tag:blogger.com,1999:blog-21308815.post1893253395235735435..comments2021-04-20T11:14:11.434+00:00Comments on Beyond Necessity: The Perils of AnalysisEdward Ockhamhttp://www.blogger.com/profile/07583379503310147119noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-21308815.post-46521384857832810702010-09-08T21:20:28.858+00:002010-09-08T21:20:28.858+00:00OK, thanks, that's interesting. I ought to ge...OK, thanks, that's interesting. I ought to get McKay.David Brightlyhttps://www.blogger.com/profile/06757969974801621186noreply@blogger.comtag:blogger.com,1999:blog-21308815.post-15676088685505918032010-09-08T20:55:07.382+00:002010-09-08T20:55:07.382+00:00Hi David - the only person whose work I am familia...Hi David - the only person whose work I am familiar with in any detail is Tom McKay.<br /><br />On your point about the similarity with naive set theory - well McKay has an axiom of unrestricted comprehension that he claims is not vulnerable to the paradoxes but it's some time since I have read him. (Sorry I can't help further).Edward Ockhamhttps://www.blogger.com/profile/07583379503310147119noreply@blogger.comtag:blogger.com,1999:blog-21308815.post-32418341857832893152010-09-08T13:42:53.405+00:002010-09-08T13:42:53.405+00:00Hi O,
(1) This seems very sensible. But deciding...Hi O,<br /><br />(1) This seems very sensible. But deciding on a 'logical form' would be choosing one of two extremes---mere plurality or composite individual---of what seems to be a spectrum. Consider<br /><br />an asteroid belt, a boulder field, a scree, a pile of stones, a dry-stone wall, a Pyramid, a house.<br /><br />All of these can be seen as pluralities and as wholes. Our thought seems readily to slide between the two poles.<br /><br />(2) I was struck by one of your comments at BV's:<br /><br />Some writers have developed plural or collective versions of predicate calculus, to capture statements of the form<br /><br />These people = Peter and Paul<br /><br />Or<br /><br />Some X's = A & B<br /><br />I'm wondering if these calculi are powerful enough to express<br /><br />These people = Peter and Paul<br />Those people = Paul and Mary<br />Some of these people = some of those people<br /><br />If so, then we seem precious close to an embedding of naive set theory in predicate calculus. The referring terms 'these people' and 'those people' behave analogously with sets. Isn't this what Frege, Russell, and Whitehead were aiming for?David Brightlyhttps://www.blogger.com/profile/06757969974801621186noreply@blogger.com