Explanations in biology: teleology, mathematics, and scientific practice

Abstract

Many sciences, including biology, are becoming increasingly quantitative. Although mathematization leads to important advantages in science, the mathematical methods employed do not always satisfy the specific needs of scientific fields. For this reason, it is crucial to pinpoint what these specific needs are, and mathematize in a way that fulfils them. Biology is known for employing teleological notions and explanations. Whether teleology has a legitimate place in biology is subject to ongoing philosophical discussions. However, a major difficulty of such discussions resides in that the meaning of teleology is far from unequivocal. As a result, the debate is obscured, and misguided prescriptions may make their way into scientific practice. This dissertation has three main aims. The first is to clarify what teleology is. The second is to evaluate the epistemic value and appropriateness of teleology in biology. The third is to analyze the effect on teleology of different uses of mathematics in biology. In order to achieve these objectives, I discuss previous conceptual work on teleology, draw from the philosophies of different authors like, among others, Wittgenstein, Popper and Grosholz, and carry out case studies in the contexts of mathematical modelling in scientific practices and the use of mathematical explanations in biology. The main conclusions I reach are: 1) Teleology is minimally characterized by a purpose which has explanatory power about the element which is supposed to fulfil it, 2) teleology plays an important epistemic role in biology and its removal is detrimental to it, 3) some uses of mathematics, especially mathematical modelling carried out by biologists, preserve and promote teleology, and 4) other uses of mathematics, like mathematical explanations and perhaps mathematical modelling concerned only with physical features, can eliminate teleology from biology and hence they lead to either inadequate or partial images of biology.