It is generally accepted among philosophers of science that hypothesis testing is a key methodological feature of science. As far as philosophical theories of confirmation are con...

There seem to be some very good reasons for a philosopher of science to be a deductivist about scientific reasoning. Deductivism is apparently connected with a demand for clarity and definiteness in the reconstruction of scientists' reasonings. And some philosophers even think that deductivism is the way around the problem of induction. But the deductivist image is challenged by cases of actual scientific reasoning, in which hard-to-state and thus discursively ill-defined elements of thought nonetheless significantly condition what practitioners accept as (...) cogent argument. And arguably, these problem cases abound. For example, even geometry--for most of its history--was such a problem case, despite its exactness and rigor. It took a tremendous effort on the part of Hilbert and others, to make geometry fit the deductivist image. Looking to the empirical sciences, the problems seem worse. Even the most exact and rigorous of empirical sciences--mechanics--is still the kind of problem case which geometry once was. In order for the deductivist image to fit mechanics, Hilbert's sixth problem (for mechanics) would need to be solved. This is a difficult, and perhaps ultimately impossible task, in which the success so far achieved is very limited. I shall explore some consequences of this for realism as well as for deductivism. Through discussing links between non-monotonicity, skills, meaning, globality in cognition, models, scientific understanding, and the ideal of rational unification, I argue that deductivists can defend their image of scientific reasoning only by trivializing it, and that for the adequate illumination of science, insights from anti-deductivism are needed as much as those which come from deductivism. (shrink)

Gideon Rosen, Brian Leiter, and Catarina Dutilh Novaes raise deep questions about the arguments in Morality and Mathematics (M&M). Their objections bear on practical deliberation, the formulation of mathematical pluralism, the problem of universals, the argument from moral disagreement, moral ‘perception’, the contingency of our mathematical practices, and the purpose of proof. In this response, I address their objections, and the broader issues that they raise.

Knowledge Representation and Reasoning (KR&R) is based on the idea that propositional content can be rigorously represented in formal languages long the province of logic, in such a way that these representations can be productively reasoned over by humans and machines; and that this reasoning can be used to produce knowledge-based systems (KBSs). As such, KR&R is a discipline conventionally regarded to range across parts of artificial intelligence (AI), computer science, and especially logic. This standard view of KR&R’s participating fields (...) is correct — but dangerously incomplete. The view is incomplete because, as we explain herein, sophisticated KR&R must rely heavily upon philosophy. Encapsulated, the reason is actually quite straightforward: Sophisticated KR&R must include the representation of not only simple properties, but also concepts that are routine in the formal sciences (theoretical computer science, mathematics, logic, game theory, etc.), and everyday socio-cognitive concepts like mendacity, deception, betrayal, and evil. Because in KR&R the representation of such concepts must be rigorous in order to enable machine reasoning (e.g., machine-generated and machine-checked proofs that a is lying to b) over them, philosophy, devoted as it is in no small part to supplying analyses of such concepts, is a crucial partner in the overall enterprise. To put the point another way: When the knowledge to be represented is such as to require lengthy formulas in expressive formal languages for that representation, philosophy must be involved in the game. In addition, insofar as the advance of KR&R must allow formalisms and processes for representing and reasoning over visual propositional content, philosophy will be a key contributor into the future. (shrink)

Department of Philosophy, University of California at San Diego, La Jolla, Ca 92093, U.S.A., and Center for Advanced Study in the Behavioral Sciences, Stanford, CA, U.S.A. E-mail: [email protected].

According to Bernard Williams, philosophy is a humanistic discipline essentially different from the sciences. While the sciences describe the world as it is in itself, independent of perspective, philosophy tries to make sense of ourselves and of our activities. Only the humanistic disciplines, in particular philosophy, can do this, the sciences have nothing to say about it. In this note I point out some limitations of Williams’ view and outline an alternative view.