Introduction to Logic

Course Description

PHI2100 — Introduction to Logic (titled variously across Florida institutions as Logic, Introductory Logic, or Introduction to Logic and Critical Thinking) is a 3-credit lecture course in the philosophy of reasoning. The course meets approximately 3 hours per week, with most institutions accumulating 45 total contact hours over a 15-week semester. As a course in the SCNS PHI 2xxx series, it is part of Florida's sophomore-level philosophy offerings and is widely accepted as a Florida General Education Core "Humanities" elective and as a foundational logic course for students in mathematics, computer science, philosophy, pre-law, and other reasoning-intensive disciplines.

The course is the systematic study of the principles of correct reasoning — what makes an argument valid, what distinguishes deductive from inductive inference, what makes a conclusion follow from its premises, and how to recognize and analyze logical structure in natural-language arguments. Most Florida institutions teach the course as a balanced introduction to both informal logic (argument analysis, evaluation of premises, recognition of fallacies, application to everyday reasoning) and formal logic (propositional and predicate logic, truth tables, natural deduction). The mix varies by instructor — some emphasize formal symbolic logic comparable to a discrete-mathematics introduction, while others emphasize critical thinking and informal reasoning closer to a rhetoric course.

The course is offered at approximately 17 Florida public institutions, including Florida International University, the University of Florida, Florida State University, the University of Central Florida, the University of South Florida, Florida Atlantic University, Florida Gulf Coast University, Miami Dade College, Broward College, Palm Beach State College, Valencia College, Tallahassee State College, Pensacola State College, and Daytona State College.

Learning Outcomes

Required Outcomes

Upon successful completion of this course, the student will be able to:

• Distinguish between arguments and non-arguments in written and spoken discourse; identify the premises and conclusion of an argument; recognize argument indicators ("therefore," "because," "since," "thus").
• Distinguish between deductive and inductive arguments, and the relationship between premises and conclusion in each.
• Apply the concepts of validity, soundness, strength, and cogency to evaluate arguments: distinguish a valid argument (premises guarantee the conclusion) from a sound argument (valid plus true premises); distinguish a strong inductive argument from a cogent one.
• Recognize and name common informal fallacies, including ad hominem, straw man, appeal to authority, appeal to ignorance, false dilemma, hasty generalization, post hoc, slippery slope, equivocation, and begging the question.
• Translate natural-language sentences into propositional logic using standard connectives (negation, conjunction, disjunction, conditional, biconditional).
• Construct and interpret truth tables to determine the truth value of compound propositions, identify tautologies, contradictions, and contingent statements, and test arguments for validity.
• Identify and apply common inference rules of propositional logic, including modus ponens, modus tollens, hypothetical syllogism, disjunctive syllogism, and constructive dilemma.
• Recognize and apply common equivalence rules, including DeMorgan's laws, commutation, association, distribution, and material implication.
• Analyze categorical statements and their relationships using Aristotelian (categorical) logic, including the four categorical proposition forms (A, E, I, O), the Square of Opposition, immediate inferences (conversion, obversion, contraposition), and the validity of categorical syllogisms.
• Apply introductory predicate logic, including universal and existential quantification, the translation of quantified statements into symbolic form, and the recognition of quantifier interactions.
• Analyze the structure of inductive arguments, including arguments from analogy, causal arguments, statistical generalizations, and explanatory arguments; recognize the role of inductive reasoning in scientific inquiry.
• Apply critical thinking skills to the evaluation of arguments in everyday contexts — newspaper editorials, advertising, political rhetoric, legal reasoning, scientific claims, and academic writing.

