A principle, according to which any scientific theory can be mathematized, is investigated. Social science, liberal arts, history, and philosophy are meant first of all. That kind of theory is presupposed to be a consistent text, which can be exhaustedly represented by a certain mathematical structure constructively. In thus used, the term “theory” includes all hypotheses as yet unconfirmed as already rejected. The investigation of the sketch of a possible proof of the principle demonstrates that it should be accepted rather (...) a metamathematical axiom about the relation of mathematics and reality. The main statement is formulated as follows: Any scientific theory admits isomorphism to some mathematical structure in a way constructive. Its investigation needs philosophical means. Husserl’s phenomenology is what is used, and then the conception of “bracketing reality” is modelled to generalize Peano arithmetic in its relation to set theory in the foundation of mathematics. The obtained model is equivalent to the generalization of Peano arithmetic by means of replacing the axiom of induction with that of transfinite induction. The sketch of the proof is organized in five steps: a generalization of epoché; involving transfinite induction in the transition between Peano arithmetic and set theory; discussing the finiteness of Peano arithmetic; applying transfinite induction to Peano arithmetic; discussing an arithmetical model of reality. Accepting or rejecting the principle, two kinds of mathematics appear differing from each other by its relation to reality. Accepting the principle, mathematics has to include reality within itself in a kind of Pythagoreanism. These two kinds are called in paper correspondingly Hilbert mathematics and Gödel mathematics. The sketch of the proof of the principle demonstrates that the generalization of Peano arithmetic as above can be interpreted as a model of Hilbert mathematics into Gödel mathematics therefore showing that the former is not less consistent than the latter, and the principle is an independent axiom. The present paper follows a pathway grounded on Husserl’s phenomenology and “bracketing reality” to achieve the generalized arithmetic necessary for the principle to be founded in alternative ontology, in which there is no reality external to mathematics: reality is included within mathematics. That latter mathematics is able to self-found itself and can be called Hilbert mathematics in honour of Hilbert’s program for self-founding mathematics on the base of arithmetic. The principle of universal mathematizability is consistent to Hilbert mathematics, but not to Gödel mathematics. Consequently, its validity or rejection would resolve the problem which mathematics refers to our being; and vice versa: the choice between them for different reasons would confirm or refuse the principle as to the being. An information interpretation of Hilbert mathematics is involved. It is a kind of ontology of information. The Schrödinger equation in quantum mechanics is involved to illustrate that ontology. Thus the problem which of the two mathematics is more relevant to our being is discussed again in a new way A few directions for future work can be: a rigorous formal proof of the principle as an independent axiom; the further development of information ontology consistent to both kinds of mathematics, but much more natural for Hilbert mathematics; the development of the information interpretation of quantum mechanics as a mathematical one for information ontology and thus Hilbert mathematics; the description of consciousness in terms of information ontology. (shrink)

A principle, according to which any scientific theory can be mathematized, is investigated. That theory is presupposed to be a consistent text, which can be exhaustedly represented by a certain mathematical structure constructively. In thus used, the term “theory” includes all hypotheses as yet unconfirmed as already rejected. The investigation of the sketch of a possible proof of the principle demonstrates that it should be accepted rather a metamathematical axiom about the relation of mathematics and reality. Its investigation needs philosophical (...) means. Husserl’s phenomenology is what is used, and then the conception of “bracketing reality” is modelled to generalize Peano arithmetic in its relation to set theory in the foundation of mathematics. The obtained model is equivalent to the generalization of Peano arithmetic by means of replacing the axiom of induction with that of transfinite induction. A comparison to Mach’s doctrine is used to be revealed the fundamental and philosophical reductionism of Husserl’s phenomenology leading to a kind of Pythagoreanism in the final analysis. Accepting or rejecting the principle, two kinds of mathematics appear differing from each other by its relation to reality. Accepting the principle, mathematics has to include reality within itself in a kind of Pythagoreanism. These two kinds are called in paper correspondingly Hilbert mathematics and Gödel mathematics. The sketch of the proof of the principle demonstrates that the generalization of Peano arithmetic as above can be interpreted as a model of Hilbert mathematics into Gödel mathematics therefore showing that the former is not less consistent than the latter, and the principle is an independent axiom. An information interpretation of Hilbert mathematics is involved. It is a kind of ontology of information. Thus the problem which of the two mathematics is more relevant to our being is discussed. An information interpretation of the Schrödinger equation is involved to illustrate the above problem. (shrink)

The principle of complementarity in physics can be generalized and extended to information studies. It helps explain the dilemma faced by information studies today. The prevailing endeavor that going beyond the limitation of formal theories and to develop a unified theory of information falls in the dilemma which is structurally homologous to the dilemmas in quantum physics. The dilemma is caused by an epistemological paradox called assignment paradox. The paradox can be removed through generalized complementarity. It means that the concept (...) of information embodying in different theoretical contexts are different phenomenon. They are complementary to each other. The analysis brings bad news to methodologically reductionism and fundamentalism but good news to transdisciplinary approach. (shrink)

