In papers published between 1930 and 1935. Zermelo outlines a foundational program, with infinitary logic at its heart, that is intended to (1) secure axiomatic set theory as a foundation for arithmetic and analysis and (2) show that all mathematical propositions are decidable. Zermelo's theory of systems of infinitely long propositions may be termed "Cantorian" in that a logical distinction between open and closed domains plays a signal role. Well-foundedness and strong inaccessibility are used to systematically integrate (...) highly transfinite concepts of demonstrability and existence. Zermelo incompleteness is then the analogue of the Problem of Proper Classes, and the resolution of these two anomalies is similarly analogous. (shrink)
We give a review of some works where it is shown that certain quantum-like features are exhibited by classical systems. Two kinds of problems are considered. The first one concerns the specific heat of crystals (the so called Fermi–Pasta–Ulam problem), where a glassy behavior is observed, and the energy distribution is found to be of Planck-like type. The second kind of problems concerns the self-interaction of a charged particle with the electromagnetic field, where an analog of the tunnel effect (...) is proven to exist, and moreover some nonlocal effects are exhibited, leading to a natural hidden variable theory which violates Bell's inequalities. (shrink)
Part I [sections 2–4] draws out the conceptual links between modern conceptions of teleology and their Aristotelian predecessor, briefly outlines the mode of functional analysis employed to explicate teleology, and develops the notion of cybernetic organisation in order to distinguish teleonomic and teleomatic systems. Part II is concerned with arriving at a coherent notion of intentional control. Section 5 argues that intentionality is to be understood in terms of the representational properties of cybernetic systems. Following from this, section (...) 6 argues that intentional control needs to be seen as a particular type of relationship between the system and its environment. (shrink)
In this article, I present a novel approach to the scientific understanding of consciousness. It is based on the hypothesis that the full range of phenomenal qualities is built into the frequency spectrum of a ubiquitous background field and proceeds on the assumption that conscious systems employ a universal mechanism by means of which they are able to extract phenomenal nuances selectively from this field. I set forth that in the form of the zero-point field (ZPF) physics can offer (...) a promising candidate that is qualified for playing the dual role as both the carrier of energy and consciousness. The appropriate mechanism, which rests upon the principle of dynamical coupling of ZPF modes, is a unique feature of quantum systems, suggesting that the dividing line between conscious and non-conscious systems is defined by the differentiation between quantum systems and classical systems. The presence of this mechanism in the brain is supported by the neurophysiological body of evidence, leading to a consistent explanation of the dynamical properties of the neural correlates of consciousness. Building on these findings, I lay the foundations for the conceptually coherent integration of consciousness into the physical worldview, derive an indicator for the quantity of consciousness of a given system, and outline the further steps toward a theory of consciousness. (shrink)
: Despite some questionable decisions regarding its organization, this anthology is an interesting read and a valuable general education resource concerning the intellectual history, and subsequent evolution, of systemstheory. The book details early conceptual landmarks while emphasizing latter-day developments and applications, in particular in the context of cultural studies and the socio-economical sciences. While commenting on the book’s form and content I also raise questions concerning systemstheory’s standing in relation to such themes as consciousness, (...) constructivism, and the machine metaphor. (shrink)
It is proposed that the Darwinian theoretical approach and account of living systems has not yet been clearly given. A first approximation to this is attempted, focussing on behavior in evolving environments. A theoretical terminology is defined emphasizing the mutuality of organism and environment and the existence of biologically theoretical entities.
Recently, Brass and Dix showed 143–165) that the well founded semantics WFS can be defined as a confluent calculus of transformation rules. This led not only to a simple extension to disjunctive programs 167–213), but also to a new computation of the well-founded semantics which is linear for a broad class of programs. We take this approach as a starting point and generalize it considerably by developing a general theory of Confluent LP-systems CS . Such a system CS (...) is a rewriting system on the set of all logic programs over a fixed signature L and it induces in a natural way a canonical semantics. Moreover, we show four important applications of this theory: most of the well-known semantics are induced by confluent LP-systems , there are many more transformation rules that lead to confluent LP-systems , semantics induced by such systems can be used to model aggregation , the new systems can be used to construct interesting counterexamples to some conjectures about the space of well-behaved semantics. (shrink)
Advocates of the conserved quantity (CQ) theory of causation have their own peculiar problem with conservation laws. Since they analyze causal process and interaction in terms of conserved quantities that are in turn defined as physical quantities governed by conservation laws, they must formulate conservation laws in a way that does not invoke causation, or else circularity threatens. In this paper I will propose an adequate formulation of a conservation law that serves CQ theorists' purpose.
