Biology gives us numerous examples of self-assertional systems whose essence does not precede their existence but is rather revealed through it. Immune system is one of them. The fact of behaving in order not only to satisfy external constraints as a pre-fixed set of possible environments and objectives, but also to satisfy internal “viability” constraints justifies a sharper focus. Adaptability, creativity and memory are certainly interesting “side-effects” of such a tendency for self-consistency. However in this paper, we adopted a largely pragmatic attitude attempting to find the best hybridizing between the biological lessons and the engineering needs. The great difficulty, also shared by neural net and GA users, remains the precise localisation of the frontier where the biological reality must give way to a directed design.

Problem: There is currently a great deal of mysticism, uncritical hype, and blind adulation of imaginary mathematical and physical entities in popular culture. We seek to explore what a radical constructivist perspective on mathematical entities might entail, and to draw out the implications of this perspective for how we think about the nature of mathematical entities. Method: Conceptual analysis. Results: If we want to avoid the introduction of entities that are ill-defined and inaccessible to verification, then formal systems need to avoid introduction of potential and actual infinities. If decidability and consistency are desired, keep formal systems finite. Infinity is a useful heuristic concept, but has no place in proof theory. Implications: We attempt to debunk many of the mysticisms and uncritical adulations of Gödelian arguments and to ground mathematical foundations in intersubjectively verifiable operations of limited observers. We hope that these insights will be useful to anyone trying to make sense of claims about the nature of formal systems. If we return to the notion of formal systems as concrete, finite systems, then we can be clear about the nature of computations that can be physically realized. In practical terms, the answer is not to proscribe notions of the infinite, but to recognize that these concepts have a different status with respect to their verifiability. We need to demarcate clearly the realm of free creation and imagination, where platonic entities are useful heuristic devices, and the realm of verification, testing, and proof, where infinities introduce ill-defined entities that create ambiguities and undecidable, ill-posed sets of propositions. Constructivist content: The paper attempts to extend the scope of radical constructivist perspective to mathematical systems, and to discuss the relationships between radical constructivism and other allied, yet distinct perspectives in the debate over the foundations of mathematics, such as psychological constructivism and mathematical constructivism.

Key words: Foundations of mathematics, verificationism, finitism, Platonism, pragmatism, Gödel’s Proof, Halting Problem, undecidability, consistency, computability, actualism

The specificity of human knowledge allow one to construct specific truths about human behavior. A structural notation and language for describing a complex hierarchically organized biological system was developed for the explicit purpose of analyzing the origins of health and disease. A specific application of these concepts to a specific patient (such as an individual suffering from the heritable disease, sickle cell anemia) requires a systematic formulation of a scientific truth. No universal law is applicable. The value of a clinical truth for the patient, as well as for the physician and society, is substantial. This value has moral, ethical, and legal weight. Both physics and chemistry use a universal external invariant reference system. Human beings and other living organisms function by an internal reference system that is neither invariant nor universal. In order to address the complexity of scientific truths within living systems, a mathematical graph is constructed from observations, descriptions, and symbolizations of the relevant human scientific activities and is placed in mutual coreference with three philosophical theories of truth. Consistency within the referencing relations of the graphic object creates an image of complex truths. When mapped over degrees of internal organization, the structural consistencies can form hierarchically transitive relations (many-to-one) creating redundancies that confirm one-another. Both structural and dynamic information can be composed within the graphic framework. The redundancies intrinsic to the degrees of organization notation, semantics, and syntax augment one another in the search for scientific truth. The degree of certitude emerging from structural implications increases in relation to the number of hierarchical degrees of organization invoked to represent the various behaviors of complex systems (as illustrated by the sickle cell anemia example). The successful synthesis of the complex image (or complex simple) of a scientific truth approaches the Heideggerian notion of identity in the sense that A = A and A is A.

What is being discribed as differences between organic and cultural evolution (for example that one is Darwinian, the other, Lamarckian in character) depends on the implicit agreements made on what are analogue issues in culture and life. A special consequence of the definitions used is that opposite causal mechanisms are attributed. The development of empirical scientific theories is seen as an internal adaptation to external data. Organic evolution, however, is seen as an external selection of internal modifications. Seeing science as a special cognitive tool in the sense of evolutionary epistemology (EE) which then has to evolve according to the same principles as evolution of organic tools does, would require some notional realignments in order to level the established organismic/cultural dichotomy. Central to the approach used here is the notion of reality and adaptation. The EE declares that human categories of perception and thinking (space, time, object, causality etc.) result from evolutionary adaptation to the independent structures of an ontological reality (Campbell: “natural-selection-epistemology”). Here a “Constructivist evolutionary epistemology” (CEE) is proposed which goes one step further and considers also the category of reality itself to be a special mental concept acquired phylogenetically to immunize proven ideas under the label of “reality.” According to the CEE, the evaluation criteria for strategies and theories are the consistency with the previously and phylogenetically acquired organic and mental structures, rather than the adaptation to external data. A similar view can also be held in organic evolution where the various metabolic processes and higher strategies modify the external data according to their previously established own requirements rather than changing those requirements in adaptation to external data. Thus cognitive and scientific as well as organic evolution is an enterprise of conquest rather than of discovery and reality will lose its role as a universal legislator and evaluator. The CEE implements this thought, by considering all regularities perceived and the laws of nature derived from them as invariants of mental or sensory operators. The extension of human sense organs by means of physical measurement operators leads to the completion of classical physics if the experimental and the inborn cognitive operators commute. Otherwise non-classical (i.e. “non-human”) approaches are required such as quantum mechanics, which are based on the invariants brought about experimentally. As the set of possible experimental facilities (and therefore of new invariants) is not closed it follows that evolution of science will not end in a definitive “theory of everything” but in basically endless co-evolution between experiments and their theoretical interpretations. The same applies to organic evolution which can be considered as coevolution between genomic structures and their interpretation by the epigenetic system which itself is subject to genomic modifications. This may lead to non-stable recursive processes described here as nonlinear genetics. Some general evolutionary strategies and principles are discussed with a view to being applicable in organic evolution as well as in cultural and social evolution. Special consideration is given to the view that the need to master the physical world (mainly being done by scientific efforts) may be superseded in the long run by the need to master our social environment.

