Formal sciences are formal language disciplines
concerned with formal systems, such as logic,
mathematics, statistics, theoretical computer
science, robotics, information theory, game
theory, systems theory, decision theory, and
theoretical linguistics.
Whereas the natural sciences and social sciences
seek to characterize physical systems and
social systems, respectively, using empirical
methods, the formal sciences are language
tools concerned with characterizing abstract
structures described by sign systems.
The formal sciences aid the natural and social
sciences by providing information about the
structures the latter use to describe the
world, and what inferences may be made about
them.
== History ==
Formal sciences began before the formulation
of the scientific method, with the most ancient
mathematical texts dating back to 1800 BC
(Babylonian mathematics), 1600 BC (Egyptian
mathematics) and 1000 BC (Indian mathematics).
From then on different cultures such as the
Indian, Greek, Arab and Persian made major
contributions to mathematics, while the Chinese
and Japanese, independently of more distant
cultures, developed their own mathematical
tradition.
Besides mathematics, logic is another example
of one of oldest subjects in the field of
the formal sciences.
As an explicit analysis of the methods of
reasoning, logic received sustained development
originally in three places: India from the
6th century BC, China in the 5th century BC,
and Greece between the 4th century BC and
the 1st century BC.
The formally sophisticated treatment of modern
logic descends from the Greek tradition, being
informed from the transmission of Aristotelian
logic, which was then further developed by
Islamic logicians.
The Indian tradition also continued into the
early modern period.
The native Chinese tradition did not survive
beyond antiquity, though Indian logic was
later adopted in medieval China.
As a number of other disciplines of formal
science rely heavily on mathematics, they
did not exist until mathematics had developed
into a relatively advanced level.
Pierre de Fermat and Blaise Pascal (1654),
and Christiaan Huygens (1657) started the
earliest study of probability theory.
In the early 1800s, Gauss and Laplace developed
the mathematical theory of statistics, which
also explained the use of statistics in insurance
and governmental accounting.
Mathematical statistics was recognized as
a mathematical discipline in the early 20th
century.
In the mid-20th century, mathematics was broadened
and enriched by the rise of new mathematical
sciences and engineering disciplines such
as operations research and systems engineering.
These sciences benefited from basic research
in electrical engineering and then by the
development of electrical computing, which
also stimulated information theory, numerical
analysis (scientific computing), and theoretical
computer science.
Theoretical computer science also benefits
from the discipline of mathematical logic,
which included the theory of computation.
== 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.
As opposed to empirical sciences (natural
and social), the formal sciences do not involve
empirical procedures.
They also do not presuppose knowledge of contingent
facts, 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.
Therefore, straightly speaking, formal science
is not a science.
It is a formal logical system with its content
targeted at the real things, information and
thoughts that we experienced.
As Francis Bacon pointed out in the 17th century,
experimental verification of the propositions
must be carried out rigorously and cannot
take logic itself as the way to draw conclusions
in nature.
Formal science is a method that is helpful
to science but cannot replace science.
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 – whereas, statements based on empirical
theories, such as, say, general relativity
or evolutionary biology, do not hold in all
possible worlds, and may eventually turn out
not to hold in this world as well.
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.
== See also
