HPR4759: Quine and the Application of Logic to Science

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• W.V.O. Quine and Analytical Philosophy: The American logicians vision of applying rigorous logical structures to organise and elucidate fields of human understanding. Reference: Quine, W.V.O. (1951). Two Dogmas of Empiricism, The Philosophical Review, 60(1), 20-43; Stanford Encyclopedia of Philosophy: https://plato.stanford.edu/entries/quine/

• Kurt Godel and Incompleteness Theorems: Foundational limits in formal logic where consistent systems contain unprovable true statements. Reference: Godel, Kurt (1931). Uber formal unentscheidbare Satze der Principia Mathematica und verwandter Systeme, I; Stanford Encyclopedia of Philosophy: https://plato.stanford.edu/entries/goedel/

• Russells Paradox and Formal Logic: The historical pursuit of logical foundations for mathematics and the contradictions exposed by paradoxes like the barber paradox. Reference: Russell, Bertrand, and Alfred North Whitehead (1910-1913). Principia Mathematica, Cambridge University Press; Stanford Encyclopedia of Philosophy: https://plato.stanford.edu/entries/russell-paradox/

• Abstract Syntax Trees (ASTs): Hierarchical tree data structures utilised by static analysis tools to break down, parse, and evaluate complex computer source code. Reference: Wikipedia Entry: https://en.wikipedia.org/wiki/Abstract_syntax_tree

• Formal Specifications and Software Verification: Using mathematical proofs to verify program correctness from first principles without relying solely on empirical runtime testing. Reference: Woodcock, Jim, et al. (2009). Formal Methods: Practice and Experience, ACM Computing Surveys, 41(4).

• Deterministic Systems vs. Large Language Models: The architectural divide between rule-based, deterministic logic engines and data-driven, non-deterministic neural networks.

• Steven Wolfram and Computational Irreducibility: The limits of predictability in complex computational systems and efforts to map universal rules of knowledge. Reference: Wolfram, Stephen (2002). A New Kind of Science, Wolfram Media; Wolfram Language Resource: https://www.wolfram.com/language/anks/

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