Formal Science

Formal science is involved in the study of formal systems. It includes systems theory, and theoretical computer science. The formal sciences share similarities with the other two branches by relying on objective, careful, and systematic study of an area of knowledge. They are, however, different from the empirical sciences as they rely exclusively on deductive reasoning, without the need for empirical evidence, to verify their abstract concepts. The formal sciences are therefore a priori disciplines and because of this, there is disagreement on whether they actually constitute a science. Nevertheless, the formal sciences play an important role in the empirical sciences.


1. Systems Theory

Systems theory is the interdisciplinary study of systems. A system is a cohesive conglomeration of interrelated and interdependent parts that is either natural or man-made. Every system is delineated by its spatial and temporal boundaries, surrounded and influenced by its environment, described by its structure and purpose or nature and expressed in its functioning. In terms of its effects, a system can be more than the sum of its parts if it expresses synergy or emergent behavior. Changing one part of the system usually affects other parts and the whole system, with predictable patterns of behavior. For systems that are self-learning and self-adapting, the positive growth and adaptation depend upon how well the system is adjusted with its environment. Some systems function mainly to support other systems by aiding in the maintenance of the other system to prevent failure. The goal of systems theory is systematically discovering a system's dynamics, constraints, conditions and elucidating principles (purpose, measure, methods, tools, etc.) that can be discerned and applied to systems at every level of nesting, and in every field for achieving optimized equifinality.

