Abstract
In the classical tradition, natural laws were considered as eternal truths of the world. Galileo and Newton even proclaimed them as ‘thoughts of God’ represented by mathematical equations. In Kantian tradition, they became categories of the human mind. David Hume criticized their ontological status and demanded their reduction to habituations of sentiments and statistical correlations of observations. In mainstream twentieth-century century science, laws were often understood as convenient instruments only, or even deconstructed in Feyerabend's ‘anything goes’. However, the Newtonian paradigm of mathematical laws and models seems also to be extended to the life sciences (e.g. systems biology). Parallel to the developments in the natural sciences, a change of public meaning regarding laws in society can be observed over the last few centuries. In economics, experimental, statistical, and behavioural approaches are favoured. In any case, the ontological basis of laws, sometimes blamed as ‘Platonism’, seems to be lost. At the beginning of the twenty-first century, the question arises: Are laws still important concepts of science? What is their contemporary meaning and task in different disciplines? Are there already alternative concepts or do laws remain an essential concept of science? In the following, we consider (1) the universal concept of laws; (2) the dynamical concept of laws; (3) their applications in natural and technical systems; (4) their applications in social and economic systems; and finally (5), we emphasize the instrumental concept of laws.
Highlights
The Concept of Law in Natural, Technical and Social SystemsIn the classical tradition, natural laws were considered as eternal truths of the world
In twentieth-century physics, these insights lead to the important PCT-theorem: laws of classical physics are invariant with respect to the discrete symmetry transformations of parity P, charge C, and time T
Global Symmetry of Natural Laws Global invariance of natural laws means that the form of a natural law is preserved with respect to transformation of all coordinates
Summary
Natural laws were considered as eternal truths of the world. In a mathematical rigorous sense, the Newtonian laws are universal (invariant) with respect to the Galilean transformation group. PCT-Theorem Obviously, symmetry and invariance of natural laws have fundamental consequences in the natural sciences.[7] In twentieth-century physics, these insights lead to the important PCT-theorem: laws of classical physics are invariant with respect to the discrete symmetry transformations of parity P, charge C, and time T. Global Symmetry of Natural Laws Global invariance of natural laws means that the form of a natural law is preserved with respect to transformation of all coordinates (e.g. change from a uniformly moving reference system to another one). Unification of Natural Laws[8] In quantum field theory, the strong, weak, and electromagnetic interactions have been reduced to fundamental symmetries. In a supersymmetry of all four forces, general relativity theory would have to be combined with quantum mechanics into a single theory
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