Norman Samish : > > Max Tegmark, at http://207.70.190.98/toe.pdf, published in Annals of > Physics, 270, 1-51 (1998), postulates that "all structures that exist > mathematically exist also physically."

Max Tegmark postulated or conjectured even more in that paper: that the distinction between mathematical existence and physical existence is meaningless, at least from a scientific point of view. I also had this idea about two years ago: if (this is not a small "if" but this is the assupmtion here) the universe is isomorphic to a mathematical (presumably arithmetic) object, it must be this very object since all isomorphic objects are the same object. In other words (probably inaccurately but ine can grasp the idea anyway): no matter what substance particles are made of as long as they obey a given set of equations/rules, everything that does happen as we perceive it depends only of this given set of equations/rules, and not at all of any hypothetical substance the particles would be made of. If the substance of particle does not matter, it doesn't even matter that they have any substance at all and every question (nature, existence, ...) about such hypothetical substance is purely metaphysical. There are however several assumptions behind this idea, at least the one mentionned above and another one about "arithmetical realism". Incidently, I found this mailing list (and soon after Tegmark's paper) by trying to figure how original that idea might be and how seriously it could be taken (I just entered the question "Do natural numbers exist by themselves ?" or possibly a variant of it like "Who supports the idea that natural numbers exist by themselves ?" in the general purpose question answering system: http://www.languagecomputer.com/demos/question_answering/internet_demo/index.html). Georges Quénot.