Beyond logic : Hypothetical Reasoning in Philosophy of Science, Informatics, and Law – BeyondLogic

In our Master Project we have striven to provide the logical tools used to analyse logical reasoning in the three areas of applications and investigated how these applications feed back into the concept of logic itself. In three Individual Projects, which correspond to philosophy of science, informatics, and law, we have studied the particular forms hypothetical reasoning takes in these fields. In three significant extra-logical areas, we wanted to show that the proof-theoretic investigation of hypothetical reasoning leads to new insights, ideas, and results from which these fields can directly profit. The area of philosophy of science gives paradigmatic examples within a field of philosophy that is mainly concerned with natural sciences. The area of informatics gives paradigmatic examples within a field in the formal or mathematical sciences. The area of law gives paradigmatic examples within a field outside the natural sciences which belongs to both humanities and social sciences. Thus we aim to show that logic need not be predominantly concerned with itself but reaches out into many, if not all, areas of research. As the organisational structure in our previous projects has proven successful, we have divided this project into a Master Project to which all participants equally contribute, and into Individual Projects which are allocated to different teams in our French-German group. These Individual Projects correspond to the three subject areas just mentioned: IP1. Proof-theoretic analysis of hypothetical reasoning in philosophy of science IP2. Informatics and the philosophical modelling of hypothetical reasoning IP3. Hypothetical reasoning in law.

Two members of the German team resided in Paris, Peter Schroeder-Heister in 2016, Thomas Piecha in 2018/2019, as visiting researchers at the IHPST. We had regular project meetings every year. Each meeting was devoted to one of the themes of the Main Project and themes selected from the individual projects. In addition to these internal meetings, we have organized six international conferences with external experts. Some of these conferences took the form of workshops organized in Paris, Lyon and Tübingen. The two most important ones took place, for one in Tübingen entitled «Sub-structural logic: 25 years after« in memory of the conference held in Tübingen in 1990 and which is at the origin of this field of research; the other at Cerisy la Salle in 2017. This last conference marked the end of our joint project and allowed us to highlight what we accomplished. The second of these conferences gave rise to an open access publication.

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For each individual project, we had promised two publications a year (on average), at least one in an international newspaper, the other could also be presented in an international conference. Finally, as part of the main project, IP1 and IP2, there are 18 articles and book chapters that have been published and two books. For the Main Project, we count among the publications the volume of the proceedings of the conference which has been published by the coordinators of the project and also the volume gathering the proceedings of the symposium devoted to Kreisel (Paris, June 2016) to be published by Springer.

In previous projects, we have investigated hypothetical reasoning from a logical point of view. This new project targets hypothetical reasoning in extra-logical areas. Our leading viewpoint is that logical investigations must prove useful outside logic, and conversely, that logical investigations must take into account the way logic is applied in the ‘real world’. Thus we switch from a an internal to an external perspective by considering what hypothetical reasoning is all about when we go beyond logic.
As such extra-logical areas we have chosen philosophy of science as an application within philosophy, informatics as a application within the formal sciences, and law as an application within the field of social interaction. In each of these areas the idea of hypothetical reasoning plays a prominent role which can be used as a test case for our logical theories. We are particularly interested in how far the proof-theoretic perspective we have advocated and advanced in our logical investigations pertains to these subjects.

That the notion of hypothesis plays a prominent role in philosophy of science is a platitude, as scientific theories are hypotheses subjected to empirical test and used for empirical explanation. We claim that by adopting our proof-theoretic perspective, several open questions in philosophy of science can be solved or at least more appropriately analysed, for example by using constructive notions of implication or substructural logics.

Likewise in law hypothetical reasoning is abundant, as laws are applied by deriving consequences from them as hypotheses. Here, again, we claim that our proof-theoretic perspective will prove useful, as it provides novel methods to extract content from structured bodies of sentences.

In informatics we have the situation that logic, and in particular proof theory, has been applied in various fields such as the verification of hardware and software. Here we are predominantly interested in the opposite direction, namely in how this application of logical methods shape or should shape the form of logic itself. Our claim is that this is in fact the case, leading to some sort of ‘paradigm change’ in logic where proof theory is going to play a more prominent role than it is playing currently.

In our Master Project we shall provide the logical tools used to analyse logical reasoning in the three areas of applications and investigate how these applications feed back into the concept of logic itself. In three Individual Projects, which correspond to philosophy of science, informatics, and law, we shall study the particular forms hypothetical reasoning takes in these fields.