CONTENTS

1 LOGIC IN REALITY (LIR) AS A FORMAL LOGIC.................................. 1 1.1 INITIAL AXIOMATIZATION: THE FUNDAMENTAL POSTULATE.. 1 1.2 THE REAL AND REALITY ....................................................................... 6

1.2.1 Levels of Reality ................................................................................... 7 1.2.1.1 The Ontological Approach ............................................................ 8 1.2.1.2 The Physical Science Approach .................................................... 8

1.2.2 Contradiction, Counteraction or “Countervalence”.............................. 9 1.2.3 The Senses of Reduction..................................................................... 10

1.3 LIR VERSUS STANDARD LOGICS: DEDUCTION.............................. 11 1.3.1 Bivalence: Logical Truth, Logical Constants and Logical Consequence ................................................................................................ 12 1.3.2 Semantics ............................................................................................ 16 1.3.3 First-Order Predicate Logic (FOL) ..................................................... 19

1.4 NON-CLASSICAL LOGICS ..................................................................... 20 1.4.1 Intuitionist, Paraconsistent and Paracomplete Logics ........................ 20

1.4.1.1 Intuitionist Logic and Paracompleteness..................................... 20 1.4.1.2 Paraconsistent Logic.................................................................... 21

1.4.2 Many-Valued and Fuzzy Logics ......................................................... 22 1.4.3 Modal Logic ........................................................................................ 24 1.4.4 Relevance and Natural Logics ............................................................ 26

1.4.4.1 Relevance (or Relevant) Logics .................................................. 26 1.4.4.2 Natural Logic............................................................................... 27

1.4.5 The Metalogic, Imaginary Logic and Empirical Logic of Vasiliyev.. 28 1.5 INDUCTIVE LOGIC AND ABDUCTIVE LOGIC: PROBABILITY ..... 30

1.5.1 Inference and Abductive Logic........................................................... 33 1.6 QUANTUM LOGIC................................................................................... 34

1.6.1 The Quantum Formalism of Aerts ...................................................... 35 1.7 THE FORMAL AXIOMATIZATION OF LIR ......................................... 36

2 LIR AS A FORMAL SYSTEM....................................................................... 41 2.1 THE NON-CLASSICAL CALCULUS OF LIR: IMPLICATION............ 41 2.2 TRUTH VALUES, CONTRADICTION AND REALITY VALUES ...... 43

2.2.1 Other Theories of Truth ...................................................................... 46

v

Foreword……...............………………………………………………………….. xi

Acknowledgments……………………………………………………………….. xv

INTRODUCTION...............................................................................................xvii 1. REALITY AND LOGIC .............................................................................xvii 2. THE OBJECTIVE AND PLAN OF “LOGIC IN REALITY”..................... xix

vi CONTENTS

2.2.2 Verificationism ................................................................................... 47 2.3 IMPLICATION BETWEEN THE LIMITS............................................... 49

2.3.1 The Transfinite.................................................................................... 50 2.3.2 Ortho-deductions................................................................................. 52

2.3.4 Operational Aspects of the LIR Calculus: Logical Necessity ............ 54 2.4 CONJUNCTION AND DISJUNCTION ................................................... 56

2.4.1 A Classification Table for Connectives .............................................. 58 2.4.2 The Calculus of Events and Relations ................................................ 60

3 LIR AS A FORMAL ONTOLOGY ............................................................... 63 3.1 REALISM AND FORMAL ONTOLOGIES............................................. 63 3.2 THE LIR ONTOLOGICAL PREDICATES: DUALITY.......................... 65 3.3 THE DOMAIN OF ENTITIES: LEVELS OF REALITY......................... 66

3.3.1 Complexity Versus Levels of Reality ................................................. 67 3.4 LIR AS AN INTERPRETED FORMAL SYSTEM .................................. 67 3.5 THREE CRITICAL CONCEPTS .............................................................. 68

3.5.1 Dynamisms.......................................................................................... 68 3.5.2 Processes ............................................................................................. 69 3.5.3 Properties ............................................................................................ 69

3.5.3.1 Intrinsic Versus Extrinsic Properties: Relations.......................... 72 3.6 SOME METALOGICAL CONSIDERATIONS ....................................... 73 3.7 THE LOGIC OF BEING............................................................................ 75

3.7.1 Abstract, Non-real, Non-existent and Non-spatio-temporal Objects.. 78

4 THE CATEGORIES OF LIR......................................................................... 81 4.1 THE DEFINITION AND FUNCTION OF ONTOLOGY ........................ 81

