Lydia Patton

Detlefsen (1986) reads Hilbert's program as a sophisticated defense of instrumentalism, but Feferman (1998) has it that Hilbert's program leaves significant ontological questions unanswered. One such question is of the reference of individual number terms. Hilbert's use of admittedly "meaningless" signs for numbers and formulae appears to impair his ability to establish the reference of mathematical terms and the content of mathematical propositions (Weyl (1949); Kitcher (1976)). The paper traces the history and context of Hilbert's reasoning about signs, which illuminates Hilbert's account of mathematical objectivity, axiomatics, idealization, and consistency.

The conception of a ‘law of nature’ is a human product. It was created to play a role in natural philosophy, in the Cartesian tradition. In light of this, philosophers and scientists must sort out what they mean by a law of nature before evaluating rival theories and approaches. If one’s conception of the laws of nature is yoked to metaphysical notions of truth and explanation, that connection must be made explicit and defended. If, on the other hand, one’s aim is to disentangle laws from truth or from explanation, that must be stated and defended as well. If philosophers do not make such assumptions, intuitions, and methodological commitments clear, then it will be impossible to identify the source of disagreement in debates about the laws of nature. Are the conflicts rooted in disagreement about the conclusions reached, or do the background commitments of the combatants block any resolution to the dispute in principle or in practice?

Ernst Mach’s defense of relativist theories of motion in Die Mechanik involves a well-known criticism of Newton’s theory appealing to absolute space, and of Newton’s “bucket” experiment. Sympathetic readers (Norton 1995) and critics (Stein 1967, 1977) agree that there’s a tension in Mach’s view: he allows for some constructed scientific concepts, but not others, and some kinds of reasoning about unobserved phenomena, but not others. Following Banks (2003), I argue that this tension can be interpreted as a constructive one, springing from Mach’s approach to scientific reasoning. Mach’s “economy of science” allows for a principled distinction to be made, between natural and artificial hypothetical reasoning, and Mach defends a division of labor between the sciences in a 1903 paper for The Monist, “Space and Geometry from the Point of View of Physical Inquiry”. That division supports counterfactual reasoning in Mach’s system, something that’s long been denied is possible for him.

Philosophy, Science, and History: A Guide and Reader is a compact overview of HOPOS that aims to introduce students to the groundwork of the field. Part I of the Reader begins with classic texts in the history of logical empiricism, including Reichenbach's discovery-justification distinction. With careful reference to Kuhn's analysis of scientific revolutions, the section provides key texts analyzing the relationship of HOPOS to the history of science, including texts by Santayana, Rudwick, and Shapin and Schaffer. Part II provides texts illuminating central debates in the history of science and its philosophy. These include the history of natural philosophy (Descartes, Newton, Leibniz, Kant, Hume, and du Châtelet in a new translation); induction and the logic of discovery (including the Mill-Whewell debate, Duhem, and Hanson); and catastrophism versus uniformitarianism in natural history (Playfair on Hutton and Lyell; de Buffon, Cuvier, and Darwin). The editor's introductions to each section provide a broader perspective informed by contemporary research in each area, including related topics.

What is the origin of the concept of a law of nature? How much does it owe to theology and metaphysics? To what extent do the laws of nature permit contingency? Are there exceptions to the laws of nature? Is it possible to give a reductive analysis of lawhood, or is it a primitive? Twelve brand-new essays by an international team of leading philosophers take up these and other central questions on the laws of nature, whilst also examining some of the most important intuitions and assumptions that have guided the debate over laws of nature since the concept's invention in the seventeenth century. Laws of Nature spans the history of philosophy and of science, contemporary metaphysics, and contemporary philosophy of science. Contents: 1. Intuitions and Assumptions in the Debate over Laws of Nature, Walter Ott and Lydia Patton 2. Early Modern Roots of the Philosophical Concept of a Law of Nature, Helen Hattab 3. Laws of Nature and the Divine Order of Things: Descartes and Newton on Truth in Natural Philosophy, Mary Domski 4. Leges sive natura: Bacon, Spinoza, and a Forgotten Concept of Law, Walter Ott 5. Laws and Powers in the Frame of Nature, Stathis Psillos 6. Laws and Ideal Unity, Angela Breitenbach 7. Becoming Humean, John W. Carroll 8. A Perspectivalist Better Best System Account of Lawhood, Michela Massimi 9. Laws: An Invariance Based Account, James Woodward 10. How the Explanations of Natural Laws Make Some Reducible Physical Properties Natural and Explanatorily Powerful, Marc Lange 11. Laws and their Exceptions, Stephen Mumford 12. Are laws of nature consistent with contingency?, Nancy Cartwright and Pedro Merlussi

Hermann von Helmholtz allows for not only physiological facts and psychological inferences, but also perspectival reasoning, to influence perceptual experience and knowledge gained from perception. But Helmholtz also defends a version of the view according to which there can be a kind of “perspectival truth” revealed in scientific research and investigation. Helmholtz argues that the relationships between subjective and objective, real and actual, actual and illusory, must be analyzed scientifically, within experience. There is no standpoint outside experience from which we can reason, no extra-sensory knowledge of the constitution of the “ideal subject” or of the properties of “real objects.” In the tradition of psychophysics inherited by Helmholtz, we can arrive at a kind of perspectival analysis of perceptual experience, which embeds an account of that experience within the context of the history and situation of the perceiving subject. That analysis is relative to the perceiving subject, but the perspectival explanations Helmholtz constructs are not thereby relativist: in fact, for Helmholtz, the more squarely the perceiving subject is placed in a scientific, perspectival context, the more facts we are able to learn about her experience and the objects with which she interacts.