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Full Description
This volume presents a bold new framework for the foundations of mathematics by integrating constructivism with countablism — the view that all sets are countable and that uncountable 'sets' such as the real line are best treated as proper classes. This unified approach offers a mathematically rigorous way to avoid classical paradoxes and rethink central assumptions in set theory, truth theory, and the philosophy of mathematics.It shows how constructivist principles allow for a global classical truth predicate, long believed impossible since Tarski, while countablism eliminates much of the traditional set-theoretic pathology associated with unrestricted abstraction. It provides definitive, technically grounded resolutions to both the liar paradox and Russell's paradox, clarifying their implications for assertibility, predicativity, and the concept-object distinction.The second half develops core areas of mathematics within this constructive and countablist foundation, demonstrating that despite its philosophical and technical restrictions, the framework preserves the structure and power of mainstream mathematics. This volume offers a major rethinking of mathematical ontology, abstract objects, and the iterative conception of sets, with implications for constructivism, intuitionism, platonism, and nominalism.
