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Carnap's Conventionalism CARNAP'S CONVENTIONALISM: LOGIC, SCIENCE, AND TOLERANCE Noah Friedman-Biglin A Thesis Submitted for the Degree of PhD at the University of St Andrews 2014 Full metadata for this item is available in St Andrews Research Repository at: http://research-repository.st-andrews.ac.uk/ Please use this identifier to cite or link to this item: http://hdl.handle.net/10023/6334 This item is protected by original copyright This item is licensed under a Creative Commons Licence Carnap's Conventionalism: Logic, Science, and Tolerance Noah Friedman-Biglin This thesis is submitted in partial fulfilment for the degree of PhD at the University of St Andrews December 16th, 2013 Declarations Candidate's Declarations: I, Noah Friedman-Biglin, hereby certify that this thesis, which is approximately 75,000 words in length, has been written by me, that it is the record of work carried out by me and that it has not been submitted in any previous applica- tion for a higher degree. I was admitted as a research student in September, 2009 and as a candidate for this degree in May, 2010; the higher study for which this is a record was carried out in the University of St Andrews between 2009 and 2013. Date: 16 December, 2013 Signature: Supervisor's Declaration: I hereby certify that the candidate has fulfilled the conditions of the Resolution and Regulations appropriate for the degree of Doctor of Philosophy in the Uni- versity of St Andrews and that the candidate is qualified to submit this thesis in application for that degree. Date: 16 December, 2013 Signature: Permission for Electronic Thesis Publication: In submitting this thesis to the University of St Andrews I understand that I am giving permission for it to be made available for use in accordance with the regulations of the University Library for the time being in force, subject to any copyright vested in the work not being affected thereby. I also understand that the title and the abstract will be published, and that a copy of the work may be made and supplied to any bona fide library or research worker, that my thesis will be electronically accessible for personal or research use unless exempt by award of an embargo as requested below, and that the library has the right to migrate my thesis into new electronic forms required to ensure continued access to the thesis. I have obtained any third-party copyright permissions that may be required in order to allow such access and migration, or have requested the appropriate embargo below. The following is an agreed request by candidate and supervisor regarding the electronic publication of this thesis: Embargo on part of both printed copy and electronic copy for the same fixed period of two years on the grounds that publication would preclude future pub- lication. Date: 16 December, 2013 Signature of Candidate: Signature of Supervisor: Abstract In broadest terms, this thesis is concerned to answer the question of whether the view that arithmetic is analytic can be maintained consistently. Lest there be much suspense, I will conclude that it can. Those who disagree claim that accounts which defend the analyticity of arithmetic are either unable to give a satisfactory account of the foundations of mathematics due to the incomplete- ness theorems, or, if steps are taken to mitigate incompleteness, then the view loses the ability to account for the applicability of mathematics in the sciences. I will show that this criticism is not successful against every view whereby arithmetic is analytic by showing that the brand of \conventionalism" about mathematics that Rudolf Carnap advocated in the 1930s, especially in Logical Syntax of Language, does not suffer from these difficulties. There, Carnap de- velops an account of logic and mathematics that ensures the analyticity of both. It is based on his famous \Principle of Tolerance", and so the major focus of this thesis will to defend this principle from certain criticisms that have arisen in the 80 years since the book was published. I claim that these criticisms all share certain misunderstandings of the principle, and, because my diagnosis of the critiques is that they misunderstand Carnap, the defense I will give is of a primarily historical and exegetical nature. Again speaking broadly, the defense will be split into two parts: one primar- ily historical and the other argumentative. The historical section concerns the development of Carnap's views on logic and mathematics, from their beginnings in Frege's lectures up through the publication of Logical Syntax. Though this material is well-trod ground, it is necessary background for the second part. In part two we shift gears, and leave aside the historical development of Carnap's views to examine a certain family of critiques of it. We focus on the version due to Kurt G¨odel,but also explore four others found in the literature. In