A Course in Analytic Philosophy

Explain Plato's Theory of Forms and its epistemological implications.

Analyze the Allegory of the Cave as an illustration of Plato's epistemology.

Describe Aristotle's critique of Platonic Forms and his alternative account of universals.

Identify the basic structure of Aristotelian syllogistic logic.

Apply Aristotelian syllogistic rules to determine the validity of simple arguments.

Distinguish between Plato's rationalist and Aristotle's empiricist approaches to knowledge.

Reconstruct Descartes' method of doubt and the 'cogito' argument.

Explain the rationalist claim that some knowledge is a priori and independent of experience, using examples from Descartes or Leibniz.

Explain Leibniz's principle of sufficient reason and its role in his metaphysics.

Describe Hume's distinction between relations of ideas and matters of fact.

Analyze Hume's problem of induction and its skeptical implications for science.

Compare rationalist and empiricist approaches to the sources of knowledge and justification.

Distinguish between analytic/synthetic judgments and a priori/a posteriori knowledge.

Explain Kant's 'Copernican Revolution' and the project of reconciling rationalism and empiricism.

Define the 'synthetic a priori' and explain its importance to Kant's project.

Describe the role of the categories of understanding in structuring experience.

Analyze Kant's response to Hume's problem of induction via synthetic a priori principles.

Explain the distinction between phenomena and noumena and its consequences.

Explain how Frege's predicate logic surpassed the limitations of Aristotelian syllogistic logic.

Apply Frege's distinction between sense (Sinn) and reference (Bedeutung) to solve puzzles about identity and meaning.

Describe the logicist project of reducing arithmetic to logic as pursued by Frege and Russell.

Explain Russell's Paradox and its devastating impact on Frege's foundational project.

Reconstruct Russell's Theory of Descriptions as a paradigm of philosophical analysis.

Apply the Theory of Descriptions to analyze sentences containing definite descriptions.

Describe G.E. Moore's defense of common sense and his critique of idealism.

Explain Wittgenstein's 'picture theory' of meaning from the Tractatus and its influence on logical positivism.

Explain the verificationist criterion of meaning and its use in attacking metaphysics.

Analyze the self-refutation objection to the verification principle.

Reconstruct Quine's critique of the analytic-synthetic distinction in 'Two Dogmas of Empiricism'.

Describe Quine's holistic 'web of belief' model of scientific theories.

Contrast the positivist view of language with Quine's holistic empiricism.

Contrast Wittgenstein's later concept of 'meaning as use' with his earlier 'picture theory'.

Explain the concepts of 'language-games' and 'family resemblance' with examples.

Analyze the rule-following considerations and their skeptical implications for understanding.

Reconstruct the private language argument and its conclusion that meaning must be public.

Apply Wittgensteinian analysis to dissolve a traditional philosophical problem (e.g., the problem of other minds).

Explain how ordinary language philosophy shifted the method of philosophical inquiry.

Explain the use of possible worlds semantics to analyze statements of necessity and possibility.

Define 'rigid designator' and distinguish it from 'non-rigid designator' using Kripke's examples.

Explain Kripke's modal and epistemic arguments against descriptivist theories of proper names.

Describe the causal-historical theory of reference for proper names and natural kind terms.

Explain Putnam's Twin Earth thought experiment and its argument for semantic externalism.

Apply Grice's theory of conversational implicature to distinguish what is said from what is implicated.

Compare the core theses of Logicism, Formalism, and Intuitionism as foundational programs for mathematics.

Describe how Russell's theory of types was designed to avoid paradoxes within the logicist project.

Explain Hilbert's formalist program and the goal of proving the consistency of arithmetic via finitary means.

Explain Brouwer's intuitionist rejection of the law of excluded middle for infinite domains.

Analyze the philosophical differences between classical and intuitionistic logic.

Apply constructive reasoning to a simple mathematical proof.

Describe the iterative conception of the set-theoretic universe underlying ZFC.

Explain the statement of the Axiom of Choice and give an example of its use.

Construct Cantor's diagonal argument to prove the uncountability of the real numbers.

Explain the distinction between syntax and semantics in the context of formal systems.

Explain the philosophical implications of the Incompleteness Theorems for Hilbert's program and logicism.

Explain mathematical Platonism and Benacerraf's epistemological challenge to it.

Describe mathematical structuralism as an alternative to Platonism.

Explain the Quine-Putnam indispensability argument for the existence of mathematical objects.

Explain mathematical fictionalism and its strategy for accounting for the applicability of mathematics.

Evaluate the key strengths and weaknesses of Platonism versus structuralism.

Analyze how Wittgenstein's rule-following considerations challenge traditional views on mathematical truth.

Explain the problem of universals and distinguish between realist and nominalist solutions.

Analyze the 'Third Man Argument' against simple forms of realism about universals.

Explain Gettier's counterexamples to the 'justified true belief' analysis of knowledge.

Distinguish between internalist and externalist theories of epistemic justification.

Describe reliabilism as a prominent externalist theory of knowledge.

Analyze the role of epistemic luck in Gettier-style cases.

Identify the premises, conclusion, and logical form of a complex philosophical argument from a primary text.

Evaluate the soundness of a philosophical argument by assessing its premises and inferential strength.

Construct a formal argument for a given philosophical thesis, anticipating and addressing potential objections.

Apply modal reasoning (possible worlds, rigid designators) to evaluate a metaphysical claim about identity or necessity.

Compare how a Platonist and a Fictionalist would interpret the truth of a specific mathematical theorem (e.g., Fermat's Last Theorem).