Logic and Methodology of Scientific Knowledge
Formal logic
Know the difference between deduction (validity guarantees truth transmission) and induction (ampliative, probabilistic). Be able to identify validity vs. soundness, and common forms: modus ponens, modus tollens, disjunctive syllogism, and the fallacies of affirming the consequent and denying the antecedent. Understand categorical propositions and the square of opposition, and the basics of propositional and predicate logic.
Scientific method
Know hypothetico-deductivism, falsificationism (Popper: demarcation by falsifiability, not verifiability), Kuhn's paradigms and normal science versus revolution, Lakatos' research programmes, and Feyerabend's methodological anarchism. Understand explanation (deductive-nomological, causal, teleological), confirmation, underdetermination, and theory-laden observation.
Induction and its problem
Hume's problem: induction cannot be justified deductively or inductively without circularity. Responses include Popper's rejection of inductive confirmation, Bayesian probabilistic accounts, and pragmatic justifications.
Traps
(a) Calling an invalid argument "false" - arguments are valid/invalid, statements true/false; (b) confusing falsifiability with falsity; (c) treating Kuhn as claiming science is irrational; (d) confusing correlation with causation in methodological questions.
Rule of thumb
To test validity, try to imagine premises true and conclusion false; if you can, the form is invalid. To test a scientific claim, ask what observation would count against it.
Worked example: "If it rains, the ground is wet. The ground is wet; therefore it rained." Invalid - affirming the consequent. The ground could be wet for another reason.