The Eleatic non‐stick frying pan
In his book Infinity: An Essay in Metaphysics José Benardete described a rather unusual book [1964: 236‐7]. The book has an infinite number of pages, all made from infinitely divisible matter. The first page is half a unit thick; page 2 is a quarter unit thick; page 3 is one eighth of a unit thick, and so on to infinity. The book therefore has a thickness of one unit and although it has a first page it has no last page. For simplicity I shall discuss a version of Benardete's book that has no cover and the pages are not fastened together; it is nothing more than a pile of pages. Because of the way it is constructed, the back of the book has a topologically open surface (henceforth open surface, i.e. it has no outermost layer of points). The front of the book has a topologically closed surface (henceforth closed surface, i.e. it has an outermost later of points) provided the pages themselves have closed surfaces, which I stipulate to be the case. I shall stipulate, further, that each page is perfectly rigid and non‐ porous and that no page is transparent, no matter how thin it is. 1 Benardete asks the following question: if the book is placed face‐down with the first page at the bottom and one looks at the book from above, what does one see? Since there is no last page, one does not see a page. Benardete concluded that one sees nothing. I would like to consider a different question. Take a piece of sticky tape with a closed surface, where 'sticky' means roughly that if the sticky surface of the tape made contact with any surface made of the same material as the pages then an extra force of magnitude F (>0) 1 Benardete also describes other objects with the same properties such as a pile of slabs of stone and a board made of sheets of wood, and some equally (perhaps more) bizarre phenomena with analogous temporal properties [1964: chapter 6].