Johannes Lenhard

Es soll ein Beitrag zur epistemischen Charakterisierung von Computersimulationen als jenseits von Experiment und Theorie geleistet werden. Es wird argumentiert, dass die in der Simulationstechnik eingesetzten Verfahren nicht numerische Lösungen liefern, sondern deren Dynamik mittels generativer Mechanismen imitieren. Die Computersimulationen in der Klimatologie werden als systematisches wie historisches Fallbeispiel behandelt. Erst "Simulationsexperimente" gestatten es, mittels Modellen eine Dynamik zu imitieren, ohne deren Grundgleichungen zu "lösen". /// Computer simulations will be characterized in epistemic respect as a method between experiment and theory. It will be argued that simulations do not provide numerical solutions, rather they use generative mechanisms to imitate a dynamics. Climate science will be considered as a case both systematically and historically. Only simulation experiments allow to build models that imitate a dynamics without solving the relevant equations.

Two conflicting interpretations of modern axiomatics will be considered. The logico-analytical interpretation goes back to Pasch, while the model-theoretical approach stems from Hilbert. This perspective takes up the distinction between logic as calculus ratiocinator versus lingua characterica that Heijenoort and Hintikka placed emphasis on. It is argued that the Heijenoort-Hintikka distinction can be carried over from logic to mathematical axiomatics. In particular, the model-theoretical viewpoint is deeply connected to a philosophy of mathematics that is not committed to a foundational perspective, but oriented more at applications and at mathematical practice.

This book puts forward a new role for mathematics in the natural sciences. In the traditional understanding, a strong viewpoint is advocated, on the one hand, according to which mathematics is used for truthfully expressing laws of nature and thus for rendering the rational structure of the world. In a weaker understanding, many deny that these fundamental laws are of an essentially mathematical character, and suggest that mathematics is merely a convenient tool for systematizing observational knowledge. The position developed in this volume combines features of both the strong and the weak viewpoint. In accordance with the former, mathematics is assigned an active and even shaping role in the sciences, but at the same time, employing mathematics as a tool is taken to be independent from the possible mathematical structure of the objects under consideration. Hence the tool perspective is contextual rather than ontological. Furthermore, tool-use has to respect conditions like suitability, efficacy, optimality, and others. There is a spectrum of means that will normally differ in how well they serve particular purposes. The tool perspective underlines the inevitably provisional validity of mathematics: any tool can be adjusted, improved, or lose its adequacy upon changing practical conditions.

We claim that adjustable parameters play a crucial role in building and applying simulation models. We analyze that role and illustrate our findings using examples from equations of state in thermodynamics. In building simulation models, two types of experiments, namely, simulation and classical experiments, interact in a feedback loop, in which model parameters are adjusted. A critical discussion of how adjustable parameters function shows that they are boon and bane of simulation. They help to enlarge the scope of simulation far beyond what can be determined by theoretical knowledge, but at the same time undercut the epistemic value of simulation models.

This paper discusses how computational modeling combines the autonomy of models with the automation of computational procedures. In particular, the case of ab-initio methods in quantum chemistry will be investigated to draw two lessons from the analysis of computational modeling. The first belongs to general philosophy of science: Computational modeling faces a trade-off and enlarges predictive force at the cost of explanatory force. The other lesson is about the philosophy of chemistry: The methodology of computational modeling puts into doubt claims about the reduction of chemistry to physics.

The role mathematics plays in the sciences has been assessed differently and in conflicting ways. Put very roughly, a strong view holds that mathematically formulated laws of nature refer to or reveal the rational structure of the world. By contrast, a weak view denies that these fundamental laws are of an essentially mathematical character, and rather suggests that mathematics is merely a tool for systematizing observational knowledge. We put forward a position that combines features of both viewpoints. The tool perspective is provisional and contextual, rather than ontological.

The goal of the present article is to contribute to the epistemology and methodology of computer simulations. The central thesis is that the process of simulation modeling takes the form of an explorative cooperation between experimenting and modeling. This characteristic mode of modeling turns simulations into autonomous mediators in a specific way; namely, it makes it possible for the phenomena and the data to exert a direct influence on the model. The argumentation will be illustrated by a case study of the general circulation models of meteorology, the major simulation models in climate research.

We claim that adjustable parameters play a crucial role in building and applying simulation models. We analyze that role and illustrate our findings using examples from equations of state in thermodynamics. In building simulation models, two types of experiments, namely, simulation and classical experiments, interact in a feedback loop, in which model parameters are adjusted. A critical discussion of how adjustable parameters function shows that they are boon and bane of simulation. They help to enlarge the scope of simulation far beyond what can be determined by theoretical knowledge, but at the same time undercut the epistemic value of simulation models.

Es soll ein Beitrag zur epistemischen Charakterisierung von Computersimulationen als jenseits von Experiment und Theorie geleistet werden. Es wird argumentiert, dass die in der Simulationstechnik eingesetzten Verfahren nicht numerische Lösungen liefern, sondern deren Dynamik mittels generativer Mechanismen imitieren. Die Computersimulationen in der Klimatologie werden als systematisches wie historisches Fallbeispiel behandelt. Erst "Simulationsexperimente" gestatten es, mittels Modellen eine Dynamik zu imitieren, ohne deren Grundgleichungen zu "lösen". /// Computer simulations will be characterized in epistemic respect as a method between experiment and theory. It will be argued that simulations do not provide numerical solutions, rather they use generative mechanisms to imitate a dynamics. Climate science will be considered as a case both systematically and historically. Only simulation experiments allow to build models that imitate a dynamics without solving the relevant equations

This paper starts by looking at the coincidence of surprising behavior on the nanolevel in both matter and simulation. It uses this coincidence to argue that the simulation approach opens up a pragmatic mode of understanding oriented toward design rules and based on a new instrumental access to complex models. Calculations, and their variation by means of explorative numerical experimentation and visualization, can give a feeling for a model's behavior and the ability to control phenomena, even if the model itself remains epistemically opaque. Thus, the investigation of simulation in nanoscience provides a good example of how science is adapting to a new instrument: computer simulation.

Two conflicting interpretations of modern axiomatics will be considered. The logico-analytical interpretation goes back to Pasch, while the model-theoretical approach stems from Hilbert. This perspective takes up the distinction between logic as calculus ratiocinator versus lingua characterica that Heijenoort and Hintikka placed emphasis on. It is argued that the Heijenoort-Hintikka distinction can be carried over from logic to mathematical axiomatics. In particular, the model-theoretical viewpoint is deeply connected to a philosophy of mathematics that is not committed to a foundational perspective, but oriented more at applications and at mathematical practice.