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Brenner J. Logic in Reality

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Logic in Reality
Logic in RealityJoseph E. Brenner
© 2008 Springer Science + Business Media B.V.No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work.springer.comISBN 978-1-4020-8374-7e-ISBN 978-1-4020-0000-0
CONTENTS vii 4.7 THE CATEGORY OF T-STATES..........................................................1064.7.1 The Duality of Quantum Spin...........................................................1084.8.1 Self and Other: Self-Reference.........................................................112AXIOM FIT....................................................................................................1134.9.1 A Check-List of Principal Dynamic Relationships...........................1174.10 THE INTERPRETATION OF LIR........................................................119STRUCTURE AND EXPLANATION...1235.1 THE CORE THESIS OF LIR...................................................................124 RELATIONAL ANALYSIS.......1265.2.1 Mereology.........................................................................................1285.2.2 Inter- and Intra-theoretic Relationships............................................129IN PARALLEL...........................1325.4 THE STRUCTURE OF REALITY IN LIR.............................................1355.4.1 The Categorial Structure of Reality in LIR.......................................1365.4.1.1 Morphisms and Functors...........................................................1365.4.2 The Structure of the Domains of Application: Set Theory...............1405.4.3 The Metaphysical Structure of Reality in LIR..................................1425.4.4 Figure Versus Ground: Gestalt Theory.............................................1445.4.5 Form Versus Matter: Catastrophe Theory........................................1455.5 WHAT IS AN EXPLANATION?............................................................1505.5.1 Two General Failures of Explanation...............................................1505.5.1.1 ‘Both-at-Once’...........................................................................1505.5.1.2 Spontaneity................................................................................1515.5.2 The LIR View of Explanation...........................................................1535.5.3 Explanation and Metaphysics...........................................................155INCTION IN LIR.......................1565.6.1 The Inferential Role Description.......................................................1585.6.2 The Syntactic – Semantic Distinction – and Conjunction................1606 LIR, METAPHYSICS AND PHILOSOPHY..............................................163DETERMINISM..............................1636.2 CAUSALITY IN LIR...............................................................................1646.2.1 The Metaphysics of Causation..........................................................1676.2.2 Non-contradictory Causalities in Science and Philosophy...............1706.2.3 Finality..............................................................................................1716.2.4 Dispositions and Powers...................................................................1736.2.5 Probabilistic Causation.....................................................................1756.2.6 Possibility, Potentiality and Probability............................................1786.2.7 Actualism and Possibilism................................................................179
4.8 THE CATEGORIES OF SUBJECT, Ontological Links......................................................................139
CONTENTS ix 7.5.1 Two Complementary Logics of Complementarity...........................2477.5.2 Relational Quantum Mechanics........................................................2527.5.3 Quantum Physics and Consciousness...............................................2537.6 TOWARD A LOGICAL COSMOLOGY................................................2557.6.1 Space-Time in General Relativity.....................................................2567.6.2 The Dual Role of the Metric Field....................................................2577.6.2.1 Simultaneity: A Comparison of Dynamics...............................2607.6.3 Structural Realism and the Metaphysics of Relations......................2627.6.4 A Cyclic Model of the Universe.......................................................264S AND CLOSURE.............................2698.1 INTRODUCTION....................................................................................2698.1.1 Emergence.........................................................................................2698.1.2 Opposition in the Physics and Chemistry of Living Systems...........2718.2 THE LIR APPROACH TO EMERGENCE.............................................2738.2.1 The Category of Emergence.............................................................2738.2.2 Emergence and Dualism Under Attack.............................................2748.2.3 A Peircean Perspective......................................................................2758.2.3.1 Virtual Logic and Organic Logic..............................................2768.3 EMERGENCE IN PERSPECTIVE..........................................................2778.3.1 Physical Emergence..........................................................................2828.3.2 Normative Emergence.......................................................................2828.3.3 Catastrophe Theory and Emergence.................................................2838.4 EXPLAINING EMERGENCE.................................................................2848.4.1 Emergence Is a Dogmatic Concept?.................................................2858.4.2 The Emmeche Synthesis...................................................................2868.4.3 Biosemiotics......................................................................................2898.4.4 Quantum Morphogenesis..................................................................2908.3.5 Half of the Story................................................................................2918.5 CLOSURE IN LIVING SYSTEMS.........................................................2928.5.1 Defining Closure...............................................................................2928.5.2 The Category of Closure...................................................................2938.5.3 Opening Up Closure..........................................................................2948.6 DOWNWARD CAUSATION.................................................................2958.6.1 The Category of Downward Causation.............................................2958.6.2 Synchronic Reflexive Downward Causation....................................2968.7 EVOLUTION AND THE ORIGIN OF LIFE..........................................2998.7.1 The Absence of Logic in Biological Science....................................3008.7.2 Natural Selection...............................................................................3018.7.3 The Epistemic Cut.............................................................................3028.7.4 Semantic Closure: The Matter-Symbol Problem..............................3058.7.5 Code Duality: Bridging the Epistemic Cut.......................................3068.7.6 A Systems Picture.............................................................................308
7.5 QUANTUM MECHANICS.....................................................................246
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 task of the book to elaborate such a caxiomatics and the importance of building open and uninterpreted formal dynamisms (chapters 1 and 2): ii) the role of a rigorous interpreted formal sider, in term of both “logic in reality” and “new energy ontology”, the problems tion of phenomenology is fruitfully taken into account), and physics, where
xii FOREWORDrare in the current research in logic and epistemology: logic is grounded in many vements of current culture and science. lian philosophy, non-standard analysis and traditionally debated philosophical problems such as the analytic/synthetic distinction, determinism/indeterminism, a new relation between logic and space-time is suggested. To take another
attempt to explain and understand the phenomena of existence in all their diversity structures, actions, thoughts, interactions, in a word the physical and mental enti-study as lying on a scale between reality itself and the most abstract representations 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 scriptions of reality; and finally, descriptions of reality based on experiment, 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 tially to the linguistic and mathematical domains, not those of entities, events or portant practical applications of standard logics, for example, in computer science
“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). 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
involves this same real physical-metaphysical but also logical principle. The first positions in philosophy and science have been blocked by classical logical de-scriptions of the domain of these theories and the consequent classical ontologies, non-classical calculus to be used will be introduced. I will then briefly review the details of the non-classical calculus applied to the logical operations of implication,
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 structure of the world, I mean that all metaphysical, philosophical but
example), to take an attitude of openness and tolerance toward what may be unex-ture often encounters resistance that goes far beyond dispassionate and reasoned I will naturally be comparing LIR with existing theories, but my intention 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 Anglophone analytical tradition take a less conservative attitude. Mulligan et al. providing an adequate picture of reality. Continental philosophy is also criticized 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 The theory in this book takes these various attitudes into account. Ac- xxi
non-classical logics, including fuzzy and modal logics, in order to bring out the ability is suggested, and the LIR axioms are restated in formal probabilistic terms. disconnected both from processes of scientific inference and from ordinary ex-valid inference to provide insight into the foundations of mathematics. Logical re-of bivalence, absolute non-contradiction and the law of the excluded middle. These three principles can be summarized by the corresponding axioms of classical logic, as follows:
Dialectics can be considered neither more, nor less, than the generalization and mental expression of conflicts in nature and civilization, and their resolution, that (Lupasco 1979) (For Heraclitus, conflict did not mean the splitting or destruction orderly principle according to which all change takes place is a binding-together. relations between abstract objects, thoughts and concepts: the second, as a theory
Presence … Absence Actuality … Potentiality
One … Many Identity … Diversity
Subjective … Objective Internal … External
Local … Global Proximity … Distance only because they formally articulate aspects of our experience, but because we their opposites or ‘contradictions’. In the original formulation by Stéphane Lupasco judgment which thinks of it, the proposition which expresses it, to the sign which symbolizes it must always be associated, structurally and functionally, a logical antiphenomenon, or
1.1 INITIAL AXIOMATIZATION: THE FUNDAMENTAL POSTULATE 3 actually experience them. Being self-evident, they are thus a further rationale, for
LIR5:Functional Association: Every real logical element e … objects, pro-
cesses, events … always exists in association, structurally and functionally,
with its anti-element or contradiction, non-e; in physics terms, they are con-
identity and diversity.4
LIR6:Asymptoticity: No process of actualization or potentialization of any
element goes to 100% completeness.
of change, that is, emergence of a new entity or phenome-and, in particular, of truth, in view of the central position of truth values in any
CLIR1:Contradiction: Contradiction can never be considered as absolute,
because it never takes place between rigorously actual terms, between
absolutely contradictory elements, such as those of classical logic and mathe-
matics. Contradiction never occurs except between antagonistic dynamisms.
Alternatively, no element, no logical variable or event is rigorously non-
contradictory; it always involves some contradiction such that, no matter
how much developed, the non-contradiction is always relative and limited.
CLIR2:Truth and Falsity: A truth cannot be absolute, because it can never

concept that has direct bearing on the current debate about the individuation of quantum parti- The axioms could be considered as a new way of looking at regularity in the immanent connec-1.1 INITIAL AXIOMATIZATION: THE FUNDAMENTAL POSTULATE 5
offers us all that surprising.Ž The most useful approach may be to maintain a description of to question, is a major issue of scientific realism. The logic of/in reality is relevant of being. Without some indication of what constitutes being, what it means for something to exist, and why something exists rather than nothing, any description ontological and physical pictures that postulate the emergence and existence of levels, which follow different detailed laws, as a natural consequence of the fun-
ten or eleven fundamental dimensions, etc.) are in the domain of reality, as are the objects and 1.2 THE REAL AND REALITY 7 not veiled(DEspagnat 1979). quantum mechanics. While there always can and will be arguments about the
natural. Most people would also agree that another kind of illogical or a-logical ‘rules’ apply in the areas of affectivity, love and religious faith. A concept of levels of reality, however, in all of which at least some of the same basic principles are instantiated, suggests a possible isomorphism of the underlying laws of nature. For purposes of this analysis, I will take the view that
Microphysical or quantum mechanical.
Macrophysical, characterized energetically by global entropy and
gradual homogenization of its components.
Biological, characterized by local negentropy and the emergence of
new forms (heterogenization).
Human mental or psychological.
Human social.
the cuts between levels, an additional principle seems necessary, namely, to ex-Porphyry, and the Aristotelian Square of Opposition. These concepts are useful for above all of phenomena involving dynamics, that is, phenomena involving some
Here and subsequently, I use the term mechanism in an informal descriptive sense without implying that computable models exist for all the transitions between levels that I will examine. Indeed, I argue that such models for living organisms 1.2 THE REAL AND REALITY 9
tal and non-fundamental aspects, the former being at a higher level of complexity than the latter. The process of reduction, in my view, is also governed by the prin-ciple of dynamic opposition, that is, when fundamental aspects are actualized, of asymptotic rea-soning developed by Batterman (2002) is useful. The limits of identity and diver-asymptotically are instances of at which the tenets of reduction and those of classical logic apply. The movement toward an equal actualization and poten-tialization of two opposing elements results in a state of maximum contradic-tion. This limit, at which emergence is possible, is As Batterman suggests, the features of this state (critical point) cannot be under-modynamically governed processes. I will return to this in the discussion of the The axioms of LIR and the related notions of interactive contradiction in-volving real entities imply major innovations and modifications to the form and
It is possible to say, using the philosophers definition, that binary, standard logic ternary logic, but the real problem may be that at this point, reduction has lost all intuitive 1.3 LIR VERSUS STANDARD LOGICS: DEDUCTION 11 lized for simple phenomena. Is a logic of reality present in standard logic in poten-
D2:There exist circumstances under which a formula and its contradic-
tion are both true and false, but not wholly so at the same time.
D3: There exist circumstances under which a formula and its contradic-
tion are not wholly false together, but generate a third term, an included
reduced to two sets, one containing what is false and possible and the other what is true.
In LIR, the notion of truth is defined logically by non-contradiction and
contradiction. The term false is not applicable to real processes and enti-
own right. These include the connectives, the group most commonly composed of signs for negation, conjunction, disjunction, conditionality and, in first-order predi- … are indifferent to content. However, if logic is universally applicable constant in and thus may contribute to the non-logical, variable content of that limited number of expressions and argument forms that have been used tradition-that the distinction does not exist, but no principled criterion has been found for it. 1.3 LIR VERSUS STANDARD LOGICS: DEDUCTION 13
absolute distinction between general and topic-dependent rules, this subject
will be a further introduction to how far-reaching for logic the implications
bivalence of classical logic, in various forms, underlie arguments in all areas of sions in this book, the fact that certain interpretations in classical logic are explicable tions. The properties of conditionals for natural-language propositions in this usual oppositional relation between two elements will always be expressed by implica-
A Pe e. I use the bar and not to refer to the real element non-erather than the negation of classical logic.
D7: The connectives of implication, conjunction and disjunction all corre-

I also do not wish to use the connective ~ that formalizes negations from natural language in 1.3 LIR VERSUS STANDARD LOGICS: DEDUCTION 15 The essential elements we are dealing with in standard, classical logic are
parameters of the real elements that constitute the domain of LIR, the rela-
tions between which elements, in the object language, are defined, at this
point, by the above Axioms and by the connectives as operators.
Comment: Some readers may object that, at least in the area of deductive
logic, a semantics can deal only with propositions and their standard truth-
values, propositions having the possibility of being combined via the stan-
dard connectives into more complex propositions. I agree in part, but also
feel that the relation between classical logic and what a proposition isŽ is
much more complex, as I have just shown.
2.Symbols of the Object Language of the Calculus
CL: an infinite number of propositional parameters or variables, the connec-
tives, and the punctuation marks.
LIR: a transfinite number of reality parameters corresponding to real-world
entities, processes and events (phenomena) and their accompanying actual-
ized and potentialized contradictions, e0A,e1A,ƒ;non-e0P, non-e1Pƒ, the LIR
connectives and the punctuation marks, the sequence of real numbers 0, 1,
ƒ referring to the first, second and subsequent instances of the pairs of vari-
ables or parameters. A and P stand here for the actualization and potentiali-
zation respectively of the reality parameters, whereby the other sequence, in
whiche and non-e are inverted, is understood.
CL: the (well-formed) formulas of the language comprise all, and only,
strings of symbols that can be generated recursively from the propositional
parameters by the following rule: if A and B are formulas, so are
A, (A
B), (A B), (A B), (A B).
LIR: the formulas of the language comprise the strings of symbols that can
be generated from the connectives indicated in D7, the signs for actual, po-
tential and T-state, that is, the reality parameters The resulting inference
rules are that, where e is any real-world element, eA (e actualized) implies
non-eP (non-e potentialized) and vice versa; both imply that contradiction is
potentialized and non-contradiction actualized;
the parameter eT implies non-eT which implies that contradiction is actual-
ized and non-contradiction is potentialized.

