Nominalistic Systems

ISBN-13: 9789401033169 / Angielski / Miękka / 2011 / 226 str.

Rolf A. Eberle

Opis

1. 1. PROGRAM It will be our aim to reconstruct, with precision, certain views which have been traditionally associated with nominalism and to investigate problems arising from these views in the construction of interpreted formal systems. Several such systems are developed in accordance with the demand that the sentences of a system which is acceptable to a nominalist must not imply the existence of any entities other than individuals. Emphasis will be placed on the constructionist method of philosophical analysis. To follow this method is to introduce the central notions of the subject-matter to be investigated into a system governed by exact rules. For example, the constructionist method of investigating the properties of geometric figures may consist in formulating a system of postulates and definitions which, together with the apparatus of formal logic, generates all necessary truths concerning geometric figures. Similarly, a constructionist analysis of the notion of an individual may take the form of an axiomatic theory whose provable assertions are just those which seem essential to the role played by the concept of an individual in system atic contexts. Such axiomatic theories gain in interest if they are supple mented by precise semantical rules specifying the denotation of all terms and the truth conditions of all sentences of the theory."

Spis treści

1 / Introduction.- 1.1. Program.- 1.2. Historical Background.- 1.3. Formal Preliminaries.- 1.3.1. Summary of Elementary Set-Theoretic Notions.- 1.3.2. Formal Systems, their Syntax and Semantics.- 2 / Individuals.- 2.1. Outline of Goodman’s Conception.- 2.2. Part-Whole Relations.- 2.3. Atomistic Universes of Individuals.- 2.4. The Leonard-Goodman Calculus of Individuals LGCI.- 2.5. The General Calculus CII of Atomistic Individuals.- 2.5.1. The Vocabulary and the Axioms of CII.- 2.5.2. Some Theorems of CII.- 2.5.3. The Semantics of CII.- 2.5.4. The Semantical Adequacy of CII*.- 2.6. Finite Sums and Products: The Calculus CIII.- 2.6.1. The Vocabulary and the Axioms of CIII.- 2.6.2. The Semantics of CIII.- 2.6.3. The Semantical Adequacy of CIII*.- 2.7. Infinite Sums and Products: The Calculus CIIII.- 2.7.1. The Vocabulary and the Axioms of CIIII.- 2.7.2. Some Theorems of CIIII.- 2.7.3. The Semantics of CI II.- 2.7.4. The Semantical Adequacy of CIIII*.- 2.8. Non-Atomistic Universes of Individuals.- 2.9. The Non-Atomistic Calculus CIIV and some Extensions.- 2.9.1. The Vocabulary and the Axioms of CIIV.- 2.9.2. The Semantics of CIIV.- 2.9.3. The Semantical Adequacy of CIIV*.- 2.9.4. Extensions of CIIV.- 2.10. Sequential Individuals and the Calculus of Individual Relations.- 2.10.1. Order Implied by Different Part-Whole Relations.- 2.10.2. Order Implied by the Existence of Certain Composites.- 2.10.3. Order Implied by Positional Parts.- 2.10.4. Order Implied by Relational Individuals and their Calculus.- 3 / Ontological Commitment and Designata of Expressions.- 3.1. Ontological Implications of Theories.- 3.2. One-Place Predicates and their Extensions.- 3.3. Truth Conditions and Relations of Predication.- 3.4. Expressions of Relations and Operations.- 3.5. Denotationless Symbols and Nominalistic Models.- 4 / Bundles of Qualities, Qualities, and Concreta.- 4.1. Bundles of Qualities and their Calculus CB.- 4.1.1. Background.- 4.1.2. The Vocabulary of CB *.- 4.1.3. The Semantics of CB with Informal Discussion.- 4.1.4. The Axioms of CB.- 4.1.5. The Semantical Adequacy of CB*.- 4.2. Resemblance and its Calculus CR.- 4.2.1. Background.- 4.2.2. The Vocabulary and the Axioms of CR.- 4.2.3. The Semantics of CR.- 4.2.4. The Semantical Adequacy of CR*.- 4.3. Qualities and their Calculus CQ.- 4.3.1. Background.- 4.3.2. The Meta-Theory of CQ.- 4.3.3. The Interpreted System CQ*.- 4.4. Concreta.- 4.5. Further Problems and Conclusion.- Symbolic Notation.- Index of Names.- Index of Subjects.