forall x Calgary: An Introduction to Formal Logic
Subject: Logic and Critical Reasoning
Author or source: P. D. Magnus, Tim Button, Robert Trueman and Richard Zach; contributions by J. Robert Loftis and Aaron Thomas-Bolduc
Updated:
Complete 437-page open textbook introducing formal logic, arguments, truth tables, first-order logic, natural deduction and further topics, with exercises.
Overview of the complete resource
Source page 1–437
This complete textbook develops methods for analysing arguments and constructing formal proofs. It begins with premises, conclusions, validity and related concepts, then introduces truth-functional notation, truth tables, first-order logic with identity and natural deduction. Later sections extend the discussion to modal logic and metatheory. The hosted file retains the original exercises, appendices, references and authorship. Its cover identifies the Fall 2025 edition; the copyright page identifies revision bb86fe9 dated 22 October 2026. A useful study sequence is to attempt a symbolisation or proof before consulting the original solutions linked by the authors. Record the notation used in your own course because different textbooks can use different symbols and proof rules. This publication supports logic and critical reasoning study; it does not teach Indian procedural law or predict judicial decisions. Related lectures and practice resources are supplementary and are not presented as lessons for each PDF page.
Original textbook: introduction preview
Source page 12
CHAPTER 1 Arguments Logic has many uses, as mentioned in the preface. What we will be focusing on here is its use in evaluating arguments; sorting the good from the bad. In everyday language, we sometimes use the word ‘argument’ to talk about belligerent shouting matches. If you and a friend have an argument in this sense, things are not going well between the two of you. Logic is not concerned with such teeth-gnashing and hair-pulling. They are not arguments, in our sense; they are just disagreements. An argument, as we will understand it, is something more like this: Either the butler or the gardener did it. The butler didn’t do it. ∴The gardener did it. We have here a series of sentences. The three dots on the third line of the argument are read ‘therefore.’ They indicate that the final sentence expresses the conclusion of the argument. The two sentences before that are the premises of the argument. If you be- lieve the premises, and you think the conclusion follows from the premises—that the argument, as we will say, is valid—then this (perhaps) provides you with a reason to believe the conclusion. 2