Physics, Theoretical Knowledge and Weinberg's Grand Reductionism

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.     

Gould, Hull, and the Individuation of Scientific Theories

When is conceptual change so significant that we should talk about a new theory, not a new version of the same theory? We address this problem here, starting from Gould’s discussion of the individuation of the Darwinian theory. He locates his position between two extremes: ‘minimalist’—a theory should be individuated merely by its insertion in a historical lineage—and ‘maximalist’—exhaustive lists of necessary and sufficient conditions are required for individuation. He imputes the minimalist position to Hull and attempts a reductio: this position leads us to give the same ‘name’ to contradictory theories. Gould’s ‘structuralist’ position requires both ‘conceptual continuity’ and descent for individuation. Hull’s attempt to assimilate into his general selectionist framework Kuhn’s notion of ‘exemplar’ and the ‘semantic’ view of the structure of scientific theories can be used to counter Gould’s reductio, and also to integrate structuralist and population thinking about conceptual change.     

A Proposal for a Coherent Ontology of Fundamental Entities

We argue that the distinction between framework and interaction theories should be taken carefully into consideration when dealing with the philosophical implications of fundamental theories in physics. In particular, conclusions concerning the nature of reality can only be consistently derived from assessing the ontological and epistemic purport of both types of theories. We put forward an epistemic form of realism regarding framework theories, such as Quantum Field Theory. The latter, indeed, informs us about the general properties of quantum fields, laying the groundwork for interaction theories. Yet, concerning interaction theories, we recommend a robust form of ontological realism regarding the entities whose existence is assumed by these theories. As an application, we refer to the case of the Standard Model, so long as it has proved to successfully inform us about the nature of various sorts of fundamental particles making up reality. In short, although we acknowledge that both framework and interaction theories partake in shaping our science-based view of reality, and that neither would do by itself the work we expect them to accomplish together, our proposal for a coherent ontology of fundamental entities advances a compromise between two forms of realism about theories in each case.     

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.     

"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.     

Towards a Theory of Mathematical Argument

In this paper, I assume, perhaps controversially, that translation into a language of formal logic is not the method by which mathematicians assess mathematical reasoning. Instead, I argue that the actual practice of analyzing, evaluating and critiquing mathematical reasoning resembles, and perhaps equates with, the practice of informal logic or argumentation theory. It doesn’t matter whether the reasoning is a full-fledged mathematical proof or merely some non-deductive mathematical justification: in either case, the methodology of assessment overlaps to a large extent with argument assessment in non-mathematical contexts. I demonstrate this claim by considering the assessment of axiomatic or deductive proofs, probabilistic evidence, computer-aided proofs, and the acceptance of axioms. I also consider Jody Azzouni’s ‘derivation indicator’ view of proofs because it places derivations—which may be thought to invoke formal logic—at the center of mathematical justificatory practice. However, when the notion of ‘derivation’ at work in Azzouni’s view is clarified, it is seen to accord with, rather than to count against, the informal logical view I support. Finally, I pose several open questions for the development of a theory of mathematical argument.     

Embedding Quantum Mechanics into a Broader Noncontextual Theory

Scholars concerned with the foundations of quantum mechanics (QM) usually think that contextuality (hence nonobjectivity of physical properties, which implies numerous problems and paradoxes) is an unavoidable feature of QM which directly follows from the mathematical apparatus of QM. Based on some previous papers on this issue, we criticize this view and supply a new informal presentation of the extended semantic realism (ESR) model which embodies the formalism of QM into a broader mathematical formalism and reinterprets quantum probabilities as conditional on detection rather than absolute. Because of this reinterpretation a hidden variables theory can be constructed which justifies the assumptions introduced in the ESR model and proves its objectivity. When applied to special cases the ESR model settles long-standing conflicts (it reconciles Bell’s inequalities with QM), provides a general framework in which previous results obtained by other authors (as local interpretations of the GHZ experiment) are recovered and explained, and supports an interpretation of quantum logic which avoids the introduction of the problematic notion of quantum truth.     

Bridging the Gap Between Argumentation Theory and the Philosophy of Mathematics

We argue that there are mutually beneficial connections to be made between ideas in argumentation theory and the philosophy of mathematics, and that these connections can be suggested via the process of producing computational models of theories in these domains. We discuss Lakatos’s work (Proofs and Refutations, 1976) in which he championed the informal nature of mathematics, and our computational representation of his theory. In particular, we outline our representation of Cauchy’s proof of Euler’s conjecture, in which we use work by Haggith on argumentation structures, and identify connections between these structures and Lakatos’s methods.     

Gödel's Incompleteness Theorems and Computer Science

In the paper some applications of Gödel's incompleteness theorems to discussions of problems of computer science are presented. In particular the problem of relations between the mind and machine (arguments by J.J.C. Smart and J.R. Lucas) is discussed. Next Gödel's opinion on this issue is studied. Finally some interpretations of Gödel's incompleteness theorems from the point of view of the information theory are presented.     

