{"id":594,"date":"2016-11-25T23:30:20","date_gmt":"2016-11-26T04:30:20","guid":{"rendered":"http:\/\/aristotle2digital.blogwyrm.com\/?p=594"},"modified":"2016-11-25T19:33:38","modified_gmt":"2016-11-26T00:33:38","slug":"the-more-things-change","status":"publish","type":"post","link":"https:\/\/aristotle2digital.blogwyrm.com\/?p=594","title":{"rendered":"The More Things Change…"},"content":{"rendered":"

The scope of human knowledge has certainly changed over the last 3000 years.\u00a0 Daily, we manipulate electrons and beam electromagnetic signals to and fro.\u00a0 Large scale distribution networks move goods between highly specialized production centers.\u00a0 Information flows from one corner of the globe to another in a matter of seconds.\u00a0 Clearly, we live in an age of wonder.\u00a0 But interestingly, while what we have learned has increased over the centuries, the methods of inquiry into obtaining new knowledge really haven\u2019t changed all that much; certainly what we know has changed greatly but not how we learn it.<\/p>\n

Case in point, it the use of regression or recursion as a tool for understanding the world in a philosophical way.\u00a0 The applications of this approach are numerous due to the wide utility and the fruitful applications of it.<\/p>\n

For example, Aristotle argued for that Man must have a purpose<\/a> by using a type of regression argument whose spirit, although not its explicit nature, goes something like this.\u00a0 Consider the bones of the hand; their function is to provide stiffness.\u00a0 Likewise, the ligaments, tendons, and muscles provide the articulation.\u00a0 The nerves provide the sense of touch and the flesh provides a means of touching, gripping, and holding as well as a unity and an encapsulation for the other parts.\u00a0 All of these pieces have a function to perform in the greater existence that is the hand.\u00a0 Likewise, one can find smaller parts serving limited roles within limbs, organs, and systems within the human body:\u00a0 the eye serves to see; the nose to smell and breath; the mouth to chew, taste, drink, eat, breathe, and talk; and so on.\u00a0 Since each piece contributes, through its function, to the greater function of the thing to which it is a part, isn\u2019t reasonable to assume that the completed whole, the sum of all these individual parts within parts, also has a function or purpose?\u00a0 This argument, put forward approximately 2500 years ago, is still compelling and persuasive.<\/p>\n

Saint Thomas Aquinas, one the great philosophers of the medieval world, put forward arguments greatly influenced and cast in the form of Aristotle\u2019s arguments.\u00a0 In his Cosmos section of the Summa Theologica<\/em>, Aquinas offers five proofs for the existence of God<\/a> based on the concept of regression.\u00a0 In outline form<\/a> they are:<\/p>\n

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  1. Argument from Motion\/Change<\/u><\/em>: changing things depend on their interaction with other things (a plant depends on sunlight which, in turn, depends on ongoing fusion, and so on).\u00a0 Since no change can start itself, things react when acted on by an external mover.\u00a0 The only way to avoid an infinite regression of things depending on yet more things (all operating simultaneously) is to assume that there is a prime or unmoved mover.<\/li>\n
  2. Argument from Efficient Causes<\/u><\/em>: current effects are brought about by prior causes, which are, in turn, effects of causes one level more removed.\u00a0 The only way to avoid an infinite regression of things causing other things is to assume that there was a first cause not caused by anything else.<\/li>\n
  3. Argument from Possibility and Necessity<\/u><\/em>: beings come and go into and out of existence; they are contingent \u2013 having a limited time during which they exist.\u00a0 Given infinite time in the past, there must have been a time where all things were absent implying nothing could exist now.\u00a0 Given the current state of existence, the only way to avoid this contradiction is to assume the existence of a non-contingent being.<\/li>\n
  4. Argument from Gradation of Being<\/u><\/em>: natural objects are understood and ranked by quantities or qualities; this object is hotter than that one, this thing is better than another (better constructed, better conceived, and so on). Ranking requires a maximum (e.g. hottest object) from which all are measured.\u00a0 The only way to judge something as better is if there is a best that exists.<\/li>\n
  5. Argument from Design<\/u><\/em>: natural objects seem to work towards a goal that they themselves don\u2019t or can\u2019t know and so are directed by a higher intelligence. The only way to avoid an infinite regression of greater intelligences directing lesser ones is to assume that there is a master intelligence that directs all.<\/li>\n<\/ol>\n<\/div>\n

    In all of these arguments, Aquinas identifies the thing that prevents an infinite regress, that stops the chain of thinking at a well-defined point, as God.<\/p>\n

    These kinds of logical arguments are not limited to the purely metaphysical realm.\u00a0 One of the crowning achievements of mathematics is the development of set theory, which depends heavily on the type of arguments put forward above.\u00a0 The presence of a run-away regress, one that never stops, is a sign of issues within set theory.\u00a0 This typically, although not exclusively, happens when dealing with infinite collections or sets of things and leads to many paradoxes that must be resolved in order for mathematics to be put on a firm foundation.<\/p>\n

    Perhaps the most famous example is Russell\u2019s paradox<\/a>.\u00a0 The paradox is based on defining two types of sets:<\/p>\n

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