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Deflating Existential Consequence - A Case for Nominalism (Paperback)
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Deflating Existential Consequence - A Case for Nominalism (Paperback)
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If we must take mathematical statements to be true, must we also
believe in the existence of abstracta eternal invisible
mathematical objects accessible only by the power of pure thought?
Jody Azzouni says no, and he claims that the way to escape such
commitments is to accept (as an essential part of scientific
doctrine) true statements which are about objects that don't exist
in any sense at all.
Azzouni illustrates what the metaphysical landscape looks like
once we avoid a militant Realism which forces our commitment to
anything that our theories quantify. Escaping metaphysical
straitjackets (such as the correspondence theory of truth), while
retaining the insight that some truths are about objects that do
exist, Azzouni says that we can sort scientifically-given objects
into two categories: ones which exist, and to which we forge
instrumental access in order to learn their properties, and ones
which do not, that is, which are made up in exactly the same sense
that fictional objects are. He offers as a case study a small
portion of Newtonian physics, and one result of his classification
of its ontological commitments, is that it does not commit us to
absolute space and time.
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