tag:blogger.com,1999:blog-1834133093226640255.post4373751201253904829..comments2024-01-20T10:50:57.236-08:00Comments on there could be snakes in here: The Dilthey Prizetechnicalitieshttp://www.blogger.com/profile/01695260271886267461noreply@blogger.comBlogger6125tag:blogger.com,1999:blog-1834133093226640255.post-41886310288721152502011-03-10T17:31:07.864-08:002011-03-10T17:31:07.864-08:00Grrr, posting things when I am angry is silly! We...Grrr, posting things when I am angry is silly! Well really it is quite interesting but I'm curious as to what degree the proof would be required for it to be accepted. I mean, maths can be embedded within the lambda calculus (or at least all the maths we know now...) and the lambda calculus can be described using logic. So you've got to wonder nowadays what the value is in such theories; when instead you could be could be compiling either logic or math into turing machines.spoonhttps://www.blogger.com/profile/09887815934706618874noreply@blogger.comtag:blogger.com,1999:blog-1834133093226640255.post-25867897301976794202011-03-10T14:53:57.512-08:002011-03-10T14:53:57.512-08:00Ahhh, I see what you were getting at now. To be h...Ahhh, I see what you were getting at now. To be honest, it's not a question that interests me really. Unless you have a specific problem that requires one to be treated as the other, it's a bit mad to force one to be a subset of the other.spoonhttps://www.blogger.com/profile/09887815934706618874noreply@blogger.comtag:blogger.com,1999:blog-1834133093226640255.post-38305690437787623632011-03-03T13:46:45.458-08:002011-03-03T13:46:45.458-08:00Hehe, I'll have to read the rest later. It is...Hehe, I'll have to read the rest later. It is long. I was happy my example provided something useless! Hehe!spoonhttps://www.blogger.com/profile/09887815934706618874noreply@blogger.comtag:blogger.com,1999:blog-1834133093226640255.post-73786379818894675242011-03-03T13:14:11.903-08:002011-03-03T13:14:11.903-08:00The title of the post could have been "Nobel ...The title of the post could have been "Nobel Prize for the Mardy Sciences"technicalitieshttps://www.blogger.com/profile/01695260271886267461noreply@blogger.comtag:blogger.com,1999:blog-1834133093226640255.post-28877649701020471512011-03-03T09:24:32.973-08:002011-03-03T09:24:32.973-08:00Oh, I ken it's useful, and highly homologous: ...Oh, I ken it's useful, and highly homologous: that's why the result was so surprising. Flick down and you'll see that folk are still trying...technicalitieshttps://www.blogger.com/profile/01695260271886267461noreply@blogger.comtag:blogger.com,1999:blog-1834133093226640255.post-12403154644072101502011-03-03T08:41:59.499-08:002011-03-03T08:41:59.499-08:00Hey man, only started to read the first part of th...Hey man, only started to read the first part of this!<br /><br />It's not just an old fashioned thing to describe numbers with logic. Well, perhaps it is, but it is also a recreational form of mathematics particularly among computer scientists. For instance, the natural numbers can be defined as sets, and subtraction can be defined as logical predicates as follows:<br /><br />It isn't required for the logic, but:<br /><br />Let Zero be the empty set.<br />And in this way, 0 = {}. 1 = {{}}. 2 = {{{}}}.<br /><br />Subtraction is performed as follows.<br />For some set X, for some set Y, Subtract(X, Y) implies:<br />Either X or Y being empty implies X.<br />otherwise,<br />for some set A, such that A is a child of X,<br />for some set B such that B is a child of Y,<br />then Subtract(A, B) is implied.<br /><br />Example, subtracting one from two<br />Subtract({{{}}}, {{}}) implies<br />Subtract({{}}, {}) implies<br />{{}}. Or 1 as we like to call it.spoonhttps://www.blogger.com/profile/09887815934706618874noreply@blogger.com