Preface. Almost fifty years ago, in 1948, when I was an undergraduate at Queens College in New York and a student of Carl G. Hempel's, I received from his hands an offprint of his now-classic but then just-published paper “Studies in the Logic of Explanation”, written in collaboration with Paul Oppenheim and then just published in Philosophy of Science.1 This paper greatly impressed me—and I was not alone. We have here one of those unusual publications that sets the agenda for (...) a whole generation of investigators. It set in train an enormous body of discussions and publications which shaped the course of deliberations about scientific explanation over the next decades—an effort to which my own work also made some contributions. However my present aim is not to consider what came out of the Hempel-Oppenheim paper but what went into it. I want, in sum, to consider the prehistory of that era of scientific explanation studies—and to look more closely at the background ramifications of this paper that launched a thousand others. (shrink)

Dual aspect theory has conceptual advantages over alternative mind-body notions, but difficulties of its own. The nature of the underlying psychophysical ground, for one, remains problematic either in terms of the principle of complementarity or if mind and matter are taken to be aspects of something like energy, movement, or information. Moreover, for a dual aspect theory to be plausible it should avoid the four perils of all mind-body theories: epiphenomenalism, reductionism, gross panpsychism, and the problems of emergence. An alternative (...) dual aspect theory, patterned process theory, is introduced and defended in neurological and individuality terms. The concept is grounded in a brain model of hierarchies wherein consciousness is conceived to be a cognitive aspect of the highest emergent brain inter-module activity, which is situated in the context of a living organism coping with a changing environment. The notion of individuals as psychophysical units unfolding as patterned processes is shown to constitute an integrative approach to brain, consciousness, and behavior that can avoid the conceptual perils and meet the ontological requirements of dual aspect reality and thereby advance the foundations of an integrative mind-body science. (shrink)

Some contemporary theorists such as Mazzocchi, Theise and Kafatos are convinced that the reformed complementarity may redefine how we might exploit the complexity theory in 21st-century life sciences research. However, the motives behind the profound re-invention of “biological complementarity” need to be substantiated with concrete shreds of evidence about this principle’s applicability in real-life science experimentation, which we found missing in the literature. This paper discusses such pieces of evidence by confronting Bohr’s complementarity and ion channel modeling practice. We examine (...) whether and to what extent this principle might assist in developing ion channel models incorporating both deterministic and stochastic solutions. According to the “mutual exclusiveness of experimental setups” version of Bohr’s complementarity, this principle is needed when two mutually exclusive perspectives or approaches are right, necessary in a particular context, and are not contradictory as they arise in mutually exclusive conditions (mutually exclusive experimental or modeling setups). A detailed examination of the modeling practice reveals that both solutions are often used simultaneously in a single ion channel model, suggesting that the opposite conceptual frameworks can coexist in the same modeling setup. We concluded that Bohr’s complementarity might find applications in these complex modeling setups but only through its realistic phenomenological interpretation that allows applying different modes of description regardless of the nature of the underlying ion channel opening process. Also, we propose the combined use of complementarity and Complex thinking in building the multifaceted ion channel models. Overall, this paper’s results support the efforts to establish a more general form of complementarity to meet today’s complexity theory-inspired life sciences modeling demands. (shrink)

Ontology, the ideas we have about the nature of reality, and epistemology, our concepts about how to gain knowledge about the world, are interdependent. Currently, the dominant ontology in science is a materialist model, and associated with it an empiricist epistemology. Historically speaking, there was a more comprehensive notion at the cradle of modern science in the middle ages. Then “experience” meant both inner, or first person, and outer, or third person, experience. With the historical development, experience has come to (...) mean only sense experience of outer reality. This has become associated with the ontology that matter is the most important substance in the universe, everything else—consciousness, mind, values, etc., —being derived thereof or reducible to it. This ontology is insufficient to explain the phenomena we are living with—consciousness, as a precondition of this idea, or anomalous cognitions. These have a robust empirical grounding, although we do not understand them sufficiently. The phenomenology, though, demands some sort of non-local model of the world and one in which consciousness is not derivative of, but coprimary with matter. I propose such a complementarist dual aspect model of consciousness and brain, or mind and matter. This then also entails a different epistemology. For if consciousness is coprimary with matter, then we can also use a deeper exploration of consciousness as happens in contemplative practice to reach an understanding of the deep structure of the world, for instance in mathematical or theoretical intuition, and perhaps also in other areas such as in ethics. This would entail a kind of contemplative science that would also complement our current experiential mode that is exclusively directed to the outside aspect of our world. Such an epistemology might help us with various issues, such as good theoretical and other intuitions. (shrink)