Scientific formalism
Scientific formalism is a broad term for a family of approaches to the presentation of science
Science is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe...

. It is viewed as an important part of the scientific method
Scientific method
Scientific method refers to a body of techniques for investigating phenomena, acquiring new knowledge, or correcting and integrating previous knowledge. To be termed scientific, a method of inquiry must be based on gathering empirical and measurable evidence subject to specific principles of...

, especially in the physical sciences.

Levels of formalism

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
Scientific theory
A scientific theory comprises a collection of concepts, including abstractions of observable phenomena expressed as quantifiable properties, together with rules that express relationships between observations of such concepts...

 at this level, one starts with a well defined set of axioms, and from these follows a formal system
Formal system
In formal logic, a formal system consists of a formal language and a set of inference rules, used to derive an expression from one or more other premises that are antecedently supposed or derived . The axioms and rules may be called a deductive apparatus...


However, at a higher level, scientific formalism also involves consideration of the axioms themselves. These can be viewed as questions of ontology
Ontology is the philosophical study of the nature of being, existence or reality as such, as well as the basic categories of being and their relations...

. For example, one can, at the lower level of formalism, define a property
Property (philosophy)
In modern philosophy, logic, and mathematics a property is an attribute of an object; a red object is said to have the property of redness. The property may be considered a form of object in its own right, able to possess other properties. A property however differs from individual objects in that...

 called 'existence'. However, at the higher level, the question of whether an electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...

 exists in the same sense that a bacterium exists still needs to be resolved.

Some actual formal theories on fact
A fact is something that has really occurred or is actually the case. The usual test for a statement of fact is verifiability, that is whether it can be shown to correspond to experience. Standard reference works are often used to check facts...

s have been proposed.

In modern physics

The scientific climate of the twentieth century revived these questions. From about the time of Isaac Newton
Isaac Newton
Sir Isaac Newton PRS was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian, who has been "considered by many to be the greatest and most influential scientist who ever lived."...

 to that of James Clerk Maxwell
James Clerk Maxwell
James Clerk Maxwell of Glenlair was a Scottish physicist and mathematician. His most prominent achievement was formulating classical electromagnetic theory. This united all previously unrelated observations, experiments and equations of electricity, magnetism and optics into a consistent theory...

 they had been dormant, in the sense that the physical sciences could rely on the status of the real number
Real number
In mathematics, a real number is a value that represents a quantity along a continuum, such as -5 , 4/3 , 8.6 , √2 and π...

s as a description of the continuum
Continuum (theory)
Continuum theories or models explain variation as involving a gradual quantitative transition without abrupt changes or discontinuities. It can be contrasted with 'categorical' models which propose qualitatively different states.-In physics:...

, and an agnostic view of atom
The atom is a basic unit of matter that consists of a dense central nucleus surrounded by a cloud of negatively charged electrons. The atomic nucleus contains a mix of positively charged protons and electrically neutral neutrons...

s and their structure. Quantum mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...

, the dominant physical theory after about 1925, was formulated in a way which raised questions of both types.

In the Newtonian
Newtonian refers to the work of Isaac Newton, in particular:* Newtonian mechanics, also known as classical mechanics* Newtonian telescope, a type of reflecting telescope* Newtonian cosmology* Newtonian dynamics...

 framework there was indeed a degree of comfort in the answers one could give. Consider for example the question of whether the Earth
Earth is the third planet from the Sun, and the densest and fifth-largest of the eight planets in the Solar System. It is also the largest of the Solar System's four terrestrial planets...

 really goes round the Sun
The Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...

. In a frame of reference
Frame of reference
A frame of reference in physics, may refer to a coordinate system or set of axes within which to measure the position, orientation, and other properties of objects in it, or it may refer to an observational reference frame tied to the state of motion of an observer.It may also refer to both an...

 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. Before Newton, Galileo would draw the consequences, from the Copernican
Copernican means of or pertaining to the astronomer Nicolaus Copernicus* For the Copernican system of astronomy, see heliocentrism* For the philosophical principle, see Copernican principle* For the lunar geological period, see Copernician...

 heliocentric model. He was, however, constrained to call his work (in effect) scientific formalism, under the old 'description' saving the phenomena. To avoid going against authority, the elliptic orbits of the heliocentric model could be labelled as a more convenient device for calculations, rather than an actual description of reality.

In general relativity
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...

, Newton's inertial frames are no longer privileged. In quantum mechanics, Paul Dirac
Paul Dirac
Paul Adrien Maurice Dirac, OM, FRS was an English theoretical physicist who made fundamental contributions to the early development of both quantum mechanics and quantum electrodynamics...

 argued that physical models were not there to provide semantic constructs allowing us to understand microscopic physics in language comparable to that we use on the familiar scale of everyday objects. His attitude, adopted by many theoretical physicists, is that a good model is judged by our capacity to use it to calculate physical quantities that can be tested experimentally. Dirac's view is close to what Bas van Fraassen calls constructive empiricism
Constructive empiricism
In philosophy, constructive empiricism is a form of empiricism. Bas van Fraassen is nearly solely responsible for the initial development of constructive empiricism; its historically most important presentation appears in his The Scientific Image...



A physicist who took the issues involved seriously was Pierre Duhem
Pierre Duhem
Pierre Maurice Marie Duhem was a French physicist, mathematician and philosopher of science, best known for his writings on the indeterminacy of experimental criteria and on scientific development in the Middle Ages...

, writing at the beginning of the twentieth century. He wrote an extended analysis of the approach he saw as characteristically British, in requiring field theories of theoretical physics to have a mechanical-physical interpretation. That was an accurate characterisation of what Dirac (himself British) would later argue against. The national characteristics specified by Duhem do not need to be taken too seriously, since he also claimed that the use of abstract algebra
Abstract algebra
Abstract algebra is the subject area of mathematics that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras...

, namely quaternion
In mathematics, the quaternions are a number system that extends the complex numbers. They were first described by Irish mathematician Sir William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space...

s, was also characteristically British (as opposed to French or German); as if the use of classical analysis methods alone was important one way or the other.

Duhem also wrote on saving the phenomena. In addition to the Copernican Revolution
Copernican Revolution
The Copernican Revolution refers to the paradigm shift away from the Ptolemaic model of the heavens, which postulated the Earth at the center of the galaxy, towards the heliocentric model with the Sun at the center of our Solar System...

 debate of "saving the phenomena" (σώζειν τα φαινόμενα) versus offering explanations that inspired Duhem was Thomas Aquinas, who wrote, regarding eccentrics and epicycles
Deferent and epicycle
In the Ptolemaic system of astronomy, the epicycle was a geometric model used to explain the variations in speed and direction of the apparent motion of the Moon, Sun, and planets...

, that
Reason may be employed in two ways to establish a point: firstly, for the purpose of furnishing sufficient proof of some principle [...]. Reason is employed in another way, not as furnishing a sufficient proof of a principle, but as confirming an already established principle, by showing the congruity of its results, as in astronomy the theory of eccentrics and epicycles
Deferent and epicycle
In the Ptolemaic system of astronomy, the epicycle was a geometric model used to explain the variations in speed and direction of the apparent motion of the Moon, Sun, and planets...

 is considered as established, because thereby the sensible appearances of the heavenly movements can be explained; not, however, as if this proof were sufficient, forasmuch as some other theory might explain them. [...]

The idea that a physical interpretation in physics is not an ultimate condition has as descendant modern structural realism on science.
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