In this paper we investigate ignorance in relation to our capacity to justify our beliefs. To achieve this aim we specifically address scientific misconceptions, i.e. beliefs that are considered to be false in light of accepted scientific knowledge. The hypothesis we put forward is that misconceptions are not isolated false beliefs, but rather form part of a system of inferences—an explanation—which does not match current scientific theory. We further argue that, because misconceptions are embedded in a system, they cannot be (...) rectified simply by replacing false beliefs with true ones. To address our misconceptions, we must rather act on the system of beliefs that supports them. In the first step of our analysis, we distinguish between misconceptions that are easy to dispel because they represent simple errors that occur against the background of a correct explanatory apparatus and misconceptions that are, on the contrary, very difficult to dispel because they are the product of pseudo explanations. We show that, in the latter case, misconceptions constitute an integral part of an incorrect explanation and the reasons that support such misconceptions are deeply misleading. In the second step, we discuss various approaches that have been adopted to address the problem of misconceptions. Challenging the notion that directly addressing and criticizing specific misconceptions is an effective approach, we propose that critical thinking is the most fruitful means to deal with misconceptions. We define the core competences and knowledge relevant for the practice of critical thinking and discuss how they help us avoid misconceptions that arise from accepting beliefs that form part of a mistaken explanation. (shrink)

Although mathematicians often use it, mathematical beauty is a philosophically challenging concept. How can abstract objects be evaluated as beautiful? Is this related to their visualisations? Using an example from graph theory, this paper argues that, in making aesthetic judgements, mathematicians may be responding to a combination of perceptual properties of visual representations and mathematical properties of abstract structures; the latter seem to carry greater weight. Mathematical beauty thus primarily involves mathematicians’ sensitivity to aesthetics of the abstract.