Commensurability (philosophy of science) in the context of "Formulas"

In science, a formula is a concise way of expressing information symbolically, as in a mathematical formula or a chemical formula. The informal use of the term formula in science refers to the general construct of a relationship between given quantities.

The plural of formula can be either formulas (from the most common English plural noun form) or, under the influence of scientific Latin, formulae (from the original Latin).

Pluralism is a term used in philosophy, referring to a worldview of multiplicity, often used in opposition to monism (the view that all is one) or dualism (the view that all is two). The term has different meanings in metaphysics, ontology, epistemology and logic. In metaphysics, it is the view that there are in fact many different substances in nature that constitute reality. In ontology, pluralism refers to different ways, kinds, or modes of being. For example, a topic in ontological pluralism is the comparison of the modes of existence of things like 'humans' and 'cars' with things like 'numbers' and some other concepts as they are used in science.

In epistemology, pluralism is the position that there is not one consistent means of approaching truths about the world, but rather many. Often this is associated with pragmatism, or conceptual, contextual, or cultural relativism. In the philosophy of science it may refer to the acceptance of co-existing scientific paradigms which though accurately describing their relevant domains are nonetheless incommensurable. In logic, pluralism is the relatively novel view that there is no one correct logic, or alternatively, that there is more than one correct logic. Such as using classical logic in most cases, but using paraconsistent logic to deal with certain paradoxes.

In philosophy, neutrality is the tendency to not take a side in a conflict (physical or ideological), which may not suggest neutral parties do not have a side or are not a side themselves. In colloquial use, neutral can be synonymous with unbiased. However, bias is a favoritism for one side, distinct from the tendency to act on that favoritism. Neutrality is distinct (though not exclusive) from apathy, ignorance, indifference, doublethink, equality, agreement, and objectivity. Apathy and indifference each imply a level of carelessness about a subject, though a person exhibiting neutrality may feel bias on a subject but choose not to act on it. A neutral person can also be well-informed on a subject and therefore need not be ignorant. Since they can be biased, a neutral person need not feature doublethink (i.e. accepting both sides as correct), equality (i.e. viewing both sides as equal), or agreement (a form of group decision-making; here it would require negotiating a solution on everyone's opinion, including one's own which may not be unbiased). Objectivity suggests siding with the more reasonable position (except journalistic objectivity), where reasonableness is judged by some common basis between the sides, such as logic (thereby avoiding the problem of incommensurability). Neutrality implies tolerance regardless of how disagreeable, deplorable, or unusual a perspective might be.

In moderation and mediation, neutrality is often expected to make judgments or facilitate dialogue independent of any bias, emphasizing on the process rather than the outcome. For example, a neutral party is seen as a party with no (or a fully disclosed) conflict of interest in a conflict, and is expected to operate as if it has no bias. Neutral parties are often perceived as more trustworthy, reliable, and safe. Alternative to acting without a bias, the bias of neutrality itself is the expectation upon the Swiss government (in armed neutrality), and the International Federation of Red Cross and Red Crescent Societies (in non-interventionism). The Oxford English Dictionary documents that, by at least 1897, "neutral" meant applying the rules to the facts, as in football "Neutral linesmen shall officiate in all games." In the Supreme Court decision Board of Regents of the University of Wisconsin System v. Southworth based on the United States Constitution's First Amendment, the court decided some funding decisions should be made through a neutral viewpoint.

Thomas Samuel Kuhn (/kuːn/; July 18, 1922 – June 17, 1996) was an American historian and philosopher of science whose 1962 book The Structure of Scientific Revolutions was influential in both academic and popular circles, introducing the term paradigm shift, which has since become an English-language idiom.

Kuhn made several claims concerning the progress of scientific knowledge: that scientific fields undergo periodic "paradigm shifts" rather than solely progressing in a linear and continuous way, and that these paradigm shifts open up new approaches to understanding what scientists would never have considered valid before; and that the notion of scientific truth, at any given moment, cannot be established solely by objective criteria but is defined by a consensus of a scientific community. Competing paradigms are frequently incommensurable; that is, there is no one-to-one correspondence of assumptions and terms. Thus, our comprehension of science can never rely wholly upon "objectivity" alone. Science must account for subjective perspectives as well, since all objective conclusions are ultimately founded upon the subjective conditioning/worldview of its researchers and participants.