University of Massachusetts Amherst ScholarWorks@UMass Amherst Doctoral Dissertations 1896 - February 2014 1-1-1975 An analysis of the stone paradox. David E. Schrader University of Massachusetts Amherst Follow this and additional works at: https://scholarworks.umass.edu/dissertations_1 Recommended Citation Schrader, David E., "An analysis of the stone paradox." (1975). Doctoral Dissertations 1896 - February 2014. 2138. https://scholarworks.umass.edu/dissertations_1/2138 This Open Access Dissertation is brought to you for free and open access by ScholarWorks@UMass Amherst. It has been accepted for inclusion in Doctoral Dissertations 1896 - February 2014 by an authorized administrator of ScholarWorks@UMass Amherst. For more information, please contact [email protected]. AN ANALYSIS OF THE STONE PARADOX A Dissertation Presented By DAVID EUGENE SCHRADER Submitted to the Graduate School of the University of Massachusetts in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY June 1975 Philosophy ii (c) David Eugene Schrader 1975 All Rights Reserved iii AN ANALYSIS OF THE STONE PARADOX A Dissertation By DAVID EUGENE SCHRADER Approved as to style and content by: Mary Sirridge, Member George Urch, Member Robert Sleigh, Acting Department Head June 1975 , iv ACKNOWLEDGEMENTS I should like to express my appreciation to the members of my com- mittee: Robert Paul Wolff, John Robison, Mary Sirridge and George Urch for the help and guidance they have given me in preparing this disserta- tion. I should also like to thank Gareth Matthews, who has given me a great deal of valuable criticism in my work on the stone paradox, and Edmund Gettler, Michael Jubien and Robert Ackermann, with whom I have discussed various topics relating to the development of this work. I must add a special note of thanks to J.L. Cowan, of the University of Arizona, with whom I have carried on a very pleasant and provocative correspondence over the past six months concerning points made in his article, "The Paradox of Omnipotence Revisited". Finally, I want to add a special not of thanks to Robert Paul Wolff for all the help and encouragement he has given me over the past four years. Without that help and encouragement, this present work would never have been started, to say nothing of completed. V ABSTRACT In this dissertation I shall present an analysis of a very old argument wnich has come to be well known among both philosophers and non-philosophers. The argument is: 15 Create a one “!! that He lift or God cannot create a stone that He cannot lift.,^ 2) If God can create a stone that He cannot lift, then He is not onmipo- L GH tl • 3) If God cannot create a stone that He cannot lift, then He is not omni- potent. 4) Therefore, God is not omnipotent. The argument, which has come to be known as the stone paradox, has often proven to be a frustration to the religious believer and a puzzle- ment to the philosopher. Despite this fact, the stone paradox has re- ceived very litde careful analysis from any contemporary philosopher. received a fair amount of attention in the contemporary philoso- phical journals, but the treatment it has been given has generally been rather fascile. In this dissertation I plan to provide an adequate ac- count of the stone paradox. By this I do not mean that I intend to provide an adequate account of all the crucial theological notions that lie behind the stone paradox, nor even that I intend to provide an ade- quate account of the nature of divine agency. Rather I intend to provide an adequate analysis of the logic of the argument of the stone paradox and a decisive answer to the question of its soundness. This dissertation falls fairly naturally into three divisions. Chapters I-IV constitute what might be called "the Preparation". Chap- ter I will consider whether and why the stone paradox is of interest and vi will lay out the plan of the dissertation in some detail. Chapter II will deal with the relationship between Cod and logical truth. Chapter III will settle 1 on a definition of 'omnipotent and provide some justi- fication for that choice of definition. And Chapter IV will consider whether "God is omnipotent" is either provable or true by definition. Chapters V-VII give a topical survey of the recent literature on the argument. Chapter V deals with the form of the argument. Chapter VI with the first premise, and Chapter VII with the third premise. There is no chapter on the second premise of the argument, since that premise has received no comment in the recent literature. It has been assumed to be innocuously true. Finally, Chapters VIII-XI give my own analysis of the argument. In Chapter VIII I develop a formal language, with