The Role of Mathematics in Francis Bacon's Natural Philosophy
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The Role of Mathematics in Francis Bacon’s Natural Philosophy Ünsal Çimen A thesis submitted for the degree of Doctor of Philosophy at the University of Otago, Dunedin, New Zealand. April 2016 Abstract In this study, I discuss the role of mathematics in Francis Bacon’s natural philosophy. Bacon was one of the important figures of early modern philosophy and has been accepted as one of the frontier philosophers of modern science. The increasing role of mathematics in natural philosophy was an important development of this period of time, which raises the question of whether Bacon approved of the new role of mathematics in natural philosophy. The new role of mathematics in natural philosophy was mainly developed by astronomers such as Copernicus, Galileo, and Kepler, and can be defined as ‘making natural philosophical claims through mathematics’. I will examine the role of mathematics in Baconian natural philosophy by considering the following questions: Can Bacon’s attitude towards the role of mathematics be accepted as Aristotelian? Were there similarities between Bacon and al–Bitruji in their ideas of how an astronomical model should be established? Is there any difference in Bacon’s attitude towards mathematics between his earlier and later works? Can we use Bacon’s approach to arithmetical quantification to refute the claim that he was against the new role of mathematics? i Was there any similarity between the attitude of Bacon and neo-Platonist chemical philosophers towards mathematics? Is there any relation between the non–mechanical character of Bacon’s philosophy and his attitude towards mathematics? Is there any relation between his matter theory and his attitude towards mathematics? Throughout this thesis, I emphasise that Bacon attached importance to applying mathematics to natural philosophy, however, was against the idea of making natural philosophical claims through mathematics. I argue that he had two fundamental commitments for being distrustful towards mathematics’ ability in making natural philosophical claims; his first being the consistency between the human mind and the course of logic and mathematics, and the second being the inconsistency between the course of nature (matter) and the course of logic and mathematics. ii Acknowledgements Primarily, I would like to thank my supervisors, Michael LeBuffe, Peter Anstey, and Alan Musgrave for their guidance and support. I would also like thank other academic staff, postgraduate students and administrative staff in the Philosophy Department of Otago University. Many thanks to Orna Harari, for her helpful discussion regarding issues arising from her fine book ‘Knowledge and demonstration: Aristotle’s posterior analytics’; to Sophie Weeks, for many helpful suggestions regarding mathematical models and philosophical mechanics for mathematical sciences; and to Çig dem Du ru şken and C. Cengiz Çevik, for their Latin translations. Additional thanks to the University of Otago for providing the financial support through its postgraduate scholarship, and for funding me with a travel grant to attend the Philhist ‘15, II. International History of Philosophy Conference in Istanbul. iii Table of Contents Introduction…………………………………………………………………………….................1 1 The Relation between the Mathematical Sciences and Natural Philosophy, and the Aristotelian Facet of Francis Bacon…......………….9 1.1 The development of the distinction between mathematical sciences and natural philosophy……………………...……….………………….................10 1.2 The place of mixed mathematics in Baconian natural philosophy…………………………………………………………….………………….15 1.3 Bacon’s loyalty to the Aristotelian disciplinary boundary between mathematical sciences and natural philosophy …….………..…………..21 1.4 Summary………………………………………………………………………................27 2 Two Reasons Bacon Disapproved of Making Natural Philosophical Claims through Mathematics……………….………………………………………..29 iv 2.1 Rational method, the errors of the human mind and the properties of matter …………………………………………………………………………………..29 2.1.1 Searching for the properties of matter beyond nature ….....29 2.1.2 Finding rest among the general axioms…………………………...38 2.1.3 Mathematics as a way to attribute excessive orderliness to nature……………………………………………………………………………40 2.2 The human mind and the subtlety of matter…………………....……........43 2.3 Bacon’s inductive experimental method and the errors of the human mind……………………………………………………………………………...48 2.4 Summary………………………………….…………………..…………………………...52 3 Francis Bacon: A Physical Realist..…………………….……..…………………..54 3.1 Physical realists vs. Mathematical realists …….……………………...........55 3.2 Arabic opposition to Ptolemy..……………………………………...