Pierre Duhem in the context of "Theory-ladenness"

European science in the Middle Ages comprised the study of nature, mathematics and natural philosophy in medieval Europe. Following the fall of the Western Roman Empire and the decline in knowledge of Greek, Christian Western Europe was cut off from an important source of ancient learning. Although a range of Christian clerics and scholars from Isidore and Bede to Jean Buridan and Nicole Oresme maintained the spirit of rational inquiry, Western Europe would see a period of scientific decline during the Early Middle Ages. However, by the time of the High Middle Ages, the region had rallied and was on its way to once more taking the lead in scientific discovery. Scholarship and scientific discoveries of the Late Middle Ages laid the groundwork for the Scientific Revolution of the Early Modern Period.

According to Pierre Duhem, who founded the academic study of medieval science as a critique of the Enlightenment theory of a 17th-century anti-Aristotelian and anticlerical scientific revolution, the various conceptual origins of that alleged revolution lay in the 12th to 14th centuries, in the works of churchmen such as Thomas Aquinas and Buridan.

The Vienna Circle (German: Wiener Kreis) of logical empiricism was a group of elite philosophers and scientists drawn from the natural and social sciences, logic and mathematics who met regularly from 1924 to 1936 at the University of Vienna, chaired by Moritz Schlick. The Vienna Circle had a profound influence on 20th-century philosophy, especially philosophy of science and analytic philosophy.

The philosophical position of the Vienna Circle was called logical empiricism (German: logischer Empirismus), logical positivism or neopositivism. It was influenced by Ernst Mach, David Hilbert, French conventionalism (Henri Poincaré and Pierre Duhem), Gottlob Frege, Bertrand Russell, Ludwig Wittgenstein and Albert Einstein. The Vienna Circle was pluralistic and committed to the ideals of the Enlightenment. It was unified by the aim of making philosophy scientific with the help of modern logic. Main topics were foundational debates in the natural and social sciences, logic and mathematics; the modernization of empiricism by modern logic; the search for an empiricist criterion of meaning; the critique of metaphysics and the unification of the sciences in the unity of science.

Most scientific and technical innovations prior to the Scientific Revolution were achieved by societies organized by religious traditions. Ancient Christian scholars pioneered individual elements of the scientific method. Historically, Christianity has been and still is a patron of sciences. It has been prolific in the foundation of schools, universities and hospitals, and many Christian clergy have been active in the sciences and have made significant contributions to the development of science.

Historians of science such as Pierre Duhem credit medieval Catholic mathematicians and philosophers such as John Buridan, Nicole Oresme and Roger Bacon as the founders of modern science. Duhem concluded that "the mechanics and physics of which modern times are justifiably proud to proceed, by an uninterrupted series of scarcely perceptible improvements, from doctrines professed in the heart of the medieval schools". Many of the most distinguished classical scholars in the Byzantine Empire held high office in the Eastern Orthodox Church. Protestantism has had an important influence on science, according to the Merton Thesis, there was a positive correlation between the rise of English Puritanism and German Pietism on the one hand, and early experimental science on the other.

In philosophy of science, the Duhem–Quine thesis, also called the Duhem–Quine problem, says that unambiguous falsifications of a scientific hypothesis are impossible, because an empirical test of the hypothesis requires one or more background assumptions. Rather than disproving the main hypothesis, the blame can be placed on one of the background beliefs or "auxiliary" hypotheses. It is named after French theoretical physicist Pierre Duhem and American logician Willard Van Orman Quine, who wrote about similar concepts.

In recent decades, the set of associated assumptions supporting a thesis sometimes is called a bundle of hypotheses, i.e. a hypothesis and its background assumptions. Although a bundle of hypotheses as a whole can be tested against the empirical world and be falsified if it fails the test, the Duhem–Quine thesis says it is impossible to isolate a single hypothesis in the bundle, a viewpoint called confirmation holism.

A thermodynamic potential (or more accurately, a thermodynamic potential energy) is a scalar quantity used to represent the thermodynamic state of a system. Just as in mechanics, where potential energy is defined as capacity to do work, similarly different potentials have different meanings. The concept of thermodynamic potentials was introduced by Pierre Duhem in 1886. Josiah Willard Gibbs in his papers used the term fundamental functions. Effects of changes in thermodynamic potentials can sometimes be measured directly, while their absolute magnitudes can only be assessed using computational chemistry or similar methods.

One main thermodynamic potential that has a physical interpretation is the internal energy U. It is the energy of configuration of a given system of conservative forces (that is why it is called potential) and only has meaning with respect to a defined set of references (or data). Expressions for all other thermodynamic energy potentials are derivable via Legendre transforms from an expression for U. In other words, each thermodynamic potential is equivalent to other thermodynamic potentials; each potential is a different expression of the others.

In philosophy of science and in epistemology, instrumentalism is a methodological view that ideas are useful instruments, and that the worth of an idea is based on how effective it is in explaining and predicting natural phenomena.According to instrumentalists, a successful scientific theory reveals nothing known either true or false about nature's unobservable objects, properties or processes. Scientific theory is merely a tool whereby humans predict observations in a particular domain of nature by formulating laws, which state or summarize regularities, while theories themselves do not reveal supposedly hidden aspects of nature that somehow explain these laws. Instrumentalism is a perspective originally introduced by Pierre Duhem in 1906.

Rejecting scientific realism's ambitions to uncover metaphysical truth about nature, instrumentalism is usually categorized as an antirealism, although its mere lack of commitment to scientific theory's realism can be termed nonrealism. Instrumentalism merely bypasses debate concerning whether, for example, a particle spoken about in particle physics is a discrete entity enjoying individual existence, or is an excitation mode of a region of a field, or is something else altogether. Instrumentalism holds that theoretical terms need only be useful to predict the phenomena, the observed outcomes.

In philosophy of science, confirmation holism, also called epistemological holism, is the view that no individual statement can be confirmed or disconfirmed by an empirical test, but rather that only a set of statements (a whole theory) can be so. It is attributed to Willard Van Orman Quine who motivated his holism through extending Pierre Duhem's problem of underdetermination in physical theory to all knowledge claims.

Duhem's idea was, roughly, that no theory of any type can be tested in isolation but only when embedded in a background of other hypotheses, e.g. hypotheses about initial conditions. Quine thought that this background involved not only such hypotheses but also our whole web of belief, which, among other things, includes our mathematical and logical theories and our scientific theories. This last claim is sometimes known as the Duhem–Quine thesis.