4.1.1 Formal and Material Categories.......................................................... 82 4.2 THE ESTABLISHMENT AND CONSTRUCTION OF CATEGORIES. 84 4.3 THE PHYSICS OF REALITY: THE FUNDAMENTAL DUALITIES ... 85 4.4 THE CATEGORY OF ENERGY .............................................................. 87

4.4.1 The Duality of Energy ........................................................................ 88 4.4.1.1 Intensity and Extensity ................................................................ 90 4.4.1.2 Identity and Diversity: Homogeneity and Heterogeneity ........... 92 4.4.1.3 Actuality and Potentiality............................................................ 93 4.4.1.4 Locality and Globality................................................................. 95 4.4.1.5 Energy Is Dual and Antagonistic ................................................ 96

4.4.2 The Fundamental Principle of LIR ..................................................... 97 4.5 THE CATEGORY AND SUB-CATEGORIES OF DYNAMIC OPPOSITION................................................................................................... 99

4.5.1 Non-separability................................................................................ 100 4.5.2 Is There a Mathematical Physics of LIR?......................................... 102

4.6 THE CATEGORY OF PROCESS: CHANGE ........................................ 104 4.6.1 Three Current Views of Process ....................................................... 104

2.3.3 Para-deductions................................................................................... 53

CONTENTS vii

4.7 THE CATEGORY OF T-STATES .......................................................... 106 4.7.1 The Duality of Quantum Spin........................................................... 108

4.8.1 Self and Other: Self-Reference ......................................................... 112 4.9 LIR AS A FORMAL ONTOLOGY: NEO AND THE CATEGORY-AXIOM FIT.................................................................................................... 113

4.9.1 A Check-List of Principal Dynamic Relationships........................... 117 4.10 THE INTERPRETATION OF LIR........................................................ 119

5 THE CORE THESIS OF LIR: STRUCTURE AND EXPLANATION ... 123 5.1 THE CORE THESIS OF LIR................................................................... 124 5.2 A TWO-LEVEL FRAMEWORK OF RELATIONAL ANALYSIS....... 126

5.2.1 Mereology ......................................................................................... 128 5.2.2 Inter- and Intra-theoretic Relationships ............................................ 129

5.3 ONTOLOGY AND METAPHYSICS IN PARALLEL........................... 132 5.4 THE STRUCTURE OF REALITY IN LIR ............................................. 135

5.4.1 The Categorial Structure of Reality in LIR....................................... 136 5.4.1.1 Morphisms and Functors ........................................................... 136

5.4.2 The Structure of the Domains of Application: Set Theory ............... 140 5.4.3 The Metaphysical Structure of Reality in LIR.................................. 142 5.4.4 Figure Versus Ground: Gestalt Theory............................................. 144 5.4.5 Form Versus Matter: Catastrophe Theory ........................................ 145

5.5 WHAT IS AN EXPLANATION?............................................................ 150 5.5.1 Two General Failures of Explanation ............................................... 150

5.5.1.1 ‘Both-at-Once’........................................................................... 150 5.5.1.2 Spontaneity ................................................................................ 151

5.5.2 The LIR View of Explanation........................................................... 153 5.5.3 Explanation and Metaphysics ........................................................... 155

5.6 THE ANALYTIC/SYNTHETIC DISTINCTION IN LIR....................... 156 5.6.1 The Inferential Role Description....................................................... 158 5.6.2 The Syntactic – Semantic Distinction – and Conjunction ................ 160

6 LIR, METAPHYSICS AND PHILOSOPHY .............................................. 163 6.1 INTRODUCTION: CAUSE AND DETERMINISM .............................. 163 6.2 CAUSALITY IN LIR............................................................................... 164

6.2.1 The Metaphysics of Causation.......................................................... 167 6.2.2 Non-contradictory Causalities in Science and Philosophy ............... 170 6.2.3 Finality .............................................................................................. 171 6.2.4 Dispositions and Powers ................................................................... 173 6.2.5 Probabilistic Causation ..................................................................... 175 6.2.6 Possibility, Potentiality and Probability............................................ 178 6.2.7 Actualism and Possibilism ................................................................ 179

4.8 THE CATEGORIES OF SUBJECT, OBJECT AND SUBJECT-OBJECT........................................................................109

5.4.1.2 Ontological Links ...................................................................... 139

viii CONTENTS

6.2.8.1 Intervention................................................................................ 182 6.2.8.2 Some Remarks on Self-Organization........................................ 183

