Formal Sciences: Language Tools for Abstract Structures
Formal sciences are disciplines that study abstract structures described by formal systems, such as logic, mathematics, and statistics. Unlike natural sciences that investigate physical systems and social sciences that focus on social systems, formal sciences employ language tools to characterize abstract structures. These sciences play a vital role in providing information about the structures used to describe the physical world and facilitate inferences about them.
Formal sciences are non-empirical, relying on axioms and definitions to deduce theorems. Rudolf Carnap's epistemological theory classifies theories in these sciences as consisting solely of analytic statements rather than empirical ones. This distinguishes them from natural and social sciences, where laws are subject to empirical evidence and debate.
Branches and Unique Characteristics
Formal sciences encompass various branches, including logic, mathematics, statistics, computer science, and information theory. One key feature that sets mathematics apart is the absolute certainty of its laws, which are considered indisputable. This certainty stems from the reliance on axioms and definitions, which are not subject to empirical verification or refutation.
Contributions to Other Sciences
Formal sciences support natural and social sciences by providing insights into the structures used to describe physical and social systems. They enable researchers to make inferences about the systems' behavior and predict their future states. For example, mathematical models in economics help predict economic growth and market trends.
Historical and Philosophical Perspectives
C. West Churchman, Mario Bunge, and Stephen Leacock have extensively studied formal sciences. Churchman emphasized the role of logic in formal science, while Bunge focused on the philosophical implications of the non-empirical nature of these sciences. Karl Popper's work on scientific discovery highlighted the importance of formal methods in hypothesis testing.