exhaustive values of truth and falsity. This does not mean, however, that propositions when they 1.3 LIR VERSUS STANDARD LOGICS: DEDUCTION 17
Their purpose was to represent valid deductive arguments, also in mathematics statement logic – quantifiers and predicate variables and constants. The axioms are one refers to reasoning involving quantified statements, and other describes the for which the first-order predicate calculus suffices as the logical basis. Predicate logics of the second order essentially permit quantification over the quantifications ts are pro-positional or mathematical variables of some kind, the underlying classical logical concepts of truth and bivalence, remain unchanged. There is no implication that () ()()xxxx
 zment. This makes it a logical truth that there is at least one thing, but not that there ture of there being at least two things, namely, an element and its contradictory
The subsequent development of basic FOL is enormously complex, for example, the attempts 1.3 LIR VERSUS STANDARD LOGICS: DEDUCTION 19 There are two ways of looking any logic, namely, how it is built up, and how
shown by Priest and others, intuitionist logic remains closely related (congruent) negation can be deduced from a given set of hypotheses, the set must remain non-trivial, that is, not require the deduction of anything. The characteristics of the ne-native, paraconsistent logic based on the existence of dialetheias … true contradic-contexts (Priest 1987). A logic in which the inference from A and non-A to any arbitrary conclusion (explosion) is not valid is called paraconsistent (Priest 2000). major revolution in human thought and to important new kinds of theory within 1.4 NON-CLASSICAL LOGICS 21 at the same time, hence the contradiction. In LIR, if A is (predominantly) actualized,
absent. The only similarity between many-valued logics and LIR is that both Perhaps the first three-valued logic that contained a value other than 0, that of Peirce (Hammer 2002). Similarly, in the three-valued logic of Lukasiewicz, logics. It involves a combination of the formalism of non-standard mathematical applied to evidence and belief, and generalizations of fuzzy sets, taking on values something that is neutral (hence the name, neutrosophic logic) with respect to A and temporal and deontic neutrosophic logics can be constructed accordingly, NL
On the other hand, it is impossible to ignore the vast number of practical applications that 1.4 NON-CLASSICAL LOGICS 23
standpoint. In all cases, however, what is at issue are the kind of beliefs in the truth of statements or attributions, not the states of the objects of belief tems of calculi, for modal logics. However, the basic notions of interest, truth, are unchanged in these non- or neo-classical systems. Non-modal logics characterize the difference between valid and invalid tables. A semantics for modal logics can be defined through the concept of possi-being considered. Priest (2001) has described the problems involved in trying to The difficulties associated with possible worlds interpretations of modal logics have already motivated the abandonment of some classical rules in favor of of the logics discussed in this section, over formulas of the standard predicate of actualization and potentialization of necessity and contingency that is quanti-(see Section 1.7 on the reality function). I agree with Freges statement that no-
language-in-use. A distinction is made in the domain of application of natural logic … to first person experience … and that of formal logic … to scientific observa-point from facts, but without further relation to reality. An absolute concept of truth is implicit in that premises are stated as such and their establishment is not required, in my view, was because such logics do not in fact adequately describe action and
30 1 LOGIC IN REALITY (LIR) AS A FORMAL LOGIC here, now there. It is difficult to foretell the future.Ž ƒ future generations will totle or a scientific revolution.Ž (Poli 1993) I leave it to the reader to position Vasiliyevs work, and LIR, on this scale. lution of their instantiation. The contrast I am making between LIR and other While the standard deductive logics, as shown in the previous Section do pear to address aspects of real situations. In the next two Sections, I will call atten-lation of the relation between deduction and induction is the following: there is just one form of logical argument, namely, a set of propositions, one of which is induction was reasoning from the particular to the general. A simple modern formu- Classically, deduction was reasoning from the general to the particular, and
32 1 LOGIC IN REALITY (LIR) AS A FORMAL LOGIC I introduce these axioms because of their relation to the concept of
D9: In LIR, the function is a probability-like reality function, Rl, a meas-
ure function over an algebra of the non-propositional formulas of actualiza-
At the interface between induction and probability, Jaeger (2005) uses probabilities. The objective in an infinite series of proofs”, but this can be shown to be compatible with a traditional statistical point of view, that is, one describing the real world. Both overall probability, but it is not a great step from here to the idea that they are con-tia” of each of us, that is to say the intensity (in both senses!) of our repugnance to
Other sets of axioms can be written for probabilistic inductive logic that consider probability duction) have been developed to combine evidential reasoning (abduction) with causal reasoning
34 1 LOGIC IN REALITY (LIR) AS A FORMAL LOGIC viewed negatively. In my LIR theory, intuition is a process of thought related dia-lectically to knowledge, and has a non-trivial logical and ontological status. A further discussion of inference and explanation is presented with the ontological It has been necessary to make the above comparisons of LIR with various those logics to reality. Further, that the statement that the logic of/in reality reduces cepted that a logic can exist for non-classical systems. Quantum logic, the logic of the elements of reality studied by quantum mechanics, provides such a formal be preferred. I claim that the logic of/in reality is a quantum-type logic with the zation and potentialization of dynamically contradictory states. As in probabilistic
36 1 LOGIC IN REALITY (LIR) AS A FORMAL LOGIC dled readily by the mathematical model. The criteria for analysis that develop violations of Bells inequalities in language, Aerts says that not only are they not substratesin the world (Aerts and Aerts 2004). This approach does insist on the importance ofthe metaphysical positions, and his theory will help to illuminate several aspects of
38 1 LOGIC IN REALITY (LIR) AS A FORMAL LOGIC B,and physical systems are represented by probabilistic models, composed of the interaction at the biological and mental levels cannot be described by classical logic and classical physics. Although quantum mechanical entities are not di-ponents, a description of their behavior using something like the probability values discussion of the application of measurement theory to propositions, linguistic ex-though measurement theoretic propositions are abstract entities, they measure it linear feedback is present which, as I proposed above, involves a non-Boolean al-
40 1 LOGIC IN REALITY (LIR) AS A FORMAL LOGIC Gabora, Liane and Diederik Aerts. 2005. Evolution as context-driven actualization of potential. 30: 69…88. Logique naturelle et communications. , ed. Edward N. Zalta. http://plato.stanford.edu/archives/win2002/entries/peirce-logic/Philosophy Significance of Universal LogicNorthwestern Polytechnic University of China Press. SYNTHESELa logique.Que sais-je? Lupasco, Stéphane. 1987. Narens, Louis. 2005. A Theory of Belief for Scientific Refutations. Albany, NY:State University of 12:3…4.Poli, Roberto. 1993. Vasilév, Nicholas A., Logic and Metalogic. Imaginary (non-Aristotelian) Nicolescu, Basarab. 1982. Sociologie et mécanique quantique. 1: March-April. ous, la particule et le monde
. In other words, what is ‘true’ about the two ele-In LIR, there are thus four ‘true things’ that exist. To avoid confusion of ’ the term or element truth of the potentialization. The term truth is to be preferred over validity since ),the four true terms (truths) of the quadruple are also relative, like the par-truth of existential potentialization. This means that potentialization must be given than an operator. The concept of a contradictory ‘negative’ truth does not imply 2.2 TRUTH VALUES, CONTRADICTION AND REALITY VALUES 43
Alternatively, since the implications are reciprocal:
AP+A-P-A+P ; AP+T-s-T-s(C.C) (. ) (. )(C.C) (. )Š›ŠVVVVVVpotentialized as a consequence. If there is a contradiction, then there are two con-ing the degree of actualization, potentialization and T-state. Starting with (2.6), the
e e e eTrue False A PFalse True T T P AThe following table combines the above with the concept of contradic-non-contradiction is always partial, incomplete, and when two contradictory ele-ments are neither actual nor potential, non-contradiction is potentialized, as in
the dynamic phenomena and their evolution and secondarily on sentences
sential part of something is so of analytical necessity and not because of natural,
little to a description of the underlying reality and seems to retain some of the idealism of con-cepts of individuals and universals that tropes were purported to obviate (cf. article “Tropes” in The quotation defines an interesting domain of philosophical inquiry, but I will not comment on 2.2 TRUTH VALUES, CONTRADICTION AND REALITY VALUES 47
survey should be seen as another of the several attempts I have made and will
1. One version of verificationism states that what is true can be known – all
truths are knowable. However, this anti-realist position leads to the logical
conclusion that all truths are known. According to Marton (2006), some anti-
realists claim that if classical logic proves that verificationism is untenable,
then classical logic must be wrong. The verificationist counter is to invoke
intuitionist logic and the concept of something being true that is completely
different from being a realist fact. These facts are not truths, but are some-
how involved in their definition. This view, however, has additional prob-
lems with it. Simply, my conclusion is the same as that of Marton: this kind
of verificationism should be limited to theoretical areas where no contingent
facts (that is, no areas of reality of the kind with which LIR is concerned)
are considered.
2. Verificationism, for Dummett (1993), is a theory of meaning of sentences
that replaces a truth-conditional meaning theory in which truth is the central
notion. This leads rapidly to circularity. Verificationism defines a variety of
alternative methods that establish a sentence as true, such as observation or
argument. Verification is to say that “that in which an understanding of the
sentence consists in an ability to recognize, whenever presented with it,
whatever we take to count as establishing its truth” (the ‘criterion’). The re-
sulting notion of truth, significantly for this study, is not subject to the prin-
ciple of bivalence, since it is the observation that sentences exist in the
language that can neither be verified nor falsified is one reason for rejecting
the truth-conditional theory of meaning. This stance remains an anti-realist
one (see Chapter 6), since it claims that if our statements and thoughts are
not all determinately true or false, reality itself is (fundamentally) indeter-
minate. However, in an anticipation of some of the positions in this book,
Dummett suggests that the verificationist who is not satisfied with this result
“will adopt a semantic theory yielding a non-classical logic – quantum logic
or, more probably, intuitionist logic“. LIR is, of course, my preferred candi-
date for this job.
3. Ladyman and Ross (2007) state that their naturalist metaphysics, a “dia-
lectical combination of realism and empiricism”, is equivalent to adopting a
verificationist attitude to both science and metaphysics. These authors’ veri-
ficationism, however, is verificationism about epistemic value derived from
empirical science and the empirically measured boundaries of the real, not
about meaning. Verificationists, on this view, restrict acceptability in meta-
, as opposed to a logical or mathe-
matical perspective. “No empirical science is responsible for counter examples 48 2 LIR AS A FORMAL SYSTEM
This should be read: if an implication is actualized, an exclusion or nega-tive implication is potentialized; if a negative implication is actualized, an affirma-neither actualized or potentialized, a negative implication cannot be potentialized One can therefore proceed, as previously for elements, to construct a ta- (2.9)
APAPTTAPAPTT . ; . ; . ; and ( ) ŠŠŠŠŠŠŠŠ›ŠŠ›ŠŠreal processes and systems. The LIR concept of real processes is that they are The term infinite refers to a set of elements, such as the integers, which 50 2 LIR AS A FORMAL SYSTEM
AAPAPPetc. ( ) ( ) .... ()ŠŠŠŠŠŠŠŠŠŠ(ee)
APA P() to: eeŠŠŠŠ A and P
absolute and definitive negation, nothing. It is a theorem of LIR that both identity The first of the three sets of chains illustrated by (2.12) shows progressive actualization of positive implication and potentialization of negative implication, the second the inverse progressive actualization of negative implication and poten-tialization of positive implication and the third a progressive semi-actualization semi-potentialization of the two contradictory implications. Lupasco called these the
Positive Ortho-Deduction
The first is oriented toward the limit of infinite or absolute actualization of
positive implication, which is approached asymptotically, in other words, that
of classically positive and tautological deduction. It is a model for the struc-
ture of physical causality and classical physical theory, and, by extension, of 52 2 LIR AS A FORMAL SYSTEM
which develop transfinitely without any particular orientation. Lupasco identified these with the multiple combinations of linkages and ruptures (negative links) that The para-deductive chains are thus an integral part of logic. As can be de-
APAPTT()() ()() ()()ŠŠŠ›ŠŠŠ›ŠŠŠ One sees here the real meaning of disjunction: it is the mechanics of dia-lectics: no dialectic without disjunction and implied by the fundamental postulate that permits the dialectic, and the dialectic But disjunction itself, as discussed in the next section, also cannot be absolute and rigorous. Para-deductions, will always accompany, to some extent, The above series of series of symbols are at the heart of the LIR represen-in Section 1.2.2 toward non-contradiction (identity, homogeneity or diversity, het-(relatively) stable physical objects. Note in this view, an identity, a stable “object” 54 2 LIR AS A FORMAL SYSTEM
described by the dialectic alternation of a contradictional conjunction and a con-

(e V e) (e e)
(e V e) (e e)
e V e
e e
A P(e V e) (e e) By eliminating the element tion and disjunction as for implication, always based on the existence of a point T, ,that is (V) ()TTTTV; V/ŠŠ/56 2 LIR AS A FORMAL SYSTEM
APAAV ee; VV e V effff/Š{/{Š/{{ The conjunction and the disjunction of exclusion of classical logic are One can further characterize LIR as a formal logic by classifying the val-
the negative and operation inversed. This duality, however, still refers to abstract entities. Aand B may also be semantic elements provided there is some dynamic interaction between them. Jakobson distinguishes between trait excludes its opposite (principle at the same time of exclusion and participation, of disjunc-58 2 LIR AS A FORMAL SYSTEM
characteristics. These are alternately actualized and potentialized like the opposing ‘overlap’, ‘meets’, ‘begins-before’ and ‘ends-before’. Subsequent work has refined certain technical aspects of this logic, to which the many publications on the topic between propositions and meaning, which are directly relevant to my brief discus-can appear as arguments in predicates. Events are initiated, terminated and negated 60 2 LIR AS A FORMAL SYSTEM
The components of LIR that will constitute it as a formal ontology, an completed in this chapter. The three components are: (1) its axioms; (2) the ‘language’ ‘brand’ of realism. Formal ontologies are generally divided into three kinds: repre-senttational – a framework to represent information in as formal a mathematical a theory that is intended not only as description of the entities of reality but how realist system. about the ontological structure of the world. As such, it is subject to division into
64 3 LIR AS A FORMAL ONTOLOGY The combination of logic and reality in the one phrase I have used to characterize my logical system might accordingly lead to a possible misunder-are endowed with real characteristics. On this view, logical forms and relations with a mode of being that is analogous to that of predicable concepts: they are not “objective” as assumed in logical realism. On the contrary, I consider
Intensity – extensity Internal – external
Local – global Neighborhood–distance+xtensity
If the axioms indeed apply to these predicates, then one must accept, at logical predicates has been given, except that intuitively all predicates shown refer relationships are involved will emerge from the further construction of the categories which case bivalent logic holds ‘to all intents and purposes’, or in states which instantiate contradiction or opposition between the two elements, eventually leading,
68 3 LIR AS A FORMAL ONTOLOGY and discussion of three critical terms to be used, namely, dynamisms, processes I first propose that the term ‘dynamism’, used to designate intensity and extensity means, combining the dictionary definitions, that they are not only pro-cesses or mechanisms of the operation of energy, responsible for its development and motion, but also theoretical constructs that describe the universe in terms of that of dynamics, since they are themselves forces that together, in an antagonistic or contradictorial relation (conjunction), cause motion, activity and change. If this is accepted, then what are the definitions and characteristics of actuality and potentiality and homogeneity and heterogeneity? These would appear to be intensive properties of real elements or entities to which could be assigned complex values as observables. At the same time, however, I have described change actualization (or actualizing, homogenizing and so on). My preferred answer to this point is itself an illustration of LIR: the two terms, the noun and verb forms cannot be considered as totally separate and independent and one is not
2 Lowe (2006) has developed an alternate formal ontology as a basis of metaphysics. This approach retains, however, standard notions of categories and their underlying predicate logic that limit its applicability to real phenomena.
70 3 LIR AS A FORMAL ONTOLOGY discussions of reality and description of reality in terms of laws of nature. In natureestablishedfollowing, recognizing that each of these points itself has given rise to debates,
Properties include relations, as well as attributes, qualities and fea-
tures of phenomena. Processes are instantiated or exemplified and
the ‘things’ – processes, objects, relations, etc. – that exemplify a
property are instances of it.
