From 61f898d8a9308ccf7ad19b7f4ccf7b1546794678 Mon Sep 17 00:00:00 2001 From: Lucian Mogosanu Date: Wed, 14 Aug 2013 10:15:26 +0300 Subject: [PATCH] posts: 008 --- ...ligion-and-the-closed-world-assumption.markdown | 76 ++++++++++++++++++++ 1 file changed, 76 insertions(+) create mode 100644 posts/y00/008-religion-and-the-closed-world-assumption.markdown diff --git a/posts/y00/008-religion-and-the-closed-world-assumption.markdown b/posts/y00/008-religion-and-the-closed-world-assumption.markdown new file mode 100644 index 0000000..a762617 --- /dev/null +++ b/posts/y00/008-religion-and-the-closed-world-assumption.markdown @@ -0,0 +1,76 @@ +--- +postid: 008 +title: Religion and the closed world assumption +author: Lucian Mogoșanu +date: August 11, 2013 +tags: cogitatio +--- + +Among the various arguments used to invalidate the existence of God, and +implicitly religion, the one that atheists seemingly consider to be fundamental +is closely related to Occam's razor: as there has been no proof of God's +existence until now, it is superfluous to state that God exists. The argument +is so strong that theists have no other option but to simply ignore it, an +uncivilized attitude that is however the healthiest approach for their own +good. + + + +Occam's razor being nothing more than a principle based on common sense, the +argument doesn't stand by itself. Rather, it is based on a formalized model of +the world called the closed world assumption. One can guess from its name that +it is also more of a principle than an actual truth, since it poses other hard +questions such as, if the universe is closed, then is it possible for it to be +finite? If it's finite, then what is "outside" of the universe? Is there a +naked singularity? And so on, and so forth. + +The notion of "closed world" can be easily explained using set theory (or +category theory) and logic. Let $U$ be a possibly infinite set of objects, say, +logical predicates, which we will use for simplicity, without sacrificing the +model's validity. More exactly, $U$ describes the set of predicates which hold +in a given, possibly infinite, universe. The closed world assumption states +that all other predicates except those in $U$ are considered to be false. +Therefore if we have a set $U = \{p_1, p_2, p_3\}$ and another predicate $p_4$, +then $p_4$ will be necessarily false in $U$. This might seem trivial, but it +isn't. + +The opposite assumption is that of an "open world", a set $U$ split in three +disjoint sets $U_t, U_f, U_u$. The first two contain predicates that are +necessarily true or false respectively. The third set contains predicates whose +truth values are yet unknown. Trivial? Definitely not. An observation is that +the open world assumption is more closely related to agnosticism than to pure +theism. + +The advantage of the closed world assumption is that not only is it simpler, +but it's also more convenient to use in practice. For example, the animal brain +uses it to discriminate useful information from noise, an approach without +which it would certainly overload. Prolog uses negation as failure to construct +a Turing machine based on first-order logic, thus using the boolean false as a +default value for undefined variables, which is essential for theorem proving. + +However, the closed world assumption is not sufficient for a big part of +real-world applications, specifically those that deal with partial information. +In such situations, representing unknown information in the model can lead to +much better solutions: for example, no one can know what each person on Earth +is thinking right now. Assuming that they aren't thinking about anything (or +that they aren't thinking *at all*) can be useful in some situations and +disastruous in others, such as language interpretation, the typical example +here being search engine optimization. Moreover, some models use uncertainty as +a measure for the lack of information, particularly statistical and +probabilistical models. + +So maybe asking whether God exists isn't quite the right question from the +purest scientifical point of view, since it's now pretty clear that it's not +something one can find out even with state of the art tools. The question +should, I believe, rather be relaxed to "is God really necessary?", or "how +much God should we allow into our lives?". It makes much more sense, as God is +mainly a social construct, and it reevaluates religion not from a rigid, +scientific point of view, but from an utilitarian one. It is also a proven +method, given that statistically speaking, God is much more popular in +undeveloped countries, while educated people prefer ditching it (or Him, or +Her, or whoever that is) altogether. + +Then again, in our mystical/spiritualistic conception of religion, we've +deprived the concept of God of its worship-related semantics, or it's just that +we're worshipping our own gods without calling them "God". But this is another +story. -- 1.7.10.4