It is generally agreed upon today that scientific reasoning, like everyday reasoning, proceeds in a dynamic way: inferences derived at some stage in the reasoning process may at a later stage be rejected. This dynamics may be extrinsic or intrinsic. I shall call it extrinsic when previously derived conclusions are rejected on non-logical grounds, and intrinsic when their rejection is based on a purely logical analysis.

A logic of diagnosis proceeds in terms of a set of data and one or more (prioritized) sets of expectancies. In this paper we generalize the logics of diagnosis from [27] and present some alternatives. The former operate on the premises and expectancies themselves, the latter on their consequences.

Creativity is commonly seen as beyond the scope of rationality. In the present paper, it is argued that available insights in epistemology and available results in logic enable us to incorporate creativity within an independently sensible view on human rationality.

Brown (The laboratory of the mind. Thought experiments in the natural science, 1991a , 1991b ; Contemporary debates in philosophy of science, 2004 ; Thought experiments, 2008 ) argues that thought experiments (TE) in science cannot be arguments and cannot even be represented by arguments. He rest his case on examples of TEs which proceed through a contradiction to reach a positive resolution (Brown calls such TEs “platonic”). This, supposedly, makes it impossible to represent them as arguments for logical reasons: (...) there is no logic that can adequately model such phenomena. (Brown further argues that this being the case, “platonic” TEs provide us with irreducible insight into the abstract realm of laws of nature). I argue against this approach by describing how “platonic” TEs can be modeled within the logical framework of adaptive proofs for prioritized consequence operations. To show how this mundane apparatus works, I use it to reconstruct one of the key examples used by Brown, Galileo’s TE involving falling bodies. (shrink)

In this paper I propose a new approach to the foundation of mathematics: non-monotonic set theory. I present two completely different methods to develop set theories based on adaptive logics. For both theories there is a finitistic non-triviality proof and both theories contain (a subtle version of) the comprehension axiom schema. The first theory contains only a maximal selection of instances of the comprehension schema that do not lead to inconsistencies. The second allows for all the instances, also the inconsistent (...) ones, but restricts the conclusions one can draw from them in order to avoid triviality. The theories have enough expressive power to form a justification/explication for most of the established results of classical mathematics. They are therefore not limited by Gödel’s incompleteness theorems. This remarkable result is possible because of the non-recursive character of the final proofs of theorems of non-monotonic theories. I shall argue that, precisely because of the computational complexity of these final proofs, we cannot claim that non-monotonic theories are ideal foundations for mathematics. Nevertheless, thanks to their strength, first order language and the recursive dynamic (defeasible) proofs of theorems of the theory, the non-monotonic theories form (what I call) interesting pragmatic foundations. (shrink)

Pluralism has many meanings. An assessment of the need for logical pluralism with respect to scientific knowledge requires insights in its domain of application. So first a specific form of epistemic pluralism will be defended. Knowledge turns out a patchwork of knowledge chunks. These serve descriptive as well as evaluative functions, may have competitors within the knowledge system, interact with each other, and display a characteristic dynamics caused by new information as well as by mutual readjustment. Logics play a role (...) in the organization of the chunks, in their applications and in the exchange of information between them. Epistemic pluralism causes a specific form of logical pluralism. Against this background, the occurrence of inconsistencies will be discussed together with required reactions and systematic ways to explicate them. Finally, the place of inconsistencies in the sciences will be considered. Seven theses will be proposed and argued for. The implications of each of these for pluralism will be considered. The general tenet is that paraconsistency plays an important role, bound to become more explicit in the future, but that the occurrence of inconsistencies does not basically affect the need for pluralism. (shrink)