## Logic in RealityThis book is both dif?cult 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 en- 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 lo- 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. |

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### Contents

1 | |

12 THE REAL AND REALITY | 6 |

121 Levels of Reality | 7 |

1211 The Ontological Approach | 8 |

122 Contradiction Counteraction or Countervalence | 9 |

123 The Senses of Reduction | 10 |

DEDUCTION | 11 |

Logical Truth Logical Constants and Logical Consequence | 12 |

627 Actualism and Possibilism | 179 |

Manipulability and Intervention | 180 |

6281 Intervention | 182 |

6282 Some Remarks on SelfOrganization | 183 |

63 CONTINUITY AND DISCONTINUITY | 185 |

632 The Problem of Differential Calculus | 186 |

633 Paracontinuity and Paradiscontinuity | 188 |

634 Smooth Infinitesimal Analysis SIA | 189 |

132 Semantics | 16 |

133 FirstOrder Predicate Logic FOL | 19 |

14 NONCLASSICAL LOGICS | 20 |

1412 Paraconsistent Logic | 21 |

142 ManyValued and Fuzzy Logics | 22 |

143 Modal Logic | 24 |

144 Relevance and Natural Logics | 26 |

1442 Natural Logic | 27 |

145 The Metalogic Imaginary Logic and Empirical Logic of Vasiliyev | 28 |

PROBABILITY | 30 |

151 Inference and Abductive Logic | 33 |

16 QUANTUM LOGIC | 34 |

161 The Quantum Formalism of Aerts | 35 |

17 THE FORMAL AXIOMATIZATION OF LIR | 36 |

References | 39 |

LIR AS A FORMAL SYSTEM | 41 |

22 TRUTH VALUES CONTRADICTION AND REALITY VALUES | 43 |

221 Other Theories of Truth | 46 |

222 Verificationism | 47 |

23 IMPLICATION BETWEEN THE LIMITS | 49 |

231 The Transfinite | 50 |

232 Orthodeductions | 52 |

233 ParaDeductions | 53 |

Logical Necessity | 54 |

24 CONJUNCTION AND DISJUNCTION | 56 |

241 A Classification Table for Connectives | 58 |

242 The Calculus of Events and Relations | 60 |

LIR AS A FORMAL ONTOLOGY | 63 |

DUALITY | 65 |

LEVELS OF REALITY | 66 |

331 Complexity Versus Levels of Reality | 67 |

35 THREE CRITICAL CONCEPTS | 68 |

352 Processes | 69 |

Relations | 72 |

36 SOME METALOGICAL CONSIDERATIONS | 73 |

37 THE LOGIC OF BEING | 75 |

371 Abstract Nonreal Nonexistent and Nonspatiotemporal Objects | 78 |

THE CATEGORIES OF LIR | 81 |

411 Formal and Material Categories | 82 |

42 THE ESTABLISHMENT AND CONSTRUCTION OF CATEGORIES | 84 |

THE FUNDAMENTAL DUALITIES | 85 |

44 THE CATEGORY OF ENERGY | 87 |

441 The Duality of Energy | 88 |

4411 Intensity and Extensity | 90 |

Homogeneity and Heterogeneity | 92 |

4413 Actuality and Potentiality | 93 |

4414 Locality and Globality | 95 |

4415 Energy Is Dual and Antagonistic | 96 |

442 The Fundamental Principle ofLIR | 97 |

45 THE CATEGORY AND SUBCATEGORIES OF DYNAMIC OPPOSITION | 99 |

451 Nonseparability | 100 |

452 Is There a Mathematical Physics of LIR? | 102 |

CHANGE | 104 |

47 THE CATEGORY OF TSTATES | 106 |

471 The Duality of Quantum Spin | 108 |

48 THE CATEGORIES OF SUBJECT OBJECT AND SUBJECTOBJECT | 109 |

SelfReference | 112 |

NEO AND THE CATEGORYAXIOM FIT | 113 |

491 A CheckList of Principal Dynamic Relationships | 117 |

410 THE INTERPRETATION OF LIR | 119 |

THE CORE THESIS OF LIR STRUCTURE AND EXPLANATION | 123 |

51 THE CORE THESIS OF LIR | 124 |

52 A TWOLEVEL FRAMEWORK OF RELATIONAL ANALYSIS | 126 |

521 Mereology | 128 |

522 Inter and Intratheoretic Relationships | 129 |

53 ONTOLOGY AND METAPHYSICS IN PARALLEL | 132 |

54 THE STRUCTURE OF REALITY IN LIR | 135 |

541 The Categorial Structure of Reality in LIR | 136 |

5412 Ontological Links | 139 |

Set Theory | 140 |

543 The Metaphysical Structure of Reality in LIR | 142 |

Gestalt Theory | 144 |

Catastrophe Theory | 145 |

55 WHAT IS AN EXPLANATION? | 150 |

5512 Spontaneity | 151 |

552 The LIR View of Explanation | 153 |

553 Explanation and Metaphysics | 155 |

56 THE ANALYTICSYNTHETIC DISTINCTION IN LIR | 156 |

561 The Inferential Role Description | 158 |

562 The Syntactic Semantic Distinction and Conjunction | 160 |

LIR METAPHYSICS AND PHILOSOPHY | 163 |

62 CAUSALITY IN LIR | 164 |

621 The Metaphysics of Causation | 167 |

622 Noncontradictory Causalities in Science and Philosophy | 170 |

623 Finality | 171 |

624 Dispositions and Powers | 173 |

625 Probabilistic Causation | 175 |

626 Possibility Potentiality and Probability | 178 |

64 STATISM AND DYNAMISM | 192 |

65 DETERMINISM AND INDETERMINISM | 194 |

651 A Philosophical Argument | 195 |

Bohmian Determinism | 196 |

66 REALISM AND EXPERIENCE | 197 |

661 Generic Realism | 198 |

662 Scientific Realism | 199 |

