Climbing Ladders, Building Bridges: Mathematical Philosophy at Work
• German Center for Research and Innovation (GCRI)
• German University Alliance (GUA)
On September 2, 2014, Prof. Stephan Hartmann, Chair of Philosophy of Science at the Ludwig-Maximilians-Universität München, gave an evening lecture on mathematical philosophy and its applications to science and public policy. He set the stage by questioning how we can better understand scientific reasoning, trace decision-making in scientific communities, and design fair and efficient voting procedures. This evening lecture was part of “Bridges 2014,” an LMU-organized transcontinental meeting in mathematical philosophy from September 2-3, 2014, in New York City, and was co-sponsored by the German Center for Research and Innovation (GCRI) and the German University Alliance (GUA). Prof. Branden Fitelson, Professor of Philosophy at Rutgers University and the event’s moderator, introduced the evening’s speaker Prof. Hartmann, whom he has collaborated with for many years. Prof. Fitelson is currently a visiting professor at the Munich Center for Mathematical Philosophy at the LMU Munich.
Prof. Hartmann’s evening lecture began with a brief introduction on the history of using mathematical methods in philosophy and the conceptual motivations that exist for applying scientific strategies to philosophical dilemmas. One key question within this discussion, he noted, is: What is the proper method of philosophy? Many philosophers believe that philosophy is an armchair activity and the exact methods of the natural and social sciences cannot guide philosophical research. Scientific philosophy, on the other hand, maintains that philosophical theses and arguments should be just as clear and precise as scientific ones: philosophers ought to build theories and models just as much as scientists do.
Prof. Hartmann then introduced the methodology used at the Munich Center for Mathematical Philosophy, which includes logic, probability theory, set theory, topology, modeling, and simulation. Knowing which method will be useful, of course, depends on the problem at hand. The problems that mathematical philosophy addresses hail from many different fields, ranging from epistemology and the philosophy of science to metaphysics, ethics, and social and political philosophy. Prof. Hartmann reminded audience members that the use of mathematical philosophy isn’t new. In fact, many of the world’s great philosophers were also mathematicians. For example, when confronted with a problem, the great German philosopher Gottfried Wilhelm Leibniz once proclaimed, “Let’s calculate.”
Prof. Hartmannthen illustrated what this field of philosophy entails by providing three examples from science and public policy. His first example concerned designing fair and efficient voting procedures for decision-making in the E.U.’s heterogeneous structure. The E.U. is currently comprised of 28 member states – some of which are large like Germany with a population of 82 million and others which are small like Malta with a population of 0.42 million. Keeping these differences in mind, these states must still find a way to make important joint decisions. The Treaties of Nice and Lisbon are examples of specific proposals that were designed to address the question of what a fair assignment of voting weights entails. One factor to consider is: What kind of union is the E.U.? Is it a union of states (equal representation), a union of people (proportional representation), or something in between (degressive proportionality or qualified majority)? The Treaty of Nice concluded that the E.U. was essentially sometype of qualified majority.
Prof. Hartmann’s second example referenced the group psychology “anchoring effect” that occurs during group deliberations. Suppose that a group has to reach a decision on a factual issue, such as the maximally tolerable amount of CO2 emissions. In the course of the deliberation, the group members try to convince each other of their opinions, but everyone is also open to change his or her mind in light of the others’ arguments. In many cases, a consensus eventually emerges. However, does the final outcome of the deliberation depend on the order in which group members speak? According to Prof. Hartmann, one often empirically observes that one speaker dominates the group by jumping up first to speak, thus setting the tone for the rest of the discussion. In other words, he or she essentially “anchors” the deliberation. Is it possible that a group of rational agents is actually irrational? Based on studies, research shows that the probability of the initial assignment of the first speaker is higher than that of all other group members, quite independently of the probabilities.
In his third example, Prof. Hartmann cited well-known methods used in scientific reasoning, such as deduction, induction, and abduction (or “inference to the best explanation”) before questioning whether “non-empirical” ways to assess scientific theories exist. Traditionally, scientific theories have been assessed in light of empirical data. However, this does not work well in some cases, such as in fundamental physics. Prof. Hartmann then provided theory assessments of the Hypothetico-deductive Model and Bayesian Confirmation Theory before introducing a new type of reasoning known as the “no-alternatives argument.”
In his concluding remarks, Prof. Hartmann emphasized that the aforementioned examples have a philosophical as well as a scientific dimension and addressing them requires a combination of methods from both fields. A lively discussion moderated by Prof. Fitelson ensued based on questions from the audience.