Metamathematics and the Philosophical Tradition is the first work
to explore in such historical depth the relationship between
fundamental philosophical quandaries regarding self-reference and
meta-mathematical notions of consistency and incompleteness. Using
the insights of twentieth-century logicians from Goedel through
Hilbert and their successors, this volume revisits the writings of
Aristotle, the ancient skeptics, Anselm, and enlightenment and
seventeenth and eighteenth century philosophers Leibniz, Berkeley,
Hume, Pascal, Descartes, and Kant to identify ways in which these
both encode and evade problems of a priori definition and
self-reference. The final chapters critique and extend more recent
insights of late 20th-century logicians and quantum physicists, and
offer new applications of the completeness theorem as a means of
exploring "metatheoretical ascent" and the limitations of
scientific certainty. Broadly syncretic in range, Metamathematics
and the Philosophical Tradition addresses central and recurring
problems within epistemology. The volume's elegant, condensed
writing style renders accessible its wealth of citations and
allusions from varied traditions and in several languages. Its
arguments will be of special interest to historians and
philosophers of science and mathematics, particularly scholars of
classical skepticism, the Enlightenment, Kant, ethics, and
mathematical logic.
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