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Inconsistent Mathematics (Paperback, Softcover reprint of hardcover 1st ed. 1995)
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Inconsistent Mathematics (Paperback, Softcover reprint of hardcover 1st ed. 1995)
Series: Mathematics and Its Applications, 312
Expected to ship within 10 - 15 working days
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without a properly developed inconsistent calculus based on
infinitesimals, then in consistent claims from the history of the
calculus might well simply be symptoms of confusion. This is
addressed in Chapter 5. It is further argued that mathematics has a
certain primacy over logic, in that paraconsistent or relevant
logics have to be based on inconsistent mathematics. If the latter
turns out to be reasonably rich then paraconsistentism is
vindicated; while if inconsistent mathematics has seri ous
restriytions then the case for being interested in
inconsistency-tolerant logics is weakened. (On such restrictions,
see this chapter, section 3. ) It must be conceded that
fault-tolerant computer programming (e. g. Chapter 8) finds a
substantial and important use for paraconsistent logics, albeit
with an epistemological motivation (see this chapter, section 3).
But even here it should be noted that if inconsistent mathematics
turned out to be functionally impoverished then so would
inconsistent databases. 2. Summary In Chapter 2, Meyer's results on
relevant arithmetic are set out, and his view that they have a
bearing on G8del's incompleteness theorems is discussed. Model
theory for nonclassical logics is also set out so as to be able to
show that the inconsistency of inconsistent theories can be
controlled or limited, but in this book model theory is kept in the
background as much as possible. This is then used to study the
functional properties of various equational number theories."
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