Theory and History of Ontology
by Raul Corazzon - e-mail: raul.corazzon[at]formalontology.it
For an overview see the Index of the Pages, the SITE MAP or the Alphabetical Index of the
Philosophers: A-F - G-O - P-Z; You can also
download this page as 
Table of Contemporary Ontologists 
(click on the image to see the PDF file)
I wish to thank Professor Cocchiarella for helping me to complete this bibliography.
Index of the Section: "The Rediscovery of Ontology in Contemporary Thought"
Table of Formal and Descriptivists Ontologists (PDF - from Bernard Bolzano to present time)
Ontologists of the 19th and 20th Centuries (a selection of critical judgments about some of the greatest philosophers of the recent past)
Living Ontologists (a list of authors with an interest in ontology, with synthetic bibliographies)
Annotated bibliography of Nino Cocchiarella
INTRODUCTION
"Conceptual realism, as opposed to conceptualism simpliciter , does provide the general framework of a formal ontology that can accommodate both a natural realism and an intensional realism, as in conceptual natural realism and conceptual Platonism — or, instead of conceptual Platonism, as in conceptual intensional realism , where abstract objects are intensional objects that come about as products of cultural evolution. But the representation of the different ontological categories by logico-grammatical categories is not given in the direct and simple way in conceptual realism as it is in logical realism or nominalism. Instead, conceptual realism must represent the different formal modes of being in an indirect way. It is the explanation of this indirect way that is our primary concern in this essay."
From: Nino Cocchiarella - Conceptual Realism as a Formal Ontology (1996) p. 4.
BOOKS
FOR OTHER PUBLICATIONS SEE: Annotated bibliography of Nino Cocchiarella
PUBLICATIONS AVAILABLE ON LINE (PDF)
Conceptual Realism as a Formal Ontology - in: Roberto Poli & Peter Simons (eds.) "Formal Ontology" - Kluwer, Dordrecht/Boston/London 1996) pp. 27-60 - Nijhoff International Philosophy Series. vol. 53. (256 KB) - This essay is reproduced with the kind authorization of Kluwer
Logic and Ontology - in: Axiomathes vol. 12, (2001) pp. 117-150.
Infinity in Ontology and Mind - in: Axiomathes vol. 18, (2008) pp. 1-24.
Mass nouns in a logic of classes as many - in: Journal of Philosophical Logic vol. 38 (2009) pp. 343-361.
I am grateful to Professor Nino Cocchiarella, Dr. Woosuk Park (editor of the Korean Journal of Logic) and to Professor Inkyo Chung, President of Korean Association of Logic for the permission to publish to following essay:
Logical necessity based on Carnap's criterion of adequacy - Korean Journal of Logic - vol. 5 n. 2 (2002) - pp. 1-21
The following papers are posted with the kind permission of Professor Nino Cocchiarella:
Conceptual Realism and the Nexus of Predication - Metalogicon 16, 2, 2003, pp. 45-70.
Denoting concepts. reference, and the logic of names, classes as many, groups and plurals - Linguistics and Philosophy 28, 2, 2005, pp. 135-179
Deontic logic - Unpublished notes based on a course given on modal logic in the late 1960s at the State University of California at San Francisco
Gustav Bergmann on Ideal Languages - Unpublished lecture presented at Indiana University at the Gustav Bergmann Memorial Conference (October 30-21, 1992)
ARTICLES AVAILABLE ON LINE AT PROJECT EUCLID
PRE-PRINT AVAILABLE ON LINE: Axiomathes. An International Journal in Ontology and Cognitive Systems
INDEX OF THE BOOKS
Tense Logic: A Study of Temporal Reference (VI, 251 pages) Ph. D. Dissertation, University of California - Los Angeles, January 7, 1966). Committee in charge: Richard Montague, Charmain, Alfred Horn, Donald Kalish, Abraham Robinson, Robert Stockwell.