  • Abstract systems theory (also see: formal system)
    It is a mathematical theory of systems based on the "top-down"-formalization-approach of formal systems. A formal system is used to infer theorems from axioms according to a set of rules. These rules used to carry out the inference of theorems from axioms are known as the logical calculus of the formal system. A formal system may represent a well-defined system of abstract thought. Spinoza's Ethics imitates the form of Euclid's Elements. Spinoza employed Euclidean elements such as "axioms" or "primitive truths", rules of inferences, etc., so that a calculus can be built using these
  • Action Theory
    In sociology, action theory is the theory of social action presented by the American theorist Talcott Parsons. Parsons established action theory to integrate the study of social order with the structural and voluntaristic aspects of macro and micro factors. In other words, he was trying to maintain the scientific rigour of positivism, while acknowledging the necessity of the "subjective dimension" of human action incorporated in hermeneutic types of sociological theorizing. Parsons sees motives as part of our actions. Therefore, he thought that social science must consider ends, purposes and ideals when looking at actions. Parsons placed his discussion within a higher epistemological and explanatory context of systems theory and cybernetics.
  • Adaptive systems theory (also see: complex adaptive system)
    An adaptive system is a set of interacting or interdependent entities, real or abstract, forming an integrated whole that together are able to respond to environmental changes or changes in the interacting parts, in a way analogous to either continuous physiological homeostasis or evolutionary adaptation in biology. Feedback loops represent a key feature of adaptive systems, such as ecosystems and individual organisms; or in the human world, communities, organizations, and families.
  • Applied general systems theory (also see: general systems theory)
    It is a multidisciplinary formal approach to modelling of systems and processes of ‘Applied Systems Theory’ makes it suitable for managers, engineers, students, researchers, academics and professionals from a wide range of disciplines. Applied systems theory can be used to describe, analyze,  and design biological, engineering and organizational systems as well as getting a better understanding of societal problems. It covers areas like abductive reasoning, the relevance of systems theories for research methods and problem analysis and solving based on systems theories.
  • Applied multidimensional systems theory
    Is a study of Multidimensional signal processing. Multidimensional systems or m-D systems are the necessary mathematical background for modern digital image processing with applications in biomedicine, X-ray technology and satellite communications.
  • Archaeological systems theory (also see: Systems theory in archaeology)
    Systems theory in archaeology is the application of systems theory and systems thinking in archaeology. It originated with the work of Ludwig von Bertalanffy in the 1950s, and is introduced in archaeology in the 1960s with the work of Sally R. Binford & Lewis Binford's "New Perspectives in Archaeology" and Kent V. Flannery's "Archaeological Systems Theory and Early Mesoamerica".
  • Systems theory in anthropology
    Systems theory in anthropology is an interdisciplinary, non-representative, non-referential, and non-Cartesian approach that brings together natural and social sciences to understand society in its complexity.
  • Associated systems theory
  • Behavioral systems theory
    Behavioral Systems Theory (BST) is the confluence of principles from behavior analysis and dynamical systems theory applied to human development. BST takes a natural science approach to the study of the changes in behavior/environment relationships over the lifespan. In BST, simple mechanisms produce complex developmental outcomes. The parallelism between natural selection and learning is emphasized and the importance of principles of operant learning in development is stressed. Development is considered to be multidirectional, multiply determined and multileveled. Among the BST principles described are reciprocal determinism, nonlinearity, coalescent organization, leading parts, control parameters, and attractor states. The role of contingencies in organizing patterns of behavior is presented. Weight is placed on development as skills learning. 
  • Biochemical systems theory
    Biochemical systems theory is a mathematical modelling framework for biochemical systems, based on ordinary differential equations (ODE), in which biochemical processes are represented using power-law expansions in the variables of the system.
  • Biomatrix systems theory
    Biomatrix systems theory claims to be an integrated systems theory. It was developed through an interdisciplinary PhD programme at the University of Cape Town. The aim being to identify generic organizing principles of all systems and the differences between social, natural and technological systems.
  • Body system
    Throughout the course of human evolution, humans have been solving complex problems. Various system theories such as General Systems Theory, Chaos Theory, Complex-Adaptive Systems, and Integral Theory apply and are discussed within the context of the human body. Different systems of varying context, such as: (1) when facilitating sustainable changes in organizations; (2) when promoting the unification of health care teams to enhance patient care; and (3) when explaining treatment principles in oncology arr working examples. Systems theory has many applications, not only in leadership and organization, but also in oncology.
  • Complex adaptive systems theory (also see: complex adaptive system)
  • Complex systems theory[(also see: complex systems)
  • Computer-aided systems theory
  • Conceptual systems theory (also see: conceptual system)
  • Control systems theory(also see: control system)
  • Critical systems theory (also see: critical systems thinking, and critical theory)
  • Cultural Agency Theory
  • Developmental systems theory
  • Distributed parameter systems theory
  • Dynamical systems theory
  • Ecological systems theory (also see: ecosystem, ecosystem ecology)
  • Economic systems theory (also see: economic system)
  • Electric energy systems theory
  • Family systems theory (also see: systemic therapy)
  • Fuzzy systems theory (also see: fuzzy logic)
  • General systems theory
  • Human systems theory (see: human systems)
  • Infinite dimensional systems theory
  • Large scale systems theory
  • Liberating systems theory
  • Linear systems theory (also see: linear system)
  • Living systems theory
  • LTI system theory
  • Macrosystems theory
  • Mathematical systems theory
  • Medical ethics systems theory
  • Modeling systems theory
  • Modern control systems theory
  • Modern systems theory
  • Multidimensional systems theory
  • Nonlinear stochastic systems theory (also see: stochastic modeling).General system approach
  • Operating systems theory(also see: operating system)
  • Open systems theory(also see: open system)
  • Pattern language
    Was also first conceived by an Austrian and has many similarities with systems thinking. It too is a way of describing how things work holistically, but disaggregated into patterns which interact to give emergent properties. Originally applied to architecture it has been extended into many other fields.
  • Physical systems theory (also see: physical system)
  • Pulley system
  • Retrieval system theory
  • Social systems theory (also see: social system)
  • Sociotechnical systems theory
  • Social rule system theory
  • Transit systems theory
  • World-systems theory

2. Computer Science

Computer science is the theory, experimentation, and engineering that form the basis for the design and use of computers. It involves the study of algorithms that process, store, and communicate digital information. A computer scientist specializes in the theory of computation and the design of computational systems.

Its fields can be divided into a variety of theoretical and practical disciplines. Some fields, such as computational complexity theory (which explores the fundamental properties of computational and intractable problems), are highly abstract, while fields such as computer graphics emphasize real-world visual applications. Other fields focus on challenges in implementing computation. For example, programming language theory considers various approaches to the description of computation, while the study of computer programming itself investigates various aspects of the use of programming languages and complex systems. Human–computer interaction considers the challenges in making computers and computations useful, usable, and universally accessible to humans.