Scientific formalism

Scientific formalism is a family of approaches to the presentation of science. It is viewed as an important part of the scientific method, especially in the physical sciences. There are multiple levels of scientific formalism possible. At the lowest level, scientific formalism deals with the symbolic manner in which the information is presented. To achieve formalism in a scientific theory at this level, one starts with a well defined set of axioms, and from this follows a formal system. However, at a higher level, scientific formalism also involves consideration of the axioms themselves. These can be viewed as questions of ontology. For example, one can, at the lower level of formalism, define a property called 'existence'. However, at the higher level, the question of whether an electron exists in the same sense that a bacterium exists still needs to be resolved. Some actual formal theories on facts have been proposed. The scientific climate of the twentieth century revived these questions. From about the time of Isaac Newton to that of James Clerk Maxwell they had been dormant, in the sense that the physical sciences could rely on the status of the real numbers as a description of the continuum, and an agnostic view of atoms and their structure. Quantum mechanics, the dominant physical theory after about 1925, was formulated in a way which raised questions of both types. In the Newtonian framework there was indeed a degree of comfort in the answers one could give. Consider for example the question of whether the Earth really goes round the Sun. In a frame of reference adapted to calculating the Earth's orbit, this is a mathematical but also tautological statement. Newtonian mechanics can answer the question, whether it is not equally the case that the Sun goes round the Earth, as it indeed appears to Earth-based astronomers. In Newton's theory there is a basic, fixed frame of reference that is inertial. The 'correct answer' is that the point of view of an observer in an inertial frame of reference is privileged: other observers see artifacts of their acceleration relative to an inertial frame (the inertial forces).