ABSTRACT: This work is concerned with the logical analysis of topological or non-metrical temporal reference. The specific problem with which it successfully deals is a precise formalization of (first-order) quantificational tense logic wherein both an appropriate formal semantics is developed and a meta-mathematically consistent and complete axiomatization for that semantics given. The formalization of quantificational tense logic herein presented adheres to all the canons of logical rigor by being carried out entirely as a definitional extension of (Zermelo-Fraenkel) set theory. Model-theoretical techniques are utilized in the semantics given and the notion of a history is formally developed as the tense-logical analogue of the notion of a model for standard first-order logic with identity. Corresponding to the key semantical concept of satisfaction (and consequently of truth) in a model, by means of which the central standard notion of logical truth is defined, the notion of satisfaction (and consequently of truth) in a history at a given moment of that history is developed, from which development, in turn, the central notion of tense-logical truth is defined. An axiomatic characterization of derivability within tense logic, or t-derivability, is then presented and proved to be both consistent and complete, i.e. , it is shown that an arbitrary tensed formula is tense-logically true if and only if it is t-derivable from zero premises, i.e., if and only if it is a theorem of the given axiomatic system. Quantification within tense logic introduces issues in no manner confronted on the sentential level. Recognition is made that quantification over objects existing prior to the time of assertion is to be distinguished from quantification over objects existing at the time of assertion, both of which in turn are to be distinguished from quantifying over objects existing at the time of assertion. Such distinct kinds of quantification are readily distinguishable within tense logic by means o£ incorporation of what is here called the logic of actual and possible objects. Precise semantical and syntactical formalization of this double quantification is presented prior to its use within tense logic, and completeness theorems are given for both the full system. and the restricted logic of actual objects, the latter of which may separately be taken as a formalization of a logic which can accommodate denotationless names. These several kinds of quantificational logic lead to separate completeness theorems stated and established for tense logic, depending on the several kinds of quantificational bases possible for this logic.
TABLE OF CONTENTS
Vita, Publications and Field of Study V
Abstract 1
Chapter 1. The Metalanguage 3
§ 1. Terminology 3
§ 2. Syntax 8
Chapter 2. Formalization of a Logic of Actual and Possible Objects 15
§ 1. Semantics 17
§ 2. Logical Axioms, Derivations and Theorems 23
§ 3. Completeness of the Logic of Actual and Possible Objects 35
§ 4. Standard Logic and the Logic of Denotationless Terms 47
Chapter 3. The Semantics of Tense Logic 59
§ 1. Histories, Moments and Momentary States 60
§ 2. Satisfaction, Truth and Validity in a History 66
§ 3. Tense-Logical Truth 76
§ 4. R-Validity 78
Chapter 4. An Axiomatic Formulation of Tense Logic 95
§ 1. Tense-Logical Axioms, t-theorems and t-derivations 96
§ 2. Partial Histories, Historical Sequences and Complete Decompositions 141
§ 3. A Completeness Theorem for Tense Logic 217
§ 4. Tense Logic with Quantification only over Possibilia 231
§ 5. Tense Logic with Quantification only over Actual Objects 233
Bibliography 250
Logical Investigations of Predication Theory and the Problem of Universal s, (265 pages), Naples, Bibliopolis, 1986.
