Research
Three papers comprise the core of my dissertation research. I am bridging this dissertation into research into some classic problems in philosophy of science from a novel direction, using cross-domain model transfer. The process of model transfer poses a fertile starting place to investigate and understand the epistemology of science and interdisciplinarity.
In this paper I propose a new notion - the landing zone - in order to identify conceptual features that allow modelers to transfer mathematical tools across disciplinary borders. Discussion on model transfer refers to the transferable models as ‘templates’. Templates are functions, equations, or computational methods that are capable of being generalized from a particular subject matter. There are formal and conceptual prerequisites for the transfer of a template to a new domain. A landing zone is an ontology that contributes to the satisfaction of these conditions for successful transfer.
To make this point I use a case study on a model in chemistry - the Quantum Theory of Atoms in Molecules (QTAIM) - that makes use of transferred templates from physics - the virial theorem and the wave function. The landing zone in this case is a new ontological notion, that of the topological atom, which prepares ground for the use of the virial theorem and the wave function in chemistry. The virial theorem requires that there exists in-principle stability to the system that it represents, and the wave function requires transformation in its representation that is justified. The ontology of QTAIM – the landing zone for these templates – grounds the scientific use of these templates in the context of chemistry.
There exists a dynamic between the thing that is transferred and the thing to which transferrable templates apply that influences conceptual development in the sciences. The use of a transferable template in a new domain requires reconception of domain-specific phenomena. This paper examines two cases of model transfer, the use of the ideal gas law in biology by R.A. Fisher and the use of the virial theorem in chemistry by Richard Bader. These two stories of model transfer in biology and chemistry indicate a dimension to conceptual progress related to this dynamic. Using discourse on model transfer affords philosophers a novel approach for depicting the invention of, for instance, chemical concepts and resulting disputes.
Paper 3: Using a Scientific Model of Problem Solving to Solve the Problem of Scientific Model Transfer
There are two discussions in philosophy of science about modeling that this paper seeks to combine into a new perspective on the epistemology of science. One discussion is about the transfer of models across scientific disciplines. Certain models seem capable of transfer across scientific domains while others do not. Philosophical accounts for model transfer identify the features that transferable models share – a mathematical core for instance – and explain why these features drive transfer, for example, affording less computational demanding methods for mathematical modeling. Research so far provides a framework for investigating the scientific practice of model transfer, revealing unique modes of conceptual strategizing in the sciences.
The other discussion is about the role of idealizing in scientific modeling. Idealizations are distorting features of models that seemingly involve misrepresentations or false claims about phenomena. This conflicts with the face-value role of scientific models as accurately and truthfully depicting nature. If idealizations are in tension with a model’s accuracy or truthfulness, then it is puzzling that scientists so often choose to idealize. Philosophers of science resolve this tension by proposing epistemic aims like non-factive explanation or understanding as what idealizing contributes towards.
This paper offers a smaller scale alternative, made salient by analysis of a case of model transfer, for the epistemic role of idealizing: constraint tuning. Constraint tuning is new concept I introduce that identifies the practice of delimiting the area of application of a mathematical model through idealizing. It is a method that scientists use to forward their modal knowledge of a target system by making explicit what counts as a representation. This process involves thoughtful conceptualization and drawing up formal mathematical constraints, and fits in a developing philosophical discussion on conceptual strategizing in the sciences.
To illustrate how constraint tuning is another epistemic aim of idealizing, I introduce a new case study on the transfer of the virial theorem to astrophysics in the 1960s. Model transfer, instead of being for reasons to do with tractability, involves affording new modal knowledge to a domain. The transferred model does so by allowing scientists to delimit a new region for modal exploration. In this case, the transferrable model core - the virial theorem - consists of an equation that modelers use as a formal mathematical constraint for drawing up principled idealizations. In astrophysics, the introduction of the virial theorem allowed scientists to explore the supposition that interstellar clouds were essentially stable things – an idealization. This transfer of the virial theorem then allowed other modelers to piggyback on this supposition, using this idealization in models of stellar evolution, generating hypotheses and inferences about the time scale for the birth of stars. What modelers introduced to astrophysics when they began using the virial theorem was a new way to delimit which things in model systems were stable clouds. This allows scientists to explore, by varying initial conditions and other parameters, how clouds may possibly evolve.
[JP1]Michael thought at this point: would have thought isolation was the point here.