The problem of induction is closely connected with the idea of an ontological reality as the regularities we perceive can be generalised to the laws of an independent nature only by means of inductive methods. A constructivist evolutionary epistemology (CEE) is proposed which considers all regularities perceived and the laws of nature derived from them as invariants of mental operators, similar to quantum mechanics which defines the properties of subjects as invariants of measuring operators. Then the laws of physics are specific to human beings. This will apply even for the law of the conservation of energy if it is derived from the homogeneity of time and therefore will depend on the phylogenetically evolved mental mechanisms defining the metric of time perception. Also mathematical regularities and the laws of logic are not universal. Rather they have to be seen as invariants of certain human mental operators. If these mathematical and perceptual operators are phylogenetic homologa, we have the possibility of explaining why mathematical methods are so successful in extrapolating experimental data or, as Davies put it, why the universe is algorithmically compressible. The possible relationship is discussed between the continuity of all physical motion as perceived by men and a special constructivist approach of counting processes. As the laws found in higher physics are invariants of the experimental facilities applied they can neither be derived from nor are they determined by the given functional structure of the brain. The CEE, therefore, does not suggest teleological ideas. The view is taken that the evolution of science is as open and endless as organic evolution is.

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.

Abstract: Under the aspect of constructivism evolution generates the varying boundary conditions to which evolution itself then is subject. This applies for organic as well as for cognitive evolution. The currently valid conditions for cognitive evolution we describe as laws of nature brought about by an independent reality. Within the constructivist evolutionary epistemology CEE), however. the regularities we perceive and which we condense to the laws of nature are seen as the invariants of phylogenetically formed cognitive operators. The extension of the inborn operators by means of experimental operators (i.e. by mea­surement facilities) will lead to the consolidation of the classical world picture if both _are _commutable. Otherwise there will be invariants which cannot be described in classical terms and, which therefore, will require non-classical theories. Likewise mathematical and logical structures can be seen as invariants of cognitive operators. It is shown that the propositions of Gödel would deal with what can be considered as the analogy of non-classical phenomena in physics. To renounce reality as an element of physical metatheory requires some rearrangements of those notions which explicitly refer to reality such as acting and perceiving, learning and adapting, and, partially, language. It turns out that the distinction between acting and perceiving is not unambiguous as it is in the “theory of reality.” Similarly we can see learning as a process of adaptation to the given environment as well as an independent development into something for which an appropriate environment or application still has to be found. It will be shown that both “adaptive” and “initiative” evolution occur in organic as well as in cultural evolution. Within CEE, language is seen as a “generative” theory rather than as a tool to portray independently existing facts. Its competence is based on the fact that it is generated by mechanisms closely related to those generating our phy­sical perceptions. A similar genetically grounded relationship between mental operators enables mathematics to compress empirical data into a generating theory, and then, based on this theory, to extrapolate them (problem of induction). The lin­guistic equivalent of algorithmic data compression and the subsequent extrapolation is the recognition of a text’s meaning, and the subsequent drawing of conclusions from it, or semantic extrapolation as proposed to say. Accordingly, communication can be defined. Some parallels are discussed between verbal, cultural and genetic communication.

Key words: Reality, Gödel, language, mathematics, communication, meaning, learning

The constructivist evolutionary epistemology (CEE) has taken up the demand of modern physics that theoretical terms have to be operationalizable (i.e. the description of nature should comprise only quantities, variables or notions which are defined by means of measurement facilities or other physical processes) and extended it by the idea that operationalisation is something general which must be the constituting basis also for observational terms. This is realised by considering the regularities we perceive and which we condense to the laws of nature as the invariants of phylogenetically formed mental cognitive operators. Experimental operators (i.e. measurement facilities) can be seen as extensions of these inborn operators. This will lead to the consolidation of the classical world picture if the mental and the experimental operators involved are commutable. Otherwise there will be invariants which cannot be described in classical terms and, therefore, will require non-classical approaches such as the uncertainty principle in quantum mechanics enunciated by Heisenberg. As the development of experimental facilities will never be completed and, therefore, will continue to bring about novel invariants, evolution of science cannot converge towards what many physicists envisage as the “theory of everything” describing definitively the structure of reality (Feynman, 1965; Hawking, 1979). So, both organic and scientific evolution are entirely open and non-deterministic. When seeing also mathematical objects and structures as invariants of mental operators we must expect similar phenomena. Indeed: Just as experimental operators, though constructed entirely according to the rules of classical physics, may lead to results which cannot be described in classical terms, there are also mathematical calculuses which, though based entirely on well tested axioms, can lead to statements which cannot be proven within the context of these axioms as shown by Gödel.