6.3 CONTINUITY AND DISCONTINUITY................................................ 185 6.3.1 The Continuum Hypothesis .............................................................. 185 6.3.2 The Problem of Differential Calculus............................................... 186 6.3.3 Paracontinuity and Paradiscontinuity ............................................... 188 6.3.4 Smooth Infinitesimal Analysis (SIA) ............................................... 189

6.4 STATISM AND DYNAMISM ................................................................ 192 6.5 DETERMINISM AND INDETERMINISM............................................ 194

6.5.1 A Philosophical Argument................................................................ 195 6.5.2 Contingency and Necessity: Bohmian Determinism........................ 196

6.6 REALISM AND EXPERIENCE ............................................................. 197 6.6.1 Generic Realism................................................................................ 198 6.6.2 Scientific Realism ............................................................................. 199 6.6.3 Structural Realism............................................................................. 201 6.6.4 The LIR Extension: Scientific Structural Realism (SSR)................. 202 6.6.5 Semantic Realism.............................................................................. 206

6.7 THE PRINCIPLE OF DYNAMIC OPPOSITION AND LAWS OF NATURE........................................................................................................ 208

6.7.1 Dynamic Opposition: Constitutive and Regulative .......................... 209 6.7.2 Dynamic Opposition as a Scientific Principle: Linking Physics and Statistics ..................................................................................................... 210 6.7.3 Dynamic Opposition as a Law of Nature.......................................... 211 6.7.4 Metaphysical Positions ..................................................................... 212 6.7.5 Laws of Nature in Use ...................................................................... 213

6.8 FRIEDRICH HEGEL: IDEALISM AND/OR CONTRADICTION? ..... 216 6.9 THE LIR APPROACH TO PHILOSOPHY ............................................ 219

6.9.1 The Philosophy of Mind ................................................................... 224 6.9.2 The Naturalization of Phenomenology ............................................. 225

7.1 TIME AND SPACE: PRELIMINARY REMARKS ............................... 229 7.2 THE LIR THEORY OF SPACE-TIME................................................... 231

7.2.1 The LIR Categories of Time ............................................................. 231 7.2.2 The LIR Categories of Space............................................................ 233 7.2.3 Simultaneity and Succession............................................................. 234

7.2.3.1 Synchronic and Diachronic Logic............................................. 236 7.3 SOME ALTERNATIVE VIEWS OF TIME............................................ 237

7.3.1 Time in Philosophy ........................................................................... 237 7.3.2 Time in Phenomenology ................................................................... 238

7.4 BEING AND BECOMING IN MODERN PHYSICS............................. 239 7.4.1 Tensers Versus Detensers ................................................................. 240 7.4.2 Being and Becoming Revisited......................................................... 241

7 LIR AND PHYSICAL SCIENCE: TIME, SPACE AND COSMOLOGY 229

6.2.8 Potentiality and Micro-causation: Manipulability and Intervention.. 180

CONTENTS ix

7.5.1 Two Complementary Logics of Complementarity ........................... 247 7.5.2 Relational Quantum Mechanics ........................................................ 252 7.5.3 Quantum Physics and Consciousness ............................................... 253

7.6 TOWARD A LOGICAL COSMOLOGY................................................ 255 7.6.1 Space-Time in General Relativity..................................................... 256 7.6.2 The Dual Role of the Metric Field .................................................... 257

7.6.2.1 Simultaneity: A Comparison of Dynamics ............................... 260 7.6.3 Structural Realism and the Metaphysics of Relations ...................... 262 7.6.4 A Cyclic Model of the Universe ....................................................... 264

8 EMERGENCE, LIVING SYSTEMS AND CLOSURE ............................. 269 8.1 INTRODUCTION .................................................................................... 269

8.1.1 Emergence......................................................................................... 269 8.1.2 Opposition in the Physics and Chemistry of Living Systems........... 271

8.2 THE LIR APPROACH TO EMERGENCE............................................. 273 8.2.1 The Category of Emergence ............................................................. 273 8.2.2 Emergence and Dualism Under Attack............................................. 274 8.2.3 A Peircean Perspective...................................................................... 275

8.2.3.1 Virtual Logic and Organic Logic .............................................. 276 8.3 EMERGENCE IN PERSPECTIVE.......................................................... 277

8.3.1 Physical Emergence .......................................................................... 282 8.3.2 Normative Emergence....................................................................... 282 8.3.3 Catastrophe Theory and Emergence ................................................. 283

8.4 EXPLAINING EMERGENCE................................................................. 284 8.4.1 Emergence Is a Dogmatic Concept? ................................................. 285 8.4.2 The Emmeche Synthesis ................................................................... 286 8.4.3 Biosemiotics...................................................................................... 289 8.4.4 Quantum Morphogenesis .................................................................. 290 8.3.5 Half of the Story................................................................................ 291

