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The Rise of Modern Logic: from Leibniz to Frege, Volume 3 (Hardcover, REV and)
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The Rise of Modern Logic: from Leibniz to Frege, Volume 3 (Hardcover, REV and)
Series: Handbook of the History of Logic
Expected to ship within 12 - 17 working days
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With the publication of the present volume, the Handbook of the
History of Logic turns its attention to the rise of modern logic.
The period covered is 1685-1900, with this volume carving out the
territory from Leibniz to Frege. What is striking about this period
is the earliness and persistence of what could be called 'the
mathematical turn in logic'. Virtually every working logician is
aware that, after a centuries-long run, the logic that originated
in antiquity came to be displaced by a new approach with a
dominantly mathematical character. It is, however, a substantial
error to suppose that the mathematization of logic was, in all
essentials, Frege's accomplishment or, if not his alone, a
development ensuing from the second half of the nineteenth century.
The mathematical turn in logic, although given considerable torque
by events of the nineteenth century, can with assurance be dated
from the final quarter of the seventeenth century in the
impressively prescient work of Leibniz. It is true that, in the
three hundred year run-up to the Begriffsschrift, one does not see
a smoothly continuous evolution of the mathematical turn, but the
idea that logic is mathematics, albeit perhaps only the most
general part of mathematics, is one that attracted some degree of
support throughout the entire period in question. Still, as Alfred
North Whitehead once noted, the relationship between mathematics
and symbolic logic has been an "uneasy" one, as is the present-day
association of mathematics with computing. Some of this unease has
a philosophical texture. For example, those who equate mathematics
and logic sometimes disagree about the directionality of the
purported identity. Frege and Russell made themselves famous by
insisting (though for different reasons) that logic was the senior
partner. Indeed logicism is the view that mathematics can be
re-expressed without relevant loss in a suitably framed symbolic
logic. But for a number of thinkers who took an algebraic approach
to logic, the dependency relation was reversed, with mathematics in
some form emerging as the senior partner. This was the precursor of
the modern view that, in its four main precincts (set theory, proof
theory, model theory and recursion theory), logic is indeed a
branch of pure mathematics. It would be a mistake to leave the
impression that the mathematization of logic (or the logicization
of mathematics) was the sole concern of the history of logic
between 1665 and 1900. There are, in this long interval, aspects of
the modern unfolding of logic that bear no stamp of the imperial
designs of mathematicians, as the chapters on Kant and Hegcl make
clear. Of the two, Hcgel's influence on logic is arguably the
greater, serving as a spur to the unfolding of an idealist
tradition in logic - a development that will be covered in a
further volume, British Logic in the Nineteenth Century.
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