Logic and Critical Thinking
Logic and Critical Thinking trains learners to construct, evaluate, and communicate arguments rigorously by covering propositional logic, truth tables, validity and soundness, categorical syllogisms, informal fallacies, evidence evaluation, cognitive biases, and Bayesian probability. The course develops both formal analytical skills and practical epistemic habits for navigating the information-rich modern world.
Who Should Take This
This course is ideal for undergraduates in any discipline who want to reason more clearly, professionals who regularly evaluate arguments or evidence in their work, and anyone preparing for standardized tests with logical reasoning sections such as the LSAT or GRE. No mathematical background beyond arithmetic is required; intellectual curiosity and a willingness to examine one's own assumptions are the only prerequisites.
What's Included in AccelaStudy® AI
Adaptive Knowledge Graph
Practice Questions
Lesson Modules
Console Simulator Labs
Exam Tips & Strategy
13 Activity Formats
Course Outline
1Propositional Logic 8 topics
Identify propositions as declarative statements with a definite truth value, distinguishing them from questions, commands, and expressions that cannot be assigned true or false
State the five logical connectives (negation, conjunction, disjunction, conditional, biconditional), their symbolic notation, and the truth conditions that define each connective
Translate English sentences containing 'not', 'and', 'or', 'if...then', and 'if and only if' into symbolic form using propositional variables and logical connectives accurately
Apply the inclusive-or vs. exclusive-or distinction and identify when natural language 'or' is inclusive, explaining how this affects the truth conditions of compound propositions
Analyze the logical relationships among a conditional statement and its converse, inverse, and contrapositive, explaining which pairs are logically equivalent and which are not
Apply De Morgan's Laws to distribute negation over conjunction and disjunction, and simplify complex negated compound propositions to their equivalent forms
Evaluate the truth conditions for 'if...then' statements including the paradoxes of material implication where a false antecedent makes the conditional true regardless of the consequent
Identify necessary and sufficient conditions in natural language statements and translate them correctly into conditional or biconditional form, avoiding common direction errors
2Truth Tables and Logical Equivalence 7 topics
Describe the structure of a truth table including how the number of rows is determined by 2 to the power n for n variables, and why each row represents a unique truth-value assignment
Construct truth tables for compound propositions with two or three variables, evaluating intermediate subformulas before computing the final column
Identify tautologies, contradictions, and contingent propositions by inspecting the final column of a truth table and explain what each classification reveals about the proposition's logical status
Verify logical equivalence of two propositions using truth tables by checking that the final columns are identical across all truth-value assignments
Analyze the validity of a deductive argument using a truth table by testing whether every row that makes all premises true also makes the conclusion true, identifying any counterexample rows
Compare the truth table method with informal semantic methods for evaluating argument validity, explaining when shortcut methods (looking for counterexamples) are more efficient
Simplify a compound proposition to its simplest logically equivalent form using De Morgan's laws, double negation, and absorption laws, reducing the number of connectives required
3Validity, Soundness, and Argument Structure 8 topics
Describe the distinction between validity (logical form guarantees the conclusion given true premises) and soundness (valid plus premises actually true) and provide clear examples of each combination
Identify the premise(s) and conclusion of an argument expressed in natural language, using indicator words (therefore, because, since, hence) and paraphrasing to reveal the logical structure
Apply the modus ponens and modus tollens inference rules to evaluate whether a deductive argument is valid and explain why denying the antecedent and affirming the consequent are fallacies
Distinguish deductive arguments (validity guarantees truth transfer) from inductive arguments (premises support but do not guarantee the conclusion) and evaluate argument strength accordingly
Identify hidden (implicit) premises in enthymemes by reconstructing the unstated assumption needed to make the argument valid, and evaluate whether that hidden premise is plausible
Evaluate the overall strength of an inductive argument by assessing sample representativeness, the strength of causal evidence, and whether alternative explanations have been ruled out
Apply the hypothetical syllogism and disjunctive syllogism inference forms to extend chains of reasoning and identify when these forms are used implicitly in everyday argumentation
Identify the structure of arguments by diagramming relationships between sub-conclusions, main conclusions, and supporting premises using a standard argument map format
4Categorical Logic and Syllogisms 6 topics
Identify the four categorical proposition types (A: All S are P, E: No S are P, I: Some S are P, O: Some S are not P) and state the distribution status of the subject and predicate in each
Apply Venn diagrams with two or three overlapping circles to represent categorical propositions and visually test the validity of categorical syllogisms by checking whether the diagram forces the conclusion
Evaluate the validity of a standard-form categorical syllogism by testing the three rules (undistributed middle, illicit major/minor, two negative premises) or by Venn diagram method
Translate ordinary-language categorical arguments into standard syllogistic form by identifying the major and minor terms, middle term, and writing each premise and conclusion as a categorical proposition
Analyze the relationship between categorical logic and propositional logic by showing how syllogistic validity can be modeled as propositional validity and identifying where the frameworks differ
Apply the square of opposition relationships (contradiction, contrariety, sub-contrariety, subalternation) among the four categorical proposition types to infer truths from known truths
5Informal Fallacies 8 topics
Name and describe ten common informal fallacies including ad hominem, straw man, false dilemma, slippery slope, appeal to authority, begging the question, hasty generalization, post hoc, red herring, and tu quoque
Identify specific informal fallacies in written or spoken arguments by labeling the fallacy, explaining why the move from premises to conclusion fails, and suggesting how the argument could be repaired
