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The Logic of Sortals - A Conceptualist Approach (Hardcover, 1st ed. 2019)
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The Logic of Sortals - A Conceptualist Approach (Hardcover, 1st ed. 2019)
Series: Synthese Library, 408
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Sortal concepts are at the center of certain logical discussions
and have played a significant role in solutions to particular
problems in philosophy. Apart from logic and philosophy, the study
of sortal concepts has found its place in specific fields of
psychology, such as the theory of infant cognitive development and
the theory of human perception. In this monograph, different formal
logics for sortal concepts and sortal-related logical notions (such
as sortal identity and first-order sortal quantification) are
characterized. Most of these logics are intensional in nature and
possess, in addition, a bidimensional character. That is, they
simultaneously represent two different logical dimensions. In most
cases, the dimensions are those of time and natural necessity, and,
in other cases, those of time and epistemic necessity. Another
feature of the logics in question concerns second-order
quantification over sortal concepts, a logical notion that is also
represented in the logics. Some of the logics adopt a constant
domain interpretation, others a varying domain interpretation of
such quantification. Two of the above bidimensional logics are
philosophically grounded on predication sortalism, that is, on the
philosophical view that predication necessarily requires sortal
concepts. Another bidimensional logic constitutes a logic for
complex sortal predicates. These three sorts of logics are among
the important novelties of this work since logics with similar
features have not been developed up to now, and they might be
instrumental for the solution of philosophically significant
problems regarding sortal predicates. The book assumes a modern
variant of conceptualism as a philosophical background. For this
reason, the approach to sortal predicates is in terms of sortal
concepts. Concepts, in general, are here understood as
intersubjective realizable cognitive capacities. The proper
features of sortal concepts are determined by an analysis of the
main features of sortal predicates. Posterior to this analysis, the
sortal-related logical notions represented in the above logics are
discussed. There is also a discussion on the extent to which the
set-theoretic formal semantic systems of the book capture different
aspects of the conceptualist approach to sortals. These different
semantic frameworks are also related to realist and nominalist
approaches to sortal predicates, and possible modifications to them
are considered that might represent those alternative approaches.
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