Unity of Science. From the Idea to the Configurations

Olga Pombo
(Faculty of Sciences, Lisbon University, Portugal)

Unity of Science is both a regulative idea and a task. That is why it has been grasped through the most extreme metaphors of an invisible totality and has gave rise to several epistemological programs and intellectual mouvements. However, before to mount up to such exemplary issues, I will pay attention to the deep, institutional configurations of Unity of Science (Library, Museum, "République des Savants", School and Encyclopaedia) and to their polyedric articulations. More than a game of complementarities, what seems to be interesting is to show that their strucured relationship is endowed with important descriptive and normative capacity.

Dealing with Uncertainty in Modern Science

Dinis Pestana 
(Philosophy Department, Lisbon University, Portugal)

For a while, scientists tried to alienate Heraclitus legacy, that contingence and ephemerety are at the core of reality. But quantification has been Science’s way, and metrological issues have brought to the forefront errors in measurements and the protagonism of uncertainty, and by 1920 Pólya christened the asymptotic results on the “normal” approximation  as the central limit theorem, recognizing that it is the ultimate weapon to measure with the accuracy we need, insofar as we can pay for a long run of measurements. This isn’t but one well-known instance where composing with uncertainty pays much better dividends than trying to avoid it.

Since their appearance as branches of Mathematics, Probability and Statistics have been part of the toolbox used by scientists in all fields to cut through the deep complexity of data, accompanying and sometimes preceding the advancement of science. The total probability theorem is, in fact, Descartes’ method of dealing with a complex problem, splitting it in simpler sub-problems to work out a solution as the blending of partial solutions of these sub-problems; and three centuries latter, Fisher’s analysis of variance is a brilliant and pathbreaking example that Descartes’ method can be inappropriate, that some problems must be solved as a whole, and cannot be splitted out in sub-problems. Fisher’s work also has shown that science had to move from observational gathering of data to the production of relevant data, with the new discipline he invented, Design of Experiments, since this way of dealing with information is much more rewarding in knowledge building.

In fact, information is important insofar as it is at the root of knowledge building —  and Probability and Statistics have a large share in the toolbox of methodologies that allow us to extract knowledge from the available data. In a sense, Probability and Statistics are our resources in taming uncertainty, sometimes in using its patterns as a source of knowledge by itself. Unfortunately, the formal training of scientists relies much more on the ability of dealing with ad hoc techniques than on deep understanding of the principles involved in statistical thinking. There is far too much “random search” of significant results, with few critical appraisal of the information needed to achieve conclusions, proper consideration of confounding concerns, and poor understanding of the essential role of repeatability in the experimental method.

We discuss the importance of planning experiments, issues on appropriate sample sizes, and concerns arising in metha-analytical methods, as well as the limits of of statistical tools in the construction of science from empirical evidence.

More information regarding this Colloquium may be obtained from the website