Some central philosophical issues concern the use of mathematics in putatively non-mathematical endeavors. One such endeavor, of course, is philosophy, and the philosophy of mathematics is a key instance of that. The present article provides an idiosyncratic survey of the use of mathematical results to provide support or counter-support to various philosophical programs concerning the foundations of mathematics.

Natural kinds have been a constant topic in philosophy throughout its history, but many issues pertaining to natural kinds still remain unresolved. This paper considers one of these issues: the epistemic role of natural kinds in scientific investigation. I begin by clarifying what is at stake for an individual scientific field when asking whether or not the field studies a natural kind. I use an example from life science, concerning how biologists explain the similar body shapes of fish and cetaceans, to show that natural kinds play a central epistemic role in scientific explanations that cannot be delegated to other explanatory factors. A task for philosophy, then, is to come up with a theory of natural kinds that adequately accounts for the epistemic role of natural kinds in science. After having sketched the spectrum of available philosophical theories of natural kinds, I argue that none of the available theories adequately performs this task and that therefore the search is still open for a theory that does.

The introductory section discusses supervenience and the role it plays in formulating contemporary physicalism. The section concludes with the definition of local supervenience used by Kim in the causal-exclusion argument. The second section outlines an abstract model for the analysis of supervenience, associating total mental states with total states of the nervous system. It is argued that Kim’s formulation confuses two orders of necessity: a metaphysical necessity attaching to the supervenience of the total mental state, and a nomological necessity attaching to the correlation of particular elements of the concurrent physical and mental states. A central idea is the degree of resolution of the description of the state of the nervous system. This serves as a metaphor for the idea of multiplelevels of physical description, and in the third section it is argued that any formulation of supervenience that was attached to a particular level of description would risk error if changes at a more fundamental level of the subvening base proved to be significant for supervenience. In the fourth section it is argued that the problem of levels of properties and description cannot be avoided by a retreat from local to global supervenience. Loewer’s notion of a duplicate world may help, but an alternative weaker formulation is proposed that does avoid the difficulty.

I critically discuss the contextualist approach to essentialism, which was developed as an explanation of the seeming inconstancy of our essentialist intuitions. The problem is supposed to be that we vacillate a great deal in judging what properties an object has essentially from one occasion to another, which obviously undermines the reliability of our essentialist intuitions. Contextualists solve the problem by combining the metaphysical view that objects have essential properties with the semantic thesis that the term “essentially” is a context sensitive expression. Once we are aware of the context shifting, the conflict of intuitions turns out to be onlyapparent. My aim is to show that contextualism is not the answer that a proponent of essentialism should adopt. First, I outline the contextualist strategy and argue by help of an example that our linguistic practice does not seem to support the contextualist claim that “essentially” is a context-sensitive term. Secondly, the contextualist strategy deals only with the vacillation of intuitions in one person, but offers a very unfavorable explanation of the conflict of intuitions among different persons. Thus, contextualists face the challenge of proving the reliability of essentialist intuitions nevertheless. I conclude with David Lewis’s proposal in order to illustrate that the contextualist approach only provides the appearance, but not the real essentialism.

The article critically examines Jaegwon Kim’s book Physicalism, or Something Near Enough (Princeton: Princeton University Press, 2005). It recognizes the »near enough type of physicalism« involving functional reduction and covering the relational properties of qualia. Its intrinsic qualites are left out, but since it is qualia’s differences and similarities that matter, i.e. which affect our cognition and behaviour, this is, according to Kim, “no big loss”. While appreciating the book’s effort to offer an intelligible physicalistic theory of the world, the paper concludes that it fails to do so.

The central issue of the presentation is two questions: the first one is related to the issue of competences which are currently penetrating into philosophy curricula. The second, also related to the first one, is the issue of formulation of curriculum objectives and consequently of teaching methodology and practice. The controversial thesis that “the practice of philosophy is a whole which can not be divided into parts, procedures and techniques” is discussed and the reasons for more articulated learning objectives are offered. On the level of the curriculum a reflective approach to objectives-driven curriculum and the inclusion of process-driven curriculum is offered as a solution. On the level of the teaching methodology and practice the need for appropriately articulated learning objectives for the purpose of the conceptualisation of the process is shown.