LIR: Being actual or potential, or being actualized or potentialized are thus
Properties can be cited to explain or account for change, as well as
other phenomena of philosophical interest, provided adequate
reference is made to additional background assumptions or un-
derlying mechanisms rather than only state observations (pale skin
yesterday, red skin today, but red due to staying in the sun too long,
rather than just because paleness and redness were exemplified at
different times). Properties are intensional entities that describe the
intensional aspects of phenomena, and in this sense provide a picture
of reality that is not ‘abstract’.
LIR: My explanation of energy in Chapter 4 in terms of extensity and
intensity as properties is metaphysical, since such properties are clearly not
observables, for example, in the case of some electromagnetic radiation, but
also physical since they are postulated by the best available physical theories.
I will show later that LIR supports a specific kind of scientific realism. No
properties or elements are invoked in LIR’s account of properties that are
outside the laws of physics, but the existence of dynamic opposition pro-
vides an additional element of structure.
Properties can explain sentences in terms of a concept of logical
linguistic form, and compound properties can be built up from simpler
ones by logical operations equivalent to conjunction, negation, etc.
72 3 LIR AS A FORMAL ONTOLOGY same or different. They reciprocally define each other according to whether one The definition is not circular since in reality, neither process not property return to the exact point of departure. Compound processes and properties been standard, consistent, bivalent logics from which any principle of contradiction, intents-and-purposes, without the absoluteness of identity as an properties can themselves instantiate properties, each property is part of a des- of exemplified properties refers to where they are instantiated in space-time. The principle of instantiation implies that properties are located in their instances, but they can be of two kinds, intrinsic or extrinsic. Intrinsic properties are normally defined as being those which an object may possess independently of everything else that exists. Typical properties are the mass and charge of particles in properties are extrinsic or relational: weight, which depends on the presence of depend on the state of the system and extrinsic properties do. form of dynamic interaction, that is, at the quantum level and the biological and
Similar considerations apply, I believe, to category and category feature, particularly in the case no obvious disadvantages except to theory, I am inclined to take a pragmatic position on this
it means for something to be or exist, that is, an answer to the question of being, ment that stamps me as someone capable of discerning what does and does not Well-known attempts to provide answers to the questions of being are .Sartre (1943) developed an ontology consisting of two distinct, irreducible and mutually exclusive cate-these existential views are phenomenological, requiring a human a human observer, phical ontological question of existence before defining its various possible catego-that is, to carefully define, as far as possible, a concept of being as a matter of
There are many deep intuitions in Sartre of duality and alternating potentiality and actuality as (Sartre 1943). He is unable, however, to avoid the consequence of his total separation of the and the resulting contradiction in the appearance of consciousness in the seen as an explanation of his phrase “everything happens as if the for how this “absolute event arrived that crowned the individual adventure which is the existence of
and the insights of Jacquette partly converge. It thus may not be possible, with a approach opposition to, non-being. To understand being means to me not only Rather than referring to standard ‘pure’ logical objects to further characterize bivalent logic, but it can by LIR. LIR is perhaps less purely than Jacquette’s system, but it is in my view the most that can still capture the real world. In other Jacquette, yet making any ontological specification of what any of the things in the universe are, I note the existence of duality, two-ness, even in bivalence. Another way quirement that one thing must exist but not that two must exist. This aspect of people would say that the difference between the properties of existence and non- The philosophical problem thus focuses on the nature of the relation bivalent, multivalent, intuitionist, paraconsistent, etc. are neither more nor less
exist, it would (or could) casually interact with us. Examples of the former category changes that are different from simple iteration, adding 1 to 3 to get 4 and eventu-properties of both have the same structure, and bridge laws or principles, which objects and physical states. What, however, might these bridge principles be that would be general enough to insure that one has the right properties in the right the correlation and the co-evolution of the objects in the ‘two worlds’. Theories The conclusion of this discussion is that both of the above approaches being, with a logical basis in either standard classical or paraconsistent propositional the formal ontology of LIR. Before proceeding with this construction, some further
of formal ontology as “the systematic, formal, more than formal existence to the entities of this ontology, much less any interactive or processual
effective quantum field description of quantum phenomena. The categories of a New Energy Ontology (NEO) are established, including the essential categories of Dynamic Opposition, Process and T-state (emergent included middle) and SubObject that are both formal and physically meaningful. The categories are shown Ontology can be defined as the study of what exists, what entities compose reality and also what the most general features and relations of these entities are. It therefore overlaps the concept of metaphysics, as suggested in the Introduction. converts these assumptions, concepts and theories, which are of course expressed
82 4 THE CATEGORIES OF LIR reasoning and patterns of inference. In doing this I follow the suggestions of Seibt relationships between linguistic expressions in a language, natural or scientific: cation of the achievements of contemporary science. My conception of onto-logy those whose ‘source’ is in our conceptualizations of reality. One may say in both reading of the term ‘category’. In both of these readings, ontological categories are constituents (individual, properties, and relations) in a particular domain or region
See however my discussion of truth-makers in Chapter 2.
84 4 THE CATEGORIES OF LIR Among other things, the formal ontological approach is a way of seeing defending the claim that even standard logic does have an ontology and, by regulating inquiry, says something directly empirical about the world, namely about higher As suggested by Seibt (2004), an adequate ontological theory should these nouns include, in addition to reality and phenomenon, property, process, construction of a set of categories is, in general, carried out with the eventual fit with a set of axioms in mind, including the metalogical principles they embody,
1.Definition of a general philosophical worldview including the – for
me – unavoidable features of inconsistency, incompleteness and
contradiction in the dynamic sense I have given.
2.Outline of a physical, obviously today, a quantum mechanical
picture of the world.
3.An intuitive, that is, non-axiomatic introduction of categories based
on 1 and 2.
86 4 THE CATEGORIES OF LIR In Section 3.1, I listed Smith’s material categories: Body, Wave, Mass, Particle. To these should be added Information, but all these categories can be seen as physical energy in various forms and aspects. Elementary particles exist that can be more or less well characterized; flows of such particles can take place, netic and nuclear that exert forces on one another. I am concerned with grounding a much clearer concept of the origin of duality, opposition and an included middle, field is, there are many hints from different approaches that (1) such a dualism ex-configuration space-time. The structure of their causal relations will in general combination of differential and integral equations of second-order cybernetics, and their underlying dynamics by a theory of topological structure, which
88 4 THE CATEGORIES OF LIR (3) that duality and antagonism translate into oppositional relationships throughout dualities I am analyzing are real and not somehow artifacts of prior approaches. The basic a form of energy are thus a consequence of the physics of reality discussed above.
Electrical charges are only positive or negative. In an atom, the
positive charge of the protons is balanced by the negative charge of
orbital electrons. The positron, the ‘anti-particle’ of the electron,
has a positive charge, and in semi-conductors, the negative charge
of electrons is offset by defects or holes with positive charge. Like
charges repel one another; unlike charges attract.
Magnets have two poles, called by convention North and South. As
do charges, two like magnetic poles repel one another, unlike poles
attract, a physical instantiation of duality of ‘forces’.
Finally, depending on the energy level, there are always and only
two types of quarks bound within a quantum particle, given more
or less picturesque names (top and bottom; charmed and strange,
etc.). The forces between two quarks are mediated by a third
particle, a gluon, and the overall dynamics can be considered as
instantiating a T-state. In this case, the gluon is the energy state
emerging from the interaction between quarks at another level of
reality or complexity.
nature. For a discussion see Section 6.8.
90 4 THE CATEGORIES OF LIR metaphysicalbe taken into account, and the most fundamental of these are intensity and extensity. It was recognized early that different forms of energy had properties that and extension respectively, in a different sense from their use in classical logic notion of physical movement, a tendency to further development of an identity, sive contains the notion of power, power-for-itself, hence subjective (cf. the always defined by difference and gravitational and electric potential by complex In fact, energy, the underlying entity, is nothing other than extensity. Everything that is attributed to it – unicity, permanence, homogeneity, conservation, etc., characterize extensity and nothing else. In postulating the fundamental unicity of energy, with all its properties, one postulates the primordiality, the substantiality, the monism of extensity
Carnap divided the meaning of an expression into independent components of extension or denotation and of intension or connotation. The former corresponds to its understanding or comprehension and the latter is determined by empirical investigation.
92 4 THE CATEGORIES OF LIR a tendency toward a single undifferentiated state of affairs as exemplifying identity energy, as apparently indistinguishable electrons, shows a fundamental duality results in the existence of nuclear spin isomers (Hougen and Oka 2005). The ‘heterogenizing’ process, a diversification. Combining this idea with the one in the acterize the process of extensity, and heterogeneity, interiority and subjectivity place. Further, the ‘coefficients’ of homogenization and heterogenization define a relation of contradiction or opposition since they imply the coexistence, in the energetic constituents of the phenomenon, of identity and non-identity. A cell (an notions of rationality, reality in a limited, classical sense, invariance and classical logic and tautology. The opposite process of diversity or diversification refers reality that instantiate diversity constitute an integral part of the total logical
94 4 THE CATEGORIES OF LIR refers to its two crucial instants, namely, the start of the movement or conception and I can agree with her formulation that change is not a ‘product’ but a process process and state is justified from the NEO categorial standpoint: some physical objects are macrophysically more stable than others, and the ‘perdurationist’ view uncertainty principle. The principle of dynamic opposition, Lupasco thought, Other authors, including Russell and Schrödinger, saw the necessity of
Heisenberg considered that the probability wave of quantum mechanics was a ,a new kind of physical reality “halfway between the massive reality of matter and the intellectual reality of the idea”, and the reduction of the probability wave during measurement was a data, without necessarily being data to any mind” (Bitbol 1991).
96 4 THE CATEGORIES OF LIR relative change in the phase of a wave function of the electrons produced by the in LIR of elements related by dynamic opposition: potential is a real component of I describe again the principle of antagonism in energy as follows: whatever such that the actualization of non-A implies the potentialization of A, and For a chemical reaction to take place, for example, a certain quantity of energy must for all phenomena, there will be a point of equilibrium between the two tendencies, ‘on the way from one to the other’, which can be considered as the third element complex processes will become apparent in the next section. Examples and further categories of things, variant and invariant, real and apparent, internal and external.
extensities, are easier and more normally grasped, whereas variance appears as unreal or to a reaction taking place, has been overcome by an input of energy – heat, favored products can also be formed, but to a much smaller extent, unless further energy is made available in some form, for example, by the use of a catalyst with a unique molecular or
98 4 THE CATEGORIES OF LIR structure and function. The contradictory logic of energy is a real logic, that is, a science of logical facts and operations, and not a psychology, phenomenology or epistemology. or avoid contradiction of any kind, is not adequate to describe real systems, all of amples of the operation of the fundamental principle. For example, LIR provides a concept of judgment that emphasizes the existence, for any judgment, for the the possibility of emergence of a third, new judgment that would still embody aspects of the other two. Any autonomous judgment would be one rigorously, reality. It would no longer be a judgment, that is, a dynamic event. A judgment in this view is constituted or essentially composed of two inverse, contradictory reality. An appearance is something relational, what something is for something
100 4 THE CATEGORIES OF LIR is a form of category error. I thus claim that non-separability at the macroscopic level, like that being macroscopic phenomena that has been neglected. The functional non-separability level systems, membranes, ions and neurotransmitters, down to the level of funda-mental particles. Moving in the other direction, this view has consequences for the relation between the neurophysiological level and the higher level, non-reducible, but also at biological and cognitive levels would require a chapter in itself to do it whole, and one says in this case that the whole – an object or process with its own set of properties and relations – does not supervene on its parts. Since I am talking : The state assigned to a compound physical system at any time is supervenient on the states then assigned to its component subsystems (the latter are the
102 4 THE CATEGORIES OF LIR existent basic physical parts, following a principle of physical closure (cf. Chapter 6). The ideas in the literature and LIR can now be directly compared: (1) it is not parts; (2) the former state that some physical entities that we take to be composed but none has been made. In Chapter 1, I suggested that the appropriate forma- In quantum mechanics, the elements of the algebras, their ‘structure’ – As pointed out by Krause (2007), while physics has moved its paradigm distinguishable objects, that is, sets, describable by set theory. Macroscopic object “relative identity” is introduced to convey the notion that classical identity cannot
Krause has suggested (private communication) that the appropriate mathematical concepts to describe LIR are the “uniform structures” of Günther Ludwig. These concepts, lie somewhere between topological and metrical structures. The theory has the intriguing characteristic that the structures of the infinitely large and small have no physical meaning, but are tools to
104 4 THE CATEGORIES OF LIR The further material categories of Process, the structure of change, Subject, “whose model is no longer a portion of physical stuff but a process.” Like other From the LIR standpoint, I introduce the new category of ‘Process’ logical predicate or category feature of LIR in Chapter 3, as something in common of process, namely, its partial reliance on idealized, abstract objects of reality. Free
106 4 THE CATEGORIES OF LIR commonsense logic, the law of the excluded middle, is the crucial innovation of At a single level of reality, the second and third axioms of classical logic are essentially equivalent: there are no contradictions in the same time and place. In my extension of logic, a T-state resolves a contradiction at another level of mutually exclusive, antagonistic pairs that can be seen as resulting from the or third term in that it is located in the model at an intermediate point in a complex deploy their own time and space, or space-time as I will claim in Chapter 7. The reality. A given T-state (which effects the unification of A and non-A) is associated . The application of the logic
succession that is the consequence of the fundamental postulate applied to ‘space-time’. Computational logic now includes concepts of formal systems as open, capable of handling changing or evolving information, replacing the Hilbert concept of formal systems as closed.
108 4 THE CATEGORIES OF LIR actualized and macro-physical potentialized, but at There is an additional fundamental physical duality to which I should call Quantum entities exist in two classes defined by the quantity of a property called reality. In the case of bosons, of which most common one is the photon, this the photon are completely defined mathematically, as a combination or ‘super-
ceeds from potential to actual, that actualizes an energy, monopolizes, so to speak, tence, a subject. The dynamism that is potentialized is displaced from this center (Lupasco 1951). Formalizing this, actualizations (A), potentializations (P) and
formulas previously shown. The existence of a subject-object as an included
e e i d S O S O S OSO SO SO SO SO SOO S O S O S I am aware that this is just a notation replacing one symbol with another etc.) on the one hand, and diversity or heterogeneity (variance, differentiation, etc.) can be respectively subject and object. The indeterminacy relations of is the momentum of a quantum
112 4 THE CATEGORIES OF LIR other, but this is a trivial coincidence. The key point is that, in LIR, applied to real In real situations, however, use of the term in ‘self-reference’ requires further explanation. How can a real self refer to itself unless the self is somehow
The Lebnizian form of argument can also be used in relation to knowledge. note Jung’s foundational view of 1912–1916 (Jung 1971). He stated that the problem of energies and gradients. The self was “characterized as a kind of compensation for (or result of) the conflict between inside and outside”, and even suggested that the self “can claim the value of a hypothesis analogous to the structure of the atom”. This may be one of the earliest
114 4 THE CATEGORIES OF LIR Hartmann defines Process as a category that is intermediate between ‘real as a fundamental category, the ‘dynamic substratum’, together with another equally categorial concepts that receive added meaning from their relation with the phy-seen that energy instantiates all of the opposing ontological predicates. The concept
Nicolescu has suggested the term ‘onto-logic’ to characterize the logic of the included middle, as being a logic that is ‘open’ to ontology, but other workers in other contexts have also used this
Rule 1: The opposition of three elements A, B and C can be reduced by
induction to that between three pairs of two elements, as seen in nature,
eventually with each element being the included middle between the other
Rule 2: Given three elements A, non-A and their included middle T, an
included fourth term T1 is not possible: any fourth term T1 added to A, non-
A and T, can be decomposed into two structures of included third terms (A,
non-A and T) and (A1, non-A1 and T1) (Nicolescu 2002). This agrees with a
theorem of Peirce that he demonstrated by the use of graphs: all ‘four-tailed’
etc. If there are three, two together, or their resultant T-state interact with the third. processes of differentiation depend on further progressively dissymmetric dualities.
