Aaron Lercher

Haskell Curry’s philosophy of mathematics is really a form of “structuralism” rather than “formalism” despite Curry’s own description of it as formalist (Seldin 2011). This paper explains Curry’s actual view by a formal analysis of a simple example. This analysis is extended to solve Keränen’s (2001) identity problem for structuralism, confirming Leitgeb’s (2020a, b) solution, and further clarifies structural ontology. Curry’s methods answer philosophical questions by employing a standard mathematical method, which is a virtue of the “methodological autonomy” emphasized by Curry (1951, 1963) and more recently with greater clarity by Maddy (1997, 2007).

This dissertation gives an account of the goals of inquiry of Descartes's 1637 Geometry. This account of the goals of inquiry is based on historical study of what is actually achieved by the mathematical work done in the Geometry. This account of the Geometry is a contribution toward a naturalistic understanding of mathematical inquiry in general. ;This dissertation first examines an account by Putnam of goals of mathematical inquiry. This dissertation argues that this extension of a realist view of mathematics results in a contrived interpretation of the achievement of the Geometry and is rejected. Instead this dissertation argues that Kuhn's view of the historical development of inquiry can be interpreted as an account of the goals of scientific inquiry and this account can be extended to the mathematical inquiry of the Geometry. ;This dissertation explains this extension of Kuhn's account of inquiry by examining the variety of solutions to a single long-standing and relatively simple mathematical problem. With respect to the most general goals of mathematical inquiry, Descartes's solution of the cube duplication problem is at the midpoint in a development extending from the ancient Greeks to a contemporary abstract view. ;This account of mathematical inquiry is also extended to a study of the applied mathematics of Descartes's geometrical optics. This account of applied mathematics circumvents the problem of understanding the ontology of the mathematics involved

By making use of a distinction between “making something happen” and “allowing it to happen,” a polluting act can be defined as making something happen with widely scattered externalized costs. Not all polluting acts are blameworthy, but we can investigate which polluting acts are sufficiently badly performed as to be blameworthy. This definition of polluting act permits us to justify the belief we often have that behavior concerning pollution may be blameworthy, even when we do not know whether the behavior caused harm

By making use of a distinction between “making something happen” and “allowing it to happen,” a polluting act can be defined as making something happen with widely scattered externalized costs. Not all polluting acts are blameworthy, but we can investigate which polluting acts are sufficiently badly performed as to be blameworthy. This definition of polluting act permits us to justify the belief we often have that behavior concerning pollution may be blameworthy, even when we do not know whether the behavior caused harm.

Electronic health records are likely to improve health care but in the U.S. they will also enable health insurers to be more selective in deciding to whom to deny coverage or whose premiums to increase. In a Rawlsian social contract (1971) the veil of ignorance does not conceal general scientific information from the hypothetical contracting parties. Nonetheless, this paper shows that social contract considerations rule out risk selection as morally impermissible. Since modern health care must in effect be paid for by public or private insurance, and doing so is efficient, this is a basic part of health care justice. But for information ethics this argument does not extend beyond cases in which provision of information serves to deny a social primary good to members of society

Our concern for nonhuman nature can be justified in terms of a human right to liberty of ecological conscience. This right is analogous to the right to religious liberty, and is equally worthy of recognition as that fundamental liberty. The liberty of ecological conscience, like religious liberty, is a negative right against interference. Each ecological conscience supports a claim to protection of the parts of nonhuman nature that are current or potential sites of its active pursuit of natural value. If we acknowledge the fallibility of each conscience in its pursuit of genuine natural value, a policy of indefinitely extensive conservation can be justified. Destruction of an object of current or potential natural value is like destroying a church, mosque, temple, or other holy place. This justification for environmental conservation is analogous to the standard justification for individual negative rights, as upheld by the liberal tradition of Locke, Mill, and Rawls.

This paper extends the argument in H.L.A. Hart's 'Are there any natural rights?' to argue that there is an environmental moral right against pollution. This right is composed of a right against negligent, reckless or intentional risk imposition, together with the liberty to act in a way that does not negligently, recklessly or intentionally impose risks on others. This right is understood as overrideable or prima facie, and this paper does not claim that this right is the only basis of moral judgment in the cases it considers. The hypothesis that there is a right against pollution does, however, explain some moral reasoning about pollution that otherwise is difficult to explain

Our concern for nonhuman nature can be justified in terms of a human right to liberty of ecological conscience. This right is analogous to the right to religious liberty, and is equally worthy of recognition as that fundamental liberty. The liberty of ecological conscience, like religious liberty, is a negative right against interference. Each ecological conscience supports a claim to protection of the parts of nonhuman nature that are current or potential sites of its active pursuit of natural value. If we acknowledge the fallibility of each conscience in its pursuit of genuine natural value, a policy of indefinitely extensive conservation can be justified. Destruction of an object of current or potential natural value is like destroying a church, mosque, temple, or other holy place. This justification for environmental conservation is analogous to the standard justification for individual negative rights, as upheld by the liberal tradition of Locke, Mill, and Rawls.