Language, Truth And Logic In Mathematics

The foundations of mathematics are examined by reference to such crucial concepts as the informational independence of quantifiers, the standard-nonstandard distinction, completeness, computability, parallel processing and the extremality of models.

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A dozen essays, most previously published, critique the concepts that mathematicians use, particularly their logical and linguistic tools. Typically finds that the concept under scrutiny needs revision or reconsideration. Argues that quantification theory has been only partially and inadequately captured by the received first-order logic, that much of the discussions of the implications of G<:o>del-type incompleteness results are superficial and misleading, that the characterization of Hilbert as a formalist hides rather than reveals the true dynamics of his thought, and that implication of the contrast between standard and non-standard interpretations of higher-order logics have remained largely unacknowledged. Also offers several alternative concepts. No index. Annotation c. by Book News, Inc., Portland, Or.

Jaakko Hintikka is the author or co-author of thirty volumes and of some 300 scholarly articles in mathematical and philosophical logic, epistemology, language theory, philosophy of science, history of ideas and history of philosophy, including Aristotle, Descartes, Leibniz, Kant, Peirce, The Bloomsbury Group, Husserl and Wittgenstein. He has also been active in international scholarly organizations, most recently as the First Vice-President of FISP, Vice-President of IIP and Co-Chair of the American Organizing Committee of the Twentieth World Congress of Philosophy. He has been Editor-in-Chief of the International Journal Synthese and the Managing Editor of Synthese Library since 1965.