Here is an old reply to Russell Standish and Stephen Paul King.
Russell Standish wrote: >I have often said myself the plenitude is not a set, however when >trying to write up some of this work for another audience, I tried >following up the web documents on set theory, I came up with nothing, >so in the end simply didn't raise the issue. I agree it is foolish to see the plenitude as a *set* and I have explain why before. Now, you can perhaps *modelize* the plenitude by a set, but *big* set are notoriously difficult to handle. So you need a set theory. Now, and this is a subtil point hardly understood, a model of a set theory is called *universe�* and is intuitively a collection of *all* possible sets. If we want to say "Group Theory" instead of Transformation Theory we should say "Universe Theory" instead of Set Theory!!! In most set theories, (like ZF, NBG, ...), the universe is not itself a set. There exists set theories with "universal sets" in which the universe is a set. The best known is NF (Quine's New Foundation), build from some works by Church. Well NF is not even known by some specialist of set theory, and to study NF you need great familiarity with mathematical logic. But sets are not enough. Even in mathematics there are mathematical object which are to big to put in a universe (model) of ZF. For exemples some categories. Do you know category theory? It is mathematical structure intermediate between group and lattices. They are bridge between logic, topology, Algebra, etc. Stephen Paul King wrote: > Oppps, I forgot to mention the notion of expressiveness... >I am trying >to keep my posts concise... Please >read this paper by Peter Wegner which explains the notions of >expressiveness and introduces Non-Well Founded >sets, my thinking draws strongly from it: > > http://www.cs.brown.edu/~pw/papers/math1.ps Formidable idea, let's do math. Non-Well Founded sets are certainly interesting ... but it can lead us in the forest of mathematical mermaids and keep us with some beautiful songs away from our search toward a theory of everything. It seems to me that many-worlder should so some modal logic, if only to taste the second part of my thesis :-) But even without my thesis I think that modal logic is a formidable tool for rigorous philosophy. See my last post to George Levy. Bruno PS I have also problem to load http://www.cs.brown.edu/~pw/papers/math1.ps I will try with the recent suggestion by Russell.
