Abstract Objects: An Introduction to Axiomatic MetaphysicsIn 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. |
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 |
| 190 | |
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Common terms and phrases
2-expressions A-objects a₁ abbreviate abstract objects abstract properties actual world atomic formula believes Chapter clause Consequently context defined definite description DICTO E-IDENTITY Eext encodes a property encoding formulas example existing objects extranuclear fact fails to exemplify formal language free object free object variable Frege interpretation intuitions Lauben Leibniz logical axioms logically true Meinong metaphysical modal monads n-place relation term n-tuple names necessarily notion nuclear object encodes object exemplifies object term object which encodes object which exemplifies objects of type Parsons philosophers Plato PLUG possible world primitive principle proof proper axioms propositional attitude propositional formula quantifiers Raskolnikov reading restricted rules of inference Russellian satisfies with respect schema schemata Section semantics sentences Socrates story subformula suppose term of type theorem theory of abstract translate truth type theory unique v₁ vacuous properties variable ranging weak correlate wife of Tully