Title: Logic And Critical Thinking — LearnCoachAssist

Q: What is formal logic?
A: Formal logic is the study of inference with purely formal content, where the validity of an argument depends solely on its logical form rather than the meaning of its terms.

Q: What is an argument in logic?
A: An argument is a set of statements (premises) offered as reasons to support a conclusion.

Q: What is a premise?
A: A premise is a statement in an argument that provides evidence or reasons for the conclusion.

Q: What is a conclusion in an argument?
A: The conclusion is the statement that the premises of an argument are intended to support or prove.

Q: What is a valid argument?
A: A valid argument is one where if all the premises are true, the conclusion must necessarily be true. Validity concerns logical structure, not actual truth.

Q: What is a sound argument?
A: A sound argument is one that is both valid and has all true premises. Soundness guarantees a true conclusion.

Q: What is the difference between deductive and inductive reasoning?
A: Deductive reasoning moves from general premises to a specific, certain conclusion. Inductive reasoning moves from specific observations to a general, probable conclusion.

Q: Give an example of deductive reasoning.
A: All mammals are warm-blooded. Dogs are mammals. Therefore, dogs are warm-blooded. The conclusion follows necessarily from the premises.

Q: Give an example of inductive reasoning.
A: Every swan I have observed is white. Therefore, all swans are probably white. The conclusion is probable but not certain.

Q: What is a syllogism?
A: A syllogism is a form of deductive reasoning consisting of two premises and a conclusion, typically involving a major premise, a minor premise, and a conclusion.

Q: What are the three terms in a categorical syllogism?
A: The major term (predicate of conclusion), minor term (subject of conclusion), and middle term (appears in both premises but not the conclusion).

Q: What is a truth table?
A: A truth table is a mathematical table used to determine the truth value of a compound proposition for every possible combination of truth values of its components.

Q: What is logical conjunction (AND)?Conjunction (P ∧ Q) is true only when both P and Q are true
A: false in all other cases.

Q: What is logical disjunction (OR)?Disjunction (P ∨ Q) is true when at least one of P or Q is true
A: false only when both are false.

Q: What is logical negation (NOT)?
A: Negation (¬P) reverses the truth value of a proposition: if P is true, ¬P is false, and vice versa.

Q: What is a conditional (IF…THEN) in logic?A conditional (P → Q) is false only when P is true and Q is false
A: true in all other cases.

Q: What is a biconditional (IF AND ONLY IF)?
A: A biconditional (P ↔ Q) is true when both P and Q have the same truth value (both true or both false).

Q: What is modus ponens?Modus ponens: If P then Q
A: P is true; therefore Q is true. (P → Q, P ⊢ Q)

Q: What is modus tollens?Modus tollens: If P then Q
A: Q is false; therefore P is false. (P → Q, ¬Q ⊢ ¬P)

Q: What is a hypothetical syllogism?If P then Q
A: if Q then R; therefore if P then R. (P → Q, Q → R ⊢ P → R)

Q: What is a disjunctive syllogism?Either P or Q
A: not P; therefore Q. (P ∨ Q, ¬P ⊢ Q)

Q: What is a tautology?
A: A tautology is a compound statement that is true for every possible assignment of truth values to its variables (e.g., P ∨ ¬P).

Q: What is a contradiction in logic?
A: A contradiction is a compound statement that is false for every possible assignment of truth values (e.g., P ∧ ¬P).

Q: What is a contingency in propositional logic?
A: A contingency is a proposition that is neither a tautology nor a contradiction—its truth value depends on the values of its variables.

Q: What is the fallacy of affirming the consequent?If P then Q
A: Q is true; therefore P is true. This is invalid because Q could be true for reasons other than P.

Q: What is the fallacy of denying the antecedent?If P then Q
A: P is false; therefore Q is false. This is invalid because Q might be true independently of P.

Q: What is an informal fallacy?
A: An informal fallacy is an error in reasoning whose flaw lies in the content, context, or delivery of the argument rather than its logical form.

