Differences From Other Forms of Science
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. —Albert EinsteinAs opposed to empirical sciences (natural, social), the formal sciences do not involve empirical procedures. They also do not presuppose knowledge of contingent fact, or describe the real world. In this sense, formal sciences are both logically and methodologically a priori, for their content and validity are independent of any empirical procedures.
Although formal sciences are conceptual systems, lacking empirical content, this does not mean that they have no relation to the real world. But this relation is such that their formal statements hold in all possible conceivable worlds (see valid formula) – whereas, statements based on empirical theories, such as, say, General Relativity or Evolutionary Biology, do not hold in all possible worlds, and may even turn out not to hold in this world. That is why formal sciences are applicable in all domains and useful in all empirical sciences.
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. In other words, theories in formal sciences contain no synthetic statements; all their statements are analytic.
Read more about this topic: Formal Science
Famous quotes containing the words differences, forms and/or science:
“The country is fed up with children and their problems. For the first time in history, the differences in outlook between people raising children and those who are not are beginning to assume some political significance. This difference is already a part of the conflicts in local school politics. It may spread to other levels of government. Society has less time for the concerns of those who raise the young or try to teach them.”
—Joseph Featherstone (20th century)
“You may melt your metals and cast them into the most beautiful moulds you can; they will never excite me like the forms which this molten earth flows out into. And not only it, but the institutions upon it are plastic like clay in the hands of the potter.”
—Henry David Thoreau (1817–1862)
“After sitting in my chamber many days, reading the poets, I have been out early on a foggy morning and heard the cry of an owl in a neighboring wood as from a nature behind the common, unexplored by science or by literature.”
—Henry David Thoreau (1817–1862)