It is the shared, probably incomplete understanding of these processes, unconscious or not, that facilitates consensus of what is meant by ‘brick’.
Principal Direction: Actual
Principal Entity: Identity (Homogeneity)
Principal Process: Heterogenization (Diversification, Individualization)
Principal Direction: Potential
Principal Entity: Diversity (Heterogeneity)
Principal Process: Heterogenization (Diversification, Individualization) Principle Dynamic Relationships of LIR
Potentialization Actualization
Diversity Homogenization HeterogenizationIdentity Heterogenization Homogenization
.T-states have not been put into this list since it is to be understood that
120 4 THE CATEGORIES OF LIR In the other category of phenomena, NSC, in which the dual category In practice, as we will see, it is the NSC category of dualities seen from contains the included middle T-states that emerge from the Before completing this discussion, I wish to return to the categoricity, or Whitehead’s statement of his ontological principle does not classify ‘poten-seems to me to be a similar relation between my potentiality and actuality and his potentiality and givenness as ontological predicates. There is a ‘correlation’ between are meaningless apart from the entities to which they refer, and they are require-and T-states of actuality, potentiality and T-states. Nicolescu has given an interpret- 3 matrix (Nicolescu 2002). Their domain of application may be limited to higher cognitive levels of reality, and I
27 I am grateful to Johanna Seibt for this question.
122 4 THE CATEGORIES OF LIR Krause, Décio and Steven French. 2007. Quantum Sortal Predicates. Le principe d’antagonisme et la logique de l’énergie. In H. Badescu and B. Nicolescu. Monaco: Éditions du Energy Between Past and Future State Vectors. In , eds. D. M. Greenberger and A. Zeilinger. New York: Annals of the New York Poli, Roberto. 2003. Descriptive, Formal and Formalized Ontologies. In Husserl’s Logi- , ed. D. Fisette. Dordrecht, The Netherlands: Kluwer, Stanford Encyclopedia of Philosophy (Spring physics-structuralism. Schneider, Luc. 2002. Formalized Elementary Formal Ontology. Wahrheit-System-Struktur: Auseinandersetzungen mit Metaphysik.Stuttgart, Germany: Olma Seibt, Johanna. 2003. Free Process Theory: Towards a Typology of Occurrings. In Process Netherlands:Kluwer.Trento, Italy. .Boulder, CO/San Francisco, CA: Westview. Issues in Contemporary Phenomenology and Cognitive Science.New York: Free Press.
structure of the reality to which LIR applies. In the process, we will also see that could meet Popper’s criterion of falsifiability. There are problems with the Popper approach, but the idea is still useful in many cases. In another sense, however, LIR on the absolute independence of the entities or interpretations under discussion may be biased in favor of one other, resulting in errors or omissions. For itself, 3, is the ‘semantic’ one, which sees theories as models or structures. These are phism. Real systems and their theoretical models are not totally independent enti-
of Batterman (cannot be derived from the more fundamental theories; instead, they require one to make use of a special-case theory involving elements of both the original two.
It is clear that any implied separation between these subjects and those of
Theorem 5.1: Object level and meta-level entities are contradictorially re-
To prove this, for example, in the case of matter and symbols of matter, I therefore reflect the underlying dynamic opposition that was in operation at that But in what way does matter have the properties of symbol? This requires Individuals, as part of a group, contribute their individuality to it. But the vidual. What is the ‘group part of the individual’ is something instantiated at higher, At all levels of reality, I will assume that there is a conflict or opposition respond. I may and in fact always will focus on one or the other aspect, but there
sages written in letters constituted by human features (Pamuk 1996). These principles might also be considered as being outside the domain of laws boundary conditions at real boundaries and interactions and constraints of the kind that Cat has
Even where there are no interactions of this kind, classical part-whole speak, its origins in mathematics. In non-classical extensional mereology, the absent. In its place there is a combination of two different relations between parts The two relations differ primarily insofar as the applicability of classic the normal temporal and modal world, the absolute part-whole relation, on which clude all apparently static objects, sometimes referred to as ‘continuants’, as well whole that depends on PDO is not captured by them, given the classical concep-
In LIR, continuants are regarded as processual entities, and there is no epistemic cut between
I propose the logic of/in reality, together with its PDO and associated on-tology, as a metatheoretical scheme that can deal with scientific theories and their of a field of experience, by this definition, LIR offers a structural model of at least The distinctions between inter- andintra-level reduction, like other dis- The principles of LIR could be stated in the same terms as many of Wimsatt’s heuristics for fundamental problems in philosophy and science:
Look for robust tendencies (e.g., toward identity or diversity), and
for conditions under which those tendencies are likely to be real-
ized, rather than for absolute positions.
Study context-sensitive inferences rather than ones that are context-
free, along the lines of Aerts’ analysis of non-classical contextual-
ity, in which both system and perturbation have an internal relational
structure (Aerts et al. 2002).
The role of categories in ontology, independently of the formal mathe-matical uses to which they can be put, is essential in defining LIR as a conceptual structure that has additional explanatory power. In a categorial realist conception, timately bivalent concept, based on Whorfian reciprocal relation between lan-LIR naturalizes the debate on the cultural relativism of categories, as it provides a lanffy 1969) that “they (categories) must, in a certain way and to a certain extent, Seibt’s definition of ontology is as an explanatory theory of truth-makers ontological theories specify what makes sentences of the theory true without being committed to any particular theory of truth. Ontology in this sense is best com-pared with semantic theories of inference, which discuss patterns of formal and logical and ontological theory are found relatively frequently. However, there is rarely any reference to a process of drawing the categorial inferences regarding the well as physics and being. I recall the reference to experience in the presentation 3. Because everything in reality is logical in the LIR sense of incorporating rela-logic and experience become interchangeable terms. Further, in the epistemology
I will speculate further here and suggest that in fact logic in reality, metaphorically, as a triad, each member of which is the included middle of the other. make to research on reality – in physics, ontology and metaphysics – will require prolegomenon to the much deeper analysis that is required to take into account the I assume that reality, the domains of which all theories try to describe, the previous chapter. Thus, the most important task at this point in my develop-been left undefined. The description of reality in terms of levels also has left unde-sions of structural realism in science in Chapter 6 and cosmological structure in
I have adapted this idea from the ‘trialectic view of reality‘ of Craciunescu in which each member of the triad of epistemology, poetry and metaphysics can be the included middle of the other two (Craciunescu 1999). Seibt, Johanna (2005, private communication).
NEO category of Energy, there is a classical identity morphism that maps Energy The functors, at least informally, operate as might be expected: every- Regarding the morphisms within all the categories, the mappings, it may be a consequence of the theory that they look very much like the axioms and onto-is not. If there is, they belong in the sub-category NSC of the category of Dynamic Opposition. Within NSC, the single morphism or ‘mapping’ must be interpreted as Energy, in which the function of self-mapping, which is a standard operation in in my opinion from the fact that category theory was designed to handle objects,
I accept the concept of preservation here, in contrast to its use in propositional logic; truth pres-ervation is not directly applicable in LIR. This picture nevertheless leaves place for the categorial features of both exhaustivity and ex-
it thus excludes the dynamic, contradictory properties of form, and thus does representation and goes so far as to suggest that the Husserlian categories of Fact, These fundamentally different links entail a complex structure in the category scheme. An ontology is not a catalogue or list of objects or processes , but a

Energy Equivalence
Process Change
Dynamic Opposition (SC and NSC) Qualification
Subject, Object and Subject-Object Representation
T-state Formationof entities in the sub-category of Non-Separability (NSC). In the example of Smith, 2 where formal and material categories link or apply to entities Nevertheless, the resulting conceptual structure is not unlike the one above defined in
5.4 THE STRUCTURE OF REALITY IN LIR 141Definition of Structure
jects it relates.
D2: The objective of the analysis is completely different. The relation be-
tween two elements is grounded by the Axioms of LIR and the PDO, and I
want to show what this implies for the real structure of a process. In other
terms, given two sets A and B, axiomatically a bijection f from A to B exists
such that substitution of B for A always entails similarity. In other words,
they have a similar structure since only one reality relation exists at this
meta-level, that of dynamic opposition.
Quasi-set Theory
sets) and the relations among them. Krause introduces the concept of quasi-sets in
D3: In LIR, entities are, by the fundamental axioms, both the same and dif-
ferent, both distinguishable and indistinguishable. This seems to me per-
fectly consistent with the interpretation of Krause for quantum cases. I need
to distinguish in some more formal way between macroscopic process ele-
ments involved in an ‘active’ process and objects for which the dialectics are
‘frozen’ (cf. Appendix 1) that is, subject to an input of energy, they are to all
intents and purposes in the ‘classical’ part of the LIR theory. This is similar
to the quasi-set situation, for such ‘M’ (macro) elements that are distin-
guishable, the set-theoretical description has a classical part.11
I thus arrive at a concept of structure, also, as an entity in the category of
This is again similar to the contextual concepts of Aerts. It should be considered the rule and non-classical parts.
structure?” The answer he gave was that structures are also dynamisms, not to be for its existence.” Thus, using the method with which we may by now be familiar, ), one embodying primarily bonding forces and homogenization, another primarily heterogenizing forces and a third at a T-state between the two. Any indi-vidual structure is never rigorously actual, that is absolute in any sense, given the pure structural forms, containers of containers, structures of structures, subject to an and static form; devoid of a present, going always from past to future, or even inversely, tive potentiality or T-state. Structure is thus defined by the sub-category of Non-Separability. The values (degrees) of actualization and potentialization or T-state are logical in that they depend on this syntactical structure as well as being con-sense to consider them, also, as dynamic forms, subject to potentialization and the actualization of their contradictions? I think the answer is yes and no. As
13 Lupasco designated all such processes as ‘non-ontological’, which meant everything that was becoming, experience and logic. He used ontological to refer to being, which for him consisted only of affectivity (affect).
simplified relations between terms. This would represent a reification of con-dynamic logic of the contradictory. Seeing that figures and grounds are related contradictorially, that is, alternately actualizing and potentializing one another, since every element is itself a form, it is apprehended in the form in which it is and Petitot developed a theory of morphogenesis, the origin of form, in terms of a Catastrophe theory (CT) abductively permits the classification and pre-diction of the singularities of the morphogenesis of a system, even without knowl-the natural sciences, CT was able to constitute an objectivity of phenomena of social sciences (humanities), language and thought. Petitot said that CT ‘purified’
familiar with the ideas of this book, the above separation into local and global re-neither form nor matter-energy need be considered primary in the sense that mat-of coherence, of one of the terms of a dichotomy or duality. According to my cate-gorial scheme, the Petitot-Smith approach would be applicable only to phenomena in the category SC. Indeed, most of the examples used in the paper refer to simple, tulate that these infrastructures constitute an objective correlate of the qualitative consequence is that one could go beyond the division of the subjective and the atoms, fields, etc.), governed by principles and laws capable of being defined mathe-matically from the geometry of space-time, can one ‘redescend’ from such an objective, mathematically determined reality to visible morphologies? entiated entities to be built up by and from them. Most importantly, the principles of LIR provide for what Petitot described as “reciprocal interactions between an
16 I note that these authors claim no causal predictive or explanatory power for their theory.
themselves instantiate dialectics, then they (the dialectical relations) can be ity, but then he should say so, and provide adequate characterization of those ‘virtual aspects’. My criticism of CT is not that it possesses a transcendental signi-ties.In LIR and NEO, the approach to states-of-affairs is not to seek invariants in elements undergo change. The phrase used by Cassirer of “invariants of experiencation of LIR, since LIR is proposed as theory of explanation, I must also look
As a further indication of the exclusive role of geometry, Petitot quotes Deleuze to the effect
affairs might be instantiated, and the phrase ‘both at once’ can only be understood being at the same time digital and analog, discontinuous and continuous, and , particle and wave. The part of a phenomenon is at the same time smaller and larger than the whole, and inversely. An intuition of intermediate states is pre-quantum measurement, he saw that quantum entities had to be described as both ‘both (A and not-A) at once’. This interpretation is now generally conceded to be Bohm’s underlying unity; Varela’s autopoiesis; the ‘creative spontaneity’ of Rescher; Popper’s propensities; Kauffman’s spontaneous computational ‘order for
A recent example (Miller 2006) is the search for a ‘bridge’ between two traditionally opposed hypotheses about how we infer the mental states of others: simulation theory (mirror activity) sive, the theories may describe “two processes we can mix together”.
artificial barriers between the classical disciplinary divisions in and between the under study. If LIR were only a restatement of the intuition of the prevalence of human affairs, it would not have much new explanatory value. The essential addi-in the physics of the universe that can be formalized as a logic or logical theory. In namic opposition at cognitive levels would in my view already be likely to be in-is frequently, or always, followed by one toward anti-reductionism is nothing such that former provides the basic concepts used in the latter. Both types of recognized theories, laws and ‘facts’ from other disciplines, the essence of my
5.5.3 Explanation and Metaphysics One debate about the nature of explanation can be readily approached
Subjectivist (S-explanation): explanation = act of explaining and
what is provided by that act; anti-metaphysical – explanations are
not natural objects and do not constitute part of the way things are;
typically, incomplete; the relation between explanandum and ex-
planans is syntactic.
Objectivist (O-explanation): explanation = natural phenomenon in-
dependent of subject; deals with the way laws and facts relate
metaphysically; typically, complete; relation of semantic entail-
ing most significant, but their theory has been severely criticized by many authors, relations of dependence. As evidence, these authors point to explanations made in causality playing any role in them. This is probably true, but it does not mean that stantiated by causal relations, and it is only at this second level that explanatori-
This discussion, I believe, is essential because LIR statements look like statements, that is, ones whose truth depends on matters, Meaning arises from the syntax and rules of the language used. Quine of meaning is both circular and non-naturalist, in my terms; it lacks a link to real-ity. Because there is no principled way of distinguishing cognitive processes lism’, since there is no way of selecting which of the causal relations involved in Naturalistic theories of mental states define their meaning in terms of behavior. This is the causal-role theory of content in cognition. If one assumes that other factors, but some way is still required for making this distinction. The way to that such structural relations need to be defined as immutable and independent of spatial and temporal location for human beings. Such distinctions My claim is that LIR provides support to a naturalistic, causal-role theory is possible to say, now, that an analytic statement is true in virtue of the causal consequence is that an absolute distinction between analytic and synthetic state-
21 This means that there is not a single rigorously identical concept that all subjects must share.
Energy: Effective Quantum Fields
T-state: Emergent Included Middle
6. The Fit of the Definitions of the Categories to the Inferential Roles of
‘Perception’: The categories assign meaning to all aspects of the mental rep-
resentations that constitute, for me, my patterns of inference-making about
‘Perception’, e.g., that it can lead to new notions or that I may be overloaded
and make erroneous judgments and arguments.

7. The Capture of the Content of the Scientific Concepts of ‘Perception’ by
the Definitions of the Categories: In the concepts of ‘Perception’ we have:
energy in micro- and macro-physical, chemical and electrochemical form;
dialectic of excitation-inhibition; changes at surfaces; a subject-object rela-
tionship between the energy and the perceiver; plans and ideas as T-states.
