Symbolic Logic I Course Description
Logic, parts of which form a branch of mathematics and parts of which form a branch of philosophy, is the science of reasoning, the science of separating good arguments from bad ones. A good or logical argument is one that is truth-preserving, i.e. one that always takes us from true premises to a true conclusion. Logic allows us to determine whether the premises of an argument support the conclusion of it.
This is a first course in formal, deductive reasoning. You will learn to symbolize and evaluate deductive arguments. Topics include symbolization in sentential and predicate logic, truth tables, and proofs in sentential and predicate logic.
The following passage, taken from the introduction to Language, Proof and Logic by Jon Barwise and John Etchemendy, neatly summarizes the role and importance of modern symbolic logic:
What do the fields of astronomy, economics, finance, law, mathematics, medicine, physics, and sociology have in common? Not much in the way of subject matter, that's for sure. And not all that much in the way of methodology. What they do have in common, with each other and with many other fields, is their dependence on a certain standard of rationality. In each of these fields, it is assumed that the participants can differentiate between rational argumentation. based on assumed principles or evidence, and wild speculation or nonsequiturs, claims that in no way follow from the assumptions. In other words, these fields all presuppose an underlying acceptance of basic principles of logic.
... all rational inquiry depends on logic, on the ability of people to reason correctly most of the time, and, when they fail to reason correctly, on the ability of others to point out the gaps in their reasoning. While people may not all agree on a whole lot, they do seem to be able to agree on what can legitimately be concluded from given information. Acceptance of these commonly held principles of rationality is what differentiates rational inquiry from other forms of human activity.
The importance of logic has been recognized since antiquity. After all, no science can be any more certain than its weakest link. If there is something arbitrary about logic, then the same must hold of all rational inquiry. Thus it becomes crucial to understand just what the laws of logic are, and even more important, why they are laws of logic. These are the questions that one takes up when one studies logic itself.