In previous projects, we have investigated hypothetical reasoning from a logical point of view. This 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 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 an 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.