Logic is the study of valid inference and reasoning. It is used in many intellectual activities but is primarily studied in philosophy, mathematics, semantics, and computer science. In the 19th century, logic became mathematized by British mathematicians such as George Boole, who developed an algebra of logic featuring operators like and, or, not, and exclusive or. Boole saw the potential of applying this algebraic logic to solve problems and argued that logic was a discipline of mathematics rather than philosophy alone.

1. Prepared by:
Nathaniel T. Sullano
BS Math – 3

2. is a science that deals with the principles
and criteria of validity of inference and
demonstration.
is the formal systematic study of
the principles of valid inference and
correct reasoning.
Logic is used in most intellectual
activities, but is studied primarily in the
disciplines
of philosophy, mathematics, semantics,
and computer science.

3. has became mathematized in the 19th century, in the
work of mostly British mathematicians such as George
Peacock (1791-1858), George Boole (1815-1864),
William Stanley Jevons (1835-1882), and Augustus de
Morgan, and a few Americans, notably Charles Sanders
Peirce.
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 goes
back 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 Boole‟s work of
incorporating logic and
mathematics 1806-1871
• formally stated the laws of
set theory

6. •

7. Lagrange‟s algebraic approach to analysis (Thinking of Taylor‟s
Theorem).
Where Df(x) = f’(x), and comparing with the Taylor‟s series of the
exponential 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 the
algebra to the solution of
processes of analysis
logical problems. Boole's
does not depend upon
1847 work, 'The
the interpretation of the
Mathematical Analysis of
symbols which are
Logic', not only expanded
employed but solely upon
on Gottfried Leibniz' earlier
the laws of their
speculations on the
combination…”
correlation between logic
and math, but argued that
logic was principally a
discipline 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 X‟s and Y‟s”
• This language rather blurs the distinction between a set,
its members, and the properties that determine what the
members are.

11. •

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