A conceptual system is a conceptual model. Such systems may be related to any topic from formal science to individual imagination. Conceptual systems may be found within the human mind, as works of art and fiction, and within the academic world. Indeed, this article may be understood as a conceptual system because it includes a set of interrelated concepts.
Broadly, when a conceptual system includes a range of values, ideas, and beliefs the conceptual system is said be a view of the world. In psychology and social work, a conceptual system may refer to an individual's mental model of the world. In humans, a conceptual system may be understood as kind of a metaphor for the world. In science, there are many forms of conceptual systems including laws, theories, and models. Those conceptual systems may be developed through inductive reasoning, deductive reasoning, and empirical analysis.
The idea that the human mind might contain conceptual systems goes back at least as far as Kelly's personal construct theory in 1955. More recently, many scholars discuss conceptual systems and the importance of understanding them (c.f. Bateson, Luhmann, Senge, Quine, Eco, Umpleby, and Wallis). On the personal level, the human mind is generally held to contain a wide range of conceptual systems although they are not well organized. Indeed, our minds are full of conflicting mental models which makes decision making unreliable - particularly in large-scale, complex situations.
Within the academic literature, each theory may be understood as a conceptual system. Conceptual systems are generally held to have greater value when they are more useful, based on more research, and are more systemically interrelated.
Generally, that validity may also be described in terms of its internal coherence and the correspondence between the conceptual system and other systems (e.g. social systems or physical systems). Coherence may be tested by Integrative complexity (for individuals) and by Integrative Propositional Analysis (for academic theories). Correspondence is generally tested by empirical analysis and conditions of falsifiability. The conceptual system may then be said to model the physical or social system and serve as a guide for individual behavior or academic research.
Examples of conceptual systems include:
A concept is an abstract idea or a mental symbol, typically associated with a corresponding representation in language or symbology, that denotes all of the objects in a given category or class of entities, interactions, phenomena, or relationships between them. Concepts are abstract in that they omit the differences of the things in extension, treating them as if they were identical. They are universal in that they apply equally to everything in their extension. Concepts are also the basic elements of propositions, much the same way a word is the basic semantic element of a sentence. Unlike perceptions, which are particular images of individual objects, concepts cannot be visualized. Because they are not, themselves, individual perceptions, concepts are discursive and result from reason. They can only be thought about, or designated, by means of a name. Words are not concepts. Words are signs for concepts.
A conceptual model is a representation of some phenomenon, data or theory by logical and mathematical objects such as functions, relations, tables, stochastic processes, formulas, axiom systems, rules of inference etc. A conceptual model has an ontology, that is the set of expressions in the model which are intended to denote some aspect of the modeled object. Here we are deliberately vague as to how expressions are constructed in a model and particularly what the logical structure of formulas in a model actually is. In fact, we have made no assumption that models are encoded in any formal logical system at all, although we briefly address this issue below. Moreover, the definition given here is oblivious to whether two expressions really should denote the same thing. Note that this notion of ontology is different from (and weaker than) ontology as is sometimes understood in philosophy; in our sense there is no claim that the expressions actually denote anything which exists physically or spatio-temporally (to use W. Quine's formulation).
For example, a stochastic model of stock prices includes in its ontology a sample space, random variables, the mean and variance of stock prices, various regression coefficients etc. Models of quantum mechanics in which pure states are represented as unit vectors in a Hilbert space include in their ontologies observables, dynamics, measurement operators etc. It is possible that observables and states of quantum mechanics are as physically real as the electrons they model, but by adopting this purely formal notion of ontology we avoid altogether this question.
A conceptual framework is used in research to outline possible courses of action or to present a preferred approach to a system analysis project. It has also been defined as the organization of ideas to achieve a purpose The framework is built from a set of concepts linked to a planned or existing system of methods, behaviors, functions, relationships, and objects. A conceptual framework might, in computing terms, be thought of as a relational model.
For example, a conceptual framework of accounting "seeks to identify the nature, subject, purpose and broad content of general-purpose financial reporting and the qualitative characteristics that financial information should possess".