"Białkowski Panel" - Introduction and Acknowledgements

The two main points of this contribution are the following: (1) Applied mathematical theories might complement physical theories in an essential way; some applied mathematical theories allow us to understand phenomena we are unable to explain by resorting to physical theories alone, (2) In the case of social sciences it might be necessary to account for examined phenomena by resorting to the idea of goal-oriented activity (the causal approach typical for natural science might be unsatisfactory). Weinberg's idea of grand reductionism ignores the two above mentioned facts and hence overestimates the foundational role of physics and its methodology. This revised version was published online in July 2006 with corrections to the Cover Date.     

Reduction and Understanding

Reductionism, in the sense of the doctrine that theories on different levels of reality should exhibit strict and general relations of deducibility, faces well-known difficulties. Nevertheless, the idea that deeper layers of reality are responsible for what happens at higher levels is well-entrenched in scientific practice. We argue that the intuition behind this idea is adequately captured by the notion of supervenience: the physical state of the fundamental physical layers fixes the states of the higher levels. Supervenience is weaker than traditional reductionism, but it is not a metaphysical doctrine: one can empirically support the existence of a supervenience relation by exhibiting concrete relations between the levels. Much actual scientific research is directed towards finding such inter-level relations. It seems to be quite generally held that the importance of such relations between different levels is that they are explanatory and give understanding: deeper levels provide deeper understanding, and this justifies the search for ever deeper levels. We shall argue, however, that although achieving understanding is an important aim of science, its correct analysis is not in terms of relations between higher and lower levels. Connections with deeper layers of reality do not generally provide for deeper understanding. Accordingly, the motivation for seeking deeper levels of reality does not come from the desire to find deeper understanding of phenomena, but should be seen as a consequence of the goal to formulate ever better, in the sense of more accurate and more-encompassing, empirical theories. This revised version was published online in July 2006 with corrections to the Cover Date.     

中国古代的异常天象观

异常天象在中国古代受到高度重视，是历代天文观测的一项重要内容。象人类对所有事物的认识一样，中国古代对异常天象的认识也是以最初自发的直觉认识为开端，形成异常天象的概念，在阴阳说、五行说、元气说等关于自然的理论形成以后，对异常天象的解释随之产生。此外，按照占星术理解异常天象是中国古代异常天象观的一个重要侧面。     

Scientific Discovery: Between Incommensurability of Paradigms and Historical Continuity

Discoveries in physics imply two elements. The firstone is the belief that formal tools, already foundedin the framework of existing mathematical theories,may offer the solution to a puzzling anomaly. Thesecond one is the ability to assign a physical meaningto the adopted formalism, and to consider all itstheoretical implications.Discussing an historical case where the adoption of aparticular formalism represents the real motor of thecreative intuition, we mean to delineate scientificdiscovery both as a discontinuous change with respectto previous achievements and as a linear process ofknowledge enrichment.On March 1948, during the Pocono conference thatfollowed the one held in Shelter Island, Feynmananalysed the electron-photon interaction formulatingit in terms of the Lagrangian formalism. Thedevelopment of Feynman's idea draws attention to thepoint that novel theoretical discoveries may be theresult of applying existing formal tools. They may bethe result of giving different interpretations toprevious scientific thinking (according to thehermeneutical point that not even scientific textshave a single, absolute meaning but are given amultiplicity of possible readings by different peoplein different contexts).     

Axiomatization and Models of Scientific Theories

In this paper we discuss two approaches to the axiomatization of scientific theories in the context of the so called semantic approach, according to which (roughly) a theory can be seen as a class of models. The two approaches are associated respectively to Suppes’ and to da Costa and Chuaqui’s works. We argue that theories can be developed both in a way more akin to the usual mathematical practice (Suppes), in an informal set theoretical environment, writing the set theoretical predicate in the language of set theory itself or, more rigorously (da Costa and Chuaqui), by employing formal languages that help us in writing the postulates to define a class of structures. Both approaches are called internal, for we work within a mathematical framework, here taken to be first-order ZFC. We contrast these approaches with an external one, here discussed briefly. We argue that each one has its strong and weak points, whose discussion is relevant for the philosophical foundations of science.     