……………57 3.3 The hide of an ox: astronomy which presents only the exterior part of the heavens………………………………………………………………...…………62 3.4 Did Bacon adopt al–Bitruji’s mathematical model of the heavens before he developed his physical model?....................................................72 v 3.5 Bacon’s physical statements and his astronomical theory…….……..74 3.6 Summary……………………………………………………………………………….….78 4 Geometrical Abstraction vs. Arithmetical Quantification……..………80 4.1 Arithmetical quantification in Bacon’s natural historical works……81 4.1.1 Examples of quantification from the writings of Bacon…......83 4.1.2 Mathematical instances (instances of measurement)…..……85 4.2 Can we use Bacon’s arithmetical quantitative works to refute the argument that he denied the new role of mathematics in the sciences?......................................................................................................................99 4.3 Do the arithmetical quantitative works of Bacon call his distrust of the entire quasi–deductive structure of mathematical sciences into question?.........................................................................................................106 4.4 Summary…………………………...…….…………………………..…………………..109 5 Clarification of the Role of Mathematics in Baconian Natural Philosophy by Considering Active and Passive Matter Theories..111 5.1 The chemical philosophy on the unmoved mover and vi Mathematics…………………………………………………………………………..112 5.2 Active matter as the reason for being against logical and mathematical methods in natural inquiries………………………….......118 5.2.1 Action at a distance, motion through the impact of particles, and the role of mathematics in natural philosophy….........124 5.2.2 Did Bacon think that Democritus’ doctrine of atoms was a mechanical account of motion in matter?................................129 5.3 Summary…………………………...……………………………………………………133 6 External Mechanics and Mathematics………………….…………………..…136 6.1 External mechanics and philosophical mechanics…………….............138 6.2 The Baconian labyrinth–like nature, geometrically structured nature, and their relation with external mechanics and the system of machinery………………...…………………………………………………………142 6.3 Summary……………..…………………….……………………………………………149 Conclusion…………………………………………………………….………………………….151 References……………………………………………………………………………………….156 vii List of Figures Figure 1 Speculative part of Bacon’s natural philosophy…………………….......16 Figure 2 The distinction between pure and mixed mathematics in the Baconian schema………………………………………………………………….…19 Figure 3 Detailed schema of speculative and operative part of Bacon’s natural philosophy.................................................................................................19 Figure 4 Three types of velocity represented geometrically by Oresme….……………………………………………………………………..............102 Figure 5 Ascending and descending parts of Bacon’s natural philosophy……………….…………………………………………………………….139 viii Introduction Bacon’s attitude towards the role of mathematics in natural philosophy is an ongoing debate among scholars. Some researchers have argued that Bacon neglected the role of mathematics in sciences. For example, John William Draper, in his A History of the Intellectual Development of Europe states: Ignorant himself of every branch of mathematics, he presumed that they were useless in science, but a few years before Newton achieved by their aid his immortal discoveries (Draper, 1875, p. 233). Another example can be given from Lynn Thorndike: He [Bacon] complained that Aristotle had mixed it [natural philosophy] with logic; Plato, with natural theology; and the Neo– Platonists, with mathematics. This suggests what from the standpoint of modern science was his chief defect, his total disregard of mathematical method. He spoke of pure mathematics as, like the game of tennis, of no use in itself but as good exercise to cure intellectual defects (Thorndike, 1958, pp. 66–7).1 However, there are other more recent scholars who have argued against this view. Graham Rees was the most important scholar, whose works has been important in improving our understanding of Bacon. More recently, Peter Urbach’s (1987), Stephen Gaukroger’s (2001), Mary Domski’s (2013) and 1. For similar views on Bacon and mathematics, see also Hochberg (1953, p. 322). 1 Dana Jalobeanu’s (2016b) works have extended our views regarding Bacon’s attitude towards mathematics’ role in natural philosophy. All of these scholars are in agreement that Bacon gave an auxiliary role to mathematics in natural inquiries, and this agreement has come about due to Bacon’s statement in the De Augmentis Scientiarum (1623): I have thought it better to designate Mathematics, seeing that they are of so much importance both in Physics and Metaphysics, and Mechanics and Magic, as appendices and auxiliaries to them all (Bacon, De augmentis,