It is widely understood in physics that evaluation criteria for empirical theories are determined by what is called the objective structures of an outside and real world, and on this basis, discussions ensue as to whether our scientific efforts to condense observations into theories will eventually result in a “theory of everything” (Feynman 1965, Hawking 1979, Barrow 1990, Chalmers 1982) reflecting precisely these structures. “Unless one accepts that the regularities (we perceive) are in some sense objectively real, one might as well stop doing science” (Davies 1990a). I.e., reality is seen as a prerequisite for a non arbitrary and reasonable development of theories. Without reality “anything goes” – which is the downright unacceptable in physics. On the other hand, if regularities are objective in the sense that they depend on the structures of an objective outside world, it remains unclear why mathematics which obviously does not include any information on these structures is nevertheless so helpful in describing them in such a way that purely mathematical extrapolations will lead to correct predictions. This is the old question about “the unreasonable effectiveness of mathematics in the natural sciences” (Wigner 1960), or, as Davies (1990b) put it, “why the universe is algorithmicly compressible” (i.e. why the obviously complex structure of our world can be described in so many cases by means of relatively simple mathematical formulae). This question is closely linked to why induction and, therefore, science at all, succeeds. It is difficult to avoid asking whether mathematics, as the outcome of human thinking has its own specificity which, for what ever reason, fits to the specificity of what man would see or experience. As long as this question is not comprehensively answered science may explain much – but not its own success. But how can such entirely disparate categories as perceiving and thinking be linked with each other? This question will be discussed here in the context of a new constructivist version of evolutionary approaches to epistemology (Diettrich 1991, 1993), which will lead to a revised notion of reality, as well as to some rather unexpected links between the phenomena of non-classical physics and the mathematical findings of Gödel.

The unsolved problem of induction is closely linked to “the unreasonable effectiveness of mathematics in the natural sciences” (Wigner 1960) and to the question “why the universe is algorthmicly compressible” (Davies 1960). The problem of induction is approached here by means of a constructivist version of the Evolutionary Epistemology (CEE) considering both, the perceived regularities we condense to the laws of nature and the mathematical structures we condense to axioms, as invariants of inborn cognitive and mental operators. A phylogenetic relationship between the mental operators generating the perceived and the mathematical regularities respectively may explain the high suitability of mathematical tools to extrapolate observed data. The extension of perceptional operators by means of experimental operators, i.e., by means of measurement devices) would lead to the completion of the classical world picture if both the cognitive and the physical operators are commutable in the sense of operator algebra (quantitative extensions). Otherwise the physical operators will have invariants which no longer can be described in classical terms, and, therefore, would require the formation of non-classical theories (qualitative extension), exceeding the classical world picture. The mathematical analogon would be the algorithmic extension of elementary mathematical thinking exceeding the axiomatic basis previously established according to Gödel’s incompleteness theorem. As a consequence there will be neither a definitive set of axioms in mathematics, nor will be there a definitive theory of everything in physics.

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 <constructivist evolutionary epistemology’ (CEE): In analogy to physics where observables are defined as invariants of experimental measurement operators, the CEE considers the perceived patterns and regularities from which we derive the laws of nature to be invariants of inborn cognitive (sensory) operators. Then, the so called laws of nature are the result of cognitive evolution and therefore are human specific. They nevertheless allow correct empirical predictions if the generating cognitive operators commute with the operators of human physical acting. Cognitive operators and the cognitive phenotype they represent, there-fore, do not need to develop phylogenetically in adaptation to an external world as proposed by Campbell’s ‘natural selection epistemology’. If cognitive operators are extended by means of experimental operators the result can be expressed in classical terms if both commute (quantitative extensions). Otherwise non-classical approaches such as quantum mechanics are required (qualitative extensions). As qualitative extensions never can be excluded, it follows that there will be no definitive set of theories of everything’. From applying this concept to the inborn operators of mathematical thinking and their algorithmic extensions it follows that there will be no definitive set of axioms, i. e. it would explain Gödel’s incompleteness theorem. The ontological prerequisites being the basis of the various epistemologies discussed in the philosophy of science, are replaced by the requirement of 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.

