In 1959, mathematician Mark Kac introduced a model, called the Kac ring, in order to elucidate the classical solution of Boltzmann to the problem of macroscopic irreversibility. However, the model is far from being a realistic representation of something. How can it be of any help here? In philosophy of science, it is often argued that models can provide explanations of the phenomenon they are said to approximate, in virtue of the truth they contain, and in spite of the idealisations (...) they are made of. On this view, idealisations are not supposed to contribute to any explaining, and should not affect the global representational function of the model. But the Kac ring is a toy model that is only made of idealisations, and is still used trustworthily to understand the treatment of irreversible phenomena in statistical mechanics. In the paper, my aim is to argue that each idealisation ingeniously designed by the mathematician maintains the representational function of the Kac ring with the general properties of macroscopic irreversibility under scrutiny. Such an active role of idealisations in the representing has so far been overlooked and reflects the art of modelling. (shrink)

I investigate the construction of the mathematical concept of quaternion from a methodological and heuristic viewpoint to examine what we can learn from it for the study of the advancement of mathematical knowledge. I will look, in particular, at the inferential microstructures that shape this construction, that is, the study of both the very first, ampliative inferential steps, and their tentative outcomes—i.e. small ‘structures’ such as provisional entities and relations. I discuss how this paradigmatic case study supports the recent approaches (...) to problem-solving and philosophy of mathematics, and how it suggests refinements of them. In more detail, I argue that the inferential micro-structures enable us to shed more light on the informal, heuristic side of mathematical practice, and its inferential and rational procedures. I show how they enable the generation of a problem, the construction of its conditions of solvability, the search for a hypothesis to solve it, and how these processes are representation-sensitive. On this base, I argue that: 1.the recent development of the philosophy of mathematics was right in moving from Lakatos’ initial investigation of the formal side of a mathematical proof to the investigation of the semi-formal, heuristic side of the mathematical practice as a way of understanding mathematical knowledge and its advancement. 2.The investigation of mathematical practice and discovery can be improved by a finer-grained study of the inferential micro-structures that are built during mathematical problem-solving. (shrink)

In this paper we propose a formal theory of metaphors called Constrained Semantic Transference [CST]. We start from the assumptions that metaphors are characterized by the description of one domain, called the target domain, in terms of another domain, called the source domain; and that a metaphor works by transferring a set of structural relationships from the source domain to the target domain coherently.Starting from these assumptions, we formally define the concept of T-MAPs which are partial coherent mappings from the (...) source domain to the target domain. We also define two operators, called Augmentation and Positing Structure that extend a given T-MAP by adding new structure to the target domain. (shrink)

"The term 'model' has become fashionable". What Mary Hesse characterized in the mid-1960s as a trend in logic, mathematics, and the natural sciences, applies today in general for a broad spectrum of disciplines. Today models appear to be of "extraordinary importance" compared to the first half of the twentieth century, when models were neither mentioned nor contemplated, either generally in scientific publications or specifically in the philosophy of science. It is even assumed that models are "the key to science" and (...) that today's science is largely... (shrink)

The indistinguishability of bosons and fermions has been an essential part of our ideas of quantum mechanics since the 1920s. But what is the mathematical basis for this indistinguishability? An answer was provided in the group representation theory that developed alongside quantum theory and quickly became a major part of its mathematical structure. In the 1930s such a complex and seemingly abstract theory came to be rejected by physicists as the standard functional analysis picture presented by John von Neumann took (...) hold. The purpose of the present account is to show how indistinguishability is explained within representation theory. (shrink)

The Received View of particles in quantum mechanics is that they are indistinguishable entities within their kinds and that, as a consequence, they are not individuals in the metaphysical sense and self-identity does not meaningfully apply to them. Nevertheless cardinality does apply, in that one can have n> 1 such particles. A number of authors have recently argued that this cluster of claims is internally contradictory: roughly, that having more than one such particle requires that the concepts of distinctness and (...) identity must apply after all. A common thread here is that the notion of identity is too fundamental to forego in any metaphysical account. I argue that this argument fails. I then argue that the failure of individuality and identity applies also to macroscopic physical objects, that the problems cannot be constrained to apply only within the microscopic realm. (shrink)

Since Plato’s massive critique of the Sophists rhetoric’s ill repute runs through the history of western philosophy denunciating methods of rhetoric as in large part dishonest persuasion strategies which are at most marginally interested in dealing with truths. This judgement falls way too short insofar as it distorts the historically grown stock labeled “rhetoric” not only in the Aristotelian work. With reference to Olaf Müller’s philosophical book addressing the “controversy” between Goethe and Newton about the nature of light, I will (...) study the different rhetorical models and methods used by Newton and Goethe and also Müller himself. It becomes apparent that even works attempting to decide who was right in the long run do far more than trying to evoke true “representations” of facts or truths in the reader. The specific use of language patterns provides deeper insight into an author’s mindset towards the subject area discussed in his work and generally speaking the investigation of the rhetoric of science and philosophy leads to a better understanding of different epistemic cultures both in philosophy and science. (shrink)

