A Buddhist challenge to Western conceptions of logic. This project aims to advance and defend a theory about the nature of logic and rationality. The project will draw on Buddhist logic texts and demonstrate their relevance to contemporary Western debates about the nature of logic. It seeks to show that a Buddhist theory of logic can challenge widely-entrenched but unexamined Western conceptions of the nature of logic. The project is expected to advance intellectual engagement between Buddhist a ....A Buddhist challenge to Western conceptions of logic. This project aims to advance and defend a theory about the nature of logic and rationality. The project will draw on Buddhist logic texts and demonstrate their relevance to contemporary Western debates about the nature of logic. It seeks to show that a Buddhist theory of logic can challenge widely-entrenched but unexamined Western conceptions of the nature of logic. The project is expected to advance intellectual engagement between Buddhist and Western philosophers, bring attention to texts and theories not currently available to the Western philosophical world, and demonstrate the importance of a collaborative, interdisciplinary approach to global philosophy.Read moreRead less
A Computational Solution to the Problem of Reference. This project will attack the core problem of philosophy of language by developing and applying tools from the theory of algorithmic complexity. Groundbreaking pure research at the intersection of logic, language, information and computation is the lifeblood of commercial research and development in information technology and telecommunications. The project will foster a cross-fertilisation of ideas between philosophy, computer science, math ....A Computational Solution to the Problem of Reference. This project will attack the core problem of philosophy of language by developing and applying tools from the theory of algorithmic complexity. Groundbreaking pure research at the intersection of logic, language, information and computation is the lifeblood of commercial research and development in information technology and telecommunications. The project will foster a cross-fertilisation of ideas between philosophy, computer science, mathematics, linguistics and psychology, and will provide students with skills and analytic techniques that will be valuable in future pure and applied research.Read moreRead less
The logical and metaphysical challenge of vague language. Where do we draw the line between life and death, tall and short, right and wrong? The vagueness or indeterminacy of such concepts prohibits easy answers. This projects aims to provide a philosophical analysis of such concepts which abound in natural language with a view to showing that orthodox views in logic and metaphysics are challenged by their presence. This analysis is to be published as a monograph whose significance lies in the f ....The logical and metaphysical challenge of vague language. Where do we draw the line between life and death, tall and short, right and wrong? The vagueness or indeterminacy of such concepts prohibits easy answers. This projects aims to provide a philosophical analysis of such concepts which abound in natural language with a view to showing that orthodox views in logic and metaphysics are challenged by their presence. This analysis is to be published as a monograph whose significance lies in the fact that it provides one of only four book-length treatments of the matter and does so from an entirely novel perspective.Read moreRead less
Mathematical explanation. The best mathematical proofs tell us why some mathematical fact holds, not simply that it holds. However to understand how one piece of mathematics explains another piece of mathematics is poorly understood. This project will develop a philosophical account of mathematical explanation. In particular, it will show how mathematics can explain further mathematics as well as how it can explain physical phenomena.
Mathematical notation: a philosophical account. This project will explore philosophical issues associated with mathematical notation. In particular, it will provide an account of how mathematical notation is used in mathematical applications and how it facilitates analogical reasoning in science.
A Unified Theory of 'If's. This project aims to develop a unified theory of ‘if’s. Our understanding of an uncertain and risky world requires hypothetical reasoning involving ‘if’s. They are significant theoretically: in science, history, politics, economics, psychology, computer science, linguistics, and philosophy. They are significant practically: in our planning, decision-making, policy priorities, legal judgments, environmental and medical interventions. Yet we lack a comprehensive, readily ....A Unified Theory of 'If's. This project aims to develop a unified theory of ‘if’s. Our understanding of an uncertain and risky world requires hypothetical reasoning involving ‘if’s. They are significant theoretically: in science, history, politics, economics, psychology, computer science, linguistics, and philosophy. They are significant practically: in our planning, decision-making, policy priorities, legal judgments, environmental and medical interventions. Yet we lack a comprehensive, readily implementable theory of ‘if’s. The project expects to provide such a theory, based on probability, improving on approaches from philosophy and linguistics, and benefitting both these fields. It also promises significant benefits for artificial intelligence/machine learning.
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Substructural logics for limited resources. This project aims to develop logical tools for managing reasoning and computation under conditions of bounded resources: fixed limits on the amount of time, memory, or other resources that can be allocated to a particular course of reasoning or computation. By drawing on both philosophical and computational approaches to logic, the project will develop new logical systems aimed at capturing these limitations. The expected outcome is new logical methods ....Substructural logics for limited resources. This project aims to develop logical tools for managing reasoning and computation under conditions of bounded resources: fixed limits on the amount of time, memory, or other resources that can be allocated to a particular course of reasoning or computation. By drawing on both philosophical and computational approaches to logic, the project will develop new logical systems aimed at capturing these limitations. The expected outcome is new logical methods for managing limited resources, as well as boosting interdisciplinary capacity. Anticipated benefits include developing a new programming language that will enable programmers to issue strong guarantees about the resources their programs will use.Read moreRead less
Analysis in the idealist tradition: the development of Leibniz's analytic method by Kant and Hegel and its implications for contemporary philosophy. This project investigates the development of the 'analytic' method in the idealist philosophies of Leibniz, Kant and Hegel, and compares it to 'analysis' as used in analytic philosophy. It thereby seeks to find a ground for dialogue between strands within contemporary philosophy that are usually thought to be opposed.
A Paraconsistent Approach to Vagueness. This project will utilise logical techniques that have been developed largely by Australian logicians. This techniques will be brought to bear on the problem of vagueness, one of the most important problems in the philosophy of logic. The project will thus greatly enhance Australia's already strong international reputation in logic and philosophical logic.
Logical Theory and Sentence Composition -- A General and Comparative Study of the Principal Sentential Connectives. The aims are to get clear about the semantic and logical properties of
the basic sentence connectives, and to adjudicate several debates on
these matters. The significance is that the logic of sentence
connectives is fundamental for the whole of logic. The expected aim is a large book - probably to be called *The Connectives* - in which all of this is set out.