Theories and languages have in common that they aim at describing the world and the experiences made in the world. The specificity of theories is based on the fact that they code certain laws of nature. The specificity of languages is based on the fact that they code our worldview by means of their syntax. Also mathematics can be considered as theory in so far as it codes the constituting axioms. Language can achieve the objectivity postulated by analytical philosophy only if it can refer to a mathematics and logic being objective in the sense of platonism and based on a definitive set of axioms, or if the world-view concerned is definitive and based upon an objective (and therefore definitive) set of laws of nature. The first way is blocked by Goedel’s incompleteness theorem. The objectivity of the laws of nature being necessary for going the second way is questioned as well by what is called the constructivist evolutionary epistemology (CEE): the perceived patterns and regularities from which we derive the laws of nature is considered by the CEE to be invariants of inborn cognitive (sensory) operators. Then, the so called laws of nature are the result of cognitive evolution and therefore are human specific. Whether, e.g., we would identify the law of energy conservation which in physics results from the homogeneity of time, depends on the mental time-metric generator defining what is homogeneous in time. If cognitive operators are extended by means of experimental operators the result can be expressed in classical terms if both commute in the sense of operator algebra (quantitative extensions). Otherwise results would be inconsistent with the classical worldview and would require non-classical approaches such as quantum mechanics (qualitative extensions). As qualitative extensions can never be excluded from future experimental reasearch, it follows that the development of theories cannot converge towards a definitive set of laws of nature or a definitive ‘theory of everything’ describing the structure of reality. Also the structures of mathematics and logic we use have to be considered als invariants of mental operators. It turns out that the incompleteness theorem of Goedel has to be seen as analogy of the incompleteness of physical theories due to possible qualitative experimental extensions. Language, therefore, cannot be considered as an objective depiction of independently existing facts and matters but only as a theory generating propositions being consistent with our world-view. The competence of language is based on the fact that the mental mechanisms generating the ontology we use in our syntax are related to those generating our perceptions. Similar applies to the relationship between the operators generating perceived and mathematical structures enabling us to compress empirical data algorithmically (i.e. to transform them into mathematically articulated theories) and then to extrapolate them by means of the theory concerned (inductive inference). An analogue mechanism establishes our ability to compress verbal texts semantically (i.e. to reduce them to their meaning) and then to extrapolate them (i.e. to draw correct conclusions within the framework of the meaning concerned). This suggests a modified notion of meaning seing it as a linguistic analogy to theories. Similar to physical and mathematical theories also languages can be extended qualitatively particularly by means of metaphorical combinations of semantically noncompatible elements. The development of languages towards it actual richness can be seen as a process of ongoing metaphorosation. this leads to some parallels between verbal, cultural and genetic communication.

Excerpt: Concluding that cognitive structures and instruments are unconditional or arbitrary because they are not, and cannot be derived from external boundary conditions, is mistaken, since internal boundary conditions must also be taken into account. Firstly, there are the developmental constraints of cognitive evolution itself; cognitive as well as organic evolution is subject to what has been evolved before. Cognitive evolution in our time, therefore, would find rather limited degrees of freedom. Further, cognitive instruments exert themselves in continuous co-evolution with organic instruments for meeting organically defined needs and requirements. This means that cognitive systems cannot be explained by reference to what is called their object, but only through their organic genesis. This justifies efforts made to look for a closer relationship between cognitive and organic evolution.

It is shown that the method of operational definition of theoretical terms applied in physics may well support constructivist ideas in cognitive sciences when extended to observational terms. This leads to unexpected results for the notion of reality, induction and for the problem why mathematics is so successful in physics. A theory of cognitive operators is proposed which are implemented somewhere in our brain and which transform certain states of our sensory apparatus into what we call perceptions in the same sense as measurement devices transform the interaction with the object into measurement results. Then, perceived regularities, as well as the laws of nature we would derive from them can be seen as invariants of the cognitive operators concerned and are by this human specific constructs rather than ontologically independent elements. (e.g., the law of energy conservation can be derived from the homogeneity of time and by this depends on our mental time metric generator). So, reality in so far it is represented by the laws of nature has no longer an independent ontological status. This is opposed to Campbell’s ‘natural selection epistemology’. From this it is shown that there holds an incompleteness theorem for physical laws similar to Gödels incompleteness theorem for mathematical axioms, i.e., there is no definitive or object ‘theory of everything’. This constructivist approaches to cognition will allow a coherent and consistent model of both cognitive and organic evolution. Whereas the classical view sees the two evolution rather dichotomously (for ex.: most scientists see cognitive evolution converging towards a definitive world picture, whereas organic evolution obviously has no specific focus (the ‘pride of creation’).

Key words: cognitive operator theory, epistemological autoreproduction, human specific character of natural laws, incompleteness theorem of mathematics (gödel) and physics, realism.