History and Philosophy of Logic

Distinguish between the key philosophical domains of metaphysics, epistemology, and philosophy of language.

Contrast semantic realism and anti-realism as theses about the relationship between truth and meaning.

Describe the core tenets of the correspondence, coherence, and deflationary theories of truth.

Explain the analytic-synthetic distinction and its traditional role in grounding a priori knowledge.

Explain the core tenets of foundationalism and coherentism as theories of epistemic justification.

Distinguish between model-theoretic and proof-theoretic conceptions of logical consequence.

Explain Kant's view of logic as formal and his conception of analytic and synthetic judgments.

Analyse the philosophical significance of Boole's algebraization of logic.

Analyse the revolutionary impact of Frege's replacement of subject-predicate analysis with a function-argument structure.

Explain Frege's distinction between sense (Sinn) and reference (Bedeutung) using the puzzles of identity and cognitive significance.

Assess Frege's logicist thesis and the philosophical motivations for reducing arithmetic to logic.

Explain Frege's context principle and its implications for the relationship between logic and language.

Analyse the philosophical impact of Russell's paradox on Frege's logicist project.

Evaluate Russell's theory of types as a philosophical response to the paradoxes.

Analyse Russell's theory of definite descriptions as a paradigm of philosophical analysis.

Analyse the core tenets of neo-logicism, focusing on Hume's Principle as an abstraction principle.

Evaluate key philosophical challenges to neo-logicism, such as the 'bad company' objection and the Caesar problem.

Analyse the Frege-Hilbert controversy on the nature of axioms as truths versus implicit definitions.

Assess the philosophical goals of Hilbert's programme for the foundations of mathematics.

Analyse the philosophical significance of Gödel's first incompleteness theorem for Hilbert's programme.

Evaluate the claim that the first incompleteness theorem shows that mathematical truth outruns formal proof.

Assess the philosophical impact of the second incompleteness theorem on foundationalist programmes in mathematics.

Critically evaluate the Lucas-Penrose argument that Gödel's theorems refute mechanism about the mind.

Explain Tarski's semantic theory of truth, including the metalanguage/object language distinction.

Analyse Tarski's model-theoretic definition of logical consequence and its philosophical presuppositions.

Evaluate Etchemendy's critique that Tarski's account conflates logical and material consequence.

Analyse the demarcation problem: what makes a term a logical constant?

Analyse the philosophical significance of soundness and completeness theorems for relating model-theoretic and proof-theoretic consequence.

Analyse Brouwer's philosophical case against the law of excluded middle based on the nature of mathematical construction.

Evaluate the BHK interpretation as an alternative account of the meaning of logical connectives.

Analyse Dummett's argument that a theory of meaning must be grounded in the public manifestation of understanding.

Evaluate how Dummett's 'manifestation argument' provides a justification for intuitionistic logic over classical logic.

Assess whether the choice between classical and intuitionistic logic is a substantive philosophical dispute.

Distinguish between de re and de dicto modal ascriptions and explain the problem of referential opacity.

Analyse Quine's arguments against the coherence of quantified modal logic, focusing on his critique of essentialism.

Explain how Kripke semantics provides a formal framework for modal logic and analyse the metaphysical status of 'possible worlds'.

Compare David Lewis's modal realism with ersatzist alternatives as accounts of possible worlds.

Evaluate Kripke's argument for the existence of necessary a posteriori truths and its impact on the analytic-synthetic distinction.

Analyse the Liar paradox and the principle of explosion as a challenge for classical logic.

Evaluate paraconsistent logic and the dialetheist thesis that some contradictions are true.

Analyse the Sorites paradox and the challenge of vagueness for classical logic.

Evaluate supervaluationism as a response to the problem of vagueness.

Analyse the philosophical motivations for relevance logic and its critique of classical entailment.

Analyse Quine's argument for the revisability of logic and its challenge to logical apriorism.

Evaluate 'anti-exceptionalism' about logic: is logic continuous with the empirical sciences?

Define logical monism and logical pluralism, outlining the core thesis of each position.

Evaluate Beall and Restall's case-based logical pluralism and its main objections.

Analyse the debate over the status of second-order logic: is it logic or 'set theory in disguise'?

Assess whether disagreements between classical and non-classical logicians are genuine disputes or merely verbal.