Formal science
Study of abstract structures described by formal systems
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Through Social science, Theory and Empirical evidence
Whereas the natural sciences and social sciences seek to characterize physical systems and social systems, respectively, using theoretical and empirical methods, the formal sciences use language tools concerned with characterizing abstract structures described by formal systems and the deductions that can be made from them.
The formal sciences aid the natural and social sciences by providing information about the structures used to describe the physical world, and what inferences may be made about them.
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Differences from other sciences
One reason why mathematics enjoys special esteem, above all other sciences, is that its laws are absolutely certain and indisputable, while those of other sciences are to some extent debatable and in constant danger of being overthrown by newly discovered facts.
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. For this reason, in Rudolf Carnap's logical-positivist conception of the epistemology of science, theories belonging to formal sciences are understood to contain no synthetic statements, instead containing only analytic statements.