§-Unit

QLDPhilosophy and Reason← Philosophy and Reason syllabus

Unit 3: Reason and formal logic

15 dot points, in syllabus order. Each dot point has a focused answer, with exam-style questions and worked answers where available.

Which errors of reasoning come purely from an argument's form, regardless of what it is about?

identify and explain formal fallacies, including affirming the consequent, denying the antecedent and the undistributed middle

Formal fallacies. Covers what makes a fallacy formal rather than informal, the propositional fallacies of affirming the consequent and denying the antecedent, the categorical fallacy of the undistributed middle, and how to expose each by counterexample.

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What are informal fallacies, and how do we identify them when analysing real arguments?

identify and explain common informal fallacies in arguments, including fallacies of relevance, ambiguity and presumption

Informal fallacies. Covers the difference between formal and informal fallacies and explains the major fallacies of relevance, presumption and ambiguity, including ad hominem, straw man, appeal to authority, false dilemma, begging the question and equivocation, with examples.

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What is the difference between a necessary and a sufficient condition, and why does it matter for argument?

identify and distinguish between necessary and sufficient conditions and represent them using conditional statements

Necessary and sufficient conditions. Covers the definitions, how they map onto the conditional, the converse and contrapositive, the difference between the two kinds of condition, and how confusing them produces the formal fallacies of affirming the consequent and denying the antecedent.

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When several hypotheses could explain the evidence, what justifies inferring the best one as true?

explain inference to the best explanation (abduction) and evaluate hypotheses using criteria such as simplicity, explanatory scope and coherence

Abductive reasoning. Covers the structure of inference to the best explanation, the criteria for ranking explanations (simplicity, scope, coherence, testability), the role of Ockham's razor, and the limits of abduction including underdetermination.

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How does science test its theories, and what marks the boundary between science and non-science?

explain the hypothetico-deductive method and Popper's falsificationism, including the demarcation problem and the asymmetry of confirmation and refutation

Scientific method. Covers the hypothetico-deductive method, Karl Popper's falsificationism and demarcation criterion, the logical asymmetry between confirmation and refutation, the role of bold conjectures, and criticisms from Kuhn and the Duhem-Quine thesis.

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What makes an inductive argument strong, and how does inductive support differ from the certainty of deduction?

distinguish inductive from deductive reasoning and evaluate inductive arguments for strength and cogency rather than validity

Inductive reasoning. Covers the difference between deduction and induction, why inductive arguments are assessed for strength and cogency rather than validity, the role of probability, and how added evidence can defeat an otherwise strong inference.

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How do we tell whether an argument is valid, and when does validity guarantee a true conclusion?

distinguish validity from soundness, and evaluate deductive arguments for both, using premises and conclusions

Validity and soundness. Covers the structure of deductive arguments, the difference between truth and validity, what soundness adds, common valid forms such as modus ponens and modus tollens, and how to test arguments by counterexample.

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Can our reliance on induction be rationally justified, or does Hume's argument show that it cannot?

explain Hume's problem of induction and evaluate proposed responses, including the appeal to the uniformity of nature and pragmatic justifications

Problem of induction. Covers David Hume's argument that inductive inference cannot be justified without circularity, the role of the uniformity of nature, and responses including pragmatic justification, Popper's falsificationism and the limits of each.

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How do we reason from observation to a cause, and what are Mill's methods for discovering causal connections?

explain and apply Mill's methods of causal reasoning, including agreement, difference, joint method, residues and concomitant variation

Causal inference. Covers John Stuart Mill's five methods (agreement, difference, joint method, residues, concomitant variation), how each isolates a probable cause, the difference between correlation and causation, and the limits of causal induction.

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How do we extract a clear argument from messy ordinary prose so that we can evaluate it fairly?

reconstruct and map arguments from ordinary language, identifying premises, conclusions, hidden assumptions and argument structure

Argument analysis. Covers identifying premises and conclusions, indicator words, supplying hidden premises in enthymemes, distinguishing linked from convergent support, the principle of charity, and standardising and mapping arguments before evaluation.

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How should evidence change what we believe, and why do people reason so badly about probabilities?

apply basic probabilistic reasoning to evaluate arguments, including conditional probability, base rates and common statistical fallacies

Probabilistic reasoning. Covers conditional probability, the role of base rates, Bayesian updating in plain terms, and common statistical fallacies including the base-rate fallacy, the conjunction fallacy and the gambler's fallacy.

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How do we symbolise propositions and use truth tables to test arguments for validity?

translate and symbolise propositions using logical operators, and use truth tables to test propositional arguments for validity

Propositional (sentential) logic. Covers symbolisation with the five logical operators, building truth tables for negation, conjunction, disjunction, the conditional and the biconditional, and using a full truth table to test an argument for validity.

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How do categorical statements combine into syllogisms, and how do we test a syllogism for validity?

analyse categorical statements and syllogisms, including the four standard forms and the rules for valid syllogistic reasoning

Aristotelian categorical logic. Covers the four standard categorical forms A, E, I and O, the subject and predicate terms, distribution, the structure of the categorical syllogism, and the rules used to test a syllogism for validity.

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When does reasoning from one case to a similar case give a strong conclusion, and what makes an analogy break down?

analyse and evaluate arguments from analogy, assessing the relevance and number of similarities and the presence of relevant disanalogies

Analogical reasoning. Covers the structure of an argument from analogy, the criteria that make one strong (relevance, number and variety of similarities), how relevant disanalogies weaken it, and famous philosophical analogies such as Paley's watch and Thomson's violinist.

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When does evidence from a sample justify a conclusion about a whole population, and what makes a generalisation hasty or biased?

evaluate inductive generalisations by assessing sample size, representativeness and the dangers of hasty generalisation and biased sampling

Inductive generalisation. Covers the structure of generalising from a sample to a population, the criteria of sufficient size and representativeness, the fallacies of hasty generalisation and biased sampling, and why anecdotes and self-selected samples mislead.

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