Formal ScienceFormal sciences are systems of knowledge based on abstract concepts represented by symbols such that they are widely applicable to other sciences. These are often based on proofs such that these systems are internally correct with a high degree of certainty.
Natural ScienceNatural science is the use of science to understand the physical world. As these sciences deal with physical and observable phenomena these are considered hard science whereby the standard of proof is very high to have a theory accepted. Compliance with the scientific method is relatively high in the natural sciences with peer review and reproducibility required for acceptance of a theory.
Applied ScienceThe use of science to solve real world problems. This is considered with the discovery of know-how and development of actionable plans using foundational knowledge created by formal sciences and natural sciences. For example, an architect who uses physics, mathematics and material science to determine the wind load the facade of a building can tolerate.
Social ScienceSocial science is the study of societies and individuals. This is considered a soft science whereby theories may be based on informal logic, imprecise measurement or studies that lack scientific rigor. In fields such as psychology, it is common for studies that do conform to the scientific method to fail to be verified by subsequent studies†.