In mathematics and other formal sciences, first-order or first order most often means either:

The word science is used in the sense of natural, social and formal sciences - areas of research that tend toward positivism.

Although formal sciences are conceptual systems, lacking empirical content, this does not mean that they have no relation to the real world.

Formal sciences, study of rules, logic, and formal systems of information.

The formal sciences, which also include statistics and logic, are vital to the empirical sciences.

Unlike other sciences, the formal sciences are not concerned with the validity of theories based on observations in the real world.

The formal sciences discover the philosophers' stone.

As opposed to empirical sciences (natural and social), the formal sciences do not involve empirical procedures.

In other words, theories in formal sciences contain no synthetic statements; all their statements are analytic.

That is why formal sciences are applicable in all domains and useful in all empirical sciences.

Besides mathematics, which is not classified as a science, logic is another example of one of oldest subjects in the field of the formal sciences.

Folk notions of botany and zoology are presented as ethnobotany and ethnozoology alongside references from the formal sciences.

In this sense, formal sciences are both logically and methodologically a priori, for their content and validity are independent of any empirical procedures.

Formal sciences sometimes aid constructing, assessing, and testing scientific theories and scientific models, however, by revealing inconsistencies or invalid forms of inference.

In an ideal logical language, the logical form can be determined from syntax alone; formal languages used in formal sciences are examples of such languages.

Social network analysis is now one of the major paradigms in contemporary sociology, and is also employed in a number of other social and formal sciences.

Strict proof is possible only in formal sciences such as logic and mathematics, not natural sciences (where terms such as "validated" or "corroborated" are more appropriate).

Because of their non-empirical nature, formal sciences are construed by outlining a set of axioms and definitions from which other statements (theorems) are deduced.

Proof exists in formal sciences, such as a mathematical proof where symbolic expressions can represent infinite sets and scientific laws having precise definitions and outcomes of the terms.

Now we consider analysis, algebra, and geometry, but not mechanics, as parts of mathematics because they are primarily deductive formal sciences, while mechanics like physics must proceed from observation.

Singidunum University offers Bachelor's, Master's and Doctoral degree programmes in the fields of social sciences, formal sciences and applied sciences.

In addition to empirical sciences, there are the formal sciences, such as mathematics and logic, which use an a priori, as opposed to factual methodology to study formal systems.

This distinguishes sciences that cover inquiry into the world of nature from humanities such as linguistics, anthropology, literary science, and from formal sciences such as mathematics and logic.

In the formal sciences, mathematics, mathematical logic, statistics, and their applied disciplines, a boolean-valued function may also be referred to as a characteristic function, indicator function, predicate, or proposition.

Formal sciences are disciplines concerned with formal systems, such as logic, mathematics, statistics, theoretical computer science, information theory, game theory, systems theory, decision theory, and portions of linguistics.