Inconsistent Mathematics

C.E. Mortensen (Autor)

Buch | Softcover

158 Seiten

2010 | Softcover reprint of hardcover 1st ed. 1995
Springer (Verlag)
978-90-481-4480-8 (ISBN)

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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.

One Motivations.- Two Arithmetic.- Three Modulo Infinity.- Four Order.- Five Calculus.- Six Inconsistent Continuous Functions.- Seven The Delta Function.- Eight Inconsistent Systems of Linear Equations.- Nine Projective Spaces.- Ten Topology.- Eleven Category Theory.- Twelve Closed Set Sheaves and Their Categories.- Thirteen Duality.- Fourteen Foundations: Provability, Truth and Sets.- Index of Definitions and Names.

Erscheint lt. Verlag	6.12.2010
Reihe/Serie	Mathematics and Its Applications ; 312
Zusatzinfo	X, 158 p.
Verlagsort	Dordrecht
Sprache	englisch
Maße	160 x 240 mm
Themenwelt	Geisteswissenschaften ► Philosophie ► Logik
	Informatik ► Theorie / Studium ► Algorithmen
	Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre
ISBN-10	90-481-4480-9 / 9048144809
ISBN-13	978-90-481-4480-8 / 9789048144808
Zustand	Neuware