Entropy is often introduced to students through the use of the disorder metaphor. However, many weaknesses and limitations of this metaphor have been identified, and it has therefore been argued that it is more harmful than useful in teaching. For instance, under the influence of the disorder metaphor, students tend to focus on spatial configuration with regard to entropy but disregard the role of energy, which may lead their intuition astray in problem solving. Albeit so, a review of research of (...) students’ ideas about entropy in relation to the disorder metaphor shows that students can use the metaphor in developing a more nuanced, complex view of the concept, by connecting entropy as disorder to other concepts such as microstates and spreading. The disorder metaphor—in combination with other explanatory approaches—can be used as a resource for learning, in giving students an early flavour of what entropy means, so long as we acknowledge its limitations; we can put this “bad” metaphor to good use in teaching. (shrink)

The object of this paper is to look at the extent and nature of the uses of analogy during the ªrst century following the so-called scientiªc revolution. Using the research tool provided by JSTOR we systematically analyze the uses of “analog” and its cognates (analogies, analogous, etc.) in the Philosophical Transactions of the Royal Society of London for the period 1665–1780. In addition to giving the possibility of evaluating quantitatively the proportion of papers explicitly using analogies, this approach makes it (...) possible to go beyond the maybe idiosyncratic cases of Descartes, Kepler, Galileo, and other much studied giants of the so-called Scientiªc Revolution. As a result a classiªcation of types of uses is proposed. Relations between types of analogies and research ªelds are also established. In this paper we are less interested in discussing the “real nature” or “essence” or even the cognitive limitations of analogical thinking than in describing its various uses and different meanings as they changed over the course of a century. (shrink)

This paper explores the relation between scientific knowledge and common sense intuitions as a complement to Hoyningen-Huene’s account of systematicity. On one hand, Hoyningen-Huene embraces continuity between these in his characterization of scientific knowledge as an extension of everyday knowledge, distinguished by an increase in systematicity. On the other, he argues that scientific knowledge often comes to deviate from common sense as science develops. Specifically, he argues that a departure from common sense is a price we may have to pay (...) for increased systematicity. I argue that to clarify the relation between common sense and scientific reasoning, more attention to the cognitive aspects of learning and doing science is needed. As a step in this direction, I explore the potential for cross-fertilization between the discussions about conceptual change in science education and philosophy of science. Particularly, I examine debates on whether common sense intuitions facilitate or impede scientific reasoning. While contending that these debates can balance some of the assumptions made by Hoyningen-Huene, I suggest that a more contextualized version of systematicity theory could supplement cognitive analysis by clarifying important organizational aspects of science. (shrink)

The aim of this paper is to grasp the relevant distinctions between various ways in which models and simulations in Artificial Intelligence (AI) relate to cognitive phenomena. In order to get a systematic picture, a taxonomy is developed that is based on the coordinates of formal versus material analogies and theory-guided versus pre-theoretic models in science. These distinctions have parallels in the computational versus mimetic aspects and in analytic versus exploratory types of computer simulation. The proposed taxonomy cuts across the (...) traditional dichotomies between symbolic and embodied AI, general intelligence and symbol and intelligence and cognitive simulation and human/non-human-like AI. -/- According to the taxonomy proposed here, one can distinguish between four distinct general approaches that figured prominently in early and classical AI, and that have partly developed into distinct research programs: first, phenomenal simulations (e.g., Turing’s “imitation game”); second, simulations that explore general-level formal isomorphisms in pursuit of a general theory of intelligence (e.g., logic-based AI); third, simulations as exploratory material models that serve to develop theoretical accounts of cognitive processes (e.g., Marr’s stages of visual processing and classical connectionism); and fourth, simulations as strictly formal models of a theory of computation that postulates cognitive processes to be isomorphic with computational processes (strong symbolic AI). -/- In continuation of pragmatic views of the modes of modeling and simulating world affairs, this taxonomy of approaches to modeling in AI helps to elucidate how available computational concepts and simulational resources contribute to the modes of representation and theory development in AI research—and what made that research program uniquely dependent on them. (shrink)

