The Greeks, especially Aristotle, saw the value of using letters of the alphabet as variables to express the way ideas are connected in logical patterns. The particular look of modern formal logic is owing to the work of Bertrand Russell and Alfred North Whitehead in a book published in 1910. They saw their symbolic logic as a tool for the deeper study of mathematics, but with the advances in electronics after the Second World War symbolic logic took on a new importance. Philosophers still find symbolic logic (thought of as an artificial language) useful in expressing the complex logical relationships involved in natural languages, but computer scientists look to symbolic logic for the study of circuits as well as for keys to more effective techniques in programming.

In a first-semester course the usual goals are (1) acquiring skill in “translating” English sentences into symbolic form, (2) acquiring skill in testing for acceptable logical patterns, and (3) acquiring skill in presenting formal proofs that resemble the proofs students work with in high-school geometry.

Expressed more technically, we cover first-order propositional and quantifier logic through to the use of two-place predicates and an introduction to the concept of identity. What this means is that by the end of the course you should be able to symbolize and work with sentences such as “Logic is easy only if it is fun,” “All logic students are ambitious,” and “Every ambitious logic student takes some tests that are difficult.”

Next: what to study.

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