8.5 CLOSURE IN LIVING SYSTEMS......................................................... 292 8.5.1 Defining Closure ............................................................................... 292 8.5.2 The Category of Closure ................................................................... 293 8.5.3 Opening Up Closure.......................................................................... 294

8.6 DOWNWARD CAUSATION ................................................................. 295 8.6.1 The Category of Downward Causation............................................. 295 8.6.2 Synchronic Reflexive Downward Causation .................................... 296

8.7 EVOLUTION AND THE ORIGIN OF LIFE .......................................... 299 8.7.1 The Absence of Logic in Biological Science.................................... 300 8.7.2 Natural Selection............................................................................... 301 8.7.3 The Epistemic Cut............................................................................. 302 8.7.4 Semantic Closure: The Matter-Symbol Problem.............................. 305 8.7.5 Code Duality: Bridging the Epistemic Cut ....................................... 306 8.7.6 A Systems Picture ............................................................................. 308

7.5 QUANTUM MECHANICS ..................................................................... 246

x CONTENTS

8.7.7.1 Exclusion-Driven Potentialities................................................. 312 8.8 THE THERMODYNAMIC AND CYBERNETIC STANDPOINTS..... 313

8.8.1 Thermodynamics and Complexity.................................................... 314 8.8.2 Cybernetics and Information............................................................. 315 8.8.3 Teleonomy ........................................................................................ 318

CONCLUSION: NEW DIRECTIONS AND A NEW SKEPTICISM.......... 323 1. NEW DIRECTIONS .................................................................................. 325 2. A NEW SKEPTICISM............................................................................... 327

1. THE LOGIC OF FROZEN DIALECTICS ................................................ 331 2. THE AXIOM OF CHOICE........................................................................ 334

1. THE ONTOLOGICAL BASIS OF SYSTEMS IN REALITY.................. 337 1.1 The Relation of Antagonism................................................................ 337 1.2 The Relation of Contradiction ............................................................. 338 1.3 The Principle of Antagonism Applied to Energy ................................ 339

2. CYBERNETICS AND SYSTEMS THEORY........................................... 340 2.1 Feedback .............................................................................................. 340 2.2 General Systems Theory ...................................................................... 341 2.3 The Neuchâtel Model........................................................................... 343 2.4 Systems Science and Complex Systems.............................................. 345

Index .................................................................................................................... 347

8.7.7 Evolution as Context-Driven Actualization of Potential .................. 310

APPENDIX 2 THE SYSTEMS VIEWPOINT ........................................... 337

APPENDIX 1 CLASSES AND SETS: THE AXIOM OF CHOICE........ 331

xi

FOREWORD

This book is both difficult and rewarding, affording a new perspective on logic and reality, basically seen in terms of change and stability, being and becoming. Most importantly it exemplifies a mode of doing philosophy of science that seems a welcome departure from the traditional focus on purely analytic arguments. The author approaches ontology, metaphysics, and logic as having offered a number of ways of constructing the description of reality, and aims at deepening their relationships in a new way. Going beyond the mere abstract and formal aspects of logical analysis, he offers a new architecture of logic that sees it as applied not only to the “reasoning processes” belonging to the first disciplinary group – ontology – but also directly concerned with enti-ties, events, and phenomena studied by the second one – metaphysics. It is the task of the book to elaborate such a constructive logic, both by offering a logi-cal view of the structure of the reality in general and by proffering a wealth of models able to encompass its implications for science.

In turning from the merely formal to the constructive account of logic Brenner overcomes the limitation of logic to linguistic concepts so that it can be not only a logic “of” reality but also “in” that reality which is constitutively characterized by a number of fundamental dualities (observer and observed, self and not-self, internal and external, etc.): indeed the analysis of “contradic-tion” plays a central role in the book. In this perspective logic is also rooted in physical reality, as conceived by modern physics: “Accordingly, my logic is not only a logic about theories of reality as conceptualized in philosophy and metaphysics. It is also a scientific or quasi-scientific concept, to the extent that, like symmetry for example, its principles are a reflection of the underly-ing physical structure of the universe that is independent of human experience that nevertheless derives from it’’.