Kaye has criticized the inferential role account of mental content as circu-undercuts this objection since I use the concept of dynamic opposition to delineate The LIR approach thus permits a clarification of the ‘role’ of the causal tiation of the LIR two-level system of analysis: the causal role theory is itself syn-tial role theory serves in my view as form of control mechanism to check, as in the tologically interpreted a term or a process. From this, it is not too far fetched to suggest that the performance of philosophy is a dynamic and dialectical process it-that scientific findings and terms have philosophical as well as scientific rele-
parsing a string of words with syntactic categories produces a description that uses in Heidegger or the neo-Kantian phenomenology of Petitot. I have also established a framework for analysis that is broadly applicable to dualistic entities in philoso-Aerts, Diederik, Jan Broekaert, and Liane Gabora. 2002. Intrinsic Contextuality as the Crux of . Grenoble, France: Presses universitaires de Conference on Artificial IntelligenceHoffmann, Roald. 2007. What Might Philosophy of Science Look Like if Chemists Built It? The Devil in the Details. Asymptotic Reasoning in Explanation, , ed. Edward N. Zalta. http://plato.stanford.edu/archives/spr2002/entries/scientific-realism/ Boyd, Richard. 2002. Scientific Realism. The Stanford Encyclopedia of Philosophy (Summer
the PDO really is and what the meaning is of such a principle being ‘constitutive’. nature. The relationship to the dialectics of Hegel is explored, to avoid the that I will now address in detail. They are generally presented in terms of dualities, but the LIR logical system is founded on these dualities as fundamental proper- approach to the relations between them and the knowledge that this can occasion.
it. The sequence is often considered to begin concomitantly with the universe The problems of cause-effect and determinism-indeterminism are closely, conditioned, and his implied rigorous determinism was equivalent to a conception of a non-contradictory universe. No chance, then, since this would have to arise plish two tasks: (1) a basis for the existence of causality and finality is possible;
I shall use causality when focusing on the more theoretical or philosophical aspects of the phenomenon and causation on the more physical ones, but total consistency is difficult if not impossible, and I ask the reader’s indulgence in adapting his own distinctions, if any, to my ‘inconsistency’. The problem of causality has been referred to a the “black hole at the center of our universe”
The same reasoning applies to the epistemological subject: as actualiza-like idealism, both functions of the causality of antagonism. In order to visualize multi-dimensional process. Feedback occurs not only in the general systems sense, between, say a conscious objective of executing a plan of action (non-contradiction) The contradictory interaction of the two main causalities of non-contradiction generate by mutual inhibition (semi-actualization and semi-poten-make a key link with the concepts of immanence and transcendence, since (1) the be called transcendent to the extent they transcend contradiction; but (2) these manence and transcendence ‘cause’ themselves reciprocally. An essential corollary means that they are not to be separated from phenomena as such, provided
situations, tropes, states of affairs, etc. (fine-grained), and their number varies
from two to four, when it is considered to include causal alternatives
(counter-factual events, ones that could have happened but didn’t).
LIR: there are two relata that are processes, including events and some facts,
in the category of non-separable entities. Other events and facts, also with
two relata, including propositions quatheir meaning, are in the sub-category
of Separability. The former, which also may include the latter at the same
time, instantiates the two chains of causality; the latter only the standard
chain of simple proximate causes.
2.Immanence and Transcendence
Events, etc. are considered real and immanent, while facts, as true
propositions, are considered abstract and non-spatio-temporal.
LIR: immanence and transcendence are related contradictorially, and are
not absolute, but refer to the relative degree of contradiction and non-
contradiction respectively. Both facts and events can be immanent or
transcendent. If there is no antagonism, contradictorial interaction, there are
only simple causes and effects in the everyday sense.
Since absences can be involved in causal relations, they are considered
transcendent in one standard view as being non-occurrences, negative exist-
ential statements, involving negative properties, whereas another standard view
denies that absences can be causal.
LIR:It is practically a paradigm statement of the LIR view that absence can be
causal – immanent or transcendent in the sense of 2. This is what I meant
earlier by the giving adequate ontological status to the negative aspects of
Individuation (see 1.) is supposed to lie on a continuum from extreme
coarseness (simple events) to propositions, the most finely individuated.
LIR: I see the continuum in a different manner, in terms of antagonism, in
the sense that there can be coarse events with little antagonism, and fine
events involving substantial antagonism, and vice versa.
5.Relation, Determinacy and Connection
The nature of the causal link has been the source of the greatest controversy.
One finds two sharply opposing views: the causal connection is indetermin-
istic, defined in terms of probability; a cause raises the probability of an
effect (see below, probabilistic causation). The other view that is an account
that talks as in LIR about change, energy and process considers that cause is
The complexity of this approach to causality notwithstanding, it can be causality of identity, universality and necessity, because induction was its basic and appearance are attributed. It is thus not surprising that the notion of cause causality of diversification. There is no ‘science’ of this causality, but it can be of negation, chaos, irrational change, of a fundamental anarchy. Here can be found In fact, the objective inductive causality of negation or heterogeneity, the absence of an objective causality of identity and seem to behave according to
principle remains strong. The key conceptions are those of Prigogine of dissipative Although the development given here includes an explanation of how This causality of antagonism adds, to the classic unilateral causality, linear, on the surface, mono-dimensional, gliding, so to speak, from one fact to another, a second causality, in depth, of facts which are perturbed and potentialized by the antagonism of the classical causality and which are ignored by current science. To every causal sequence corresponds an antagonistic causal sequence, inherent in the nature of the energy that the domain of operation of classical causality, could be considered, in my view, a domain of processes and events that, if not abstract and transcendent, are primarily the primarily applicable causality would be one of antagonism or contradiction remained disconnected for Peirce. It is very
structures as final causes in preference to any inherent, internal constitutive dualism or
elimination of the inward-outward ‘cut’, and so on. Throughout this book, eli-category of Separability (SC) combine ‘freely’ without necessitating anything real, characterized by its diversity, and by the interaction between identity and diversity The contradictorial relation between actuality and potentiality in LIR thus My picture is supported by the position of Heil (2005), that manifestation of a disposition is the manifestation of reciprocal dispositional partners, and that in dispositional and qualitative intrinsic aspects, but he does not say why or how they This is ‘in essence’ an argument existence of some metaphysically necessary laws of nature. If electrons, for example, ing charge and spin, essentialists would claim that there is no deeper structural
I defined the logic of/in reality as, among other things, a theory of change. ralizations of standard statistical mechanics are appropriate here. As pointed probabilistic and statistical notions even in simple macrophysical systems. Non-leading to an emergent included middle (T-state). To the extent that statistical that simultaneous correlated events must have prior common causes (Arntzenius common cause that confirms the absence of such relation (screens off the correla-common is a practical impossibility and would trivialize the notion of common their parts. In the case of the flock of birds, at ‘equilibrium’, it acts more or less as
cause and effect relations, something that emerges naturally from LIR. The having probability-like properties, can be modeled by the notion of probability in the more standard sense, as here. However, there is no reason to assume that The actualization may not occur, but it would require an input of energy, via an potential from becoming actual or actualizing itself. Potentiality thus not only im-the energetic capacity, or oriented dynamisms, but also what maintains the pheno-can give the impression of a finality, a final cause, as if it were energy in potential-
On one recent view, epistemic possibility, what one knows about a possibility, is context-dependent and shades over into probability. This concept does not affect the distinction made here, since the set of binary choices still applies as the only one available.
them in terms of the potentialities of the entities present at the microphysical, .epipheno-of manipulability are avoided by a concept of an ‘intervention’ I, which does not The apparent absence of these additional causal powers provides the is causally inert. The crucial mistake in this line of reasoning is that it requires one
Definitions: For two phenomena (macro-variables) X and Y, where
X is the putative cause of Y, are associated macro-states of X and
micro-states Xij of micro-variables MSB(X), where MSB(X) is the
micro-supervenience base of X. Micro-supervenience is defined as
it difficult to decide which variables are macro- and which micro-. The relation formulation, micro-causation The LIR picture resolves, I believe, another issue, namely, whether explanations: explanatory, logical and causal ‘talk’ all follow the same principles, Intervention is defined so as to include not only counterfactual changes in back and forth between such talk and a representation in terms of variables.
184 6 LIR, METAPHYSICS AND PHILOSOPHY In self-organization at the higher level of an organism, one is dealing Under these circumstances, the most reasonable view is that self-organization is not, in and of itself, a ‘self ’-evident mode of system formation and of organization-by-external-agent, although the two are, again, dialectically rela-ted. Varela refers to something like my view of self-organization (Varela 1999) In the further dynamical systems language used by Varela (and also by organizers). Varela makes the geometry of the phase space and the trajectories of This is perhaps all right as far as it goes, but as I discuss in relation to Varela’s view of time, it does not go far enough. One is again left with critical
186 6 LIR, METAPHYSICS AND PHILOSOPHY integrated into and confirmed by mathematics, of continuity in our perception of Penrose, on the other hand, had the strong intuition that “physics and It is clear as discussed in Section 3.7.1 on abstract objects that in the the mathematical entities involved, but in the process of constituting these entities dynamic in LIR terms, between the appli-tween consistency and completeness in formal mathematical systems, the situa- A more serious critique of the above conception of the continuum is that reality is composed of ‘points’ and ‘instants’ in the sense used in the theory. If it is capturing the essential
8 Penrose saw larger cosmological structures as being possible (‘spin networks’ and ‘spin foams’).
188 6 LIR, METAPHYSICS AND PHILOSOPHY contradictory, antagonistic actions and both coexist, as inverse possibilities, demon-not measurable by extensive values. As these values are potentialized, it looks as if continuous non-identity with respect to itself; extensity is a continuous identity with dered as independent of one another, and from this point of view accessible to the homogenizing and heterogenizing respectively, but their necessary discontinuity is what constitutes their existentiality. on the availability of the Gödel theorems and the non-standard mathematical tions of differential and integral calculus using tools available from paraconsistent logic and non-standard mathematical analysis. This is an important current issue, differential equations are the most appropriate tool for modeling human behavior
The term paracontinuity is sometimes referred to as quasi-continuity.
Microscopic physical objects, biological and psychological agents
continuity and discontinuity which are both present in any phenomenon, e.g., ‘life trajectory’ of actual events are identified with the ‘linelets’ used in SIA as the fundamental units of objects in it. Linelets are too small to have either possibilities This thesis thus appears to depend on three interlocking assumptions: the infinitesimal of time can be explained by a contradictorial view of simultaneity this potential existence suffices for the development of infinitesimal analysis in
192 6 LIR, METAPHYSICS AND PHILOSOPHY than dynamism, and those who had difficulty deciding whether energy was a static quantity or a dynamic order, or neither one or the other while looking like both, or appearance of continuity in time and space with an intuition of the existence of its divisibility into “instants” of time and “points” of space of indeterminable size.
Elsewhere, Bell discusses variable sets that are intended to provide a feature of continuous unification described of the continuous and the discrete is an achievement of category theory that “Geometrodynamics”, a concept of John Archibald Wheeler, should be examined in this
194 6 LIR, METAPHYSICS AND PHILOSOPHY The further and greater difficulty is that local statistical or probabilistic causes also seem ruled out. The correlation between distant particles (cf. the Bell inequality listically. The correlation seems to be an irreducible fact, totally unlike any proposal is to change the view of causality at the nuclear level. Does this mean (1961, 1990) has shown a way out. He suggests that entities involved in quantum straightforward way” in which these entities existed or could be known than the
196 6 LIR, METAPHYSICS AND PHILOSOPHY actualization and semi-potentialization of each, an a-determinism emerges, what Lupasco called “the discontinuity immanent in logic”. (The two terms deter-minism and determinacy, for a principle and a quality respectively, exist in one each of intensity and extensity, that is, of speed or momentum and position. initially attributed the inability to determine both with the same precision not to kind of independent identity behind phenomena, either a geometric extensity, pure where and how can, even in our minds, the unpredictable, the continuous, non-identity emerge? If on the other hand, everything is indeterminate, from where and acy and indeterminacy that are related contradictorially, that is, when one is at some level to provide a necessary underpinning for an essentially statistical processes of evolution toward non-contradiction (identity and diversity) or logical or immanence, the symmetrical reciprocal inhibition of chance and necessity. If we look back at this point at some of the entities in the category of T-states, things that I have characterized as emergent included middles, ideas, works of art,
198 6 LIR, METAPHYSICS AND PHILOSOPHY something to be real?” Science is, of course, what is supposed to tell us about reality, and in this section I will try to disentangle the various concepts of the possible iterations of metaphysics of metaphysics? In my view, the origin of the concept of infinite regress, here as elsewhere, can be found in various types stop as and when no further information is added, that is, after the first few iter-independent (independence claim) of anyone’s beliefs, linguistic practices, con-Realists are open to challenges by anti-realists who reject the existence dimension of realism about a particular entity and either claim that such entities do not exist, or they exist but do not instantiate any of the properties ascribed to them.
15 Cf. Priest’s contradictions at the iterative limits of thought (Priest 2002).
200 6 LIR, METAPHYSICS AND PHILOSOPHY Scientific realism is the stance that best captures the general validity by anti-realism, and both will alternately predominate as more or less valid in (2007), I wish to support a program of a principled unification of science, in principles or patterns of physics while also involving emergent ones of their own. for me rather odd to note how often examples used to illustrate philosophical
The fluttering in the wind of a crumpled thousand-dollar bill has been used to discuss issues about fundamentalism in laws of nature. Others often used are simple, reversible ‘to-all-intents-and purposes’ physical changes of phase. I see LIR and the PDO as making accessible for and reality are involved as in the psychology of lying or cheating. scientists, validated by consensus, as representations of reality, that is, that ledge is accordingly approximate, one is justified in accepting the findings of
202 6 LIR, METAPHYSICS AND PHILOSOPHY perceived inadequacies of naïve scientific realism to respond to the problems of something The definition of structure in mathematical terms and the resulting structure/nature distinction begs the question of whether structure-as-equations be known of nature” whether there must be, in addition, meaning assigned to a debate by establishing the role of Dynamic Opposition as defining, at least in The ontic structural realism (OSR) of Ladyman and his colleagues is a complete current response to anti-realist challenges to scientific realism, since it insures that there are adequate metaphysical components that are lacking in definition by French and Ladyman of OSR was to permit a metaphysics of this theory metaphysical structural realism (MSR) appeared to totally eliminate the OSR, which morphs to Information-Theoretic Structural Realism (ITSR) answers
basis for such a connection. LIR thus opposes and argues against
anti-realism in philosophy and science. LIR accepts as reproduci-
ble, quasi-scientific evidence that people do defend one position or
the other and makes the reasonable assumption that ‘psychological
factors’ of some sort must be at work. But it thus says something
further and perhaps more interesting and important about these two
.More simply: “A pattern is a relation between data.” Ladyman’s position is that what exist are just real patterns. instances of properties. What is not of serious ontological account are un-of properties. Thus seeing phenomena not as the ‘result’ of the existence of things, but their (temporary) stability as part of the world’s modal contingency, is something that is acceptable in the LIR also accepted. There is information carried by LIR processes from one state probability-like non-Kolmogorovian inequalities, although it may not be easily The theories of mathematical structural realists like McArthur, and ontic realists like Ladyman and his colleagues might thus benefit from something like my view of structures as dynamic entities. In LIR, these are the sets of processual description of the relevant relations is lifted: the relations are the logical variables
206 6 LIR, METAPHYSICS AND PHILOSOPHY example, the components of perception indicated in Chapter 5 as empirically as a naturalistic philosophical explanation of why our beliefs based on properties allowing a certain ontological continuity accompanying a conceptual determinate, in the sense that, following the principle of bivalence, it is deter-
208 6 LIR, METAPHYSICS AND PHILOSOPHY and are subject to similar interactions in the brain, including the semantic ones that and usefulness of a distinctively realist understanding of truth.” Wait a minute. certain problems. Third, the citation places the emphasis, incorrectly in my internal and external, and suggest that many of the semantic challenges to realism
210 6 LIR, METAPHYSICS AND PHILOSOPHY chapter, that the PDO is a metaphysical structural principle. However, is PDO a 4, for both of them. Sklar calls it the “curious interworking of full laws (i.e., those The LIR position is that the PDO is just such a postulate. The locus of the intervention of statistical fluctuations (which in my view still follow, at a micro-right remains to be made. This will require a directed, appropriately designed developed for other purposes. But the concept of a scientific principle is also open systematicity in regulative terms. A scientific principle fulfills a regulative task of while being an and in relation with other entities are ontologically prior to laws of nature or not,
As quoted by Laudisa, Cassirer talked about an “ultimate common element of all possible
212 6 LIR, METAPHYSICS AND PHILOSOPHY approached by reference to the LIR treatment of identity and diversity as non-dependent on necessary connections between distinct states. The opposite, antagonistic position, as noted, is the one of Hume that no such connections exist necessity is metaphysical, grounded in the real features of the world; analytical grounded in form (syntax).
