3 February 2020
Since the emergence of modern physics, the search for ultimate-causes has increasingly given way to explanation through simple mathematical description. Indeed, the central role of formal models is widely accepted, yet there has been and still is much less agreement on what criteria may decide in favor of the objective validity of these models. While there is a spectrum of ideas about the representative role of models, when looking at physicists’ actual practice we usually notice that their models are combinations of abstractions-from-observation and of creative constructions. Models, then, are used as vehicles for surrogate reasoning to overcome the chaotic multiplicity of raw observations by applying to them the unity of concepts in the form of laws and patterns. (Countessa, 2007; Suarez, 2004)
We can detect the same pattern of inference-to-coherence-and-conceivability in Einstein’s first relativistic cosmological model, which was shaped by considerations having to do with the difficulty of formulating consistent boundary conditions at infinity. To get around this problem he proposed that the universe must have no boundary, rather it should be a spatially closed spherical world.
But how could Einstein be confident that the simplest mathematical construction we may conceive of, gives us a reliable entrance to knowledge of the natural world? Admitting as he did as well that two different formal models may explain phenomena with equal degrees of objectivity (Howard, 1985), how could he guarantee that theory construction would not degenerate into an arbitrary endeavor?
I intend to examine Einstein’s corpus of pertinent writing in order to single out the main controversial issues regarding the representation of reality in formal models. These issues can be classified along three central themes: 1- the necessity of non- inductive formalism and inferences-to-coherence-and-conceivability; 2- avoiding arbitrariness and disconnection from reality, and 3- redefining objectivity in the face of the two previous requirements.
Once having done that, I want to enrich the historical issue with a more strictly philosophical component. The main idea is this: The notion that the mere possibility of a coherent physical description of the universe as a whole poses some constraints on what kind of entity it could be (as is the case in Einstein’s no- boundary proposal), joined to the claim that, in order to be mathematically tractable, the object of scientific study has to be a certain way, yields a transcendental strategy in that it establishes a relation between the limits of our knowledge and what the world is like.
At this point Kant’s epistemological construction becomes relevant. Not, however, the standard reading of Kant, where the strong relation between objectivity and empirical verifiability still stands. Instead, Kant’s (often neglected) distinction between regulative and constitutive ideas may open vistas toward resolving the issues that Einstein was dealing with — issues which continue to be controversial in today’s philosophy of science, and which still plague post-Einstein efforts to construct one or another ‘final theory’. I argue that by reading the Kantian corpus as a whole and along the lines suggested by scholars such as Buchdahl, we can account for the formalism involved in physical-cosmological models. This will be achieved by emphasizing the complementary role of regulative-principles and their epistemic norms (namely, systematic unity, simplicity, homogeneity) in the process of theory construction and alongside the standard verification modes of objectivity. Based on this interpretation, inferences-to-coherence-and-conceivability are necessary for the overall modus operandi of model-based knowledge.
Neda Ghatrouei studied Philosophy at the University of Tehran and at University College London (2008-2017). Her MA project in Tehran dealt with the duality between necessity and contingency in the study of natural phenomena in the works of Greek philosophers. In London she studied more closely the different perspectives on ontological commitment in early modern scientific terminology, especially as culminating in the philosophy of Immanuel Kant. She is interested in historical approaches to scientific concepts, and presented several papers on these philosophical themes in Germany, Spain and the Netherlands. She has further translated works of modern philosophy from English and German into Farsi. She is now using her junior fellowship at the Descartes Centre, to be followed by a similar one at the Vossius center, to prepare a grant proposal for a NWO PhD project.