Abstract Objects: An Introduction to Axiomatic Metaphysics

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Springer Science & Business Media, Jun 30, 1983 - Philosophy - 193 pages
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In this book, I attempt to lay the axiomatic foundations of metaphysics by developing and applying a (formal) theory of abstract objects. The cornerstones include a principle which presents precise conditions under which there are abstract objects and a principle which says when apparently distinct such objects are in fact identical. The principles are constructed out of a basic set of primitive notions, which are identified at the end of the Introduction, just before the theorizing begins. The main reason for producing a theory which defines a logical space of abstract objects is that it may have a great deal of explanatory power. It is hoped that the data explained by means of the theory will be of interest to pure and applied metaphysicians, logicians and linguists, and pure and applied epistemologists. The ideas upon which the theory is based are not essentially new. They can be traced back to Alexius Meinong and his student, Ernst Mally, the two most influential members of a school of philosophers and psychologists working in Graz in the early part of the twentieth century. They investigated psychological, abstract and non-existent objects - a realm of objects which weren't being taken seriously by Anglo-American philoso phers in the Russell tradition. I first took the views of Meinong and Mally seriously in a course on metaphysics taught by Terence Parsons at the University of Massachusetts/Amherst in the Fall of 1978. Parsons had developed an axiomatic version of Meinong's naive theory of objects.
 

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Meta-magick gets founded here, as applied by the NuChwezi school.

Contents

1 THEORY DATA AND EXPLANATION
1
2 THE ORIGINS OF THE THEORY
6
ELEMENTARY OBJECT THEORY
15
1 THE LANGUAGE
16
2 THE SEMANTICS
19
3 THE LOGIC
28
4 THE PROPER AXIOMS
32
5 AN AUXILIARY HYPOTHESIS
37
3 MODELLING LEIBNIZS MONADS
84
4 MODELLING STORIES AND NATIVE CHARACTERS
91
5 MODALITY AND DESCRIPTIONS
99
THE TYPED THEORY OF ABSTRACT OBJECTS
107
1 THE LANGUAGE
109
2 THE SEMANTICS
113
3 THE LOGIC
121
4 THE PROPER AXIOMS
124

APPLICATIONS OF THE ELEMENTARY THEORY
40
1 MODELLING PLATOS FORMS
41
2 MODELLING THE ROUND SQUARE ETC
47
3 THE PROBLEM OF EXISTENCE
50
APPENDIX TO CHAPTER II
52
THE MODAL THEORY OF ABSTRACT OBJECTS WITH PROPOSITIONS
59
2 THE SEMANTICS
61
3 THE LOGIC
68
4 THE PROPER AXIOMS
73
THE APPLICATIONS OF THE MODAL THEORY
77
2 MODELLING POSSIBLE WORLDS
78
APPLICATIONS OF THE TYPED THEORY 1 MODELLING FREGES SENSESI
126
2 MODELLING FREGES SENSES II
140
3 MODELLING IMPOSSIBLE AND FICTIONAL RELATIONS
145
4 MODELLING MATHEMATICAL MYTHS AND ENTITIES
147
CONCLUSION
154
MODELLING THE THEORY ITSELF
158
MODELLING NOTIONS
167
NOTES
172
BIBLIOGRAPHY
187
INDEX
190
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