SYMBOLIC LOGIC AT MISSION COLLEGE: INTERNET VERSION
Description: Symbolic logic as we know it today was developed
at the turn of the century by the English philosophers Bertrand Russell
and Alfred North Whitehead in their Principia Mathematica. Its goal
at the time was to establish the logical foundations of mathematics and
thus develop a technique to recognize which mathematical statements could
be proved and which could not. Some time later it was shown that no type
of formal logic would be able to achieve this goal, but after the Second
World War a new purpose was found for symbolization in representing electronic
circuits. From then on symbolic logic became closely linked both with the
development of new hardware and the growth of the programming languages
for new software.
In this first semester of symbolic logic there are three tasks:
1. Learning to express statements that can be clearly described
as truth functional (meaning that whether they are true depends entirely
on their parts) through a set of symbols that include letters of the alphabet
and other signs used specifically to identify logical relationships.
2. Learning to determine through one or another technique the truth
value of individual statements and the validity of argument forms using
these statements.
3. Learning to develop and work with a particular set of rules to
show the validity of a given inference.
The goal of the course, then, is to develop skill in symbolization,
testing
for validity, and formal derivations.
Text: The complete course will be available on-line in HTML
format. There will be some interactive programs, and it will be necessary
to use a frames-enabled browser such as Netscape Navigator 3+ or Microsoft
Explorer 4+. Please note, however, that the software is copyright-protected
and may not be distributed as a totality without express permission from
the author.
Grading: Please click on the syllabus for the current semester.
Here you will find the policies for contact and testing in force at this
time.
Enrollment: Check the Mission
College homepage for the current or future schedule of courses as well
as for directions on how to register online for a course. Once you are
enrolled, please notify the instructor
with information on how to remain in contact with you. (Note that during
vacation periods you may have to wait for a reply.)
Outline: The following material will be presented in the course.
The use of letters to represent atomic propositions.
The use of connectives (including quantifiers) to express logical
relationships and so develop molecular propositions.
The assignment of truth values to propositions.
Testing for validity with arguments that do not use quantifiers.
Testing for validity with arguments that do use quantifers.
A derivation system for non-quantified expressions (propositional
calculus).
Expanding the system to include quantified expressions (predicate
calculus).
The use of a special symbol for identity.
Additional material: working with algebraic variations (a
modular system for programming truth tables as well as Boolean algebra),
understanding the connection between symbolized forms and actual circuits,
and the use of certain "normal forms" important in computer programming.
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