A comprehensive and user-friendly guide to the use of logic in
mathematical reasoning
Mathematical Logic presents a comprehensive introduction to
formal methods of logic and their use as a reliable tool for
deductive reasoning. With its user-friendly approach, this book
successfully equips readers with the key concepts and methods for
formulating valid mathematical arguments that can be used to
uncover truths across diverse areas of study such as mathematics,
computer science, and philosophy.
The book develops the logical tools for writing proofs by
guiding readers through both the established "Hilbert" style of
proof writing, as well as the "equational" style that is emerging
in computer science and engineering applications. Chapters have
been organized into the two topical areas of Boolean logic and
predicate logic. Techniques situated outside formal logic are
applied to illustrate and demonstrate significant facts regarding
the power and limitations of logic, such as:
Logic can certify truths and only truths.
Logic can certify all absolute truths (completeness theorems of
Post and Godel).
Logic cannot certify all "conditional" truths, such as those
that are specific to the Peano arithmetic. Therefore, logic has
some serious limitations, as shown through Godel's incompleteness
theorem.
Numerous examples and problem sets are provided throughout the
text, further facilitating readers' understanding of the
capabilities of logic to discover mathematical truths. In addition,
an extensive appendix introduces Tarski semantics and proceeds with
detailed proofs of completeness and first incompleteness theorems,
while also providing a self-contained introduction to thetheory of
computability.
With its thorough scope of coverage and accessible style,
Mathematical Logic is an ideal book for courses in mathematics,
computer science, and philosophy at the upper-undergraduate and
graduate levels. It is also a valuable reference for researchers
and practitioners who wish to learn how to use logic in their
everyday work.
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