Computational and Biological Analogies for Understanding Fine-Tuned Parameters in Physics

In this philosophical paper, we explore computational and biological analogies to address the fine-tuning problem in cosmology. We first clarify what it means for physical constants or initial conditions to be fine-tuned. We review important distinctions such as the dimensionless and dimensional physical constants, and the classification of constants proposed by Lévy-Leblond. Then we explore how two great analogies, computational and biological, can give new insights into our problem. This paper includes a preliminary study to examine the two analogies. Importantly, analogies are both useful and fundamental cognitive tools, but can also be misused or misinterpreted. The idea that our universe might be modelled as a computational entity is analysed, and we discuss the distinction between physical laws and initial conditions using algorithmic information theory. Smolin introduced the theory of “Cosmological Natural Selection” with a biological analogy in mind. We examine an extension of this analogy involving intelligent life. We discuss if and how this extension could be legitimated.     

On Gene’s Action and Reciprocal Causation

Advancing the reductionist conviction that biology must be in agreement with the assumptions of reductive physicalism (the upward hierarchy of causal powers, the upward fixing of facts concerning biological levels) A. Rosenberg argues that downward causation is ontologically incoherent and that it comes into play only when we are ignorant of the details of biological phenomena. Moreover, in his view, a careful look at relevant details of biological explanations will reveal the basic molecular level that characterizes biological systems, defined by wholly physical properties, e.g., geometrical structures of molecular aggregates (cells). In response, we argue that contrary to his expectations one cannot infer reductionist assumptions even from detailed biological explanations that invoke the molecular level, as interlevel causal reciprocity is essential to these explanations. Recent very detailed explanations that concern the structure and function of chromatin—the intricacies of supposedly basic molecular level—demonstrate this. They show that what seem to be basic physical parameters extend into a more general biological context, thus rendering elusive the concepts of the basic level and causal hierarchy postulated by the reductionists. In fact, relevant phenomena are defined across levels by entangled, extended parameters. Nor can the biological context be explained away by basic physical parameters defining molecular level shaped by evolution as a physical process. Reductionists claim otherwise only because they overlook the evolutionary significance of initial conditions best defined in terms of extended biological parameters. Perhaps the reductionist assumptions (as well as assumptions that postulate any particular levels as causally fundamental) cannot be inferred from biological explanations because biology aims at manipulating organisms rather than producing explanations that meet the coherence requirements of general ontological models. Or possibly the assumptions of an ontology not based on the concept of causal powers stratified across levels can be inferred from biological explanations. The incoherence of downward causation is inevitable, given reductionist assumptions, but an ontological alternative might avoid this. We outline desiderata for the treatment of levels and properties that realize interlevel causation in such an ontology.     

A Further Review of the Incompatibility between Classical Principles and Quantum Postulates

The traditional “realist” conception of physics, according to which human concepts, laws and theories can grasp the essence of a reality in our absence, seems incompatible with quantum formalism and it most fruitful interpretation. The proof rests on the violation by quantum mechanical formalism of some fundamental principles of the classical ontology. We discuss if the conception behind Einstein’s idea of a reality in our absence, could be still maintained and at which price. We conclude that quantum mechanical formalism is not formulated on those terms, leaving for a separated paper the discussion about the terms in which it could be formulated and the onto-epistemological implications it might have.     

Taming the Infinite

For over two thousand years thought about the infinite was dominated by Aristotelian hostility to the idea that the infinite could be a legitimate object of mathematical study. Then Cantor's work late in the nineteenth century seemed to overturn this orthodoxy. However, by highlighting ways in which infinitude still could not be brought under the control of mathematicians, Cantor's work may in fact have reinforced the orthodoxy.     

A Multiagent Approach to Modelling Complex Phenomena

Designing models of complex phenomena is a difficult task in engineering that can be tackled by composing a number of partial models to produce a global model of the phenomena. We propose to embed the partial models in software agents and to implement their composition as a cooperative negotiation between the agents. The resulting multiagent system provides a global model of a phenomenon. We applied this approach in modelling two complex physiological processes: the heart rate regulation and the glucose-insulin metabolism. Beyond the effectiveness demonstrated in these two applications, the idea of using models associated to software agents to give reason of complex phenomena is in accordance with current tendencies in epistemology, where it is evident an increasing use of computational models for scientific explanation and analysis. Therefore, our approach has not only a practical, but also a theoretical significance: agents embedding models are a technology suitable both to representing and to investigating reality.