Q: What is the ad hominem fallacy?
A: The ad hominem fallacy attacks the person making the argument rather than the argument itself. Example: "You can't trust John's climate data—he's not even a scientist."

Q: What is the straw man fallacy?
A: The straw man fallacy misrepresents someone's argument to make it easier to attack. The arguer refutes a distorted version instead of the actual position.

Q: What is the slippery slope fallacy?
A: The slippery slope fallacy claims that one event will inevitably lead to a chain of extreme consequences without providing evidence for each step in the chain.

Q: What is the appeal to authority fallacy (argumentum ad verecundiam)?
A: Claiming something is true because an authority figure says so, especially when the authority is not an expert in the relevant field or when experts disagree.

Q: What is the appeal to ignorance fallacy (argumentum ad ignorantiam)?
A: Claiming something is true because it hasn't been proven false, or false because it hasn't been proven true.

Q: What is the false dilemma (false dichotomy) fallacy?
A: Presenting only two options as if they are the only possibilities when, in fact, other alternatives exist.

Q: What is the red herring fallacy?
A: Introducing an irrelevant topic into a discussion to divert attention from the original issue.

Q: What is the tu quoque fallacy?
A: A type of ad hominem that deflects criticism by pointing out the opponent's hypocrisy: "You do it too!" It does not address the argument itself.

Q: What is the circular reasoning (begging the question) fallacy?
A: An argument where the conclusion is assumed in one of the premises. Example: "The Bible is true because it is the word of God, and we know it is the word of God because the Bible says so."

Q: What is the equivocation fallacy?
A: Using an ambiguous term in more than one sense within an argument, leading to a misleading conclusion.

Q: What is the hasty generalization fallacy?
A: Drawing a broad conclusion from a small or unrepresentative sample. Example: "I met two rude people from that city, so everyone there must be rude."

Q: What is the post hoc ergo propter hoc fallacy?
A: Assuming that because event B followed event A, A caused B. Correlation or sequence does not imply causation.

Q: What is the appeal to emotion fallacy?
A: Manipulating emotions (fear, pity, anger) to win an argument rather than using logical evidence.

Q: What is the bandwagon fallacy (argumentum ad populum)?
A: Arguing that something is true or good because many people believe it or do it.

Q: What is the genetic fallacy?
A: Judging something as good or bad based on where it comes from (its origin) rather than its current merit or evidence.

Q: What is the no true Scotsman fallacy?
A: Redefining a group to exclude counterexamples rather than accepting them. Example: "No true athlete would skip training"—redefining 'athlete' to protect the claim.

Q: What is the loaded question fallacy?
A: Asking a question that contains a presupposition or assumption that has not been proven. Example: "When did you stop cheating on exams?"

Q: What is a non sequitur?
A: A non sequitur is an argument in which the conclusion does not logically follow from the premises.

Q: What is the composition fallacy?
A: Assuming that what is true of the parts must be true of the whole. Example: "Every player on the team is excellent, so the team must be excellent."

Q: What is the division fallacy?
A: Assuming that what is true of the whole must be true of each part. Example: "The university is prestigious, so every department must be prestigious."

Q: What is Occam's razor?
A: Occam's razor states that among competing hypotheses, the one with the fewest assumptions should be preferred. "Do not multiply entities beyond necessity."

Q: How does Occam's razor apply to scientific reasoning?
A: It guides scientists to prefer the simplest explanation that accounts for the evidence, reducing the risk of overfitting and unnecessary complexity.

Q: What is the burden of proof in an argument?
A: The obligation falls on the person making a claim to provide evidence, rather than on others to disprove it.

Q: What is the scientific method?
A: A systematic process: observation → question → hypothesis → experiment → analysis → conclusion, designed to test ideas through repeatable, empirical investigation.

Q: What is a hypothesis in the scientific method?
A: A hypothesis is a testable, falsifiable prediction about the relationship between variables, formulated before experimentation.