Optional Outcomes

Depending on the instructor's emphasis and the textbook used, students may also:

• Construct natural-deduction proofs in propositional logic using a standard deduction system.
• Apply predicate logic proofs involving multiply-quantified statements and identity.
• Use truth trees (semantic tableaux) as an alternative to truth tables for testing validity.
• Explore modal logic introduction, including necessity, possibility, and possible-worlds semantics.
• Apply Venn diagrams systematically for categorical syllogism evaluation, including the Boolean and Aristotelian interpretations.
• Study probabilistic reasoning, including basic probability rules, Bayes' theorem, and the role of probability in scientific inference.
• Investigate logical paradoxes, including the liar paradox, sorites paradoxes, and Russell's paradox.
• Connect logic to computer science applications, including digital circuit design, formal verification, and the role of first-order logic in programming language semantics.

Major Topics

Required Topics

• Arguments, Premises, and Conclusions — identifying arguments in discourse, distinguishing arguments from explanations and conditionals, recognition of argument indicators.
• Deductive vs. Inductive Arguments — the structural difference, validity vs. strength, soundness vs. cogency.
• Informal Fallacies — fallacies of relevance (ad hominem, appeal to authority, appeal to emotion, red herring, straw man), fallacies of weak induction (hasty generalization, weak analogy, post hoc, slippery slope), fallacies of presumption (begging the question, false dilemma, complex question), fallacies of ambiguity (equivocation, amphiboly).
• Categorical Statements — the four categorical proposition forms (A: all S are P, E: no S are P, I: some S are P, O: some S are not P), the Square of Opposition, existential import.
• Categorical Syllogisms — standard form, mood and figure, validity testing through rules and Venn diagrams.
• Immediate Inferences — conversion, obversion, contraposition; the relationship between categorical statements.
• Propositional Logic — Symbolization — standard logical connectives (negation, conjunction, disjunction, conditional, biconditional), translation from English into symbolic form, well-formed formulas (WFFs).
• Truth Tables — truth-functional definition of connectives, construction of truth tables for complex formulas, classification of statements (tautology, contradiction, contingent), testing for logical equivalence, testing arguments for validity.
• Propositional Inference Rules — modus ponens, modus tollens, hypothetical syllogism, disjunctive syllogism, constructive dilemma, destructive dilemma, simplification, conjunction, addition.
• Equivalence Rules — DeMorgan's laws, commutation, association, distribution, double negation, material implication, material equivalence, transposition, exportation, tautology.
• Predicate Logic Introduction — universal and existential quantifiers, predicates and variables, translation of quantified statements, scope of quantifiers.
• Inductive Argument Forms — generalization, statistical syllogism, argument from analogy, causal arguments, inference to the best explanation.
• Critical Thinking Applications — analysis of arguments in journalism, advertising, political discourse, legal reasoning, and scientific claims.

Optional Topics

• Natural Deduction in Propositional Logic — formal proof construction using a standard system (Copi, Fitch, or similar).
• Predicate Logic Proofs — universal instantiation, universal generalization, existential instantiation, existential generalization; quantifier scope and identity.
• Truth Trees (Semantic Tableaux) — tree method for testing validity and consistency.
• Probability and Inductive Logic — basic probability rules, conditional probability, Bayes' theorem, the role of probability in scientific reasoning.
• Modal Logic Introduction — necessity, possibility, the difference between de dicto and de re modality.
• Logical Paradoxes — the liar, sorites paradoxes, Russell's paradox, Newcomb's paradox.
• History of Logic — Aristotle, Stoic logic, medieval logic, Frege and the foundations of modern logic.

Resources & Tools

• Standard textbooks — Patrick Hurley A Concise Introduction to Logic (the most widely adopted Florida textbook); Copi, Cohen, & Rodych Introduction to Logic; Bergmann, Moor, & Nelson The Logic Book; Lewis Vaughn The Power of Critical Thinking; Robert Baum Logic. Choice of textbook substantially affects the formal-vs-informal balance of the course.
• Online logic exercise platforms — many Florida institutions use Hurley's LogicCoach companion software, Carnap.io (free, open-source proof checker for propositional and predicate logic), or institutional Canvas-integrated exercise banks.
• Truth-table generators — free online tools such as TruthTableGenerator.com, useful for student self-checking.
• Open educational resources — the open textbook For All X (P.D. Magnus, with Florida-specific adaptations by various authors) covers propositional and predicate logic with formal proofs; the Stanford Encyclopedia of Philosophy provides authoritative reference entries on all major logic topics.
• Critical thinking supplements — for the informal-logic portion, supplementary readings from journalism, political speeches, advertising, and legal opinions provide application material.

