Pure Logic and Other Minor Works, Pure Logic or the Logic of Quality Apart From the Quantity

66 Pages·2013·5.73 MB·English

by  Radomir S. Stankovic

Some Historical Remarks
on
Switching Theory
Radomir S. Stanković, Jaakko T. Astola, Mark G. Karpovsky
Dept. of Computer Science, Faculty of Electronics, Niš, Serbia
Tampere Int. Center for Signal Processing, Tampere
University of Technology, Tampere, Finland
Dept. of Electrical and Computer Engineering,
Boston University, Boston, USA
Boolean algebra and Signal Processing
Many tasks in digital system design, combinatorial optimization,
mathematical logic, and artificial intelligence can be formulated in
terms of operations over small, finite domains.
By introducing a binary encoding of the elements in these
domains, the problems can be further reduced to operations over
Boolean values.
At the level of hardware realisations, we necessarily work with
Boolean representations, since nowadays technology is
based on circuits with two stable states.
Outline of the Talk
Boolean algebra – Development of Theory
Study of Logic in Great Britain in 19th century
Definition of Boolean algebra
Boolean algebra – a deep mathematical theory
Applications of Boolean algebra
First suggestions to exploit Boolean algebra
in circuit design
Switching theory
from art and skills into engineering and science
Revival of the Study of Logic in Britain
Richard Whately, 1826
John F.W. Herschel, 1830
Intuitive Logic
William Whewell, 1837, 1840
John Stuart Mill, 1843
August De Morgan
Formal Logic, 1847
x∨ y = x ∧ y x∧ y = x ∨ y
De Morgan, A., Formal logic - or the calculus
of inference, necessary and probable,
London 1847, xvi+336.
correspondence with Boole dated 1842-1864
Formal Logic in Lardner’s Cabinet Cyclopaedia,
edited by Dyonisius Lardner, Irish scientific writer,
the first Professor of Natural History and Astronomy
at University of London, he was involved in
the founding of
this University
Lardner
Publishers of the Time
The Society for the Diffusion of Useful Knowledge (SDUK),
founded in 1826, was a Whiggish (political party with Tories)
London organization that published inexpensive texts intended to
adapt scientific and similarly high-minded material for
the rapidly expanding reading public.

It was established mainly at the instigation of Lord Brougham
with the objects of publishing information to people
who were unable to obtain formal teaching, or who
preferred self-education.

SDUK publications were intended for the working class and
the middle class, as an antidote to the more radical output of the
pauper presses. It was sometimes mentioned in contemporary
sources as SDUK.
Development of Theory
John F. W. Hercshel
William Whewell
Intuitive Logic
John Stuart Mill
Richard Whately
Augustus De Morgan
George J. Boole Symbolic Logic
George J. Boole
Works by Boole
Boole
1847 Boole, G.J., "Mathematical Analysis of Logic, being an essay towards
a calculus of deductive reasoning", London and Cambridge,
spring 1847, 82 pages, Reprinted in P.E.B. Jourdain, (ed.),
George Boole's Collected Logical Works, Vol. 1,
Chicago and London, 1916.
1848 Boole, G.J., "The calculus of logic", The Cambridge and Dublin
Mathematical Journal, Vol. 3, 1848, 183-198, Reprinted in P.E.B.
Jourdain, (ed.), George Boole's Collected Logical Works, Vol.
1, Chicago and London, 1916.
1854 Boole, G., J., An Investigation of The Laws of Thought, on
which are founded the mathematical theories of logic and
probabilities, 1854, v+iv+424 pages, reprinted in P.E.B. Jourdain,
(ed.), George Boole's Collected Logical Works, Vol. 2, Chicago
and London, 1916, Reprinted by Dover Publications, Inc., New York,
USA, 1954.
Preface by Boole
That portion of this work which
relates to Logic presupposes
in its reader a knowledge of
the most important terms of
the science, as usually treated,
and of its general object. On these
points there is no better guide than
Archbishop Whately’s
“Elements of Logic,” or
Mr. Thomson’s
“Outlines of the Laws of Thought.”