The Intentionality of Formal Systems

One of the most interesting and entertaining philosophical discussions of the last few decades is the discussion between Daniel Dennett and John Searle on the existence of intrinsic intentionality. Dennett denies the existence of phenomena with intrinsic intentionality. Searle, however, is convinced that some mental phenomena exhibit intrinsic intentionality. According to me, this discussion has been obscured by some serious misunderstandings with regard to the concept ‘intrinsic intentionality’. For instance, most philosophers fail to realize that it is possible that the intentionality of a phenomenon is partly intrinsic and partly observer relative. Moreover, many philosophers are mixing up the concepts ‘original intentionality’ and ‘intrinsic intentionality’. In fact, there is, in the philosophical literature, no strict and unambiguous definition of the concept ‘intrinsic intentionality’. In this article, I will try to remedy this. I will also try to give strict and unambiguous definitions of the concepts ‘observer relative intentionality’, ‘original intentionality’, and ‘derived intentionality’. These definitions will be used for an examination of the intentionality of formal mathematical systems. In conclusion, I will make a comparison between the (intrinsic) intentionality of formal mathematical systems on the one hand, and the (intrinsic) intentionality of human beings on the other hand.     

Unification of Mathematical Theories

In this article the problem of unification of mathematical theories is discussed. We argue, that specific problems arise here, which are quite different than the problems in the case of empirical sciences. In particular, the notion of unification depends on the philosophical standpoint. We give an analysis of the notion of unification from the point of view of formalism, Gödel's platonism and Quine's realism. In particular we show, that the concept of “having the same object of study” should be made precise in the case of mathematical theories. In the appendix we give a working proposal of a certain understanding of this notion.     

Matter in Z3

In this paper, I will discuss a certain conception of matter that Aristotle introduces in Metaphysics Z3. It is often assumed that Aristotle came to distinguish between matter and form only in his physical writings, and that this lead to a conflict with the doctrine of primary substances in the Categories that he tries to resolve in Z3. I will argue that there is no such conflict. In Z3, Aristotle seems to suggest that matter is what is left over when we strip a thing of all its properties. I take it that he does not want us to strip away these properties by physical means or in our imagination. Rather, we are asked to strip a referring noun phrase of all its predicative parts. We are thus not supposed to be able to refer to something that has no qualities whatsoever, but to construct a phrase that refers to something that has properties without referring to its having them, and without implying which properties it has. The idea that there might be a way of referring to something definite without mentioning any of its qualities is platonic and it still underlies modern predicate logic. In Z3, Aristotle argues against this conception and thus against the basic idea of predicate logic. According to him, matter is at best an inseparable aspect of a primary substance, which substance is best referred to as a compound τóδε τι (“this such”). Matter is what the τóδε refers to as part of this phrase. But it cannot exist in separation from form, and we cannot refer to it by a separated term, without also referring to the substantial form of the substance of which it is an aspect.     

Mathematics as a Quasi-Empirical Science

The present paper aims at showing that there are times when set theoretical knowledge increases in a non-cumulative way. In other words, what we call ‘set theory’ is not one theory which grows by simple addition of a theorem after the other, but a finite sequence of theories T ₁, ..., T _n in which T _i+1, for 1 ≤ i < n, supersedes T _i . This thesis has a great philosophical significance because it implies that there is a sense in which mathematical theories, like the theories belonging to the empirical sciences, are fallible and that, consequently, mathematical knowledge has a quasi-empirical nature. The way I have chosen to provide evidence in favour of the correctness of the main thesis of this article consists in arguing that Cantor–Zermelo set theory is a Lakatosian Mathematical Research Programme (MRP).     

Quantum Theory and the Nature of Consciousness

Our interest focusses on the idea, that consciousness is a powerful acting entity. Up to now there does not exist a scientific concept for this idea. This is not due to problems within the field of psychology or brain research, but rather in resisting theories of modern physics. That is, why we have to search for a solution in the field of physics. A solution can be found in a new understanding of the basics of physical theory. That could be given by abstract and absolute quantum bits of information (AQI bits). To avoid the popular misunderstanding of “information” as “meaningful” it was necessary to find a new word for the free-of-meaning AQI bits: the AQI bits establish a quantum pre-structure termed “Protyposis” (Greek: “pre-formation”), out of which real objects can be formed, starting from energetical and material elementary particles. The Protyposis AQI bits provide a pre-structure for all entities in natural sciences. They are the basic entities, whereof the physical nature of the brain, on the one hand, and the mental nature of consciousness, on the other hand, were formed during the cosmological and the following biological evolution. A deeper understanding of quantum structures may help to overcome the resistance against quantum theory in the field of brain research and consciousness. The key for an understanding is the concept of Protyposis, which means an abstract quantum information free of any definite meaning. With the AQI bits of the Protyposis, both, massless and massive quantum particles can be constructed. Even quantum information with special meanings, in example grammatically formulated thoughts, eventually could be explained. As long as the fundamental basis of quantum theory is misunderstood as being formed by a manifold of some small objects like atoms, quarks, or strings, the problem of understanding consciousness has no solution. If instead we understand quantum theory as based on truly simple quantum structures, there would be no longer fundamental problems for an understanding of consciousness.     