Most of what nowadays is called evolutionary epistemology tries to explain the phylogenetic acquisition of inborn ‘knowledge’ and the evolution of the mental instruments concerned – mostly in terms of adaptation to external conditions. These conditions, however, cannot be described but in terms of what is provided by the mental instruments which are said to be brought about just by these conditions themselves. So they cannot be defined in an objective and non-circular way. This problem is approached here by what is called the consistency: our cognitive phenotype has to bring about a world picture within which the cognitive phenotype itself can be explained as resulting from an abiotic, then biotic, organic, cognitive and eventually scientific evolution. Any cognitive phenotype reproducing in this sense (together with its organic phenotype) represents a possible and consistent world together with its interpretation and mastery – and none of them is ontologically privileged.

Vico’s constructivist epistemology is compared with that of Piaget with a view to clarifying Piaget’s theory of knowledge. Piaget’s interpreters often show a lack of concern with the metaphysical foundations of cognitive structures. Vico’s emphasis on the limitations of human knowledge, therefore, is helpful in avoiding interpretive inconsistency. In Vico’s and in Piaget’s radical constructivism, knowledge is non-ontological in the sense that no claims may be made about the relation between cognitive structures and reality. Structural adequacy is derived from the consistency of the self-referencing cognitive system.

Key words: radical constructivism, history

Context: The detection of objective reality, truth, and lies are still heated topics in epistemology. When discussing these topics, philosophers often resort to certain thought experiments, engaging an important concept that can be broadly identified as “the global observer.” It relates to Putnam’s God’s Eye, Davidson’s Omniscient Interpreter, and the ultimate observer in quantum physics, among others. Problem: The article explores the notion of the global observer as the guarantor of the determinability and configuration of events in the world. It analyzes the consistency of the notion “global observer” from the standpoint of logic and philosophy, and discusses why application of this notion in some contexts poses challenges and appears to be paradoxical. Method: The paper uses conceptual methods of argumentation, such as logical (deduction) and philosophical (phenomenology) kinds of proof. Its key approach is the engagement of thought experiments. Results: The notion of a global observer is incoherent: “being global” and “being an observer” appear to be incompatible features. It is claimed that from the standpoint of global observation, there are no events occurring in the world. Furthermore, the indefiniteness of the world as a whole is asserted, which is related to the uninformedness of the global observer regarding the “true state of affairs.” “Global observation” turns out to be incompatible with the concept of the observer, blocking, as a result, the opportunity for a determinable configuration of events. It only makes sense to discuss local observations, which are limited to mutual observation or introspections, and not to assume the existence of some absolute truth, reality, or the state of affairs beyond the local observations. Constructivist content: The article emphasizes the role of the observer and observation. It opens up some problematic consequences of the core philosophical assumptions of globally observing existence. Referring to von Foerster’s and Luhmann’s idea that we can only speak reasonably about local observations, the paper argues that reality is neither external to nor independent of the observer. Implications: The paper could be productive for epistemic theories, theories of quantum physics, and theories of non-classical logic.

Key words: Global observer, ultimate observer, omniscient observer, ideal observer, omniscient interpreter, local observer, limited observer, event, truth.

Excerpt: I speak of consistency in one sense only, limited to the correspondence between behavior and thought, to the inner harmony between general principles and their application. Therefore I consider a consistent man to be simply one who, possessing a certain number of general, absolute concepts, strives earnestly in all he does, and in all his opinions about what should be done, to remain in the fullest possible accord with those concepts. A consistent man is one who considers killing evil and refuses to enter military service; one who is convinced of the superiority of monogamy over other forms of family life and so does not deceive his wife. Consistent, too, is the policeman who believes regulations must be observed and therefore gives out summonses to jaywalkers and the like.

Key words: ethics

In this article, the implications of constructivism for instructional systems design (ISD) are summarized as five principles that integrate the affective and cognitive domains of learning. In contrast to current views, it is suggested that constructivist philosophy offers instructional designers an alternative set of values that may significantly influence the emphasis of ISD methods without undermining the coherence and consistency of the ISD model. Distinguishing characteristics of the two approaches are described, based on a review of recent literature. The article concludes with the assertion that the influence of constructivist philosophy on ISD should be to focus attention on critical enabling objectives traditionally overlooked by instructional designers.

Key words: coherence system design distinguishing characteristic recent literature educational technology

In this article, the implications of constructivism for instructional systems design (ISD) are summarized as five principles that integrate the affective and cognitive domains of learning. In contrast to current views, it is suggested that constructivist philosophy offers instructional designers an alternative set of values that may significantly influence the emphasis of ISD methods without undermining the coherence and consistency of the ISD model. Distinguishing characteristics of the two approaches are described, based on a review of recent literature. The article concludes with the assertion that the influence of constructivist philosophy on ISD should be to focus attention on critical enabling objectives traditionally overlooked by instructional designers.

Key words: coherence, system design, distinguishing characteristic, recent literature, educational technology.