Brenner has a great deal to say about aspects of this logic of/in reality that relate it to standard logics as well as other disciplines: i) the centrality of axiomatics and the importance of building open and uninterpreted formal systems potentially able to account for real processes entities, properties, and dynamisms (chapters 1 and 2): ii) the role of a rigorous interpreted formal ontology as a “process ontology” (chapter 3), and iii) its relationship to the quantum-field equivalent of energy (chapter 4). Chapters 6, 7, and 8 recon-sider, in term of both “logic in reality” and “new energy ontology”, the problems of Gestalt and catastrophe theory, metaphysics (also the problem of naturaliza-tion of phenomenology is fruitfully taken into account), and physics, where

xii FOREWORD

rare in the current research in logic and epistemology: logic is grounded in many ways, but most essentially, for Brenner, it derives its rational basis from its participation in the most important achievements of current culture and science. It is this insight which drives the remainder of the text, which includes numer-ous examples of successful logical modelling; and within the context of this successful practice, the author expands the traditional logical power of logic in a number of significant ways. He spends considerable time on the analysis of many non-classical logics, abduction, quantum and relativistic physics, Hege-lian philosophy, non-standard analysis and traditionally debated philosophical problems such as the analytic/synthetic distinction, determinism/indeterminism, and the concepts of “causality” and of “scientific explanation”.

Brenner’s text is extremely complex; it is full of information about the widest range of issues relevant to his concerns. He has complex and critical presentations of various areas of current fields of philosophical, cognitive, and scientific knowledge. This presents one of the major problems for the reader. Since his argument is based on numerous examples of partially successful cognitive strategies and sees their partial success as a justification for his pro-ject, the book overwhelms the reader with references. Of course, if the reader is appropriately grounded in the vast literature that Brenner affords in a bibli-ography, the reference to particulars can be very deeply informative. The rest of us must rely on the sheer weight of putative examples, still extremely in-formative and epistemologically rewarding. Brenner offers such an account, and it is the connection between the account and the examples that ultimately gives his work its power in depicting a new perspective on “reality”. His con-cern with the actual practice of logic helps him to see the roots of reality in the manipulation of the wide interdisciplinary interplay I have indicated above. Brenner offers a truly novel contribution to the problem of reality by looking broadly to see its relational aspects within the entire context of logic, set the-ory, metaphysics, ontology, physics and biology, rather than narrowly as in the traditional logical and analytic approaches.

This excellent and demanding book opens up the door to a deeply in-formed attitude in logic and epistemology, requiring of philosophers that they do more than analyze concepts, demanding that they become familiar with the

that classical identity cannot account for in the case of quantum entities. But more important for the reader is the structure of his overall argumentation strategy. Implicit in Brenner’s work is an interdisciplinary commitment very

a new relation between logic and space-time is suggested. To take another example, a concept of “relative identity” is presented to convey those features

Lorenzo Magnani Department of Philosophy, University of Pavia, Pavia, Italy Department of Philosophy, Sun Yat-sen University, Guangzhou, P.R.China February 2008

xiii FOREWORD

plines. This is not to substitute description for normativity, but rather recon-ceptualizes what the grounds of normativity are. The author has provided a fine contribution to the renaissance of logical research aiming at directly elucidating the ancient philosophical concept of “reality”.

wealth of actual knowledge gathering practices available in the special disci-

ACKNOWLEDGMENTS

This book is the result of my improbable encounter with the theoretical physicist Basarab Nicolescu in 1998 for it is he who introduced me to the philoso-phical logic of Stéphane Lupasco. I am most indebted to Nicolescu and the historian of art and the media René Berger, co-founders with Lupasco of the International Center for Transdisciplinary Research, Paris, for their personal recollections of Lupasco, as well as access to otherwise unavailable documents. The next stage in the process was the encouragement I received to develop my interpretations of Lupasco into a book of my own. At this initial stage, I received much support and answers to my sometimes jejune questions from the ontologist Roberto Poli and the logicians Jean-Yves Béziau and Graham Priest, which has continued to this day. Since the inception of the five-year gestation period of this book, many of my most important exchanges have been with John Symons, Professor of Philosophy at the University of Texas, El Paso. His pertinent critique of an earlier version has been an essential contribution to its current structure and emphasis. That gestation, however, proved more difficult than expected, and is to Johanna Seibt, Professor of Philosophy at the University of Aarhus, that I am most grateful for the unselfish collaboration on this project that lasted almost two years. During the completion of the manuscript, I benefited in particular from many exchanges with logicians and philosophers of the Brazilian school – Itala D’Ottaviano, Walter Carnielli, Décio Krause and Otávio Bueno – which were very useful in the formalization of my system.

More informally, I wish to acknowledge the support and encouragement of my family and friends, including my professor of chemistry at the University of Wisconsin, Eugene van Tamelen. He is in a unique position to appreciate the con-ceptual distance between my thesis for him and the core thesis of this book.