数学真理的发展及其对自然观演变的启示

19世纪下半叶以来，数学与自然科学各自的发展及其相互关系呈现出许多新的特点。特别是20世纪以来诞生的各种数学新理论，正在逐步地改变着数学真理的传统观念。数学真理与自然法则的关系变得日益复杂和深化了。数学新的真理性质对自然观的变革产生了深远的影响。     

宇宙射线的早期研究

宇宙射线研究是天体物理学和粒子物理学的重要研究课题。对宇宙射线早期研究文献进行整理、分析 ,证明宇宙射线发现、确认的历史过程为 :(1 )库仑从验电器漏电中发现 ,电荷不可能长久保持 ,最终将会消失。根据验电器漏电现象 ,卢瑟福认为 ,漏电是由空气中穿透性极强的辐射引起的 ,成为研究的一个转折点。 (2 )沃尔夫对原有验电器进行改进 ,大大提高了实验的精度 ,为以后的研究奠定了实验基础。 (3) 1 91 1年至 1 91 3年 ,黑斯经过十次高空气球飞行 ,认为这种极强的穿透性辐射来自地球之外的空间 ,从而打开了物理学一个新的研究领域。 (4 )密立根怀疑黑斯的结论 ,在美洲大陆进行了更广泛的实验工作。实验中 ,密立根首次使用了探测气球技术 ,导致黑斯的结论得到承认     

Mathematical,Philosophical and Semantic Considerations on Infinity (I): General Concepts

In the Reality we know, we cannot say if something is infinite whether we are doing Physics, Biology, Sociology or Economics. This means we have to be careful using this concept. Infinite structures do not exist in the physical world as far as we know. So what do mathematicians mean when they assert the existence of ω (the mathematical symbol for the set of all integers)? There is no universally accepted philosophy of mathematics but the most common belief is that mathematics touches on another worldly absolute truth. Many mathematicians believe that mathematics involves a special perception of an idealized world of absolute truth. This comes in part from the recognition that our knowledge of the physical world is imperfect and falls short of what we can apprehend with mathematical thinking. The objective of this paper is to present an epistemological rather than an historical vision of the mathematical concept of infinity that examines the dialectic between the actual and potential infinity.     

Symbolic Languages and Natural Structures a Mathematician’s Account of Empiricism

The ancient dualism of a sensible and an intelligible world important in Neoplatonic and medieval philosophy, down to Descartes and Kant, would seem to be supplanted today by a scientific view of mind-in-nature. Here, we revive the old dualism in a modified form, and describe mind as a symbolic language, founded in linguistic recursive computation according to the Church-Turing thesis, constituting a world L that serves the human organism as a map of the Universe U. This methodological distinction of L vs. U helps to understand how and why structures of phenomena come to be opposed to their nature in human thought, a central topic in Heideggerian philosophy. U is uncountable according to Georg Cantor’s set theory but Language L, based on the recursive function system, is countable, and anchored in a Gray Area within U of observable phenomena, typically symbols (or tokens), prelinguistic structures, genetic-historical records of their origins. Symbols, the phenomena most familiar to mathematicians, are capable of being addressed in L-processing. The Gray Area is the human Environment E, where we can live comfortably, that we manipulate to create our niche within hostile U, with L offering overall competence of the species to survive. The human being is seen in the light of his or her linguistic recursively computational (finite) mind. Nature U, by contrast, is the unfathomable abyss of being, infinite labyrinth of darkness, impenetrable and hostile to man. The U-man, biological organism, is a stranger in L-man, the mind-controlled rational person, as expounded by Saint Paul. Noumena can now be seen to reside in L, and are not fully supported by phenomena. Kant’s noumenal cause is the mental L-image of only partly phenomenal causation. Mathematics occurs naturally in pre-linguistic phenomena, including natural laws, which give rise to pure mathematical structures in the world of L. Mathematical foundation within philosophy is reversed to where natural mathematics in the Gray Area of pre-linguistic phenomena can be seen to be a prerequisite for intellectual discourse. Lesser, nonverbal versions of L based on images are shared with animals.