Apply the distinction between legitimate appeals to expertise (appropriate authority with relevant credentials) and the appeal-to-authority fallacy (inappropriate, irrelevant, or manufactured authority)
Distinguish the straw man fallacy from a legitimate criticism by accurately restating an opponent's position before evaluating it, and recognize when a paraphrase distorts the original argument
Analyze a complex persuasive text or debate transcript by cataloging all informal fallacies present, evaluating which are most damaging to the overall argument, and rating the argument's logical quality
Evaluate whether a given slippery slope argument is a fallacy or a legitimate causal argument by examining whether each claimed step in the causal chain is empirically supported
Distinguish equivocation (exploiting ambiguous meanings of a word across premises) from other informal fallacies and identify equivocation in natural-language arguments by pinpointing the term that shifts meaning
Apply the principle of charity when interpreting an argument by attributing the strongest plausible interpretation before evaluating it, contrasting this with a straw man that targets a weakened version
6Evaluating Evidence 8 topics
List the criteria for evaluating source credibility including expertise, independence, replication, peer review, conflict of interest, and recency, and explain how each criterion affects the evidentiary weight of a claim
Apply the correlation-versus-causation distinction to evaluate research claims by identifying confounding variables, directionality problems, and why correlation alone cannot establish causal relationships
Evaluate the quality of a statistical sample by assessing size, representativeness, random selection, response rate, and the potential for sampling bias to distort conclusions
Apply the principle of confirmation bias to identify when a reasoner selects, interprets, or recalls evidence in a way that preferentially supports their existing belief rather than testing it
Analyze the hierarchy of evidence (anecdote, expert opinion, observational study, randomized controlled trial, meta-analysis) and explain why higher-quality evidence should receive greater epistemic weight
Evaluate a reported scientific finding in a news article by identifying the original study design, sample size, effect magnitude, statistical significance, and common misrepresentations in science journalism
Apply the principle of falsifiability to distinguish empirical claims that can in principle be disproved from non-falsifiable claims, explaining why falsifiability is a hallmark of scientific reasoning
Identify and explain the distinction between statistical significance and practical significance (effect size) in reported research, explaining why a statistically significant result may be trivially small
7Cognitive Biases 7 topics
Describe the availability heuristic, anchoring bias, sunk cost fallacy, overconfidence effect, framing effect, and in-group bias, giving a concrete real-world example of each
Identify specific cognitive biases operating in described decision-making scenarios by matching the pattern of error to the relevant bias and explaining the cognitive mechanism causing the error
Apply debiasing strategies including considering the outside view, pre-mortem analysis, seeking disconfirming evidence, and using base rates to counteract systematic thinking errors
Analyze the sunk cost fallacy in business, personal finance, and policy scenarios by separating past irrecoverable costs from forward-looking decision analysis and recommending the rational choice
Evaluate how framing effects in surveys, negotiations, and media can lead logically equivalent situations to produce different decisions, and design counter-framed versions to expose the bias
Identify overconfidence bias in probability estimates and calibration tasks by comparing subjective confidence intervals with actual outcomes, and apply reference class forecasting to produce more accurate predictions
Analyze the in-group bias and out-group homogeneity effect in social judgments by identifying when group membership distorts evidence evaluation and what structural conditions reduce these biases
8Bayesian Reasoning 8 topics
Describe the Bayesian framework of prior probability, likelihood, and posterior probability and explain how new evidence should rationally update the strength of a belief
Apply Bayes' Theorem using the formula P(H|E) equals P(E|H) times P(H) divided by P(E) to update a hypothesis probability given new evidence in a medical or everyday-reasoning context
Apply base rate information to diagnose base-rate neglect errors in medical testing, legal reasoning, and everyday claims where the prior probability of the hypothesis is ignored
Calculate the posterior probability in a two-hypothesis scenario using a frequency table or natural frequency representation rather than formal conditional probabilities, demonstrating both formats
Analyze the difference between strong and weak evidence by comparing the likelihood ratio P(E|H) divided by P(E|not H) and explain why evidence that is equally likely under both hypotheses provides no discriminating power
Evaluate a real-world decision or scientific claim by applying Bayesian updating iteratively, demonstrating how multiple pieces of evidence combine and how starting prior probability affects the final posterior
Compare the Bayesian approach to evaluating evidence with the deductive validity approach from propositional logic, identifying when each framework is more appropriate for assessing claims
Apply the concept of the prior probability distribution to explain why two equally rational people can reach different posterior conclusions from identical evidence if their priors differ
Scope
Included Topics
- Propositional logic (propositions, connectives, negation, conjunction, disjunction, conditional, biconditional), truth tables (constructing, evaluating, identifying tautologies and contradictions), logical equivalence (De Morgan's laws, contrapositive, converse, inverse), validity and soundness (definitions, testing arguments), deductive vs. inductive reasoning, categorical logic and syllogisms (categorical propositions, Venn diagrams, syllogism validity), argument mapping (premise identification, conclusion identification, hidden premises), common informal fallacies (ad hominem, straw man, false dilemma, slippery slope, appeal to authority, begging the question, hasty generalization, post hoc), evaluating evidence (source credibility, correlation vs. causation, sample quality, confirmation bias), cognitive biases (availability heuristic, anchoring, sunk cost, overconfidence, framing effect, in-group bias), Bayesian reasoning basics (prior and posterior probability, base rate neglect, updating beliefs with evidence)
Not Covered
- Formal predicate logic with quantifiers beyond brief introduction
- Proof theory and formal derivation systems
- Modal logic and non-classical logics
- Advanced probability theory beyond Bayes' theorem basics
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