663 Structural Realism | 201 |

Scientific Structural Realism SSR | 202 |

665 Semantic Realism | 206 |

67 THE PRINCIPLE OF DYNAMIC OPPOSITION AND LAWS OF NATURE | 208 |

Constitutive and Regulative | 209 |

Linking Physics and Statistics | 210 |

673 Dynamic Opposition as a Law of Nature | 211 |

674 Metaphysical Positions | 212 |

675 Laws of Nature in Use | 213 |

IDEALISM ANDOR CONTRADICTION? | 216 |

69 THE LIR APPROACH TO PHILOSOPHY | 219 |

691 The Philosophy of Mind | 224 |

692 The Naturalization of Phenomenology | 225 |

LIR AND PHYSICAL SCIENCE TIME SPACE AND COSMOLOGY | 229 |

72 THE LIR THEORY OF SPACETIME | 231 |

722 The LIR Categories of Space | 233 |

723 Simultaneity and Succession | 234 |

7231 Synchronic and Diachronic Logic | 236 |

73 SOME ALTERNATIVE VIEWS OF TIME | 237 |

732 Time in Phenomenology | 238 |

74 BEING AND BECOMING IN MODERN PHYSICS | 239 |

741 Tensers Versus Detensers | 240 |

742 Being and Becoming Revisited | 241 |

75 QUANTUM MECHANICS | 246 |

751 Two Complementary Logics of Complementarity | 247 |

752 Relational Quantum Mechanics | 252 |

753 Quantum Physics and Consciousness | 253 |

76 TOWARD A LOGICAL COSMOLOGY | 255 |

761 SpaceTime in General Relativity | 256 |

762 The Dual Role of the Metric Field | 257 |

A Comparison of Dynamics | 260 |

763 Structural Realism and the Metaphysics of Relations | 262 |

764 A Cyclic Model of the Universe | 264 |

EMERGENCE LIVING SYSTEMS AND CLOSURE | 269 |

812 Opposition in the Physics and Chemistry of Living Systems | 271 |

82 THE LIR APPROACH TO EMERGENCE | 273 |

822 Emergence and Dualism Under Attack | 274 |

823 A Peircean Perspective | 275 |

8231 Virtual Logic and Organic Logic | 276 |

83 EMERGENCE IN PERSPECTIVE | 277 |

831 Physical Emergence | 282 |

833 Catastrophe Theory and Emergence | 283 |

84 EXPLAINING EMERGENCE | 284 |

841 Emergence Is a Dogmatic Concept? | 285 |

842 The Emmeche Synthesis | 286 |

843 Biosemiotics | 289 |

844 Quantum Morphogenesis | 290 |

845 Half of the Story | 291 |

85 CLOSURE IN LIVING SYSTEMS | 292 |

852 The Category of Closure | 293 |

853 Opening Up Closure | 294 |

86 DOWNWARD CAUSATION | 295 |

862 Synchronic Reflexive Downward Causation | 296 |

87 EVOLUTION AND THE ORIGIN OF LIFE | 299 |

871 The Absence of Logic in Biological Science | 300 |

872 Natural Selection | 301 |

873 The Epistemic Cut | 302 |

The MatterSymbol Problem | 305 |

Bridging the Epistemic Cut | 306 |

876 A Systems Picture | 308 |

877 Evolution as ContextDriven Actualization of Potential | 310 |

8771 ExclusionDriven Potentialities | 312 |

88 THE THERMODYNAMIC AND CYBERNETIC STANDPOINTS | 313 |

881 Thermodynamics and Complexity | 314 |

882 Cybernetics and Information | 315 |

883 Teleonomy | 318 |

NEW DIRECTIONS AND A NEW SKEPTICISM | 323 |

1 NEW DIRECTIONS | 325 |

2 A NEW SKEPTICISM | 327 |

CLASSES AND SETS THE AXIOM OF CHOICE1 | 331 |

2 THE AXIOM OF CHOICE | 334 |

THE SYSTEMS VIEWPOINT | 337 |

12 The Relation of Contradiction | 338 |

13 The Principle of Antagonism Applied to Energy | 339 |

2 CYBERNETICS AND SYSTEMS THEORY | 340 |

22 General Systems Theory | 341 |

23 The Neuchâtel Model | 343 |

24 Systems Science and Complex Systems | 345 |

347 | |

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### Common terms and phrases

abstract actualization and potentialization Aerts antagonism antagonistic apply aspects axioms basis biological calculus category theory causal cause Chapter characterized classical logic complex concept consequence constitute contradiction contradictory defined described dialectics discussion diversity domain downward causation duality dynamic opposition elements emergence energy entities example existence explanation formal ontology function fundamental heterogeneity homogeneity identity implies included middle instantiate interaction interpretation intuition intuitionist logic involved levels of reality LIR view logic of/in reality logical values Lupasco mathematical matter mental metalogical metaphysical modal logics non-contradiction non-separability notion objects paraconsistent paraconsistent logic particles phenomena phenomenology philosophy physical position possible predicates principle of bivalence principles of LIR problem processes properties proposed propositional logic propositions quantum logic quantum mechanics reference relation role scientific scientific realism semantic sense space space-time standard logic structural realism structure of reality suggested T-state tion truth universe