One is often said to be reasoning well when they are reasoning
logically. Many attempts to say what logical reasoning is have been
proposed, but one commonly proposed system is first-order classical
logic. This Element will examine the basics of first-order
classical logic and discuss some surrounding philosophical issues.
The first half of the Element develops a language for the system,
as well as a proof theory and model theory. The authors provide
theorems about the system they developed, such as unique
readability and the Lindenbaum lemma. They also discuss the
meta-theory for the system, and provide several results there,
including proving soundness and completeness theorems. The second
half of the Element compares first-order classical logic to other
systems: classical higher order logic, intuitionistic logic, and
several paraconsistent logics which reject the law of ex falso
quodlibet.
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