![\"H_G\"](\"http:\/\/theskepticalzone.com\/wp\/wp-content\/ql-cache\/quicklatex.com-172016e72e40233caf752a50d58abb53_l3.png\" "\\"Rendered")
, and the evidence of complex life as ![\"L_C\"](\"http:\/\/theskepticalzone.com\/wp\/wp-content\/ql-cache\/quicklatex.com-56b6d5a61360640c49f5bd0f8e04179e_l3.png\" "\\"Rendered")
.\u00a0 What we want to know is the posterior probability that ![\"H_{G}\"](\"http:\/\/theskepticalzone.com\/wp\/wp-content\/ql-cache\/quicklatex.com-cb7b96046a1a94744653bf5e4eaafc26_l3.png\" "\\"Rendered")
is true, given , written<\/p>\nI’m going to demonstrate this using Bayes’ Rule. I will represent the hypothesis that (a non-Deist, i.e. an interventionist) God exists as , and the evidence of complex life as .\u00a0 What we want to know is the posterior probability that is true, given , written<\/p>\n
<\/span> <\/span> which, in English, is: the probability that God exists, given the evidence before us of complex life.<\/p>\n <\/p>\n By Bayes rule:<\/p>\n <\/span> <\/span> Where<\/p>\n So first of all we have to set our prior, We also have to set the likelihood of complex life existing, given the existence of an interventionist God (after all, an interventionist God might simply have decided not to bother, or to make something else, like marvellous crystal palaces, instead).\u00a0 However, I will actually set this to 1, as it seems just weird to posit an interventionist God who doesn\u2019t make complex life.<\/p>\n The first thing to note is that the term on the numerator is identical to the first term in the denominator.\u00a0 In our case we have .98*1 on the top, and .98*1 + something on the bottom.\u00a0 I will set the likelihood of Complex life given no interventionist God ( <\/span> <\/span> Which gives me a posterior probability that an interventionist God exists of .999998!<\/p>\n So, by setting the probability of complex life, given no God, very small, I have vastly increased my posterior faith that God exists!\u00a0 And if I make it still smaller, then my posterior faith in God grows still further!\u00a0 Take that, atheists!\u00a0 If IDists can show that the probability of complex life, given no God, is sufficiently tiny that it effectively cannot occur within the lifetime of the universe, that second term on the denominator will go to zero, and God becomes a certainty!<\/p>\n So far, so good. Or would be, if it were ever possible to show that something is impossible, which, 500 coins notwithstanding, it isn\u2019t. That\u2019s because there are many different nulls to reject, and there is always likely to be one you haven\u2019t thought of.\u00a0 No matter, that dead horse has been beaten enough in recent posts.<\/p>\n What I want to do here is to look at it the other way round.\u00a0 Let\u2019s say that scientists show that, far from complex life being near-impossible given no God, they discover it\u2019s a virtual certainty \u2013 we even manage to do it in a test-tube using conditions known to prevail on early earth, we find all the intermediate fossils we need to fill out the various radiations since dot, and moreoever, get a bunch of SETI signals telling us we aren\u2019t even alone as intelligent beings in the universe.<\/p>\n So instead of setting the likelihood of Complex life given no interventionist God ( <\/span> <\/span> What is my posterior probability that God exists? Well, now the denominator simply sums to unity, leaving our belief in God exactly where it started: .98.<\/p>\n In other words, finding out that life is perfectly possible in the absence of an interventionist God tells absolutely nothing at all about whether God exists.\u00a0 It simply leaves us with the faith we had in the first place.<\/p>\n The good news for theists, then, is that there is nothing to fear from naturalist science \u2013 it cannot rock your faith, no matter how good a naturalist explanation for anything scientists come up with.\u00a0 If your faith is absolute, absolute, it will remain.\u00a0 If your faith is 50:50, it can only go up, not down.<\/p>\n However, the good news for atheists is that if it starts at near zero, good naturalist explanations will keep it there. Science, therefore, as Dawkins says, allows him to be an \u201cintellectually fulfilled atheist\u201d.<\/p>\n But for theists, it can do absolutely nothing to dent your faith.<\/p>\n So have a very happy Christmas!<\/p>\n","protected":false},"excerpt":{"rendered":" I’m going to demonstrate this using Bayes’ Rule. I will represent the hypothesis that (a non-Deist, i.e. an interventionist) God exists as , and the evidence of complex life as .\u00a0 What we want to know is the posterior probability … Continue reading ![\"\[P(H_{G}|L_N)}\]\"](\"http:\/\/theskepticalzone.com\/wp\/wp-content\/ql-cache\/quicklatex.com-3f2ddf730ccbd821f6f5020f49419cdb_l3.png\" "\\"Rendered")
<\/p>\n![\"\[P(|H_G|L_C)}=\frac{P(L_C|H_G)*P(H_G)}{P(L_C|H_G)*P(H_G)+P(L_C|\neg H_G)*P(\neg H_G)}\]\"](\"http:\/\/theskepticalzone.com\/wp\/wp-content\/ql-cache\/quicklatex.com-26c8fd48de8891f67fc7bfb2bf2956e5_l3.png\" "\\"Rendered")
<\/p>\n\n
![\"P(L_C|H_G)\"](\"http:\/\/theskepticalzone.com\/wp\/wp-content\/ql-cache\/quicklatex.com-732ff0f37e9841078222f089149e8255_l3.png\" "\\"Rendered")
is the probability of complex life, given that God exists,<\/li>\n![\"P(H_G)\"](\"http:\/\/theskepticalzone.com\/wp\/wp-content\/ql-cache\/quicklatex.com-bc4c20b297998c136962a66fcdb4f0fa_l3.png\" "\\"Rendered")
, is our prior belief that God exists, expressed as a probability,<\/li>\n![\"P(L_C|\neg H_G)\"](\"http:\/\/theskepticalzone.com\/wp\/wp-content\/ql-cache\/quicklatex.com-5d3a057b7275dd9f8a7d61a37730a08e_l3.png\" "\\"Rendered")
is the probability of complex life, given that God does not exist, and<\/li>\n![\"P(\neg H_G)\"](\"http:\/\/theskepticalzone.com\/wp\/wp-content\/ql-cache\/quicklatex.com-bd930cedb9b4788e0df60a98747bc4c9_l3.png\" "\\"Rendered")
is the probability that God does not exist (which equals ![\"1-P(H_G)\"](\"http:\/\/theskepticalzone.com\/wp\/wp-content\/ql-cache\/quicklatex.com-2f8868471ddfb0858d2e5b1d60fd8504_l3.png\" "\\"Rendered")
.<\/li>\n<\/ul>\n, the probability that God exists, which I am happy to set high, for instance, at .98.<\/p>\n) at something very small, let\u2019s say .0001.\u00a0 This gives us:<\/p>\n![\"\[P(H_G|L_C)}=\frac{1*.98}{1*.98+.0001*(1-.98)}\]\"](\"http:\/\/theskepticalzone.com\/wp\/wp-content\/ql-cache\/quicklatex.com-eecbc4fd31508bb954849cb600078d1d_l3.png\" "\\"Rendered")
<\/p>\n) to something very small, let\u2019s make it 1.\u00a0 Here is our equation now:<\/p>\n![\"\[P(H_G|L_C)}=\frac{1*.98}{1*.98+1*(1-.98)}\]\"](\"http:\/\/theskepticalzone.com\/wp\/wp-content\/ql-cache\/quicklatex.com-9e73638d465348a30a0172248bc70c2c_l3.png\" "\\"Rendered")
<\/p>\n