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.
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
Decision theory in crisis. Decision theory's goals are to characterise and to guide rational decision-making—from the minor decisions of daily life, to the major decisions of industry and government— which, in its current state, it is unfit to do. This project will refine decision theory so that it may better achieve these goals.
M.C.Escher and his Contemporaries: the Genesis of the Impossible. The project aims to produce a conceptual history of the twentieth-century impossible pictures movement which developed around M.C.Escher, to classify kinds of impossible pictures, and particularly to establish priorities over who discovered what. This requires geometrical construction, and rigorous logical and mathematical analysis. The project will employ the novel techniques available within the theory of inconsistency. The sign ....M.C.Escher and his Contemporaries: the Genesis of the Impossible. The project aims to produce a conceptual history of the twentieth-century impossible pictures movement which developed around M.C.Escher, to classify kinds of impossible pictures, and particularly to establish priorities over who discovered what. This requires geometrical construction, and rigorous logical and mathematical analysis. The project will employ the novel techniques available within the theory of inconsistency. The significance of this work is that it demonstrates the rich conceptual resources available within inconsistent content. Expected outcomes are a book aimed at the general reader, technical articles in logic and mathematics journals, and a expanded understanding of our human ability to grasp inconsistent visual contents. Read moreRead less
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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Discovery Early Career Researcher Award - Grant ID: DE220100544
Funder
Australian Research Council
Funding Amount
$356,000.00
Summary
Fuzzy logics for graded reasoning in applied contexts. Many things we care about, such as friendship or safety, come in degrees, but our current systems for tracking information are not built to handle this. This project aims to enhance many-valued logic as a tool to manage graded information. It expects to generate new knowledge in the area of logical languages for fuzzy databases and finite domains using an interdisciplinary approach between philosophers, mathematicians and computer scientists ....Fuzzy logics for graded reasoning in applied contexts. Many things we care about, such as friendship or safety, come in degrees, but our current systems for tracking information are not built to handle this. This project aims to enhance many-valued logic as a tool to manage graded information. It expects to generate new knowledge in the area of logical languages for fuzzy databases and finite domains using an interdisciplinary approach between philosophers, mathematicians and computer scientists. Expected outcomes include new logical methods and modelling techniques for many-valued logics. This will provide significant benefits, such as the enhancement of fuzzy logic as a tool in artificial intelligence to handle reasoning with imprecise concepts, giving meaning to complex real-life data.Read moreRead less
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
Discovery Early Career Researcher Award - Grant ID: DE120102543
Funder
Australian Research Council
Funding Amount
$375,000.00
Summary
Models of paradox in non-classical mereotopology. Logical paradoxes have beset our best philosophical theories for millennia. In the strong tradition of Australian philosophical logic, this project will test the hypothesis that paradoxes are conceptual boundaries. Mathematical models provide a formal explanatory picture, telling us why there are logical paradoxes at all.
Qualitative models of rationality: Philosophical foundations and applications. This project aims to establish the qualitative approach to rationality as a viable and attractive choice. Mathematical models of rationality, which aim to formalise the rules of good reasoning and decision making, traditionally assume that beliefs and desires are always given in precise, quantifiable degrees of confidence and value. This assumption is implausibly strong, and alternative, qualitative frameworks have be ....Qualitative models of rationality: Philosophical foundations and applications. This project aims to establish the qualitative approach to rationality as a viable and attractive choice. Mathematical models of rationality, which aim to formalise the rules of good reasoning and decision making, traditionally assume that beliefs and desires are always given in precise, quantifiable degrees of confidence and value. This assumption is implausibly strong, and alternative, qualitative frameworks have been developed to handle the frequent situations in which it fails. These, however, remain incomplete and their foundations poorly understood. The project will address their omissions, secure their conceptual underpinnings and use them to clarify and resolve long-standing philosophical problems.Read moreRead less