2. is a science that deals with the principlesand criteria of
validity of inference anddemonstration. is the formal systematic
study ofthe principles of valid inference andcorrect reasoning.
Logic is used in most intellectualactivities, but is studied
primarily in thedisciplinesof philosophy, mathematics,
semantics,and computer science.
3. has became mathematized in the 19th century, in thework of
mostly British mathematicians such as GeorgePeacock (1791-1858),
George Boole (1815-1864),William Stanley Jevons (1835-1882), and
Augustus deMorgan, and a few Americans, notably Charles
SandersPeirce. was the creation of 19th-century analysts and
geometers,prominent among them is Georg Cantor (1845-1918),whose
inspiration came from geometry and analysis,mostly the latter.
mathematization of logic has a pre-history that goesback to
Leibniz.
4. His main contribution to mathematical analysis is his
attempt to place algebra on a strictly logical basis. Concluded
that the science of algebra has two parts arithmetical and
symbolical algebra. 1791-1858
5. developed two laws of negation (disjunction &
conjunction) interested, like other mathematicians, in using
mathematics to demonstrate logic furthered Booles work of
incorporating logic and mathematics 1806-1871 formally stated the
laws of set theory
6.
7. Lagranges algebraic approach to analysis (Thinking of
Taylors Theorem).Where Df(x) = f(x), and comparing with the Taylors
series of theexponential function, Lagrange arrived at the formal
equation Converse relation,
8. self-taught mathematician with an interest in logic
developed an algebra of logic (Boolean Algebra) featured the
operators and or not nor (exclusive or) 1815-1864
9. Boole soon began to see the He wrote that,possibilities for
applying his the validity of thealgebra to the solution of
processes of analysislogical problems. Booles does not depend
upon1847 work, The the interpretation of theMathematical Analysis
of symbols which areLogic, not only expanded employed but solely
uponon Gottfried Leibniz earlier the laws of theirspeculations on
the combinationcorrelation between logicand math, but argued
thatlogic was principally adiscipline of mathematics,rather than
philosophy.
10. Boole denoted a generic member of a class by an uppercase
X, and used the lowercase x. Then xy was to denote the class whose
members are both Xs and Ys This language rather blurs the
distinction between a set, its members, and the properties that
determine what the members are.