Mathematics and the world : explanation and representation
This thesis is about two ways in which we use mathematics to understand the non-mathematical world: in particular, mathematical explanation and mathematical representation. In chapters 1 and 2, I motivate the project by suggesting that, in addition to shedding light on the nature of explanation and representation, it is necessary to develop accounts of these two world-oriented uses of mathematics in order to evaluate competing considerations in favour of, and against, mathematical realism. In chapters 3 and 4 I discuss extra-mathematical explanation. In chapter 3, I consider and reject four recent accounts of mathematical explanation. In chapter 4 I discuss and endorse what I call the modal account of extra-mathematical explanation. I argue, in line with Jansson and Saatsi and contra Baron, Colyvan and Ripley that such an account does not require countenancing counterpossibles, I discuss in virtue of what a mathematical fact can play this role and I address whether or not extra-mathematical explanations are causal. In chapters 5 and 6 I discuss mathematical representation. In chapter 5 I consider two fundamental challenges to developing an account of mathematical scientific representation: the first is Callender
Heron, John-Hamish
Mathematics and the world : explanation and representation. This thesis is about two ways in which we use mathematics to understand the non-mathematical world: in particular, mathematical explanation and mathematical representation. In chapters 1 and 2, I motivate the project by suggesting that, in addition to shedding light on the nature of explanation and representation, it is necessary to develop accounts of these two world-oriented uses of mathematics in order to evaluate competing considerations in favour of, and against, mathematical realism. In chapters 3 and 4 I discuss extra-mathematical explanation. In chapter 3, I consider and reject four recent accounts of mathematical explanation. In chapter 4 I discuss and endorse what I call the modal account of extra-mathematical explanation. I argue, in line with Jansson and Saatsi and contra Baron, Colyvan and Ripley that such an account does not require countenancing counterpossibles, I discuss in virtue of what a mathematical fact can play this role and I address whether or not extra-mathematical explanations are causal. In chapters 5 and 6 I discuss mathematical representation. In chapter 5 I consider two fundamental challenges to developing an account of mathematical scientific representation: the first is Callender
mathematics world explanation representation two_way use mathematics non mathematical world particular mathematical explanation mathematical representation motivate project suggest addition shed_light nature explanation representation necessary develop_account world oriented mathematics order_evaluate compete consideration favour mathematical realism discuss extra mathematical explanation consider reject recent account mathematical explanation discuss endorse call modal account extra mathematical explanation argue line contra baron account require discus virtue mathematical fact play_role address_whether extra mathematical explanation causal discuss mathematical representation consider two_fundamental challenge develop_account mathematical scientific representation first