Idealization and the Laws of Nature*

The Computational Theory of the laws of nature is a rival to David Lewis' Best System Analysis. This "Best Program" analysis defines Laws in terms of Algorithmic Information Theory. This paper argues for the objectivity of Algorithmic Simplicity and explores some upshots of this understanding of laws for the logic of nomological necessity and metaphyisical disputes about Humean supervenience.

Philosophical discussions of the notion of the law of nature often spring from the attempt to identify a few necessary conditions that the notion must satisfy a priori: predictive power, universality, necessity, truth, or the satisfaction of counterfactual conditionals. 1 This manner of posing the question, however, leads to the development of theories of the laws of nature which physicists, biologists, or economists cannot recognize, simply because they do not reflect their practices in a sufficiently faithful manner. In critically presenting and evaluating the three most important philosophical positions on the laws of nature, regularism, necessitarism, and instrumentalist skepticism 2 , we must therefore keep a requisite in mind which we can refer to as being of ―faithfulness‖ to the practice, the contents, and to the overarching ends of science, i.e., the only requisite which should be presupposed by any epistemological analysis of the concept of law. Naturally, the decision to follow this method as the North Star of our investigation does not imply the recognition of a controversy as to what the end of scientific research is, what concrete use scientists make of the notion of law, or what a scientific theory is. Nor does it imply the adoption of a passive and conservative philosophical attitude with respect to the opinions that scientists implicitly defend on the laws of nature; as is obvious, the philosophy of science that they tacitly utilize is not at all homogeneous, unambiguous, and consistent. In selecting conceptions of the laws of nature implicit in the practice of scientists, and which better respond to a complete vision of the purposes of science and of its cognitive possibilities, we should obviously keep in mind some explicit philosophical reflections that are available today. In short, we should steer away from excessive philosophical timidity – and therefore unjustified 1 A counterfactual conditional is a conditional statement like, ―if p were true, then q would also be true,‖ in which the antecedent describes a situation that is contrary to fact. 2 In essence, as we will see in the next chapter, regularists hold that laws express regular associations of types of events holding everywhere in space-time; necessitarists hold that laws are necessary relations among properties regarded as universals, and instrumentalists hold that laws are simple instruments for prediction, devoid of any truth-value.

An attempt to answer the question: Why it is the case that, as Einstein had, "our experience hitherto justifies us in believing that nature is the realization of the simplest conceivable mathematical ideas" by using algorithmic complexity theory

The British Journal for the Philosophy of Science, 2011

2009

Principia: An International Journal of Epistemology, 2017

It has been argued that the fundamental laws of physics do not face a 'problem of provisos' equivalent to that found in other scientific disciplines (Earman, Roberts and Smith 2002) and there is only the appearance of exceptions to physical laws if they are confused with differential equations of evolution type (Smith 2002). In this paper I argue that even if this is true, fundamental laws in physics still pose a major challenge to standard Humean approaches to lawhood, as they are not in any obvious sense about regularities in behaviour. A Humean approach to physical laws with exceptions is possible, however, if we adopt a view of laws that takes them to be the algorithms in the algorithmic compressions of empirical data. When this is supplemented with a distinction between lossy and lossless compression, we can explain exceptions in terms of compression artefacts present in the application of the lossy laws.

2013

The idealized and abstract character of the fundamental laws of physics pose problems such as: How can they explain the physical processes within the domain of a theory? This paper analyzes the conceptual procedures of de-idealization, concretization, specialization and approximation in order to show how the models of a theory can be improved in a realistic manner. A model theoretic view of explanation is proposed: in order to explain a physical process it is required to de-idealized and concretized a model and to approximate apply it to the system that undergoes the process. Such de-idealized models provide more realistic conceptualizations of the systems while that the fundamental laws supplemented with specific laws account for the processes.

The Metaphysics Within Physics, 2007

Philosophical analyses may be pursued via a myriad of methods in service of as great a multitude of goals. Frequently the data upon which an analysis rests, and from which it receives its original inspiration, recount systematic connections between diverse realms of discourse or diverse sets of facts, events, actions, or objects. The aim of the project is elucidating the underlying logical, conceptual, or ontological structure that accounts for these connections. As an obvious example, John's beliefs about what Sarah knows covary systematically with his beliefs about what Sarah believes, about what Sarah has good evidence for, and about what is actually the case. We may explain these covariations by postulating that John at least tacitly adheres to the theory that knowledge is some species of justified true belief. The results of such a preliminary investigation of correlations among beliefs may be put to various uses. If we choose to endorse John's theory we will simply assert that what Sarah believes, what Sarah has good evidence for, and what is true determine what she knows. We may endorse John's theory, as revealed by his inferences, but criticize his particular judgements. For example, John's inferences may imply that he takes knowledge to require infallible evidence and so, by his own lights, he should not ascribe knowledge to Sarah since her evidence is not conclusive. Or we may instead endorse John's judgements and recommend that he amend his inferences accordingly. And, of course, the inferences, particular judgements, and intuitions at issue may be our own. This essay was written in 1989, but being too long for a journal and too short for a book only circulated informally. There are evident similarities to John Carroll's approach in his Laws of Nature (1994), and we have both been identified as primitivists about laws. I have not attempted a direct comparison between our views as it would not fit into the structure of the paper as originally conceived.

2006

This paper explores whether it is possible to reformulate or re-interpret Lewis's theory of fundamental laws of nature-his "best system analysis"-in such a way that it becomes a useful theory for special science laws. One major step in this enterprise is to make plausible how law candidates within best system competitions can tolerate exceptions-this is crucial because we expect special science laws to be so called "ceteris paribus laws". I attempt to show how this is possible and also how we can thereby make the first step towards a solution for the infamous difficulties surrounding the troublesome ceteris paribus clause. The paper outlines the general ideas of the theory but also points out some of its difficulties and background assumptions.

2005