Learn about the link between logical arguments and electronic circuits. Investigate the logical connectives by making and testing your own circuits and fill in the blanks in truth tables to record your findings.
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
Published December 2011,February 2011.
Venn diagrams frequently help us to make our deductions more
The Ancient Greeks were the first to really develop logic, in
particular Aristotle who lived from 384 to 322 BC. Aristotle put
forward the notion of a syllogism . This is an argument in
three parts, like the examples above. A syllogism consists of two
premises and a conclusion . The first premise must
have one thing in common with the second premise. The second
premise must have one thing in common with the first premise. The
conclusion must have one thing in common with both premises.
Aristotle's example is:
Aristotle believed that logic should be
investigated before any other areas of knowledge. He made a lot of
progress in the understanding of logic, but all of his analysis was
done in everyday language.
It wasn't until much later that Leibniz
took Aristotle's ideas a stage further. Leibniz (who lived between
1646 and 1716) was taught Aristotle's theories at school, but
wasn't satisfied with them. He suggested that a scientific language
needed to be developed which could be more precise than using
everyday words. Leibniz got a long way in creating symbolic logic which used formulae to
help work through deductions.
Boole refined these formulae to produce a
special form of algebra called Boolean algebra. Mathematicians can
use this to write and analyse logical ideas. Others followed in his
footsteps, for example Frege and Peano who were convinced that
maths could be reduced to logic. More recently, Bertrand Russell
and Alfred Whitehead wanted to prove this. In the process they
found that this could generate paradoxes . A paradox is an expression
that seems to contradict itself, like "this statement is false" or
"I am telling you the truth when I say I am a liar".
Even though Russell and Whitebread
encountered these problems with mathematical logic, it is used a
great deal in the world today. Boolean algebra has wide
applications in telephone switching and computer technology.