Career Pathways

PHI2100 supports preparation for a wide range of academic and professional pathways where rigorous reasoning is foundational:

• Pre-Law — Logic coursework is widely recommended by Florida law schools (Florida State University College of Law, University of Florida Levin College of Law, University of Miami Law School, Florida International University College of Law, Stetson University College of Law, Nova Southeastern Shepard Broad College of Law). The LSAT examination tests logical reasoning, analytical reasoning, and argument analysis directly.
• Philosophy (B.A.) — Foundational requirement for the philosophy major at all Florida public universities.
• Mathematics and Computer Science — Logical reasoning is the foundation of mathematical proof, theoretical computer science, formal verification, and programming-language semantics. CS majors particularly benefit from the propositional and predicate logic content.
• Pre-Medical and Health Professions — Critical-reasoning skills tested on the MCAT and DAT directly draw on the analytical methods developed in this course.
• Business, Finance, and Public Policy — Strategic and analytical reasoning underpins these fields; logic supports preparation for the GMAT, GRE, and CPA examinations.
• Education — K-12 teachers benefit from the meta-cognitive skills of argument analysis, which inform their ability to teach critical thinking to students.
• Journalism and Communications — Argument evaluation and fallacy recognition are foundational for journalists, communications professionals, and content creators in the post-truth era.

Special Information

Florida General Education Core

PHI2100 is widely accepted as a General Education Core Humanities elective at Florida public colleges and universities. The specific humanities requirement at the receiving institution may have additional constraints; students should verify acceptance with the receiving institution.

Articulation and Transfer

PHI2100 articulates without loss of credit between any two Florida public colleges and the State University System under the Statewide Course Numbering System. The course is widely accepted as a substantive humanities, philosophy, or critical-thinking course at receiving four-year institutions.

Course Format and Instructor Variation

The balance of formal vs. informal logic varies substantially across Florida institutions and instructors. Some institutions teach the course as a near-equivalent of a discrete-mathematics introduction with substantial symbolic-logic content; others teach it as a critical-thinking course with limited formal content. Students intending to transfer the course to satisfy a logic-major requirement (e.g., for a philosophy or mathematics major at a Florida public university) should verify the formal-content depth with the receiving institution. The course may carry the title "Logic," "Introductory Logic," or "Introduction to Logic and Critical Thinking" at different institutions — content varies even when the SCNS code is identical.

Prerequisites

Standard prerequisites include college-ready placement in reading and writing. Some institutions require completion of ENC1101 (English Composition I) as a prerequisite or corequisite. The course requires the ability to read and analyze argumentative prose at the college level.

Time Commitment

A 3-credit lecture course conventionally implies approximately 6-9 hours per week of out-of-class study (textbook reading, problem sets, proof construction, exam preparation) in addition to the 3 hours per week of class meetings. The formal-logic portions (truth tables, propositional logic, predicate logic) typically require substantial practice for mastery; students should plan to work through assigned problem sets systematically.

AI Integration

Generative-AI tools have mixed and instructive applications in introductory logic. AI tools can explain logic concepts, generate practice problems, and provide step-by-step walk-throughs of truth-table construction and propositional proofs. However, students should be aware that current generative AI tools make errors on logic problems with surprising frequency — including incorrect truth-table values, invalid proof steps, and mis-identified fallacies. The activity of evaluating an AI's logical claims is itself excellent logic practice. Students must consult institutional and instructor-specific policies on AI use; the use of AI to complete graded logic assignments without independent verification is generally a violation of academic integrity policy. The fundamental skill of thinking critically about whether a conclusion follows from its premises — including conclusions stated by AI tools — is irreducibly the student's responsibility.