(1) P is a law relative to a theory T iff P is implied by T and plays a role R
within T.
theories contain propositions that play a special role within those theories that are, fundamental laws Roberts suggests a new form that a philosophical theory of fundamental by laws of nature. This in turn depends, however, on the proposal that what it is to quantities posited by that theory are indeed measurable. But such laws, in turn, epistemic dynamics that I have proposed. Elements are part of laws, and laws are
214 6 LIR, METAPHYSICS AND PHILOSOPHY a phenomenon whose causes appear to be essentially indeterminate. The argument, The notion of propositional truth that is used is in-epistemological devices without direct implications for physical processes, and the accidents defined as undetermined events; arguments that depend on a definition characterizing both A – models of real systems, equivalent to a semantic view of basic concept that laws should not have exceptions. For this discussion, the
trivially true: the ‘law of the excluded middle’ guarantees the truth of propositions of the form is in a region in which internal structural properties of the atoms or molecules have determined the elastic constant, but the macroscopic behavior is governed by the law and its simple, non-fracture, resistance being, in this view, a potentiality dependent on the microstructure of the material, that is, on the integral of its residual potentialities at the interface between molecules. A crack is not a boundary condition, but the structural site at which macroscopic mechanical
216 6 LIR, METAPHYSICS AND PHILOSOPHY The difference between boundary conditions and constraints is that the fundamental in the first place, and the relation between a regime of boundary level of description is the center of attention. What might be considered as reality developed above to their applications in some selected areas of philosophy Hegel’s dialectics, logic and ontology that may suggest themselves to the reader, it Both Hegel and Lupasco started from a vision of the contradictorial or
At the cosmological level, the difference between a central law and an auxiliary constraint vanishes since in the effective quantum field representation of the universe, the wave function of the universe is described by the Wheeler-DeWitt equation in which time is absent.
218 6 LIR, METAPHYSICS AND PHILOSOPHY contradictorial, dynamic view of energy, provided the difference in their role and …parts and whole are not identical, each only exists in opposition to the other and in order for each to exist for itself, each must as it were reduce the other to satellite status, dependent on itself. They are related essentially: each is only itself in relation to another that is its negation. … the contradictions in it (reality) that we see by looking at part and whole show that it is in movement, that it is constantly going over from unity to multiplicity and back again. But this relation of exteriorization is that of force (energy) required demonstration of his ontology at the lowest level of simply determinate a relevant philosophical vision of “embodied subjectivity, of thought and freedom emerging from the stream of life, finding expression in the forms of social existence, and discovering themselves in relation to nature and history.” In my beings” that is, microphysical entities. Lupasco (1987b) showed that there is no
220 6 LIR, METAPHYSICS AND PHILOSOPHY the importation as noted, explicit or implicit, of principles of binary logic My catch-all definition of philosophy is that of a set of disciplines –
1.The relations between the disciplines are themselves extremely complex,
but, again pragmatically, domains can be identified in which one or the
other is the preferred form of description. In turn, this can assist the
characterization of the additional key relation, namely, between
philosophy and science as differently constituted modes of inquiry.
2.Philosophical statements must be assumed to say
about the underlying reality, physical or mental, and it is accordingly
legitimate to ask if they do so successfully or not.
3.If, on the other hand, the statements are claimed to be (nothing but)
metaphors, it is legitimate to ask what the reality is like to which the
The logic of/in reality is a logic of experience, as well as of physics, Philosophical problems are not solved by experience, for what we talk about in philosophy are not facts but things for which facts are useful. providing a smooth connection to science (Pouget 2004) through mutual
(or by which) Transcendence is specified, namely Dialectics. Term-to-term oppositions remain .Affirmation – Immanence, and Transcendence is thus specified by Dialectics, but its relation to Immanence is not Dialectics. These are not dynamic relations in the LIR sense, in which the relations between non-absolute elements constitute the ‘dialectics’, and there is no difference between opposition and dialectics.
224 6 LIR, METAPHYSICS AND PHILOSOPHY The existence of a phenomenon in the universe capable of reflecting on its own existence and referring to it symbolically is only one of the innumerable ways in which the human mind has been described. The philosophy of mind can quasi-physical aspects – biological, neural, causal, computational – and its its self-referential properties, self-consciousness. The problem is thus enormous, mental tokens that retain the properties of intentionality, “aboutness”, individua- different, here physical and mental tokens, philosophical or metaphysical, that is based on entities, physical and mental in the Philosophers of mind may, however, already see that a revision is possible of If there is a philosophical attitude endorsed by LIR, it is, certainly, one mental phenomena and their relations of partial self-reference exclude the appli-used or implied in discussions of intentionality is simply a measure, for me, of the
226 6 LIR, METAPHYSICS AND PHILOSOPHY Arntzenius, Frank. 1999. Notes to Reichenbach’s Common Cause Principle. In Bell, John L. 2006. Abstract and Variable Sets in Category Theory. In Monza, Italy: Polimetrica International Scientific Publishers. Introduction to Deleuze’s , ed. J. Khalfa.London: Continuum Editions. 149: 491–508. Conceptual Developments of 20 Century Field TheoriesCat, Jordi. 2005. Modeling Cracks and Cracking Models. Auto-organizaçao: estudos inter-Campinas, Center for Logic, Epistemology and the History of Science 30: 13. Baltimore, MD/London: Johns Hopkins University Drewery, Alice. 2005. Essentialism and the Necessity of the Laws of Nature. , ed. J. Seibt. Dordrecht, The Netherlands:, ed. M. Esfeld.Frankfurt (Main)/Germany: Hitchcock, Christopher. 2002. Probabilistic Causation. In The Stanford Encyclopedia of Philosophy (Summer , ed. Edward N. Zalta. http://plato.stanford.edu/archives/sum2005/entires/ Boyd, Richard. 2002. Scientific Realism. The Stanford Encyclopedia of Philosophy (Sum-, ed. Edward N. Zalta. http://plato.stanford.edu/archives/spr2002/entries/ 144: 343–356.
228 6 LIR, METAPHYSICS AND PHILOSOPHY Sober, Elliott and Larry Shapiro. 2007. Epiphenomenalism – The Do’s and the Don’ts. In Studies , eds. G. Wolters and P. Machamer.Pittsburgh, Varela, Francisco J. 1999. The Specious Present. In Weiner, Matthew and Nuel Belnap. 2006. How Causal Probabilities Might Fit into our ,ed.Edward N. Zalta. http://plato.stanford.edu/archives/fall2001/entries/ Salthe, Stanley N. 2004. The Spontaneous Origin of New Levels in a Scalar Hierarchy. , ed. Edward N. Zalta. http://plato.stanford.edu/archives/ Le trou noir de la causalité.PHILOSOPHIE .Cambridge:.Cambridge: Cambridge University Press.
(b) Time and energy are also related, in the sense that times closer to the Big
Bang correspond to higher energies.
(c) At the quantum level, there are additional dimensions, but they are hid-
den at the macroscopic level; correlations between states of quantum parti-
cles over arbitrary distances are possible (non-separability); and quantum
entanglement between states of particles provides a novel basis for infor-
The differences between quantum and macroscopic properties do not seem consciousness, of two estimates of ‘the’ time. I will address in what follows a Another way of stating the problem of time is that given its very real ap-inhabit, what is the relation between them? Further, is there some assumption we I will organize my analysis as follows: Section 7.2 will present the LIR conceptions of time, space and space-time derived from the fundamental postulate two ‘things’ and an oppositional relation between them. Section 7.3 is a review of will look at their implications for the philosophy of being and becoming. Section pondence of its principles with current realistic formulations of general relativity, 230 7 LIR AND PHYSICAL SCIENCE: TIME, SPACE AND COSMOLOGY
Theorem 7.2: Objects and events do not exist or take place in time, but are
identity and relations and implications are totally fixed, incompatible with time and change. Together with much else, time is relegated to the domain of the psycho-and future, but these logics do not provide a model for the dynamics of change as ential equations, but neither the realities of phenomenological time, nor physical ponding to the identifying actualizations of positive ortho-deduction, physico-, at the mid-point, corresponding to a minimum of non-contradiction and a maximum of tendency to contradiction, tities, which could provide a logical basis for the phenomenological ‘nowness’ of Varela (1999). In any event, it would be fair to say that the LIR scheme provides a more
2 See below, Section 7.6.4, on a cyclic model of the universe. 3 See Lupasco (1987).
234 7 LIR AND PHYSICAL SCIENCE: TIME, SPACE AND COSMOLOGY its logical aspects. There are both spaces and times, which are individual
Theorem 7.3: Objects and events do not exist or take place in space, but are
of the number of its elements and of their degrees of freedom; it is what links set M of the Axiom of Choice of Zermelo-Frankel set theory (cf. Appendix 2), a space that could be called photonic space; a negative or heterogenizing space of biological configurations, particles following Fermi-Dirac statistics, the sets N of choice, or electronic space; the third is the space of interactive quantum pheno-the Axiom of Choice. Let us now look at the relation between simultaneity and succession. a passage from a degree of potentialization to a degree of actualization, of a certain quantity of potential energy to a certain quantity of
236 7 LIR AND PHYSICAL SCIENCE: TIME, SPACE AND COSMOLOGY ture of time and space, are both semi-actualized and semi-potentialized, one has interpretation for so far are fundamental questions that remain as to the presence, into account the role of the gravitational field. I agree with the often made point formal. He constructed a framework for abstract notions of the epistemological properties of the human subject within which diachronic logic gives only very
I am grateful to Professor Jean-Yves Béziau for bringing the work of the Polish logician Roman
238 7 LIR AND PHYSICAL SCIENCE: TIME, SPACE AND COSMOLOGY Although Derrida makes his analysis here primarily with reference to was that of a paradoxical appearance of ‘double intentionality’, a mixture of pas-complementarity between spatial and dynamical ingredients, affect, and trajectories that the trajectories provide the “conditions for an embodied coupling, since through Phenomenological accounts of the structure of experience and their counterparts in our lived experience – Varela asks for a ‘circulation’ between them, that is, their
suggest that one should see the Derridean experience as an emergent included middle between
�Eternalism = The Block UniverseŽ Past, present and future are
An on-going debate in the standard philosophy of time revolves around pastness and futurity are attributes of events entails a vicious infinite regress and a consequent contradiction, fails to hold. McTaggart argued that time is unreal contradiction. Smith adopts a number of strategies, which will not be reproduced it is not logically necessary, as assumed by McTaggart, that events occupy moments. However, without a logic of dynamic opposition, this is an abstract statement that simply denies the commonsense intuition. More importantly, the regress, albeit concept of such a regress is not self-contradictory and hence is able to have real
11 These inherences can be understood as something like potentialities in LIR. 12 An analysans is a sentence that makes explicit something implicit in the analysandum.
242 7 LIR AND PHYSICAL SCIENCE: TIME, SPACE AND COSMOLOGY absurd, because it excludes an interactive contradictory relation between time and space. Passage is both objective and subjective (in both the broad sense, as the locus valid, what then is based his conception on human experience, but it is not a criticism to say, as I do, that it is more fundamental than Heidegger thought! Heidegger saw that
that occurs objectively can be described in science” and then argues that passage
244 7 LIR AND PHYSICAL SCIENCE: TIME, SPACE AND COSMOLOGY What I mean by adequately relativized possibilism is the following: the They perhaps describe phenomena occurring at some kind of limiting state, in The concept of the relativity of simultaneity as “the point of departure for our me-taphysical questions rather than the answer to any” cannot be supported. My view Further to this is the question of the relativization of to a frame, Is the concept of existence, then, like the concept of truth, which, when relativized (as pronouncements much like Gödels? This difficult and fundamental question has by no dynamic aspects that also apply to existence. Second, simultaneity in LIR has an retain the classical view on reality, as being the collection of all simultaneously happening events, there has not been proposed a real relativistic equivalence for reality in a serious becoming, not being. The introduction of time as a fourth geometrical dimension, perience “an actuality and not just a potentiality”. The advantage of my approach, vious discussion of simultaneity, that no appeal to travel in a relativistic space-time is required to confirm the current existence of reasonably stable future
246 7 LIR AND PHYSICAL SCIENCE: TIME, SPACE AND COSMOLOGY basis for principled avoidance of either reductionism or anti-realism as preferred circular picture of being and non-being, and being and becoming, and at the same time supports the principled extension of quantum mechanics to macroscopic Sklar suggests a different an approach that “looks for the resolution of the problems (inherent in the quantum view of the world) in a modification of our traditional thought concerning some of the most pervasive and general modes we have for describing the world”, in my terms, logic. He asks whether a revision of of logic being immutable and independent of experimental knowledge, perhaps it (logic) is just as much an empirical matter as chemistry and geometry is now taken our metaphysical picture of it. At the latter level, the one of greatest generality, the There is a hint of this in the usual description of the possibility (1) of salt dissolving in water that depends on (2) a piece of salt having an actual constitution of ions. If the structure of space depends only on the collection of all possible
248 7 LIR AND PHYSICAL SCIENCE: TIME, SPACE AND COSMOLOGY a quantum particle, and its space-time description (kinematic) and causal (dynamic) simple juxtaposition. Apart from providing no explanation or description of how The very nature of quantum theory forces us to regard space-time co-ordination and tation: phenomena or information were mentioned as being complementary, rather It is not logically unacceptable for exactly the same reason. Two answers can be If one assumes, for the sake of argument, a principle of non-contradictory 1987). This means that one or the other aspect can only be partially and never completely actualized, and the other subject to an indeterminacy that can be represented by its potentialization. Contradictory processes, identification and diversification, or attraction and repulsion, go toward the limits in both directions
250 7 LIR AND PHYSICAL SCIENCE: TIME, SPACE AND COSMOLOGY and non-separability. finition of quantum physics, although the failure of non-commutativity and non-gics, were well known. It was only in the 1980s, with the advent of paraconsistent are always contradictory, and hence this group of logics is termed paraclassical: In my view, this underlying logic for for discussing the epistemological requirements of quantum theory. However, the above discussion indicates that Bohr was also in part a realist, and made an
the Danish Order of the Elephant as well as the Nobel Prize. The Latin motto reads: Opposites and
252 7 LIR AND PHYSICAL SCIENCE: TIME, SPACE AND COSMOLOGY complementarity based on paraclassical logic, but no less deserving of serious LIR, both from the point of view of the impossibility of absolute values or isolated events, and, what amounts to the same thing, the primacy of relations in a pro- In standard QM, there is a core conceptual difficulty in reconciling the characterized by uniquely determined events. According to the theory, an ob-may have happened and at the same time may not have happened. RQM offers a way out of the dilemma. QM becomes a theory about the physical description and the
categories of existence, while the world as processŽ is the first category of explanation. One does not need to argue about the hierarchy here; what is important is the existence of a conceptual relation between relation and process.