TABLE OF CONTENTS
Preface 9
Introduction 11
§ 1. The Problem of the Predicable Nature of Universals 12
§ 2. Universality vs. Individuality 13
§ 3. Second Order Theories of Predication 15
§ 4. Predicativity vs. Impredicativity 19
§ 5. Internal vs. External Semantics 24
Notes to the Introduction 27
Chapter 1. Nominalism 29
§ 1. First Order Theories 32
§ 2. The Referential Semantics of First Order Theories 35
§ 3. Standard Predicative Second Order Logic 37
§ 4. Nominalistic Semantics for Predicative Second Order Logic 42
§ 5. Soundness and Completeness with respect to Nominalistic Semantics 44
§ 6. Nominalism and Modal Logic 47
§ 7. Logical Truth as Validity in Every Domain of Discourse 52
§ 8. The Secondary Semantics of Universal Validity 56
Notes to the Chapter 161
Chapter 2. Conceptualism 65
§ 1. Conceptualism vs. Nominalism 71
§ 2. Constructive Conceptualism 73
§ 3. Substitutivity and Definability in Constructive Conceptualism 79
§ 4. Identity in Nominalism vs. Identity in Constructive Conceptualism 82
§ 5. An External Semantics for Constructive Conceptualism 85
§ 6. Ramified Constructive Conceptualism 88
§ 7. Holistic Conceptualism 93
§ 8. An External Semantics for Holistic Conceptualism 95
§ 9. Conceptualism and the Logical Modalities 97
Notes to Chapter 299
Chapter 3. Realism 105
§ 1. Logical Realism vs. Holistic Conceptualism 108
§ 2. The Essential Incompleteness of Logical Realism 110
§ 3. Natural Realism and Conceptualism 113
§ 4. On the Logic of Natural Realism 115
§ 5. Natural Realism and Modal Logic 118
§ 6. An External Semantics for Modal Natural Realism 120
§ 7. A Completeness Theorem for Modal Natural Realism 124
§ 8. Modal Logical Realism 134
§ 9. Possibilism and Actualism in Modal Logical Realism 137
§ 10. Logical Realism and Essentialism 143
§ 11. Possibilism and Actualism in Holistic Conceptualism 150
Notes to Chapter 3 161
Chapter 4. On The Logic of Nominalized Predicates and Its Philosophical Interpretations 165
§ 1.Some Philosophical Views of Nominalized Predicates 166
§ 2. Terminology 168
§ 3. A Minimal Logic for Nominalized Predicates 170
§ 4. Russell's Paradox of Predication 173
§ 5. Identity as Syncategorematic 178
§ 6. The consistency of T* 182
§ 7. The Theories of Homogeneous, Heterogeneous and Cumulative Simple Types as Second Order Logics 188
§ 8. The Consistency of HST* Relative to Monadic HST* 193
§ 9. On the Relative Consistency of Monadic HST* 199
§ 10. On the Consistency of the Unrestricted Comprehension Principle (CP*) 205
Notes to Chapter 4 212
Chapter 5. Complex Predicates and The Lambda - Operator 215
§ 1. A Generalized Logic Syntax 215
§ 2. The Problem of Complex Predicates 218
§ 3. The Minimal Logic for Nominalized Complex Predicates 220
§ 4. Conceptual Platonic Realism and Other Extensions of λM*(*) 225
§ 5. The Theses of Extensionality and Intensionality with Nominalized Complex Predicates 232
§ 6. Modal Logic and Nominalized Complex Predicates 234
§ 7. The Principle of Rigidity Revisited 239
Notes to Chapter 5 241
Chapter 6. Two Fregean Semantics For Nominalized Complex Predicates 243
§ 1. Fregean Frames and Intensional Models 244
§ 2. A Generalized Completeness Theorem for Extensions of □M* + (□Extλ*) 248
§ 3. The Relative Consistency of □λHST* + (□Ext*) and □λT* + (□Ext*) 254
§ 4. The Relative Consistency of HST*λ□ + (□Ext*) and T*λ□ + (□Ext*) 257
§ 5. An Alternative Fregean Semantics 259
Logical Studies in Early Analytic Philosophy , (XIV, 295 pages), Columbus, Ohio State University Press, 1987.
This book deals with the development of analytic philosophy in the first quarter of the 20th century, giving both historical analyses and logical reconstructions of the logical doctrines involved in Russell's theory of types, Frege's and Russell's forms of logicism, Wittgenstein's and Russell's forms of logical atomism, and Meinong's and Russell's (pre-1905) logics of nonexistence. The text serves as a useful propaedeutic to much of the research now going on in the study of logic and language.
