tag:blogger.com,1999:blog-21308815.post7428950841886279170..comments2021-04-20T11:14:11.434+00:00Comments on Beyond Necessity: Ockham sets and infinityEdward Ockhamhttp://www.blogger.com/profile/07583379503310147119noreply@blogger.comBlogger5125tag:blogger.com,1999:blog-21308815.post-35890467455658970812012-04-22T16:48:13.823+00:002012-04-22T16:48:13.823+00:00The logical definition of 'thing'. I.e. f...The logical definition of 'thing'. I.e. for any x = for any thingEdward Ockhamhttps://www.blogger.com/profile/07583379503310147119noreply@blogger.comtag:blogger.com,1999:blog-21308815.post-67873395321687681682012-04-22T14:24:36.111+00:002012-04-22T14:24:36.111+00:00I can't figure out your definition of "th...I can't figure out your definition of "things".Anthonyhttps://www.blogger.com/profile/15847046461397802596noreply@blogger.comtag:blogger.com,1999:blog-21308815.post-64518530496051252332011-09-10T10:54:53.261+00:002011-09-10T10:54:53.261+00:00N.B. I deleted some remarks so ignore anything apa...N.B. I deleted some remarks so ignore anything apart from this comment, that you may have seen. Let's start with your point about definition:<br /><br />>>You appear to be discussing infinity without having defined it. <br /><br />OK, let's start with 'finity' first, and define recursively.<br /><br />1. Any one thing is finite in umber<br /><br />2. If any Xs are finite in number, then those Xs and some y (where y is not one of the Xs) is also finite in number.<br /><br />Thus Peter is finite in number, hence Peter and Paul are finite in number, hence Peter and Paul and John are finite in number, and so on.<br /><br />Then 'Infinite' is whatever is not finite.<br /><br />I haven't defined the terms 'one of ' and 'and'. <br /><br />The connective 'and' is primitive, and corresponds to the ordinary English 'and' which connects singular terms. Thus 'Peter and Paul preached in Athens and Jerusalem'. The relation 'is one of' can be defined in terms of 'and'. Thus <br /><br />a is one of Xs iff for some Ys, Xs = a and Ys<br /><br />Thus let the Xs be Peter and Paul and John. Then there are Ys, namely Paul and John, such that <br /><br />Xs = Peter and Ys.<br /><br />I.e. Peter is one of those three people, Peter and Paul and John.<br /><br />Note that the '=' here is a plural =, and should be read 'equal', third person plural. The mathematical equivalent, by contrast, is only singular.Edward Ockhamhttps://www.blogger.com/profile/07583379503310147119noreply@blogger.comtag:blogger.com,1999:blog-21308815.post-85830321749525519232011-09-10T09:16:55.427+00:002011-09-10T09:16:55.427+00:00Oh, and also it isn't clear how to parse "...Oh, and also it isn't clear how to parse "For any X's, there is some y such that y is not one of the X's.". I might have expected capital X to be an oset, and y to be an element. But then you say "y not one of the X's" which puts y at the same level as X, so the membership implication fails.<br /><br />Anyway, I don't know what you mean.William M. Connolleyhttps://www.blogger.com/profile/05836299130680534926noreply@blogger.comtag:blogger.com,1999:blog-21308815.post-63580628299734912982011-09-10T09:13:18.423+00:002011-09-10T09:13:18.423+00:00You appear to be discussing infinity without havin...You appear to be discussing infinity without having defined it. That way lies madness, or at least endless pointless words.William M. Connolleyhttps://www.blogger.com/profile/05836299130680534926noreply@blogger.com