tag:blogger.com,1999:blog-3891434218564545511.post2847706958222398416..comments2021-05-13T00:37:21.978-05:00Comments on Alexander Pruss's Blog: Mellor's argument against circular causationAlexander R Prusshttp://www.blogger.com/profile/05989277655934827117noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-3891434218564545511.post-15324059430122210602013-04-15T20:00:20.153-05:002013-04-15T20:00:20.153-05:00Yeah, now I think that maybe I was a bit unfair to...Yeah, now I think that maybe I was a bit unfair to Mellor.<br /><br />But I am not sure. We should expect 7.5M Es and 12.5 ~Es given 10M Cs and 10M ~Cs and no further information. But we do have further information: C is caused by E.Alexander R Prusshttps://www.blogger.com/profile/05989277655934827117noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-7389253289609240962013-04-15T18:13:23.581-05:002013-04-15T18:13:23.581-05:00This is likely the result of my own confusion, but...This is likely the result of my own confusion, but I have a thought:<br /><br />Let ‘ch(E)’ be ‘the chance that E’ <br /> <br />And further, let the following be true: <br /><br /> P = (ch(E) | C) <br /> P’ = (ch(E) | ~C)<br /> Q = (ch(C) | E) <br /> Q’ = (ch(C) | ~E) <br /><br />Mellor seems to endorse two principles: (1) If C causes E, then P is logically independent of P’ and (2) if C causes E, the fact that C causes E is logically independent of all facts that precede C and all facts that follow E.<br /><br />So suppose C causes E and E causes C. Suppose also that P = .5 and P’ = .25 and that the number of Cs is 10 million, while the number of ~Cs is 10 million. From this, we should expect to get 7.5 million E’s and 12.5 ~Es. <br /><br />Since we know that there are 10 million Cs and 10 million ~Cs, whatever numbers we plug in for Q and Q’, the probabilities must get us back to 10 million Cs and 10 million ~Cs. This means that the values for Q and Q’ are logically constrained by how many Es and ~Es there are. But ‘how many Es exist’ and ‘how many ~Es exist’ are facts that precede E causing C, so casual loops violate principle 2.<br /><br />Further, should we discover that the number of Es is indeed 7.5 million and the number of ~Es is indeed 12.5 million (exactly) and we discover that Q = .9, it follows that Q’ must = .26. So the value of Q’ is not logically independent of the value of Q and, therefore, causal loops stand in violation of principle 1. <br /><br />So if principles 1 and 2 hold for all instances of causation, causal loops are impossible.Nicholashttps://www.blogger.com/profile/13148148310896909893noreply@blogger.com