I wish also to thank Jean-Paul Bertrand, former Editor of Éditions du Rocher, Paris, for permission to reproduce the formulas of Lupasco’s calculus from those editions of Lupasco’s works, and Décio Krause for permission to re-produce citations from Niels Bohr’s work published in one of his papers. Finally, readers will note that I have made extensive use of the articles in SYNTHESE and entries in the Stanford Encyclopedia of Philosophy, and I would like express my appreciation to the editors of these authoritative ‘synthetic’ sources.

xv

INTRODUCTION

1. REALITY AND LOGIC

scientific, philosophical, artistic and religious. These have been developed in an attempt to explain and understand the phenomena of existence in all their diversity and complexity. Innumerable approaches, more or less formal, have been devel-oped to try to organize and make sense out of the processes, properties, relations, structures, actions, thoughts, interactions, in a word the physical and mental enti-ties that constitute reality in every day human existence and experience.It is possi-ble to look at the subjects and objects of knowledge and the methods for their study as lying on a scale between reality itself and the most abstract representations that are made of it, language and mathematics. All models of reality, as models, require a degree of abstraction. If one excludes, for the time being, non-linguistic representations of reality such as art, all knowledge is constituted by sets of state-ments of some kind. Starting from the side of language, farthest removed from reality, the statements consist of propositions about abstract, ideal entities; de-

scriptions of reality; and finally, descriptions of reality based on experiment, the domain of science. Increases in knowledge related to statements or beliefs about reality are involved in linguistic processes such as making arguments, inferences and judgments. Science involves increases in knowledge about reality itself, the states of real physical and non-physical systems.

The purpose of this book is to reexamine the relationships between the different disciplines concerned with the description of reality: (1) ontology, the study of being, what there is, as a systematic approach to the construction of mod-els of reality; (2) metaphysics, which is concerned with the fundamental structure of reality as a whole1; and (3) logic. Both ontology and metaphysics apply to all knowledge and reasoning.

Logic, however, is considered to apply in a formal manner to the first group of reasoning processes but not to the second, that is, as being limited essen-tially to the linguistic and mathematical domains, not those of entities, events or phenomena studied by metaphysics and science. Despite the large number of im-portant practical applications of standard logics, for example, in computer science 1 “Metaphysics is a universal discipline, in which everything, including the status and validity of ontology and metaphysics itself, is a proper subject of study” (Lowe 2002).

scriptions or models of reasoning processes; philosophical or metaphysical de-

This is a book about a theory of reality – about a theory of change and stability, being and becoming. Humans are unique in having the capacity of experi-encing reality and representing and recording it symbolically, and the recorded forms of symbolic representations constitute human knowledge organized into disciplines,

xvii

and artificial intelligence, the underlying body of logic has not undergone major modifications in the direction of a logical view of the structure of reality in general, and its implications for science. The reasons for this are primarily historical: logic has been thought of as the study of reasoning and the construction of adequate, formal descriptions of the modes of reasoning, e.g., deduction, induction and ab-duction, and the logical operations, e.g. implication, that characterize it. Modern logic was developed with the objective of modeling mathematical reasoning in as general a way as possible, without limitations as to what reality might be like. Due to their complexity, diversity and appearance of random or, at the very least, of chaotic behavior, phenomena as such have been generally considered outside the purview of logic.

In contrast to the abstractions that have constituted logic, real phenomena refer directly to human observation and human ratiocination, and the introduction of logical considerations in the corresponding disciplines, phenomenology and epistemology, has proven extremely complicated. The gap between reality – real entities – and propositions about reality remains the source of a large number of metaphysical problems. Talking about a logic of/in reality might thus be consid-ered either a contradiction or a vague metaphor, referring, but only informally, to some of the regularities in nature and science that one observes.

There is, however, no theoretical reason why this should be so. One the-sis of this book is that the limitation of logic to linguistic concepts, which do not and in fact cannot apply to real entities, should be removed. The discussion can also center, and perhaps should center, on the non-abstract and often conflictual changes characterizing real entities or phenomena as objects of analysis, while re-taining the advantages of the formal structure, rigor and generality of the logical approach. An improved reflection of reality is, in a nutshell, what I claim my pro-posed logic of/in reality (LIR) may bring to the table.

