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Borel Sets of Coordinate Quadruples Peter Forrest The Necessary Structure of the All-pervading Aether Discrete or Continuous? Simple or Symmetric? P h i l o s o p h i s c h e A n a l y s e P h i l o s o p h i c a l A n a l y s i s Herausgegeben von / Edited by Herbert Hochberg • Rafael Hüntelmann • Christian Kanzian Richard Schantz • Erwin Tegtmeier Band 49 / Volume 49 Peter Forrest The Necessary Structure of the All-pervading Aether Discrete or Continuous? Simple or Symmetric? Bibliographic information published by the Deutsche Nationalbibliothek The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available in the Internet at http://dnb.d-nb.de. North and South America by Transaction Books Rutgers University Piscataway, NJ 08854-8042 [email protected] United Kingdom, Ireland, Iceland, Turkey, Malta, Portugal by Gazelle Books Services Limited White Cross Mills Hightown LANCASTER, LA1 4XS [email protected] Livraison pour la France et la Belgique: Librairie Philosophique J.Vrin 6, place de la Sorbonne; F-75005 PARIS Tel. +33 (0)1 43 54 03 47; Fax +33 (0)1 43 54 48 18 www.vrin.fr 2012 ontos verlag P.O. Box 15 41, D-63133 Heusenstamm www.ontosverlag.com ISBN 978-3-86838-166-5 2012 No part of this book may be reproduced, stored in retrieval systems or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use of the purchaser of the work Printed on acid-free paper FSC-certified (Forest Stewardship Council) This hardcover binding meets the International Library standard Printed in Germany by CPI buch bücher.de 1 Introduction This book is an investigation into the necessary structure of the aether – the stuff that fills the whole universe. (I assure readers that it is not the sort of aether that could have a current in it – the aether wind that Mi- chelson and Morley famously failed to detect.1 ) Assuming what I call the aether exists, we lack knowledge of its structure. In fact one of my aims is to exhibit the immense variety of structures that, for all we know, it could have. Here I use the words ‘know’ and ‘knowledge’ with neither litotes nor hyperbole – we lack knowledge because the available arguments do not establish their con- clusions ‘beyond all reasonable doubt’. Nonetheless, we can form rea- sonable beliefs about its structure. I shall argue that it has no point parts: either the aether is composed of granules that are extended atoms; or it is point-free (gunky) in that every part is the sum of parts of less exten- sion (diameter).2 In particular, the aether does not have the structure of orthodox Space-time.3 To say it had that orthodox structure would be to 1 To have a current, a part of aether that exists now must be identical to some part that existed a short while ago. I deny that this can happen. If we simplify the exposition by assuming that Time is discrete then the lack of current is because: (1) a part of the aether at one time is not strictly identical to any part of the aether at the preceding time; and (2) a part of the aether x at one time is caused to exist by the sum of all the aether at the previous time that is in the past light cone from x. 2 By an atom of aether I mean a part u of the aether that is not the sum of the proper parts. If we assume classical mereology every atom is a simple, that it has no proper parts. By a granule I mean a part u of the aether that is not the sum of parts of lesser quantity (hypervolume). It is not analytic that granules are atoms, but on my preferred hypotheses they all are. 3 Because mathematicians use the term ‘space’ freely to refer to systems with properties that are reminiscent of geometry, I am adopting the convention that ‘Space’ is written with an upper case ‘S’ when used literally. Then, for the sake of uniformity, ‘Space-time’ and ‘Time’ also have upper cases. 2 say that the aether was the mereological sum of uncountably many points, and that every non-empty set of points had a mereological sum.4 The granules or gunk disjunction is more specific than the grit (i.e. discrete) or gunk thesis I have previously defended (2004). For I am able to argue against the thesis of Point Discretion, namely that every part of the aether of finite diameter has finitely many point parts. Previously, I have suggested that it an empirical question as to whether Space-time (or, better, the aether) is continuous and hence, I say, gunky, or not (Forrest, 1995). I fear the situation is more complicat- ed than that. To be sure, the empirical confirmation of (some variant on) String Theory would provide a strong case for a continuous theory. Without such confirmation, the answer will depend on how we weigh up two competing intuitions: (1) that the non-contingent structure is highly symmetric; and (2) that the non-contingent structure is simple. I shall argue that a highly symmetric non-contingent structure leads to a contin- uous point–free hypothesis. Considerations of simplicity would other- wise support granules, and specifically the hypothesis I shall call Pseu- do-set Granules. The current state of physics is highly speculative. But, for what it is worth, it supports a continuous point-free aether hypothesis unless we have a rather strong preference for simplicity over symmetry. In neither of these two cases are there any points. It is traditional, however, to think of Space, and hence Space-time, as continuous and made up of points. As already indicated, I shall consider, but reject, the thesis that the aether is likewise continuous and made up of points. I draw the conclusion that the aether should be distinguished from Space- time, which is either a fiction, or real but a construct. Not much hangs on this, however, and readers may prefer to identify the aether with Space- time and draw the conclusion that the tradition is incorrect. In this Introduction I say why I believe the aether exists, I say why we should not assume at the outset that it is the same as Space-time, I sketch the main arguments of the book, and I consider some metaphysi- cal preliminaries. 4 The Orthodoxy states rather more than this, ascribing to Space-time the structure of a topological manifold, but this manifold structure is not the ob- ject of my criticism. 3 1. The aether I used to be persuaded by Graham Nerlich’s The Shape of Space (1994) that Space-time and its parts were mind-independent substances, and that they were not dependent on spatio-temporal relations between other things. Subsequently, I have come to believe that our universe is made up of aether and that Space-time, if it exists, is best understood as a structured set of properties, namely point locations. So I stipulate that if there is some fundamental kind of stuff that fills our universe and if there is only one such fundamental kind of stuff it is to be called the ae- ther.5 It follows that substantivalists who, as I once did, hold that Space- time is itself a substance, and who deny there is anything other kind of fundamental stuff filling the universe, should identify it with the aether.6 So for them there is no change of topic. To justify the topic of this book, I need first to argue that there is precisely one kind of fundamental stuff filling the whole universe, and then argue that we should initially be open-minded as to whether it is the same as Space-time. First, then, I argue that there is some kind or kinds of stuff filling our universe. I claim no originality here and begin by not- ing the way that the topological properties of the universe – its shape, for short – have explanatory power. Thus Nerlich (1994) points out that the shape of the universe includes its being globally orientable, and so it is not possible for someone – call her Alice – to take a trip that will turn her into a mirror image of her former self when you she comes back.7 If 5 We might want to treat particles as holes in the aether. If so the aether need not fill our universe. This is a variation I shall subsequently ignore, treating particles as temporally long but spatially thin parts of the aether characterised by some special property, such as electric charge. 6 What do I mean by ‘stuff’? What do I mean by ‘fundamental’? By ‘stuff’ I mean a homoemerous substance, that is a substance all of whose parts are of the same kind, provided we do not treat differences of mereological struc- ture, of shape and of size as differences of kind. A fundamental kind is one whose members do not depend ontologically on other kinds. 7 If, to our surprise, the universe turns out to be non-orientable, then the exam- ple must be changed, but the argument still works. 4 the universe had a twist in it like a Möbius strip and so were not orienta- ble, then such a trip would be possible.8 As this example shows the shape of the universe explains otherwise mysterious facts.
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