{"id":7094,"date":"2015-06-12T17:36:55","date_gmt":"2015-06-12T17:36:55","guid":{"rendered":"https:\/\/maverickphilosopher.blog\/index.php\/2015\/06\/12\/world-god-god-a-mathematical-analogy\/"},"modified":"2015-06-12T17:36:55","modified_gmt":"2015-06-12T17:36:55","slug":"world-god-god-a-mathematical-analogy","status":"publish","type":"post","link":"https:\/\/maverickphilosopher.blog\/index.php\/2015\/06\/12\/world-god-god-a-mathematical-analogy\/","title":{"rendered":"World + God = God: A Mathematical Analogy"},"content":{"rendered":"

 The Big Henry offers the following comment on my post, World + God = God?<\/a><\/span><\/p>\n

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"<\/span>World + God = God" is (mathematically) analogous to "number + infinity = infinity", where "number" is finite. If God embodies all existence, then God is "existential infinity", and, therefore, no amount of existence can be added to or subtracted from God's totality.<\/span><\/div>\n
 <\/span><\/div>\n
The numerical concept of infinity does not comply with the rules of arithmetic addition or subtraction. Similarly, if God is presumed to be the embodiment of all existence, He does not comply with the rules of arithmetic addition or subtraction. <\/span><\/div>\n<\/blockquote>\n
To supply an example that supports Big Henry's point, 8 + \"\\aleph_0\" = \"\\aleph_0\".  \"\\aleph_0\" (aleph-nought, aleph-zero, aleph-null) is the first transfinite cardinal.  A cardinal number answers the How many? question.  Thus the cardinal number of the set {Manny, Moe, Jack} is 3, and the cardinal number of {1, 3, 5, 7} is 4.  Cardinality is a measure of a set's size. What about the infinite set of natural numbers {0, 1, 2, 3, 4 . . . n, n + 1, . . .}?  How many?  \"\\aleph_0\".  And as was known long before Georg Cantor, it is possible to have two infinite sets, call them E and N such that E is a proper<\/em> subset of N, but both E and N have the same size or cardinality.  Thus the evens are a proper subset of the naturals, but there are just as many of the former as there are of the latter, namely, \"\\aleph_0\".  How can this be?  Well, EACH element of the evens can be put into 1-1 correspondence with an element of the naturals.
<\/span><\/div>\n
 <\/span><\/div>\n
So far the analogy holds.  But I think Big Henry has overlooked the transfinite ordinals<\/em>.  The first transfinite ordinal, denoted \"omega\", is the order type<\/a> of the set of nonnegative integers.  (See here<\/a>.)  You could think of \"omega\" as the successor of the natural numbers.  It is the first number following the entire infinite sequence of natural numbers. (Dauben, 97)  The successor of <\/span> \"omega\"  is  \"omega\" + 1.  These two numbers are therefore different.  Here the analogy breaks down.  God + Socrates = God.  \"omega\" + 1 is not equal to \"omega\".
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Moreover, it is not true to say that "The numerical concept of infinity does not comply with the rules of arithmetic addition or subtraction."  This ignores the rules of transfinite cardinal arithmetic and those of transfinite ordinal arithmetic<\/a>.  Big Henry seems to be operating with a pre-Cantorian notion of infinity.  Since Cantor we have an exact mathematics of infinity.<\/span><\/div>\n
 <\/span><\/div>\n
In any case,  I rather doubt that mathematical infinity provides a good analogy for the divine infinity.  God is not a set!<\/span><\/div>\n","protected":false},"excerpt":{"rendered":"

 The Big Henry offers the following comment on my post, World + God = God? "World + God = God" is (mathematically) analogous to "number + infinity = infinity", where "number" is finite. If God embodies all existence, then God is "existential infinity", and, therefore, no amount of existence can be added to or subtracted … Continue reading “World + God = God: A Mathematical Analogy”<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[688,143,475,476],"tags":[],"class_list":["post-7094","post","type-post","status-publish","format-standard","hentry","category-cantor","category-god","category-infinity","category-mathematics"],"_links":{"self":[{"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/posts\/7094","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/comments?post=7094"}],"version-history":[{"count":0,"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/posts\/7094\/revisions"}],"wp:attachment":[{"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/media?parent=7094"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/categories?post=7094"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/tags?post=7094"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}