Q: What does falsifiability mean (Karl Popper)?
A: A statement is falsifiable if there exists a possible observation or experiment that could prove it false. Popper argued this is what distinguishes science from non-science.

Q: What is confirmation bias?
A: The tendency to search for, interpret, and remember information that confirms one's preexisting beliefs while ignoring contradictory evidence.

Q: What is anchoring bias?
A: The tendency to rely too heavily on the first piece of information encountered (the "anchor") when making decisions.

Q: What is the availability heuristic?
A: Judging the likelihood of events based on how easily examples come to mind, which can overestimate vivid or recent events.

Q: What is the Dunning-Kruger effect?
A: A cognitive bias where people with low ability overestimate their competence, while those with high ability may underestimate theirs.

Q: What is cognitive dissonance?
A: The mental discomfort experienced when holding two or more contradictory beliefs, leading people to change beliefs or rationalize to reduce the tension.

Q: What is hindsight bias?
A: The tendency to believe, after an event has occurred, that one "knew it all along", making outcomes seem more predictable than they were.

Q: What is the framing effect?
A: The tendency for people to react differently depending on how information is presented (framed)—e.g., "90% survival rate" vs. "10% mortality rate."

Q: What is groupthink?
A: A phenomenon where the desire for group harmony or conformity overrides realistic appraisal of alternatives, leading to poor decision-making.

Q: What is the sunk cost fallacy?
A: Continuing a behavior or endeavor because of previously invested resources (time, money, effort) rather than evaluating current and future value.

Q: What is motivated reasoning?
A: The tendency to arrive at conclusions that one wants to be true, using emotional biases to process information rather than objective analysis.

Q: What is an analogy in argumentation?
A: An analogy argues that because two things are similar in some respects, they are likely similar in some further respect. Strength depends on relevance of similarities.

Q: What is a counterexample?
A: A counterexample is a specific case that disproves a universal claim. One genuine counterexample is sufficient to refute a generalization.

Q: What is the difference between necessary and sufficient conditions?A necessary condition must be present for an event to occur. A sufficient condition guarantees the event occurs. Being a dog is sufficient for being a mammal
A: being a mammal is necessary for being a dog.

Q: What is abductive reasoning?
A: Abductive reasoning (inference to the best explanation) starts with observations and seeks the simplest, most likely explanation. Example: wet streets → it probably rained.

Q: How does abductive reasoning differ from inductive reasoning?
A: Abductive reasoning selects the best explanation for given data, while inductive reasoning generalizes from specific instances to broader rules.

Q: What is a reductio ad absurdum?
A: A method of argument that assumes a proposition is true and then shows it leads to a contradiction or absurd consequence, thereby proving it false.

Q: What is De Morgan's Law in logic?
A: ¬(P ∧ Q) ≡ (¬P ∨ ¬Q) and ¬(P ∨ Q) ≡ (¬P ∧ ¬Q). Negating a conjunction gives a disjunction of negations, and vice versa.

Q: What is the law of excluded middle?For any proposition P, either P is true or ¬P is true
A: there is no middle ground. (P ∨ ¬P)

Q: What is the law of non-contradiction?
A: A proposition cannot be both true and false at the same time and in the same sense. (¬(P ∧ ¬P))

Q: What is the law of identity?
A: Every object is identical to itself. In propositional logic: P ≡ P. A thing is what it is.

Q: What is a logical equivalence?
A: Two statements are logically equivalent if they have the same truth value in every possible scenario. Example: P → Q ≡ ¬P ∨ Q.

Q: What is the contrapositive of a conditional?
A: The contrapositive of P → Q is ¬Q → ¬P. A conditional and its contrapositive are logically equivalent.

Q: What is the converse of a conditional?
A: The converse of P → Q is Q → P. The converse is not logically equivalent to the original conditional.

Q: What is the inverse of a conditional?
A: The inverse of P → Q is ¬P → ¬Q. The inverse is not logically equivalent to the original but is equivalent to the converse.

Q: What is propositional logic?
A: A branch of logic dealing with propositions (statements that are true or false) and logical connectives (AND, OR, NOT, IF…THEN, IF AND ONLY IF).