自然和意义——论麦克道威尔“第二自然的自然主义”

自然主义是现代哲学的基本范式之一,这一范式的普适性受到心灵哲学的挑战。当自然主义用经验方法对心灵进行"自然化"的过程中,产生了严重的理论困难:在基于经验和因果关系解释的自然内,意义和价值变得无容身之处,同时使得理性与自然陷入紧张的分裂关系。麦克道威尔的"第二自然的自然主义"意在通过一种独特的自发性概念对自然进行全新的诠释,在捍卫知识客观性的同时恢复自然和意义的内在联系。     

Perceiving the Infinite and the Infinitesimal World: Unveiling and Optical Diagrams in Mathematics

Many important concepts of the calculus are difficult to grasp, and they may appear epistemologically unjustified. For example, how does a real function appear in “small” neighborhoods of its points? How does it appear at infinity? Diagrams allow us to overcome the difficulty in constructing representations of mathematical critical situations and objects. For example, they actually reveal the behavior of a real function not “close to” a point (as in the standard limit theory) but “in” the point. We are interested in our research in the diagrams which play an optical role –microscopes and “microscopes within microscopes”, telescopes, windows, a mirror role (to externalize rough mental models), and an unveiling role (to help create new and interesting mathematical concepts, theories, and structures). In this paper we describe some examples of optical diagrams as a particular kind of epistemic mediator able to perform the explanatory abductive task of providing a better understanding of the calculus, through a non-standard model of analysis. We also maintain they can be used in many other different epistemological and cognitive situations.     

Feedback Models of Two Classical Philosophical Positions and a Semantic Problem

The notion of feedback has been exploited with considerable success in scientific and technological fields as well as in the sciences of man and society. Its use in philosophical, cultural and educational contexts, however, is still rather meagre, even if some notable attempts can be found in the literature. This paper shows that the feedback concept can help learn and understand some classical philosophical theories. In particular, attention focuses on Fichte’s doctrine of science, usually presented in obscure terms following its inventor’s style, and on the vulgate version of Hegel’s dialectic. Also a classic problem of linguistics concerning the meaning of sentences in partially unknown languages is interpreted with the aid of feedback diagrams. Even if the analysis is only qualitative, it is believed that it may serve as a useful tool for thought for both students and researchers.     

初议工程伦理学的建设方向——来自生命伦理学的启示

我国工程伦理学正值"起步"阶段,其学科建设方向是一个热门话题。生命伦理学已经在我国"起飞",其理论和体制化建设都取得瞩目成绩,并已在医学和生命科学技术研发中开始发挥对实践的指导和规范作用。借鉴生命伦理学20年的建设经验,就工程伦理学的建设提出几个建议:工程伦理学不能等同于工程师职业伦理;工程伦理学以实践为指向,但仍然需要构建本学科的基本原则和基本方法;工程伦理学在其体制化建设中,可以借鉴生命伦理委员会的建制,通过工程评估委员会对工程合理性的评估,发挥工程伦理学宏观层面的决策指导作用。     

民国时期的大数命名及争议

大数命名是数学名词术语统一工作的一部分,也与度量衡统一工作有关。自先秦至清代,中国大数命名并无统一标准。民国时期,大数命名问题引起学界和政府的关注,并争议不断。学界多位学者和教育部、实业部等政府部门均参与其中。争议的焦点是在“兆”以上采用三位分节的千进制,还是采用四位分节的万进制。这作为民国时期中西文化碰撞与冲突一个缩影,反映了中国在现代化进程中处理本国文化习惯与国际文化习惯关系问题的不同思考。     

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。     

Script and Symbolic Writing in Mathematics and Natural Philosophy

We introduce the question whether there are specific kinds of writing modalities and practices that facilitated the development of modern science and mathematics. We point out the importance and uniqueness of symbolic writing, which allowed early modern thinkers to formulate a new kind of questions about mathematical structure, rather than to merely exploit this structure for solving particular problems. In a very similar vein, the novel focus on abstract structural relations allowed for creative conceptual extensions in natural philosophy during the scientific revolution. These preliminary reflections are meant to set the stage for the following contributions in this volume.     

Models as Points of View: The Case of System Dynamics

We propose an analysis of the notion of model as crucially related to the notion of point of view. A model in this sense would always suggest a certain way of looking at a real system, a certain way of thinking about it and a certain way of acting upon it. We focus on System Dynamics as a paradigmatic case with respect to many of the features and problems we can find in the field of modelling and simulation. We analyse in detail some of those features. All of them would be present in many other cases of construction and use of models. Furthermore, they would support the thesis that a model can be fruitfully understood as offering a point of view capable of improving our own points of view over a certain system. The point of view offered by the model could include both non-conceptual and conceptual contents, it would have a complex structure and behaviour, and it would have direct consequences on the decisions made by the subjects adopting that point of view.     

以实践为中心的两个科学抽象理论

本文分析最近卡特莱特和瑞德分别提出的两个科学抽象理论。论证两个理论的分歧来自于他们对抽象在认识论和方法论上的不同理解。这种分歧曾经十分清晰地表现在惠威尔和密尔的争论中。对这些问题的探求和解决不仅要求我们抛弃传统科学哲学中的关于抽象的观念,还要求将我们的出发点从理论转向实践。     

Contemporary Epistemic Logic and the Lockean Thesis

This paper studies the Lockean thesis from the perspective of contemporary epistemic logic. The Lockean thesis states that belief can be defined as ‘sufficiently high degree of belief’. Its main problem is that it gives rise to a notion of belief which is not closed under conjunction. This problem is typical for classical epistemic logic: it is single-agent and static. I argue that from the perspective of contemporary epistemic logic, the Lockean thesis fares much better. I briefly mention that it can successfully be extended from single-agent to multi-agent settings. More importantly, I show that accepting the Lockean thesis (and a more sophisticated version for conditional beliefs) leads to a significant and unexpected unification in the dynamic behavior of (conditional) belief and high (conditional) probability with respect to public announcements. This constitutes a methodological argument in favor of the Lockean thesis. Furthermore, if one accepts Baltag’s Erlangen program for epistemology, this technical observation has even stronger philosophical implications: because belief and high probability display the same dynamic behavior, it is plausible that they are indeed one and the same epistemic notion.