TABLE OF CONTENTS
Preface XI
Introduction 1
§ 1. On the Origin and So-Called Demise of Analytic Philosophy 1
§ 2. The Development of the Theory of Logical Types in Early Analytic Philosophy 5
§ 3. Frege, Russell, and Logicism 8
§ 4. Russell, Meinong, and the Logic of Nonexistence 11
§ 5. Russell, Wittgenstein, and Logical Atomism 12
Chapter 1. The Development of the Theory of Logical Types and the Notion of a Logical Subject in Russell's Early Philosophy 19
§ 1. Logical Subjects and the Univocity of Being in the Principles of Mathematics 20
§ 2. The Class as Many versus the Class as One 21
§ 3. The Class as Many as a Plural Logical Subject 23
§ 4. Propositional Functions as Non-Entities 25
§ 5. Propositions as Single Logical Subjects 29
§ 6. The Substitutional Theory of Classes 33
§ 7. Propositions versus Statements in the Substitutional Theory 38
§ 8. The 1908 Theory of Logical Types 43
§ 9. Russell's 1910 Multiple Relations Theory of Judgment 48
§ 10. The Theory of Ramified Logical Types 52
§ 11. Concluding Remarks on Russell's 1925 Introduction to Principia Mathematica 56
Chapter 2. Frege, Russell, and Logicism: A Logical Reconstruction 64
§ 1. Logicism and the Predicative Nature of Concepts 65
§ 2. Predication versus Functionality 70
§ 3. Existential Posits and the Laws of Logic 72
§ 4. Wertverläufe as Concept-Correlates 76
§ 5.Frege's Double Correlation Thesis and His Basic Law V 79
§ 6. Russell and Frege on Nominalized Predicates 80
§ 7. Russell's Paradox Revisited 83
§ 8. Frege's Rejection of Schröder's Hierarchy of Individuals 89
§ 9. Frege's Double Correlation Thesis and the Theory of Simple Logical Types 92
§ 10. The Theory of Homogeneous Simple Types as a Second Order Logic 94
§ 11. Frege and the Principle of Extensionality 97
§ 12. Russell and the Principle of Rigidity 99
§ 13. Frege's Contemplation of the Abelardian View 102
§ 14. A Second Reconstruction of Frege's Logicism 105
§ 15. An Intensionalized Form of Frege's Logicism 108
§ 16. Russell's Logicism as Conceptual Platonism 111
Chapter 3. Meinong Reconstructed versus Early Russell Reconstructed 119
§ 1. Meinongian Objects versus Russellian Individuals 119
§ 2. Russellian versus Meinongian Definite Descriptions 122
§ 3. An Orthodox "Picture" of Meinongian Objects 129
§ 4. A Russellian "Picture" of the Nuclear/Extra-Nuclear Distinction 133
§ 5. Why Parsons's Plugging up of Relations is Unnecessary 141
§ 6. Properties and Relations as Individuals 143
§ 7. Real Fictional Objects Please Stand Up 147
Chapter 4. Frege's Double Correlation Thesis and Quine's Set Theories NF and ML 152
§ 1. NF and the Iterative Concept of Set 153
§ 2. The Theory of Simple Types and Frege's Double Correlation Thesis 157
§ 3. Frege's Logicism as a Second Order Predicate Logic with Nominalized Predicates 160
§ 4. The Theory of Homogeneous Simple Types as a Second Order Predicate Logic 165
§ 5. Quine's Thesis and the Similarity of NF with λHST* + (Ext*) + (Q*) 169
§ 6. On Taking Urelements Seriously 172
§ 7. An Alternative Modification of Frege's Double Correlation Thesis 176
§ 8. Ultimate Classes and the Similarity of ML with HST*λ + (Ext*) + (Q*) 181
§ 9. On Mathematical Induction and the Class of Fregean Natural Numbers 186
Chapter 5. Russell's Theory of Logical Types and the Atomistic Hierarchy of Sentences 193
§ 1. The 1910 versus the 1908 Theory of Logical Types 196
§ 2. Propositional Functions as Properties and Relations in Russell's 1910-13 Principia Mathematica Ontology 200
§ 3. Russell's 1910-13 Commitment to Abstract Facts 203
§ 4. Logical Atomism and the Doctrine of Logical Types 206
§ 5. Propositional Functions as Linguistic Conveniences 211
§ 6. Russell's Weakened Form of the Principle of Atomicity 217
Chapter 6. Logical Atomism and Modal Logic 222
§ 1. Atomic Situations and Complementation 224
§ 2. Elementary Propositions and Complementation 226
§ 3. Propositional Connectives as Punctuation Marks 227
§ 4. Semantic Ascent/Or Was This Trip Really Necessary? 228
§ 5. Zeigen versus Sagen 231
§ 6. The Propositional Modal Calculus S13 238
Chapter 7. Logical Atomism, Nominalism, and Modal Logic 244
§ 1. Negative Facts and Complementary Nexuses 247
§ 2. Nominalism's View of Logical Space 252
§ 3. An Abstract Semantics for Nominalist Logical Atomism 259
§ 4. The (Onto)logical Grammar of Nominalist Logical Atomism 262
§ 5. The Problem of Identity in Logical Atomism 267
§ 6. Logical Truth versus Logical Necessity 272
§ 7. The Incompleteness of Nominalist Logical Atomism 274
Index 285
Formal Ontology and Conceptual Realism , New York, Springer, 2007.