The purpose of this paper is to present in a uniform way the commutator theory for k-deductive system of arbitrary positive dimension k. We are interested in the logical perspective of the research — an emphasis is put on an analysis of the interconnections holding between the commutator and logic. This research thus qualifies as belonging to abstract algebraic logic, an area of universal algebra that explores to a large extent the methods provided by the general theory of (...) deductive systems. In the paper the new term ‘commutator formula’ is introduced. The paper is concerned with the meanings of the above term in the models provided by the commutator theory and clarifies contexts in which these meanings occur. The work is presented in an abstracted form: main ideas are outlined but proofs are deferred to the second part of the paper. (shrink)
Of all contemporary social theorists, Luhmann has best understood the centrality of the concept of meaning to social theory and has most extensively worked out the notion's implications. However, despite the power of his theory, the theory suffers from difficulties impeding its reception. This article attempts to remedy this situation with some critical arguments and proposals for revision. First, the theory Luhmann adopted from biology as the basis of his own theory was a poor choice (...) since that theory has no explanatory power, being purely descriptive; furthermore, that theory is fundamentally flawed since it implies that viruses are impossible. Second, Luhmann's theory of meaning cannot coherently make the social domain autonomous as he desires since Luhmann does not take into account the distinction between syntax and semantics. By introducing this distinction, making clear that social systems consist of rules, not just communications, and raising the rule concept to the same prominence in social theory as those of actor and system, autonomy can be maintained while avoiding the counterintuitive aspects of Luhmann's theory. (shrink)
Recent discussions in the philosophy of science have devoted considerable attention to the analysis of conceptual issues relating to the methodology of explanation and prediction in the sciences. Part of this literature has been devoted to clarifying the very ideas of explanation and prediction. But the discussion has also ranged over various related topics, including the status of laws to be used for explanatory and predictive purposes, the logical interrelationships between explanatory and predictive reasonings, the differences in the strategy of (...) explanatory argumentation in different branches of science, the nature and possibility of teleological explanation, etc. The aim of the present article is to examine the issues involved in such questions from the specialized perspective afforded by one particular kind of physical systems--namely, systems, here to be characterized as discrete state systems, whose behavior has been studied extensively in the scientific literature under the general heading of Markov chains. These systems have been chosen as our focus because their behavior over time can be analyzed at once with great ease and with extraordinary precision. (shrink)
In this thesis I outline a view of primary legislation from a systems perspective. I suggest that systemstheory and, in particular, autopoietic theory, as modified by field theory, is a mechanism for understanding how society operates. The description of primary legislation that I outline differs markedly from any conventional definition in that I argue that primary legislation is not, and indeed cannot be, either a law or any of the euphemisms that are usually accorded (...) to an enactment by a parliament. I cite two reasons for such a conclusion. The primary reason for my conclusion is that I see primary legislation as being an output of a particular subsystem of society, while the law is the output of another subsystem of society. I argue that these outputs are the discrete products of separate subsystems of society. I argue that primary legislation should be viewed as a trinity. The first state of this trinity is that, upon enactment, primary legislation is a brute fact in that it is but a thing and the only property of this thing is that of being a text. The second state of this trinity is that following the act of enactment, the thing enacted will be reproduced and this reproduction is a separate thing that will sit in some repository until used. The third state of this trinity is that, upon use, this thing that is primary legislation will be transformed into an object and the user will attribute such functions and attributes to that object as are appropriate to the context within which the object is used. The thing has therefore become an object and an institutional fact. The second reason for my conclusion that primary legislation is not a law relates to the fact that the thing that is primary legislation is a text and the only function of a text is that it is available to be read. That is to say, of itself, a text is incapable of doing anything: it is the reader who defines the status of the text and attributes functions and attributes. Upon use, primary legislation thus becomes a censored input for future action and one of these actions may be some statement by a court of law. I assert that the view of primary legislation that has been accepted within the body politic is the product of the discourse of a particular subsystem of society that I have designated 'the legal practice', and I outline why and how this has occurred. Outlining a view about primary legislation also necessitates outlining a view as to the nature of the law. I assert that the law is a myth and I see this myth as a product of the discourse of the legal practice. I have asserted that although it is the judges that state the law, such statements flow from the discourse of those who practise the law. (shrink)
A Steiner triple system (STS) is a set S together with a collection B of subsets of S of size 3 such that any two elements of S belong to exactly one element of B. It is well known that the class of finite STS has a Fraïssé limit M_F. Here, we show that the theory T of M_F is the model completion of the theory of STSs. We also prove that T is not small and it has (...) quantifier elimination, TP2, NSOP1, elimination of hyperimaginaries and weak elimination of imaginaries. (shrink)