Logical pluralism is the view that different logics are equally
appropriate, or equally correct. Logical relativism is a pluralism
according to which validity and logical consequence are relative to
something. In Varieties of Logic, Stewart Shapiro develops several
ways in which one can be a pluralist or relativist about logic. One
of these is an extended argument that words and phrases like
'valid' and 'logical consequence' are polysemous or, perhaps
better, are cluster concepts. The notions can be sharpened in
various ways. This explains away the 'debates' in the literature
between inferentialists and advocates of a truth-conditional,
model-theoretic approach, and between those who advocate
higher-order logic and those who insist that logic is first-order.
A significant kind of pluralism flows from an orientation toward
mathematics that emerged toward the end of the nineteenth century,
and continues to dominate the field today. The theme is that
consistency is the only legitimate criterion for a theory. Logical
pluralism arises when one considers a number of interesting and
important mathematical theories that invoke a non-classical logic,
and are rendered inconsistent, and trivial, if classical logic is
imposed. So validity is relative to a theory or structure. The
perspective raises a host of important questions about meaning. The
most significant of these concern the semantic content of logical
terminology, words like 'or', 'not', and 'for all', as they occur
in rigorous mathematical deduction. Does the intuitionistic 'not',
for example, have the same meaning as its classical counterpart?
Shapiro examines the major arguments on the issue, on both sides,
and finds them all wanting. He then articulates and defends a
thesis that the question of meaning-shift is itself
context-sensitive and, indeed, interest-relative. He relates the
issue to some prominent considerations concerning open texture,
vagueness, and verbal disputes. Logic is ubiquitous. Whenever there
is deductive reasoning, there is logic. So there are questions
about logical pluralism that are analogous to standard questions
about global relativism. The most pressing of these concerns
foundational studies, wherein one compares theories, sometimes with
different logics, and where one figures out what follows from what
in a given logic. Shapiro shows that the issues are not
problematic, and that is usually easy to keep track of the logic
being used and the one mentioned.
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