semantics, which is ade- quate for the purpose of giving representation to the argument of the paradox in full formality. Chapter IX gives the formal construction of the paradox and a reappraisal of the third premise on the basis of the formal construction. In Chapter X I provide a model of the language developed in Chapter VIII on which the second premise is false. Also in Chapter X, I consider those recent writers on the stone paradox who have supported its soundness, since obviously they and I cannot both be right. Chapter XI considers other possible dilemmas which may appear to grow out of my solution to the traditional stone paradox and shows that they can be handled by the same basic procedures used on the traditional paradox in Chapters IX and X. vii TABLE OF CONTENTS Chapter I The Stone Paradox ....... page 1 Chapter II God and Logical Truth * page 15 Chapter III The Notion of Omnipotence Chapter IV Is "God is Omnipotent" Either Provable or True by Definition . page 46 Chapter V The Form of the Argument page 67 Chapter VI The First Premise and the Existence Assumption page 78 Chapter VII The Third Premise page 34 Chapter VIII A Fragment of a Formal Logic of Action . page 115 Chapter IX The Formal Argument and the Third Premise Revisited page 140 Chapter X The Second Premise . page 144 Chapter XI Orders of Ability and Further Possible Dilemmas .............. page 159 Conclusion page 169 Bibliography page 174 Appendix page 180 1 CHAPTER I THE STONE PARADOX Almost every student who has gone through an Introduction to Philo- sophy course, almost every child who has gone through a few years of religious education in Church, has at one time or another been bothered by two very closely related questions: 1) Can God create a stone that He cannot lift? and 2) Does it follow from either an affirmative or a neg- ative answer to question 1) that God is not omnipotent? The second question is clearly troublesome. (The first question is primarily of interest only insofar as it leads to the second one.) It raises the question of whether it is logically permissible to accept a fundamental article of the Christian faith. This problem has come to be known in philosophical and religious literature as "the stone paradox". While it has long been the subject of considerable discussion, the stone para- dox has received very little careful analysis. Where it has been the subject of philosophical analysis, those analyses, as I shall argue in later chapters, have been inadequate. It is my intention in this dis- sertation to provide an adequate analysis of the stone pa -adox. The basic paradox is as follows: A. (1) Either God can create a stone which He cannot lift, or He cannot create a stone which He cannot lift. (2) If God can create a stone which He cannot lift, then He is not omnipotent (since He cannot lift the stone in question). (3) If God cannot create a 3tone which He cannot lift, then He is not omnipotent (since He cannot create the stone in question). (4) Therefore, God is not omnipotent. As can be seen, nothing peculiar about God is involved in the argu- 2 ment. We could substitute any other name in place of ’God' throughout the argument and obtain a similar result. Thus, while the argument, if sound, shows that God is not omnipotent, it may be varied to show, agfin if anything, that an omnipotent being of any kind is a logical impos- sibility. However, this need not imply a denial of God's existence. The minimal conclusion which must be drawn from argument A, if sound, is that the notion of omnipotence against which the paradox is posed, a no- tion drawn largely from medieval theology and philosophy, does not apply to God. I must note at the outset that the stone paradox is largely irrele- vant to contemporary theology, especially contemporary protestant theo- logy. (The situation is somewhat different among Roman Catholic theolo- gians because of the continuing influence of medieval theology on the Roman Catholic Church.) Among modem protestant theologians, I am aware of no one who understands by 'omnipotence' any notion which would have anything to do with a task of the sort posed by the stone paradox. As typical of a more modem understanding of 'omnipotence', I cite briefly from Gustav Aulen's The Faith of the Christian Church: From this point of view God's "omnipotence" is not the causality of the divine will in relation to everything that happens, but the sovereignty of love. ... If God's sovereignty has this character, what is then implied in the omnipotence of God? It is clear at once that we need not be concerned with a number of meaningless questions about God's omnipotence which have appeared even within theology.