254 7 LIR AND PHYSICAL SCIENCE: TIME, SPACE AND COSMOLOGY as well as the intuition we have of its being something fundamental in the universe, the entire neural network that would be a superposition of the wave functions of of the former. However, up till now, there has been no alternative to seeing, in the could be seen as quantum phenomena, despite excellent biophysical evidence that understanding of consciousness, published in 1994, has by far not terminated. missing needed to incorporate central issues of human mentality within a coherent is in agreement that the strange world at the quantum level is real and permits real within physical reality, and that deeper theories will make the place of mind in the
18 The hardest problem remaining at this time is that of human individuation, why I am me and not someone else, not the behavioral aspects of consciousness.
256 7 LIR AND PHYSICAL SCIENCE: TIME, SPACE AND COSMOLOGY In Section 4.4.1 on the self-duality of the quantum field, I speculated on will provide an interpretation of the other major component of existence, the tence. General Relativity (GR) was introduced to handle the extension of relativity reduced to matter and absolute time, the absolute time “of the universe” was
In work on new foundations for geometry and computation, Michael Leyton has criticized theories, from Euclid to Einstein, that maximize invariances on the ground that they are memory-less. Leyton proposes the grounding of geometry on a concept of maximization of memory storage, that is, on shape. Leyton shows that certain shapes, described in a highly technical wide-ranging rule system for inferring history from shape (Leyton 2005). Lupasco cites the strangely significant statement by Eddington: Ž: two terms with the same ontological value, each defined by the other that opposes or negates it, and existence as a whole defined by both at once.
258 7 LIR AND PHYSICAL SCIENCE: TIME, SPACE AND COSMOLOGY epistemic part to the information encoded in the metric that must be specified in part of the gravitational field. The identity of point-events is conferred upon them intrinsic properties instantiated at those points including mass, charge, spin and dividuals however, their properties can be viewed both as extrinsic and relational, freedom of the gravitational field. “In this way both the metric field and the point-space-time in this model does not force us to abandon an entity realist stance about contradictional relation between identity, which implies indistinguishability, and ordinates (3-spaces). The reality of the vacuum space-time of GR, the dynamical
260 7 LIR AND PHYSICAL SCIENCE: TIME, SPACE AND COSMOLOGY actuali-zation and potentialization of the elements. The necessary change to the The concept I suggested above of objects (matter/energy) being the source physically, the points of a four-dimensional manifold. The gravitational field is high quantum number. In another metaphor of Lusanna and Pauri that I see as an The issue of simultaneity of events offers a good opportunity for com- The account that is emerging in GR yields an image of a complex curved dependent on the definition of a global, non-inertial frame of reference but this
24 This is in fact a form of paraconsistent logic.
262 7 LIR AND PHYSICAL SCIENCE: TIME, SPACE AND COSMOLOGY Both quantum field theory and General Relativity describe the relations involved on structure (1967) cited earlier: he said essentially that objects can neither appear (to us) nor exist except as a elements related to others. Everything is relational; nothing is self-sufficient. There is a ‘law’ of contradictory relationality, described in Appendix 2. They are: (1) the relation of antagonism or opposition, whose elements are attraction and repulsion; and (2) the relation of contradiction, tioned above in connection with Relational Quantum Mechanics (RQM), where I processes (Appendix 1). The ontological commitment to relations in LIR and OSR, space-time relations and the objects that stand in the relations, considered as
26 Esfeld and Lam (forthcoming).
264 7 LIR AND PHYSICAL SCIENCE: TIME, SPACE AND COSMOLOGY mutual ontological dependence between relations and objects regardless of what by the axioms of LIR and its fundamental principle of dynamic oppo-sition. Stated reality or being, one would, in this theory, still never find a single object ‘existing’, around the nature of the gravitational field and/or the reality of strings as fun-expanding universe have assumed an initial singularity, the Big Bang, at, or as, the origin of the universe, in which matter-energy had ‘infinite’ temperature and selected the model proposed by Steinhardt and Turok (2002) as an illustration of
27 I will not discuss here the endless speculation of how such a notion can be reconciled with the experiential notions of time and space (what was before the Big Bang). These questions are applicable only to the veiled three-dimensional view of reality that is possible to us as medium-sized macroscopic objects, and, as indicated, probably badly posed.
266 7 LIR AND PHYSICAL SCIENCE: TIME, SPACE AND COSMOLOGY principles I have been talking about, the cyclic model, in which one can see the , eds. D. Aerts et al.Dordrecht, The Netherlands: , eds. A. C. Elitzur, S. Dolev Da Costa, Newton C. A. and Décio Krause, Décio. 2004. Complementarity and Paraconsistency. .Stanford, CA: Stanford University Press. The Stanford Encyclopedia archives/ sum2002/entries/qm-copenhagen/.
suggest additional potential real-world implications entangled when at rest lose spin entanglement when accelerated to relativistic speeds, their Worldviews, Science and Us: Studies of Analytical Metaphysics. A Selection of Topics from a Methodological Per-, eds. Robrecht Vanderbeeken and Erik Weber. Dordrecht: Springer. SYNTHESE
emergence. A categorial interpretation of the related issues of closure and down-and evolution and natural selection is suggested, and the essential role of the Pauli
Inanimate Systems
Living = Perceiving Systems
Conscious Systems
Knowing Systems 269
271 reassign it to the category of separable entities. I am, of course, most interested objection that is relevant here is that my core thesis does not apply at all, either to theory or experiment. The objection has been made, for example, that it is physics. My counter-strategy will be to show, as I have in regard to these issues earlier, that theories of biological systems (cf. Appendix 2) that do not take con-biological level of reality. The processes leading, in some as yet undefined way, easily identifiable aspects of dynamic opposition, instantiated in those properties. An This postulate of the real, logical and dynamic opposition at the heart more complex levels of reality, requires that it applies to fundamental particles, protons and electrons, atoms and inorganic and organic molecules and ultimately the living organisms that are constituted by them. Everything that involves this
sub-category of Process, and Emergence as the formal category corresponding to processes are grounded in the inherent properties of energy, and statements about
result from the antagonistic interactions between the parts. Organization can be Emergence is the consequence of the overall two-level structure of principles can be applied to the three competing views outlined above. I will then
could be captured by an algorithm, this would mean, in Lupasco’s critique of similar In his discussion of causal processes, semiosis and consciousness Emmeche of signs to living systems, is that “it does not force on us a dualist metaphysics Object in which it stands itself to the same Object’. The term ‘Sign’ was used by Peirce to designate the irreducible relation between the three terms, irreducible in the standpoint, is an outstanding heuristic device for keeping track of the entities involved in biological processes (Queiroz et al.2005), but its use should not make
and Spencer-Brown (“Logic could be an encoded form of geometry.”) In my view, dealing with time series and recursion, a source is given of time series “partaking process that drive people toward one or the other monism of identity or diversity as the basis of their preferred theories of reality, existence and thought. This tendency is nowhere more clearly illustrated than in the debate in science, still in theories of evolution and emergence, classical notions of part and whole, retaining some sense of irreducibly vital qualities (O’Connor and Wong 2002). conjoint action of causes leading to: (1) a total effect equivalent to the sum of the
the theory presented in this book might at first be considered a form of NRP also, microphysical properties; (2) Completeness of Physics – all micro-physical events are
SA1: A new emergent property H is at the same time new and identical to a
combination of lower level properties.
SA2: The microphysical realizers are used up to produce something
different from and transcending them, but they are not altered or superseded.
There is transformation of these parts in building something higher, but the
parts remain what they were.
SA3: Microphysical realizers are neither unconditioned nor homogeneous,
such that the higher level entity H can have causal powers of its own.
SA4: A new emergent property H is jointly responsible with the lower level
properties in determining its causal powers. One of the fundamental realizer
properties is such that it has a conditional power whose contribution is partly
determined by the higher level property it realizes.
SA5: The determinative influence of H on the lower level property is non-
causal, instantaneous, and does not involve a force, configurational or
otherwise and/or the transfer of energy.
No longer needed in any case since Quines critique of Natural Kinds (Quine 1969), especially
8.3 EMERGENCE IN PERSPECTIVE 281 and the practical impossibility of deriving them from fundamental principles in
Postulate: All high-level principles reflect, and can be derived from, the
same basic antagonistic properties of energy that constitute the fundamental
principles of existence, including those of basic physics. Accordingly, the
phenomena of ontological emergence can be described by the former and
‘properties’ (or the event or states consisting in a system’s having a property), systems and objects as such, seen as emergent ‘included middles’ arising mination or brute fact, or emergent features could necessarily appear (supervenience), or
8.3 EMERGENCE IN PERSPECTIVE 283 power resides in such organizations; and different organizations can have different In LIR, as we have seen, a degree of organization is ascribed to particles As Bickhard shows, Hume’s argument is that norms cannot be derived mentally new can be introduced. This argument is proved to be unsound, and interpretation of the overall set of sentences. It is Humean sense data reduc- restriction to factual premises reflects the substance-ontological commitment: sub- I would simply note that a theory that gives appropriate energetic process brium, and the operation of their complex cybernetics, close to the dynamic equili- My claim is only that the operation of MEP is necessary but not suffi-principle of exclusion between like entities, of which the Pauli Exclusion Principle But they went too far; my use of the word ‘vitality’ here could be considered
minimal: the billiard ball that is struck and modified in the process is, to all intents I will therefore state, as a result of my analysis to date, the second thesis
Thesis 8.2: The logic of/in reality, LIR, and its associated new energy
ontology, NEO, provides a doctrine of emergence that is both physicalist
and dualist, but its dualism follows the category of dynamic opposition and
the axiom of Conditional Contradiction, and confirms the physical and
‘artifice’, in the same category as (standard) logic and reductionism. That life has The problem is of course real. There is as yet no agreed upon pathway small molecules produced by electrical discharges in the primitive atmosphere, to gence of polypeptides with a capacity for self-replication. There is no detailed way of understanding how “molecules acquire an order that puts them in the right place at the right time” in the organization of a pre-biological entity. For this author,
8.4 EXPLAINING EMERGENCE 287 the fuzzy, basic and problematic semantic references to the particulars of system types, in other words, the real world. The five examples given are
The theory of autopoiesis, the self-production of systems;
Non-equilibrium thermodynamics, which takes its examples
basically from the macroscopic physical world, or primitive bio-
logical entities like slime molds, which he compares, in concor-
dance with my approach, to simple syllogisms;
Dual mode theories of life, in which the hidden prototype is the
genotype-phenotype duality of classical genetics
Complexity studies, with their heavy computational bias and
agenda, leading to
Autopoiesis is the term Maturana and Varela gave to the continual pro- My critique of this approach is not so much that it fails to refer explicitly such reference would be desirable. It is that without some such concept of In the Maturana system, the result of an interaction between an organism and a stimulus external to the organism is not determined in any way by that macromolecular level, all the way up to the level of the organism, and the same is
between the “first time emergence of a primary level and later repetitions of the creations of entities”. Constitution of levels is accomplished by the application physical entities and results in a category error. The thesis of this book provides two hypotheses that are ontologically applicable: (1) that the lowest relevant level have developed in a way leading to different species. The ones we know would have been unrealized and existed as potential only. The existence mayis an alternative argument that does not require the postulation of some prior America, without the intervention of aliens from outer space. More frighteningly, it is a possible model for the development of terrorist cells in the absence of any and biological levels is a major advance toward a needed theory of emergence. If the current physical universe and its chemical elements is indeed a “particular particular way of ‘coding’ organic chemistry, and if, as discussed above, the