I take a view of reality that is neither idealist nor reductionist-materialist. I will identify structures and principles in it that are not designed to analyze or in-sure the truth-value or the pattern of inference of a set of propositions but which have, nevertheless, equivalent explanatory power and categorial authority. For ex-ample, reality seems to be characterized and/or constituted by a number of funda-mental dualities: there is the reality that is and is not accessible to our senses; the dualities of observer and observed, self and non-self, internal and external and so on. The principles of the theory that I propose, that I consider logical principles, nevertheless refer, as directly as possible, to such dualities and the relations be-tween them as providing a coherent picture of reality, human experience and the mechanisms of change. I consider that the system of thought or discipline that best captures these principles is still a logic, a logic, however, that has its origin in the characteristics of physical reality, as conceived by modern physics, although it is obviously dependent on human mental and linguistic processes to describe those characteristics.

Accordingly, my logic is not only a logic about theories of reality as con-ceptualized in philosophy and metaphysics. It is also a scientific or quasi-scientific concept, to the extent that, like symmetry for example, its principles are a reflection

xviii INTRODUCTION

of the underlying physical structure of the universe that is independent of human

also logical concepts should be compatible with, those of fundamental physics. Thus, a logico-metaphysical concept that meets this criterion also implies a change in the way one looks at the role which logic has had of organizing our reasoning. One must start by being sensitive to the biases that have been built into the analy-sis of reasoning due to the ubiquity of the essentially classical principles of stan-dard predicate, intuitionist and paraconsistent logic.

2. THE OBJECTIVE AND PLAN OF “LOGIC IN REALITY”

The title of this book, “Logic in Reality” (LIR) is thus intended to imply both (1) that the principle of change according to which reality operates is a logi-cal principle embedded in it, the logic in reality; and (2) that what logic really isinvolves this same real physical-metaphysical but also logical principle. The first objective of this book is, therefore, is to construct such a logic of and in reality. Once this logic and its related ontology are in hand, I will show that they can pro-vide some important insights into aspects of reality that have remained at the level of intuition. In particular I will be in a position to define the basis and structure of a necessary relation between reality and appearance. I will also show that many positions in philosophy and science have been blocked by classical logical de-scriptions of the domain of these theories and the consequent classical ontologies, that is, the categorizations that are made of the domains.

I will begin Chapter 1 with an informal axiomatic characterization of LIR and some initial indications as to why these axioms have been selected. The non-classical calculus to be used will be introduced. I will then briefly review the structure and major components of standard logics, showing which components can and cannot apply to LIR, or the significant reinterpretations of them that are required. The major groups will appear in the following sequence: deductive; paraconsistent; quantum; inductive – probabilistic.2 The chapter concludes with a more formal axiomatization based on a model of probabilistic logic. The differ-ences between my logical system qua system with that of both classical and non-classical logics will quickly become apparent, but the parallels that remain will be part of the justification for the consideration of LIR as a logic.

In Chapter 2, I discuss LIR as an uninterpreted formal system, including details of the non-classical calculus applied to the logical operations of implication, 2 The sequence reflects the place of the logics on the ‘line’ mentioned in paragraph 1: each logic has aspects that bring it, somewhat, closer to reality. LIR can thus be seen as continuing this process.

2. THE OBJECTIVE AND PLAN OF “LOGIC IN REALITY”

the physical structure of the world, I mean that all metaphysical, philosophical butexperience that nevertheless derives from it. Throughout this book, when I talk about

xix

conjunction and disjunction. In this theory, standard truth-values are replaced by logical values that reflect the state variables of the phenomenon under study in a novel way.

Chapter 3 develops LIR as a formal ontology and an interpreted formal system, with definitions of the critical concepts of dynamics, process and property. Ontological predicates are introduced to construct LIR as a process ontology, or process-ontological model of reality. An LIR approach to the question of being in relation to reality is compared with recent work grounding being in classical logic, and the concept of LIR as a metalogic is discussed.

Chapter 4 sets out the critical foundational notion of LIR, namely, that its fundamental postulate is based on the existence of energy, or better, its quantum field-theoretic equivalent, as the unique material category. The properties and pro-cesses associated with it as well as its most important formal categories are deve-loped, recognizing that the domain of entities involved is that of all real, physical phenomena, as well as of non-real (imaginary or fictional) entities qua their crea-tion. The categorial approach insures that LIR, as an ontological theory, has the necessary correlations to language and inference. The fit between the axioms of LIR and the New Energy Ontology (NEO) I define accordingly concludes the first

that sets forth the core thesis of LIR and provides views of key philosophical tools necessary for its development. The task of providing adequate structure to my categorization of reality is undertaken and compared with concepts from Gestaltand catastrophe theory. The ontological recategorization that LIR makes possible leads to reexamination of some issues in ontology itself. A basis for the links be-tween LIR as metaphysics and LIR as ontology will be proposed.

