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+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.
+
+<!--more-->
+
+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.