"Theories about the ontological structure of the world have generally been described in informal, intuitive terms, and the arguments for and against them, including their consistency and adequacy as explanatory frameworks, have generally been given in even more informal terms. The goal of formal ontology is to correct for these deficiencies. By formally reconstructing an intuitive, informal ontological scheme as a formal ontology we can better determine the consistency and adequacy of that scheme; and then by comparing different reconstructed schemes with one another we can better evaluate the arguments for and against them and come to a decision as to which system it is best to adopt.
This book is divided into two parts. The first part is on formal ontology and how different informal ontological systems can be formally developed and compared with one another. The main point is that a formal ontology connects logical categories -- especially the categories involved in predication -- with ontological categories.
The second part of this book is on the formal construction and defense of a particular formal ontology called conceptual realism, which is based on a unified account of general and singular reference in a conceptualist theory of predication. An intensional logic based on deactivated (nominalized) referential and predicable concepts is part of this ontology as well as an analysis of plural reference and predication in terms of a logic of classes as many. A natural realism and an Aristotelian essentialism based on a logic of natural kinds is also part of the framework, which is put forward here as the best formal ontology to adopt."
TABLE OF CONTENTS
Preface XI
Introduction XIII
I. Formal Ontology 1
1. Formal ontology and conceptual realism 3
2. Time, Being and Existence 25
3. Logical necessity and logical atomism 59
4. Formal theories of predication 81
5. Formal theories of predication part II 101
6. Intensional possible worlds 121
II. Conceptual Realism 137
7. The nexus of predication 139
8. Medieval logic and conceptual realism 169
9. On Geach against general reference 195
10. Lesniewski's Ontology 215
11. Plurals and the logic of classes as many 235
12. The logic of natural kinds 273
Afterword on Truth-Makers 295
Bibliography 297
Index 307
Modal logic. An introduction to its syntax and semantics , co-author Max A. Freund, New York, Oxford University Press, 2008.
"Modal logic is a systematic development of the logic of the various notions that are expressed in natural language by modal words and
phrases. In this text we will limit our study lo the logic of necessity and possibility, which we take to be logically dual to one another and therefore
definable in terms of one another.
These notions are represented in natural language by sentential adverbs -- that is, adverbs, such as 'necessarily' and 'possibly', or 'it is necessary that'
and 'it is possible that'. These adverbs modify whole sentences or sentential clauses with the result being a sentence or sentential clause. We do not assume
that there is but one notion of necessity (or, dually, of possibility). In fact, we maintain that there are potentially infinitely many different notions of
necessity and possibility., each of which can be expressed in natural language, and each of which has its own logic -- though some may have a logic equipollent
to one another. We shall attempt to explain this claim by formally developing the logic of a variety of modal notions."
TABLE OF CONTENTS
1. Introduction 1
2. The syntax of modal sentential calculi 15
3. Matrix semantics 45
4. Semantics for logical necessity 61
5. Semantics for S 5 71
6. Relational world systems 81
7. Quantified modal logic 119
8. The semantics of quantified modal logic 153
9. Second-order modal logic 183
10. Semantics of second-order modal logic 215
Afterword 253
Bibliography 257
Index 263
STUDIES ABOUT HIS WORK
N.B. the unpublished Ph. D. Thesis can be ordered to ProQuest Dissertation Express.
Last modified: Wednesday, March 10, 2010