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Reductionism is one of those philosophical myths that are either enthusiastically embraced or wholeheartedly rejected. And, like all other philosophical myths, it rarely gets serious consideration. Reasoning About Theoretical Entities strives to give reductionism its day in court, as it were, by explicitly developing several versions of the reductionist project and assessing their merits within the framework of modern symbolic logic. Not since the days of Carnap's Aufbau has reductionism received such close attention (albeit in a necessarily restricted and regimented setting such as that of mo

Cardinal numbers. --- Logic, Symbolic and mathematical. --- Reductionism. --- Philosophy --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Arithmetic, Cardinal --- Cardinal arithmetic --- Cardinals (Numbers) --- Numbers, Cardinal --- Transfinite numbers

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The book embeds a description and an analysis of the Old English numeral system into a broader, cross-linguistic discussion. It provides a theoretical framework for the study of numerals and numeral systems of natural languages, bridging the gap between recent findings in the cognitive sciences on numeracy and the known typological generalisations on cardinal numerals. The Old English numeral system shows a number of peculiarities not found in the present-day languages of Europe. Its detailed description is therefore an ideal locus for studying the features of linguistic number expressions in terms of their morpho-syntactic properties and of the structure of numeral systems.The approach is innovative in that it combines a detailed analysis of the numeral system with the analysis of the grammatical properties of cardinal numerals. For the description of Old English, the study focuses on aspects of information structure and of referent identification in quantificational constructions. This leads to a novel perspective on the language-internal variation in the agreement patterns between numerals and quantified nouns, allowing the author to test and refine some long standing tenets in the study of numerals and to offer alternative explanations. Rather than seeing numerals as a hybrid word class, the author argues that this variation in the morpho-syntactic behaviour follows identifiable patterns specific to the word class numeral. He accounts for these patterns by positing different, cross-linguistically uniform stages in the emergence of numeral systems, as well as varying degrees of discreteness of the quantified noun. Moreover, the author demonstrates that the constraints determining this variation in Old English have obvious parallels across languages.

English language --- Cardinal numbers. --- Numeration. --- Comparative linguistics. --- Historical linguistics. --- Diachronic linguistics --- Dynamic linguistics --- Evolutionary linguistics --- Language and languages --- Language and history --- Linguistics --- Comparative philology --- Philology, Comparative --- Historical linguistics --- Number theory --- Arithmetic, Cardinal --- Cardinal arithmetic --- Cardinals (Numbers) --- Numbers, Cardinal --- Set theory --- Transfinite numbers --- Germanic languages --- Numerals. --- History --- Cardinal numbers --- Comparative linguistics --- Numeration --- Numerals --- Grammar --- anno 500-1199 --- English /Language. --- Historical Linguistics.

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Provability, Computability and Reflection

Mathematical logic --- Algebraic logic --- Logique algébrique --- Algebra, Boolean --- Boole, Algèbre de --- Cylindric algebras --- Algèbres cylindriques. --- Set theory. --- Cardinal numbers. --- Arithmetic, Cardinal --- Cardinal arithmetic --- Cardinals (Numbers) --- Numbers, Cardinal --- Set theory --- Transfinite numbers --- Aggregates --- Classes (Mathematics) --- Ensembles (Mathematics) --- Mathematical sets --- Sets (Mathematics) --- Theory of sets --- Logic, Symbolic and mathematical --- Mathematics --- 510.22 --- 510.22 Set theory. Set theoretic approach. Theory of order types, of ordinal and cardinal numbers --- Set theory. Set theoretic approach. Theory of order types, of ordinal and cardinal numbers --- 510.64 --- 510.64 Non-classical, formal systems of logic. Modal logic. Multiple-value logics. Syllogistics. Inductive logic. Probabilistic logic --- Non-classical, formal systems of logic. Modal logic. Multiple-value logics. Syllogistics. Inductive logic. Probabilistic logic --- Recursion theory --- 510.6 --- 510.6 Mathematical logic --- Congresses --- Axiomatic set theory --- Axioms --- Congresses. --- Proof theory --- Logique algébrique --- Théorie de la preuve --- ELSEVIER-B EPUB-LIV-FT --- Cardinal numbers --- Théorie des ensembles --- Nombres cardinaux --- Théorie de la récursivité --- Congrès --- Théorie axiomatique des ensembles --- Axiomatic set theory. --- Logique mathématique. --- Récursivité, Théorie de la. --- Recursion theory - Congresses --- Numbers, cardinals --- Théorie des ensembles --- Logic, Symbolic and mathematical -- Periodicals. --- Logic, Symbolic and mathematical. --- Recursion theory - Congresses. --- Recursion theory -- Congresses. --- Physical Sciences & Mathematics --- Mathematical Theory --- Algebraic logic. --- Proof theory.