tag:blogger.com,1999:blog-2292960509733202658.post8731877661360033973..comments2017-02-18T01:53:38.046-08:00Comments on Rational Buddhism: The Emptiness of the Mind in Kadampa Buddhismseanrobsvillehttp://www.blogger.com/profile/01135048988031819619noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-2292960509733202658.post-81697974120467163662015-07-01T06:32:43.796-07:002015-07-01T06:32:43.796-07:00@ale
The article in the Catholic newspaper is pro...@ale<br /><br />The article in the Catholic newspaper is probably referring to Gödel's theorem<br /><br />From <a href="http://users.ox.ac.uk/~jrlucas/mmg.html" rel="nofollow"> Minds, Machines and Gödel by J R Lucas </a> <br /><br />'Gödel's theorem seems to me to prove that Mechanism is false, that is, that minds cannot be explained as machines. So also has it seemed to many other people: almost every mathematical logician I have put the matter to has confessed to similar thoughts, but has felt reluctant to commit himself definitely until he could see the whole argument set out, with all objections fully stated and properly met.1 This I attempt to do.<br /><br />Gödel's theorem states that in any consistent system which is strong enough to produce simple arithmetic there are formulae which cannot {44} be proved-in-the-system, but which we can see to be true. Essentially, we consider the formula which says, in effect, "This formula is unprovable-in-the-system". If this formula were provable-in-the-system, we should have a contradiction: for if it were provablein-the-system, then it would not be unprovable-in-the-system, so that "This formula is unprovable-in-the-system" would be false: equally, if it were provable-in-the-system, then it would not be false, but would be true, since in any consistent system nothing false can be provedin-the-system, but only truths. So the formula "This formula is unprovable-in-the-system" is not provable-in-the-system, but unprovablein-the-system. Further, if the formula "This formula is unprovablein- the-system" is unprovable-in-the-system, then it is true that that [256] formula is unprovable-in-the-system, that is, "This formula is unprovable-in-the-system" is true.<br /><br />The foregoing argument is very fiddling, and difficult to grasp fully: it is helpful to put the argument the other way round, consider the possibility that "This formula is unprovable-in-the-system" might be false, show that that is impossible, and thus that the formula is true; whence it follows that it is unprovable. Even so, the argument remains persistently unconvincing: we feel that there must be a catch in it somewhere. The whole labour of Gödel's theorem is to show that there is no catch anywhere, and that the result can (113) be established by the most rigorous deduction; it holds for all formal systems which are (i) consistent, (ii) adequate for simple arithmetic---i.e., contain the natural numbers and the operations of addition and multiplication---and it shows that they are incomplete--- i.e., contain unprovable, though perfectly meaningful, formulae, some of which, moreover, we, standing outside the system, can see to be true.<br /><br />Gödel's theorem must apply to cybernetical machines, because it is of the essence of being a machine, that it should be a concrete instantiation of a formal system. It follows that given any machine which is consistent and capable of doing simple arithmetic, there is a formula which it is incapable of producing as being true---i.e., the formula is unprovable-in-the-system-but which we can see to be true. It follows that no machine can be a complete or adequate model of the mind, that minds are essentially different from machines...'<br /><br /><br />For the convergence of Buddhist and Christian mysticism see The Zennist <a href="http://zennist.typepad.com/zenfiles/2015/06/where-religious-differences-end.html" rel="nofollow"> 'Where religious differences end' </a>: <br /> 'When the Buddhist mystic and the Christian mystic meet they recognize each other by the very same light'seanrobsvillehttp://www.blogger.com/profile/01135048988031819619noreply@blogger.comtag:blogger.com,1999:blog-2292960509733202658.post-25241301742680402472015-06-30T11:56:08.149-07:002015-06-30T11:56:08.149-07:00I found interesting analogy in Christian philosoph...I found interesting analogy in Christian philosophy. Founded on article on Italian catholic newspaper<br /><br /><br />Man is not a machine. Note that claim to break through this limit is linked to the identification of mathematics with formal logic, which instead is only one aspect of human reason and the logical procedures included in a computer are actually predetermined and do not have any degree of autonomy from the programmeralehttp://www.oasitech.itnoreply@blogger.comtag:blogger.com,1999:blog-2292960509733202658.post-34256756611233492692013-01-05T17:48:06.387-08:002013-01-05T17:48:06.387-08:00Buddhism is very interesting theme at your blog. I...Buddhism is very interesting theme at your blog. I like it because give an aufklarung to my knowledge.Amka Gabrielhttp://pantarhei-fithaluk.blogspot.comnoreply@blogger.com