Hilbert\u00a0On infinity<\/h1>\n

Al-Kind\u012b aimed at a mathematical contradiction in the heart of the Aristotelian issue of actual infinity. In other words, actual infinity is self-canceling, and the only thing left is infinity on the potential level. Consider this example for the sake of simplification:<\/p>\n

When we count from number 1 to number 2, we can count fractions in between such as: 1.1, 1.11, 1.12, 1.13, 1.14, . . . 1.2, . . . \u00a01.3, . . . 1.9, 1.91, 1.92, . . . 1.99, 1.999, 1.9999, and we can count 1.9n<\/sup> as long as we can count, to infinity (without reaching it, of course), but no matter how many 1.99999n<\/sup> we can count, we know that the actual end is number 2, and we are only potentially<\/em> \u00a0going between 1 and 2, and what actually<\/em> exists is the finite limit of number 1 and that is number 2. The counting of 1.99999n<\/sup> to infinity is not achievable and is actually impossible to reach; however, we can potentially assume that the process of counting could go on endlessly.<\/p>\n

Al-Kind\u012b\u2019s notion of mathematical infinity\u00a0is what revealed that Aristotelian cosmology is contradictory. Bodies that exist in actuality have a finite magnitude, and if we think about a body as infinite, that is only because it happens on the level of ideas but not in reality. Natural objects are necessarily finite.<\/p>\n

Al-Kind\u012b\u2019s appeal to pure mathematics, by refuting this metaphysical notion, is an attempt to establish belief in God. His work in metaphysics might be considered one of his most significant contributions to Islamic philosophy. Aristotle mentioned the idea that actual infinity is impossible; while al-Kind\u012b\u2019s contribution was his ability to use an Aristotelian premise in order to go beyond Aristotelian cosmology itself and establish a totally different cosmos in which God is the creator. Al-Kind\u012b also appeals to the notion of infinity in order to support religious belief by scientific knowledge, by assuming that the truth is one and could be reached by reason and revelation without contradiction. (Al-Ghaz\u0101l\u012b has a similar perspective and argument, as he explains in his book The incoherence of the philosophers<\/em> [Tah\u0101fut al-fal\u0101sifa<\/em>], which we discuss later.)<\/p>\n

Al-Kind\u012b singles out the notion of infinity in order to delve into it mathematically, apply it to the natural sciences, and address it philosophically in his metaphysics. Since the time of al-Kind\u012b, few philosophers or mathematicians addressed the notion of \u201cinfinity\u201d in depth, until the twentieth century when a great mathematician, David Hilbert (1862\u20131943), published his work \u201cOn the infinite.\u201d<\/p>\n

Hilbert says, \u201c[T]he definitive clarification of the nature of the infinite<\/em> has become necessary, not merely for the special interests of the individual sciences, but rather for the honor of the human understanding<\/em> itself.\u201d[1]<\/a><\/p>\n

He discusses infinity in both fields, microphysics and macrophysics. After he mentions physics and the divisibility of atoms, particles, electrons, quanta, and how none of these permits infinite division in an absolute and unrestricted way, he says,<\/p>\n

And the net result is, certainly, that we do not find anywhere in reality a homo-geneous continuum that permits of continued division and hence would realize the infinite in the small. The infinite divisibility of a continuum is an operation that is present only in our thoughts; it is merely an idea, which is refuted by our observation of nature and by the experience gained in physics and chemistry.[2]<\/a><\/p>\n

The infinite cannot actually be found \u201canywhere in reality,\u201d especially in physics. It exists only on the level of potentiality, \u201cin our thoughts\u201d; it is an idea. A physical object that exists outside the mind is finite. The body of the world that exists outside is finite, and thus it cannot be eternal. At the end of his paper Hilbert says: \u201cThe final result then is: nowhere is the infinite realized; it is neither present in nature nor admissible as a foundation in our rational thinking\u2014a remarkable harmony between being and thought.\u201d[3]<\/a><\/p>\n

[1]<\/a> David Hilbert, \u201cOn the infinite,\u201d in From Frege to Godel: A source book in mathematical logic, 1879\u20131931<\/em>, ed. Jean van Heijenoort (Cambridge, MA: Harvard University Press, 1967), pp. 370\u2013371.<\/p>\n

[2]<\/a> Ibid.<\/p>\n

[3]<\/a> Ibid., p. 392.<\/p>\n","protected":false},"excerpt":{"rendered":"

Similarities between al-Kind\u012b and David Hilbert\u00a0On infinity Al-Kind\u012b aimed at a mathematical contradiction in the heart of the Aristotelian issue of actual infinity. In other words, actual infinity is self-canceling, and the only thing left is infinity on the potential … Continue reading →<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11,4,8,10],"tags":[],"_links":{"self":[{"href":"http:\/\/www.muslimphilosophy.com\/ma\/wp-json\/wp\/v2\/posts\/111"}],"collection":[{"href":"http:\/\/www.muslimphilosophy.com\/ma\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.muslimphilosophy.com\/ma\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.muslimphilosophy.com\/ma\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.muslimphilosophy.com\/ma\/wp-json\/wp\/v2\/comments?post=111"}],"version-history":[{"count":1,"href":"http:\/\/www.muslimphilosophy.com\/ma\/wp-json\/wp\/v2\/posts\/111\/revisions"}],"predecessor-version":[{"id":112,"href":"http:\/\/www.muslimphilosophy.com\/ma\/wp-json\/wp\/v2\/posts\/111\/revisions\/112"}],"wp:attachment":[{"href":"http:\/\/www.muslimphilosophy.com\/ma\/wp-json\/wp\/v2\/media?parent=111"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.muslimphilosophy.com\/ma\/wp-json\/wp\/v2\/categories?post=111"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.muslimphilosophy.com\/ma\/wp-json\/wp\/v2\/tags?post=111"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}