Q: What is predicate logic (first-order logic)?
A: Extends propositional logic with quantifiers (∀ for all, ∃ there exists) and predicates to express properties of objects and relations between them.

Q: What does the universal quantifier (∀) mean?
A: ∀x P(x) means "for all x, P(x) is true." Every element in the domain satisfies the predicate P.

Q: What does the existential quantifier (∃) mean?
A: ∃x P(x) means "there exists at least one x for which P(x) is true."

Q: What is a categorical proposition?
A: A statement that asserts a relationship between two categories. The four standard forms are: All S are P, No S are P, Some S are P, Some S are not P.

Q: What is the square of opposition?
A: A diagram showing logical relationships among categorical propositions: contradictory, contrary, subcontrary, and subalternation relations.

Q: What is deductive validity vs. inductive strength?
A: A deductive argument is either valid or invalid (all-or-nothing). An inductive argument is strong or weak depending on how probable the conclusion is given the premises.

Q: What is the principle of charity in critical thinking?
A: When evaluating an argument, interpret it in the strongest, most reasonable form before critiquing it—do not attack a weak version.

Q: What is Bayesian reasoning?
A: A method of updating the probability of a hypothesis based on new evidence using Bayes' theorem: P(H|E) = P(E|H) × P(H) / P(E).

Q: What is the base rate fallacy?
A: Ignoring the general prevalence (base rate) of an event when evaluating probability, and focusing instead on specific but less informative evidence.

Q: What is the gambler's fallacy?
A: The belief that past random events affect future probabilities—e.g., thinking a coin is "due" for heads after a streak of tails. Each flip is independent.

Q: What is a self-fulfilling prophecy and how does it relate to reasoning?
A: A prediction that causes itself to become true because believing it changes behavior. It illustrates how expectations can bias outcomes and compromise objective reasoning.

Q: What is the appeal to nature fallacy?
A: Arguing that something is good because it is "natural" or bad because it is "unnatural." Naturalness alone does not determine value or correctness.

Q: What is the middle ground (argument to moderation) fallacy?
A: Assuming the truth must be a compromise between two opposing positions, regardless of the evidence for each side.

Q: What is special pleading?
A: Applying standards, rules, or principles to others while exempting oneself or one's case without adequate justification.

Q: What is the Texas sharpshooter fallacy?
A: Cherry-picking data clusters to suit a hypothesis after the fact—like drawing a target around bullet holes. It ignores the data that doesn't fit.

Q: What is whataboutism?
A: A diversionary tactic that responds to criticism by pointing to a different issue rather than addressing the original argument.

Q: What is an enthymeme?
A: An argument with an unstated (implicit) premise that the audience is expected to fill in. Example: "She's a doctor, so she's smart" (implicit: doctors are smart).

Q: What distinguishes correlation from causation?Correlation means two variables tend to occur together
A: causation means one directly produces the other. Correlation alone does not prove a causal link.

Q: What is a controlled experiment?
A: An experiment where one variable is changed (independent variable) while others are kept constant, and results are compared with a control group to isolate causal effects.

Q: What is peer review in science?
A: A process where scientific work is evaluated by independent experts in the field before publication, to check methodology, accuracy, and significance.

Q: What is reproducibility in the scientific method?
A: The ability for an experiment or study to be repeated by others with the same results, which is essential for confirming scientific findings.

Q: What is the null hypothesis?
A: The default assumption that there is no effect or no relationship between variables. Experiments aim to gather evidence to reject or fail to reject it.

Q: What is a type I error (false positive)?
A: Rejecting the null hypothesis when it is actually true—concluding there is an effect when there is none.

Q: What is a type II error (false negative)?
A: Failing to reject the null hypothesis when it is actually false—missing a real effect.

Q: What is the paradox of the heap (sorites paradox)?
A: If removing one grain from a heap still leaves a heap, when does it stop being a heap? It highlights the problem of vague predicates and unclear boundaries.