the final chapter, I develop a reading of Carnap's Principle { the `wide' reading. It is one whereby there are no antecedent constraints on the construction of linguistic frameworks. I argue that this reading of the principle resolves the purported problems. Though this thesis is not a vindication of Carnap's view of logic and mathematics tout court, it does show that the view has more plausibility than is commonly thought. For my parents, to whom I owe everything. i Analytic philosophy is ethically neutral formally; its professors do not indoctrinate their students with dogmas as to life, religion, race, or society. But analytic philosophy is the exercise of intelligence in a special field, and if the way of intelligence becomes part of the habitual nature of men, no doctrines and no institutions are safe from critical reappraisals. [. ] Analytic philosophy has thus a double function: it provides quiet green pastures for intellectual analysis, wherein its practitioners can find refuge from a troubled world and cultivate their intellectual games with chess-like indifference to its course; and it is also a keen, shining sword helping to dispel irrational beliefs and to make evident the structure of ideas. It is at once the pastime of a recluse and a terribly serious adventure: it aims to make as clear as possible what it is we really know. | Ernest Nagel, \Impressions and Appraisals of Analytic Philosophy in Europe, Part 1" The scientific world conception is characterized not so much by theses of its own, but rather by its basic attitude, its points of view and direction of research. The goal ahead is unified science. [. ] From this aim follows the emphasis on collective efforts, and also the emphasis on what can be grasped intersubjectively; from this springs the search for a neutral system of formulae, for a symbolism freed from the slag of historical languages; and also the search for a total system of concepts. Neatness and clarity are striven for, and dark distances and unfathomable depths rejected. In science there are no `depths'; there is surface everywhere [. ]. { Otto Neurath et. al., \Wissenschaftliche Weltauffassung: Der Wiener Kreis" Acknowledgments The number of people to whom I am enormously indebted for their help in producing this thesis is very large. I will, no doubt, unintentionally fail to mention some people to whom I owe many thanks. I promise this is due only to my poor memory, and a looming deadline, rather than any comment on my gratitude for all your efforts. I should first and foremost like to thank my supervisors Professor Peter Milne and Professor Peter Clark. Their efforts on my behalf, patience with me as I worked, and encouragement along the way have been not only essential, but also deeply appreciated. There is simply no way I could have successfully fin- ished this thesis without their help, and moreover it has been a genuine pleasure working with, and learning from, both of them these past years. Additionally, I would like to thank Professor Rick Creath and Dr Philip Ebert for examining this thesis. Their feedback on, and entusiasm for, my work was a wonderful end to a very rewarding few years of study. It is often said that one learns just as much from one's colleagues in graduate school as one does from the various philosophers whose work one engages with. This has been doubly true for me, as I have had the benefit of engaging with the wonderful philosophical communities in both St Andrews and Stirling. I would therefore like to thank my professors and colleagues, both in Arch´eand in the St Andrews { Stirling Graduate Programme from whom I have learned more than I could have imagined before coming to Scotland. In particular, but not in any order, I would like to thank: Professor Steven Read, Professor Stewart Shapiro, Professor Graham Priest, Dr Aaron Cotnoir, Dr Michael De, Dr Derek Ball, Dr Torfinn Huvenes, Dr Jonathan Jenkins Ichikawa, Dr Dirk Kindermann, Dr Andreas Stokke, Dr Thomas Hodgson, Dr Frederique Janssen{Lauret, Dr Julia Lankau, Dr Laura Porro, Dr Gil Sagi, Dr Rachel Sterken, Dr Margot Strohminger, Sebastin Becker, Mark Bowker, Laura Celani, Steven Hall, Nick Hughes, Bruno Jacinto, Spencer Johnston, Martin Lipman, Matthew McK- eever, Andrew Peet, Joshua Thorpe, Michael Traynor, Alex Yates, and Mrs Lynn Hynd in Arch´e. Very special thanks go to my post{docs in Arch´e,who not only were excellent role models, but were also good friends: Dr Colin Caret, Dr Toby Meadows, and Dr Ole Hjortland. In the St Andrews { Stirling com- munity more generally I would like to thank: Professor Peter Sullivan, Dr Simon Prosser, Dr Patrick Greenough, Dr Lisa Jones, Dr Jesse Tomalty, Dr Chris Macleod, Dr Simon Fokt, Dr Felix Pinkert, Dr Dan Labriola, Dr Heather Walker{Dale, Beth Curzon, Laurence Carrick, Joe Slater, Martin Sticker, Bi- hotz Barrenechea Dominguez, Bren Markey, and Brian Ho.
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