Statement Of Purpose V2

Statement of Purpose – Toby Meadows

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Statement of Purpose My career goals are to become a cutting edge researcher in mathematical and philosophical logic, and to become a successful manager of research projects, programmes and institutes. I have already come part of the way in achieving these goals and possess the talent and drive to complete them. If accepted into the PhD programme with the Group in Logic and Methodology of Science (the Group), I will hone my skills as a mathematical logician and actively contribute to the research community within the group. Presently, I am completing a PhD in philosophical logic at the University of Melbourne. My current research investigates alternative methods of characterising the concept of possibility as it is used in philosophy of language, science and metaphysics. The principal goal is to provide a coherent logical foundation for attitudes toward modality that are more in line with the ideas of Quine and Carnap. The central design requirements are: that de re quantification is explained without recourse to essentialist doctrine, and that necessity is only ever understood with reference to a background theory or set of models. As a result of these desiderata, the system uses a predicate rather than an operator to represent necessity. Coming out of this research, I am hoping to have three publications in philosophical logic by the time I would commence at Berkeley. The first provides an alternative semantics for the modal logic developed by Carnap in 1946. This approach makes a sentence possible if it is true in some first order model. While this may seem like an intuitive way of understanding possibility, the resultant logic is, for obvious reasons, unaxiomatisable. I provide a general semantics with complete proof theory by building on Henkin’s techniques for simple type theory. The second paper develops a semantic theory of necessity which allows for iteration of the necessity predicate. This work provides a response to Montague’s paradox for necessity predicates and develops out of work by Kripke, Leitgeb and Welch. The third paper develops a completeness theorem for a logic for descriptive quantification into modal contexts using a variation of the epsilon-calculus, which I have developed.

Statement of Purpose – Toby Meadows

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This line of research has led me into a number of problems in model theory, recursion theory and set theory. In order to tackle these problems I have needed to develop my mathematical skills. It has also given me an independent interest in these fields and this has been the main factor in my decision to apply to undertake a PhD with the Group. My most immediate research interests concern the theory of inductive definitions developed by Moschovakis, and in understanding the relationship between ramified accounts of forcing (as in Cohen) and contemporary approaches that rely on topology or embeddings into Boolean algebras. I would like to produce a dissertation in this area. Coming from a philosophical logic background, I have greater familiarity with effective approaches, as opposed to classical. I would eagerly address this gap during my candidature. As a graduate student at the University of Melbourne, I regularly present my material at the Melbourne Logic Seminar. I find this process invaluable as I receive feedback on my research and am able to discover any weaknesses in my ability to effectively explain or justify my material. I also work as a tutor for our undergraduate logic courses and enjoy teaching others about a topic that I think is foundational in the development of a critical attitude towards the world. I am also passionate about the value of logic and I would like to develop my skills in the administration of logic-related programs and projects. My principal goals are to learn more about successful strategies for expanding the use and influence of logic throughout the academic community and to develop

strategies for bridging

the

gaps between

distinct logical

communities, such as philosophical logic and mathematical logic. I have demonstrated my abilities as an administrator in employment as a project manager and advisor on large scale public infrastructure projects, and I would like to put these skills to use in an academic environment. Given my goals, background and career trajectory, I think the Group would be a particularly good fit for me. As a talented logician with a philosophical

Statement of Purpose – Toby Meadows

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background, I believe I have something to offer the Group and I look forward to the opportunity to contribute.