Chapter 6 discusses the relation between the principles of LIR and meta-physics, and its application to the major philosophical issues of causality, deter-minism and realism in science. I will position LIR as a broad system, an axiomatic metaphysics, for talking about both philosophical theories and real-world proc-esses. The chapter concludes with a brief discussion of the application of LIR to issues in philosophy and the naturalization of phenomenology. Chapter 7 develops the relation between LIR and modern physics. I suggest that LIR can clarify issues of complementarity, structural realism and metaphysical relations at macroscopic as well as microscopic scales, and the correspondence of LIR to some current con-cepts of space-time and cosmology is proposed. These three chapters suggest a convergence of metaphysics and physics, for which LIR provides a logical bridge.

Chapter 8 shows how the fundamental principles of LIR can define emer-gence and be applied to emergent phenomena at the increasingly complex levels of life and evolution. The book concludes with some speculations about the poten-tial consequences of the applications of LIR in philosophy and science and the proposal of a more challenging role for this extended logic in the development of knowledge.

xx I

part of the book.

of philosophical and scientific domains. Chapter 5 is a transition chapter

NTRODUCTION

The second part uses LIR and NEO re-examine problems in a number

Based on the metaphysical arguments to be developed in this book, many fundamental questions and assumptions may require a degree of redefinition, and their origin in nature and their justification may be found elsewhere than is com-monly suggested. I have made an effort to avoid reasoning according to the stan-dard dichotomies, e.g., determinism vs. indeterminism. I thus ask the reader, even if he or she has strong views on specific issues (of which determinism is a good example), to take an attitude of openness and tolerance toward what may be unex-pected or unusual in my thesis. I say this from direct experience, since even the discussion of some form of contradiction or constitutive opposition as basic to na-ture often encounters resistance that goes far beyond dispassionate and reasoned debate. I undertake to do the same with regard to my inevitable critics. But it may be considered a strength (or weakness?) of my theory that it is one that explicates and integrates its own potential critique.

I will naturally be comparing LIR with existing theories, but my intention is not to prove that any particular theory is incorrect, except in the sense that its domain of application should be clearly limited to abstract systems. For theories, views, approaches, etc. that are closer to LIR in spirit, my objective will be to support their insights and intuitions and show how they might be improved or generalized.

I will close this Introduction with a few words about the logical and philosophical environment in which this book is appearing. In his Introduction to a recent compendium that assesses current philosophy and logic (van Benthem 2006), the logician van Benthem argued for a natural and respectable process of growth of logic, in line with that in other disciplines, and cautioned against arbi-trary replacement or competition. The articles (which date back to 2002), reflect this: none go far outside established paradigms of non-classical logics applied to aspects of truth, proof, category theory and complementarity in physics, among others. In philosophy on the other hand, three significant representatives of the Anglophone analytical tradition take a less conservative attitude. Mulligan et al. (2006) castigate analytical philosophy for its failure to accept the challenge of providing an adequate picture of reality. Continental philosophy is also criticized for its lack of rigor and subordination to political agendas, which makes its use of scientific concepts anecdotal. Ladyman and Ross (2007) and their colleagues are also critical of any metaphysics or philosophy that relies on intuitions or concepts that do not take into account the most recent advances in fundamental physics. In their “naturalization of metaphysics”, they propose a picture of the world that raises the scientific standard for any theory that purports to describe and/or explain aspects of reality.

The theory in this book takes these various attitudes into account. Ac-cordingly, much of Chapter 1 is devoted to showing the principled relation to standard non-classical logics of the extension of logic that Logic in Reality repre-sents. Attention is paid to indications within standard logics that such extensions might be envisaged. Thus, in making the novel moves of extending logic to real-ity, and in showing its linkage to metaphysics and science, I have tried to maintain

2. THE OBJECTIVE AND PLAN OF “LOGIC IN REALITY” xxi

a degree of formal justification that members of the analytical philosophy com-munity could accept, in accordance with the Mulligan et al. critique.

References

Ladyman, James and Don Ross. 2007. Every Thing Must Go. Metaphysics Naturalized. Oxford: Oxford University Press.

Lowe, E. J. 2002. A Survey of Metaphysics. Oxford: Oxford University Press. Mulligan, Kevin, Peter Simons and Barry Smith. 2006. What’s Wrong with Contemporary Phi-

losophy? Topoi 25: 63–67. Van Benthem, Johan. 2006. Introduction: Alternative Logics and Classic Concerns. In The Age

of Alternative Logics, eds. J. van Benthem, G. Heinemann, M. Rebuschi and H. Visser. Dordrecht, The Netherlands: Springer.

xxii INTRODUCTION