6 For an opposing view, see again the work of Salthe, Chapter 6.
LIR: All complex systems involve feedback, enabling a parallel with Aerts
What makes our construction essentially different from the models one finds in the commutative propositions are related by uncertainty principles and are typical of systems which cannot, without an essential destruction, be separated into independent parts.Ž axiomatization of LIR. Aerts hoped that his “quantum mechanical model for the emergence. It states that it is not particles that are fundamental units of physics but quantized fields. These are processes, and processes are inherently organized, since While, as indicated, I agree with Bickhard’s conclusions, his argument makes some classical assumptions, e.g., about the relation between particles and In either the particle or field descriptions, some principle of organization seems to be involved which grounds emergence at the quantum level, and I have
The reason is, as discussed in detail in Appendix 2 on Systems Theory, that every feedback loop, natural or artificial, (cybernetics) can be viewed as a dialectics involving dynamic contradictory aggression, followed by the return to the (state of) regulation that must prevail for
objects or classes. However, also as shown by Aerts, there is a tight formal connec-Closure is defined and used by its proponents in a large variety of ways implies addressing the basic issues of the organization of matter in space and time,
Thesis 8.3: Closure is a formal sub-category of Process describing a more or
less complete set of functional relations between a system and its environ-
ment that embody the categorial features of antagonistic duality and fit the
Axioms of LIR. Closure thus is accompanied, as any real process, by its non-separable opposite of Non-Closure. Indeed, people talk freely of autonomous systems being
tific symbol systems, that is, ones that are dynamically inert. Topological semiosis, on the other hand, is a generalization of the notion of analog signaling.logical semiosis, all the interactions, responses, etc., of the organism involve logical included middle. There is no reason why this T-state cannot be, at its level, open variation that is reorganized at some higher level again into a new converse of the standard reductionist principle, namely, that the behavior of a properties: the LIR approach is an attempt to resolve the inevitable problems I thus construct the material category of processes instantiating down-
Lemke gives a useful table, with the suggestive name of Trans-organization across modes, of
recasting our basic metaphysical assumptions so as to account for the usefulness provide a way of differentiating between the causal power of mental events the intensional and extensional properties of energy to the higher levels, where closed under the laws of physics. Supervenience in this sense requires only the Using LIR, a number of illustrations of downward causation can be given, internal dialectics of concepts (Lupasco 1979), the resultant systems (of systems, (e.g., socio-political), provided the contradictory elements are in a dynamic rela- tion, and not a classical logical relation, of conjunction or disjunction (Nicolescu of knowledge. In higher, ontological levels of reality, the dynamic ‘complemen-rather than contradiction in the sense of counter-action as noted earlier. However, and biological components are (almost) absent, and those in which the latter are predominant, the category of T-states as included middles always enables, and is
ascriptions of causal relations above the (quantum) level of basic physics. I the masses of new data that have become available into an explanation of how Despite these developments, many questions over larger scales of time and
Origin of Life … the emergence of animate from inanimate matter
Evolution … the emergence of new species
Growth … the emergence of new forms in the life of an individual
The debate between mechanists and vitalists, presented earlier in this emergence itself. Descriptions of biological processes in terms of dynamic feed- My extension of logic to reality and its structuring as an ontology permits another way of approaching biology. This approach is in a sense quite novel, but I believe it may useful as a way of insuring that correct insights of conflicting views operate, whereas I propose a fundamental role for the antagonisms found at the physical and chemical levels of reality and consequently for the phenomena the establishment of the categories of Emergence, Closure and Downward Causation perspective, but was concerned that its concept of code-duality also might imply a of much neo-Darwinism. As Emmeche remarked, “the real challenge is not just to
for the description of the total system than for following its actual motion. As Without any epistemic cut, it can be argued, any use of the concepts of relation between the terms in this picture. To recall my definition, being a subject bolic control and actualization with measurement, following the approach implied The absence of a non-interactive relation between the two sides of the epistemic cut, as proposed, leads to a dead end. Pattee admits that the cut itself 8.7 EVOLUTION AND THE ORIGIN OF LIFE
tinction between matter and symbol. As implied in Chapter 5, material systems, , do not contain intrinsic symbolic activities or functions. In extreme of symbolic activity as unimportant. Computationalists are functionalists who interpret all processes in terms of computation, and the matter-symbol relation is Organisms, on the other hand, depend on internal symbolic controls, and the process of the origin of life requires, among other things, the existence of process to function, that is, have open-ended evolutionary potential, biologi- cal macro-molecules must have specific capacities for acting as templates for Semantic closure The definition of a symbol now becomes crucial: a symbol can be des-cribed as a relatively simple material structure, material including the senses of observers and individual measurements, in order to be sufficiently universal. 8.7 EVOLUTION AND THE ORIGIN OF LIFE
constraints. Parts no longer independent of each other constitute the self-organization of a higher level; as such, contextual constraints are the agents of inter-level, bottom-up causality. Acting top-down they simultaneously create new roles for those parts as they meaning in these contextual constraints. I suggest that higher level contextual operative at an early pre-biotic stage, and that most of the subsequent expansion of other such entities are real, but that there is an important sense in which they account for the evolutionary origin of any apparent epistemic cut. argues, is “the strangely overlooked key to biosemiosis.” As I suggest below in the systems model of evolution, ‘genocentrism’ is only one aspect of a general hormonal” molecules is not an inherent chemical property, but only a complex concept of code-duality as outlined here claims that the dynamic mode is basically a semiotic mode. What is essential is the “interdependence of the analog and the the temporal world, and analog codes provide the basis for interaction with the semiotic, whereas the analog twin remains in the sphere of classical dynamics, is 8.7 EVOLUTION AND THE ORIGIN OF LIFE
In the gene-centered view, genes establish and determine the direction In other words, an organism is a unique organized whole of mutually cor- Cells as biomolecular systems must have the capacity for continuous generated boundary as a condition of existence. Biological macromolecules are ontologically related to cells in the same way that organs are related to organisms. that it is proving even more difficult to duplicate. Both biomolecules and the cells The problem with this historical process view is that it is considered, one, and this is enough to render it suspect, which recourse to spontaneity is made at the lowest explanatory level, the only also instantiating, not the full set of actualized symbols that would lead, ulti-mately, to Johnson (2000) supports my critique of this systems picture in his view of a functional role of the categorial feature of diversity, specifically, in self-organizing ecosystems and their natural selection. Although a concept of diversity or quantitative understanding of diversity, like that of complexity, has been appears to be no satisfactory explanation for both local and global diversity in 8.7 EVOLUTION AND THE ORIGIN OF LIFE
Darwinian natural selection is incorrect, but it is so not because it does not exist, lism given the possibility for inheritance of acquired characteristics. I will not sug-gest specific criticisms or alternatives here. What I wish to point out is that CAP, like the theories of Pattee and other discussed above, also fails to explain “why
1. Assuming that prior to self-replication, there was random formation of
biopolymers on some template, possibly inorganic, and some of these cata-
lyzed the formation of others in an auto-catalytically closed set, some resi-
dual potentialities must have been involved derived from lower levels to
result in the high free-energy surface or structure that catalysis requires.
If there is a further requirement that some polymers adhere to one another,
to form a proto-cellular structure, it is again otiose to say that they must
have done so spontaneously. Further dialectical interaction with the context,
including some internalization of elements of the environment, also requires
that relevant potentialities be available for that process.
2. The transition from uncoded, self-organized replication to replication
per the instructions given by genetic code is indeed significant, especially in
placing restrictions on passing on acquired characteristics to the next
generation. But what on earth results in the advent of explicit self-assembly
instructionsŽ? Certainly something more than random processes are involved,
but attempts to make DNA only from small molecules in the laboratory
under biological conditions have failed. The only thing I can suggest is that
further transformation of high-energy bonds of precursors of DNA and RNA
into the additional necessary complexity occurred because such complexity
was present as potentialities. A better understanding of the interaction
between the precursors and their proto-cell environment seems necessary to
define what these were.
3. The same problem exists for the advent of sexual reproductionŽ,
although here the terminology becomes almost familiar: a mate is needed (as
context) to actualize an organisms potential for offspring. The question
remains open as to what might have been at the basis of the transition to this
principles of actuality and potentiality, and identification (homogenization) and In Appendix 2, I provide a discussion of an LIR theory of systems that is in fact another statement, in general terms, of the logical necessity of the PDO and its axiomatic consequences. I also show the relation of my theory to the General Here, I will mention some examples in chemistry and biology that
Reduction and Oxidation
Oxidation and reduction are clearly contradictorial in the LIR logical sense
since one always implies the other. One in fact always speaks of reduction-
oxidation (redox) systems. The quantity of energy-as-potential can even be
readily measured in vitro in this case: it corresponds to the standard oxida-
tion or reduction potential. Oxidation-reduction processes
characterized in addition by their tendencies to lead to homogeneity or
heterogeneity. In any case, the key point is to not to look at single values
and to represent phenomena, not in terms of substances or elements but as
processes, events and energetic actions. Photosynthesis amounts to the
reduction of carbon dioxide to carbohydrates, complex, biological polymers
by solar photons. It is a biological process that illustrates a process inverse
to the degradation of energy according to the 2nd Law of Thermodynamics,
since in it photons are up-graded to the electrons that effectuate the reduction.
Enzyme-Substrate Reactions
Most processes catalyzed by enzymes involve two or more steps. Rather
than a system acquiring energy from a high-energy bond here and using it
there to produce the desired new structure, one can talk in terms of the
actualization of the bonds energy and the potentialization of the energy of
heterogenization of the new biological systems, followed by a second step of
its actualization by another enzyme. The enzyme inherits its catalytic
to support the chemical and biological processes of life. More complex dissipative The thermodynamic view requires several supporting theories, including called variously drives, concepts, beliefs, and so on. LIR proposes: (1) the Pauli steer towards and maintain their goals, while counteracting various disturbances or
Variety, Constraint and Entropy
Variety refers to the number of states that a system can exhibit. If this
number is smaller than that potentially available, the system is said to
be constrained. A Constraint is the difference between these and as it
reduces uncertainty about the system, it is a kind of information. Variety and
The cybernetics of physical systems is characterized by a return to an identity, a constant value, invariance, or homogeneity; biological cybernetics results in a further variance, a heterogeneity. This tendency by negative feedback toward a homo- or heterogeneity is equivalent to a return to a progressive non-contradiction distributions of non-interactive systems is applicable in biology. Information can be causally effective. living substrates. This can be presented as the existence, concomitantly and has been little justification for such a distinction. One can then look at the present, as follows: in physical systems, with the increase in positive entropy, that proportion. Biological phenomena, from this standpoint, are highly improbable,
of their alternating actualization and potentialization. An alternative picture of chance and necessity, determinism and indeterminism was suggested in Chapter 6. A proponent of teleonomy may object at this point that I have made unanswered, but it may be badly posed). The creationist argumentAerts, Diederik, Jan Broekaert and Liane Gabora. 2005. A Case for Applying an Abstracted
should be and b) what might be the role of the atoms constituting the molecule.
Maurel, Marie-Christine. 2005. Lapparition de la vie. In OConnor, Timothy and Hong Yu Wong. 2002. Emergent Properties. , eds. P. B. Anderson et al.Aarhus: Aarhus University Press.Pattee, Howard H. 2001. The Physics of Symbols: Bridging the Epistemic Cut. 303:
change and provides a basis for logical inferences about them. The formal catego-associated opposites or contradictions. The former corresponds to the domain exclusivity and the entities of binary, formal, deductive logic as well as those that, value of my theory in this domain in resolving metaphysical and scientific issues , applicable to real phenomena. Classical logic is in too broad, but the classical definition of the domain of logic as too narrow. We 324 CONCLUSION: NEW DIRECTIONS AND A NEW SKEPTICISM
complexity, in which the equivalents of both efficient and final
The ideas in this book may thus offer a new approach to, for example, the nomenon. These are other areas in which a strict separation of two phenomena or plication of the contradictory links between them. The language of quantum phys-That my approach goes contrary to received wisdom in many areas is value the massive amount of knowledge garnered on the basis of non-contradiction, entific to take into consideration the contradictorial as well as the non-contradictorial sical logic is not the standard by which other logics can be judged. Classical logic consistent logics that will enable this new status to be attributed to it. And if these logics they will be the generalizations. And, in addition to their intrinsic interest, they will open 326 CONCLUSION: NEW DIRECTIONS AND A NEW SKEPTICISM
The application of this principle of skepticism applies also to theories and (Petitot-Cocorda 1992)are that the humanities same, by seeing the different ways in which the same underlying logical principles particular theories of logic, is not trivial. I conclude with a view of this matter by plementarity and the belief in the existence or non-existence of contradictions. As classicality and paraconsistency in a modal logic, namely, deontic logic. The pro-are possible, non-actual worlds in which normative conflicts (some things are both pasco said that his contradictorial logic of the included middle was the correct one “if, of course, the world is logical.” From the competition of views, from such op-Penrose says: We cannot at all draw a clear dividing line between what we call ‘matter’ or ‘substance’ and what we call ‘empty space’ – supposedly, the voids entirely free of matter of any 328 CONCLUSION: NEW DIRECTIONS AND A NEW SKEPTICISM sophical problematic of knowing if a paraconsistent logic is rival or complementary
Included Middle and Functional Association. Returning to the two-element nota-that, essentially, for any two elements or events that appear to coexist without a re-
APAPTT[() ()] [() ()] [() ()] (e,u)ŠŠŠ›ŠŠŠ›ŠŠŠŠ (App. 1.1) and can be seen as temporary arrest or interruptions in the dynamics due to the right statistical conditions (‘frozen dialectic’). The subsequent change can be seen
1 See Lupasco 1987. 331
A P A P AP ........A P A P AP ........T T T T TT ........ee(mm(nnee(mm(nnee(mm(nnxxx (App. 1.4) In this conception, all these implications of implications constitute, form in order to constitute a set. There is only a difference of degree in the principle of inclusion between a set and a class. Using Lupasco’s tables of deductions, a func-formed by dialectical freezing or ‘arrest’, identity actualized by its positive impli- The classical logic of classes takes into account only the identity of its Negative ortho-deduction forms an inverse series of classes of classes, appellations like logic of intension or inherence, or qualitative logic. The thought process involved consisted of ascribing quality or diversity to the subject, as a pas- The third contradictorial series of classes of classes, in which the values logical and esthetic experience. I then write, even more generally than before, us-
even if they use essentially classical reasoning, can be interpreted as establishing alized, for a contradictorial set theory, based on the PDO and the logic of the in-fundamental difference between LIR and all other classical or non-classical logics, is that each element of a set is a contradictory duality, composed of an element and its anti-element, such that the former expresses primarily an actualized iden-would be equivalent to a partial actualization of identity). It is the principle of
groups or systems. I will define systems as elements linked by either some internal pulsion or exclusion between elements which prevents their “agglomeration” into clusion and dissociation are equivalent terms.) Accordingly, for a system to form dissociate, to integrate and disintegrate. Every system is therefore a function of
that is a function of two antagonistic dynamisms, d, that can in principle be measured and quantified, given an adequate algorithm, in a quan-tity of antagonism, Q, as follows:
maxmax().()(.0)QsfddiifCC in the systems context, is based on the concept that every system gebra of energy” as a chain of implications expressing the above, with the addition ing from a state of actualization A to one of potentialization P, which can be
PTTAPeeeeeeŠŠŠgressive actualization of non-contradiction, and the third an actualization of con- These logical systems of energy apply to all phenomena or aspects of ex-perience, from microscopic to macroscopic, if it is agreed that antagonism and experimental, and their logic is a logic of antagonism. These logical systems are
1 The exceptions are the elements of classical mathematics and all other abstract elements, in-cluding semantic elements, such as paradoxical sentences, in which the quantity of energetic in-teraction is nil. 1. THE ONTOLOGICAL BASIS OF SYSTEMS IN REALITY 339
This information can be identified with the cybernetic operation (in its potentiality that the system senses. “The content of every potentiality is an ener-ble”. (In Chapter 8, I examined the relationship to this process of the dynamic Following the methodology of LIR, one should differentiate between a relative, partial non-contradiction in the two cases. In the dialectics of quantum or psychic phenomena, we have a third dialectic cybernetics, in which feedback leads Pattee discusses feedback in the category of causal loops that include bolic aspects of, in particular, living organisms, as discussed in Chapter 8.Systems Theory, GST), based on his fundamental research in biology and embry-study it as a system. Like the logic of/in reality discussed here, the necessity and
Lupasco’s ideas about control and cybernetics were formulated in the period 1950 to 1970, and
terms of opposites and why “our mental representation of the universe always mir-trast between structure and process breaks down in the atom as well as in the living Concomitant work by Prigogine and his school is well known (Prigogine and philosophic value to the diversity inherent in living systems. Unfortunately, due to to have fulfilled their early promise. Although von Bertalanffy’s rejected all forms of absolutism in philosophy and science, he lacked a vision of logic that was broad enough to support this. His concept of a system saw antagonistic relations among 343
Systems science developed after GST from the interaction of information new discipline that combines theoretical, practical and methodological approaches Systems science overlaps with complexity science, in that the latter is based on a definition of the complex systems that are the objects of systems sci-ternal structure as a consequence of such interaction. The non-linear interactions versity and stability, for which LIR provides an interpretation. Complexity science also looks at the dynamics of systems in transition regions of self-organized criti-grounding in dynamic opposition and potentiality that I have proposed as neces-sary to explain the functioning of such organization, as well as the ambiguity in Systems science includes aspects of such a diversity of sciences and account, in concrete systems, pairs of elements that are both conflicting and coop-
6th European Systems Science Congress, Paris, September 19–22, 2005.
actualism, 179 Bell inequalities, 36, 101 boundary conditions, 306, 317 and constraints. non-classical, 59 catastrophe theory, 192 categorial features
probability, logical discreteness, 186 continuity and discontinuity Copenhagen interpretation, 151, 197, 247 core thesis, iv, 124, 126, 136 of True and False, 277 digitalism, 307
internalization of, 311 epiphenomenalism, 180 contradictorial and non-contradictorial,configurations of, 54 explanatory power, 124, 133 as mathematical structure, 139 geometry, 145, 186
imaginary, 28 non-classical, 35
and efficient cause, 301 dualities of, 208 non-classicality, 129 of diversity, 55 non-existence, 77 imaginary, 78 non-existent, 78 applied scientific, 78
presentism, 245 Maximum Entropy Production (MEP), of determinism, 195 sub-categories of, 117 Boolean lattice of, 38
prior to relata, 202 self-consciousness, 224 mathematical theories of, 185 and classical dynamics, 302 absolute of opposing terms, 220 in philosophy, 222 paraconsistent, 334 S-matrix theory (SMT), 247 solipsism, 230 configuration, 110, 233 neo-classical, 105 stability, structural, 123
of non-standard sets, 141 2nd Law of, 38, 54, 92, 93, 191, 271 to explain life, 314 Thirdness, 275 in philosophy, 237 Unionism, 82, 225