The problem of epistemic opacity in Artificial Intelligence is often characterised as a problem of intransparent algorithms that give rise to intransparent models. However, the degrees of transparency of an AI model should not be taken as an absolute measure of the properties of its algorithms but of the model’s degree of intelligibility to human users. Its epistemically relevant elements are to be specified on various levels above and beyond the computational one. In order to elucidate this claim, I first (...) contrast computer models and their claims to algorithm-based universality with cybernetics-style analogue models and their claims to structural isomorphism between elements of model and target system. While analogue models aim at perceptually or conceptually accessible model-target relations, computer models give rise to a specific kind of underdetermination in these relations that needs to be addressed in specific ways. I then undertake a comparison between two contemporary AI approaches that, although related, distinctly align with the above modelling paradigms and represent distinct strategies towards model intelligibility: Deep Neural Networks and Predictive Processing. I conclude that their respective degrees of epistemic transparency primarily depend on the underlying purposes of modelling, not on their computational properties. (shrink)

Understanding what is distinctive about the role of models in science requires characterizing broad patterns in how these models evolve in the face of experimental results. That is, we must examine not just model statics—how the model relates to theory, or represents the world, at some point in time—but also model dynamics—how the model both generates new experimental results and is modified in response to them. Visual representations of structure play a central role in the theoretical reasoning of organic chemists. (...) Not surprisingly, these representations have changed in important ways–in response to experimental and theoretical developments– throughout the history of organic chemistry. In many cases it is appropriate to understand the visual representations used by organic chemists as models. The evolution of the structural representations of organic chemists therefore provides a clear example of the dynamics of scientific modeling. In this paper I use a conception of scientific modeling drawn from the work of Mary Hesse to examine how the concept of a molecular conformation was incorporated into the visual representations of structure used by organic chemists. (shrink)

I discuss Aristotle’s opening argument against Platonic Forms in _Metaphysics_ A.9, ‘the Razor’, which criticizes the introduction of Forms on the basis of an analogy with a hypothetical case of counting things. I argue for a new interpretation of this argument, and show that it involves two interesting objections against the introduction of Forms as formal causes: one concerns the completeness and the other the adequacy of such an explanatory project.

Based on an analysis of double hermeneutics in the human sciences, a distinction between a weak and a strong rhetorical analysis of human-scientific research is introduced, taking account of the self-reflective character of hermeneutic interpretation. The paper argues that there are three hermeneutic topics in the research process for human-scientific experience, which are associated with applying specific rhetorical tools. The three topics are described under the following rubrics: (a) bridging the gap between experience-near and experience-distant concepts; (b) achieving integrity of (...) the cultural objects dispersed in different interpretive strategies; and (c) taking into consideration that an important task of hermeneutic interpretation in human-scientific research is to give an account of the object's immanent narrative coherence. The paper is written in the conviction that a kind of re-methodologization of philosophical hermeneutics which does not rehabilitate epistemological foundationalism can provide a new philosophical identity to the human sciences. (shrink)

A theory of analogy must describe how the meaning of an analogy is derived from the meanings of its parts. In the structure‐mapping theory, the interpretation rules are characterized as implicit rules for mapping knowledge about a base domain into a target domain. Two important features of the theory are (a) the rules depend only on syntactic properties of the knowledge representation, and not on the specific content of the domains; and (b) the theoretical framework allows analogies to be distinguished (...) cleanly from literal similarity statements, applications of abstractions, and other kinds of comparisons.Two mapping principles are described: (a) Relations between objects, rather than attributes of objects, are mapped from base to target; and (b) The particular relations mapped are determined by systematicity, as defined by the existence of higher‐order relations. (shrink)

The last decade and a half has seen an ardent development of self-organised criticality, a new approach to complex systems, which has become important in many domains of natural as well as social science, such as geology, biology, astronomy, and economics, to mention just a few. This has led many to adopt a generalist stance towards SOC, which is now repeatedly claimed to be a universal theory of complex behaviour. The aim of this paper is twofold. First, I provide a (...) brief and non-technical introduction to SOC. Second, I critically discuss the various bold claims that have been made in connection with it. Throughout, I will adopt a rather sober attitude and argue that some people have been too readily carried away by fancy contentions. My overall conclusion will be that none of these bold claims can be maintained. Nevertheless, stripped of exaggerated expectations and daring assertions, many SOC models are interesting vehicles for promising scientific research.Author Keywords: Self-organised criticality; Scaling law; Models; Formal analogy. (shrink)

Veritism, the position that truth is necessary for epistemic acceptability, seems to be in tension with the observation that much of our best science is not, strictly speaking, true when interpreted literally. This generates a paradox: truth is necessary for epistemic acceptability; the claims of science have to be taken literally; much of what science produces is not literally true and yet it is acceptable. We frame Elgin’s project in True Enough as being motivated by, and offering a particular resolution (...) to, this paradox. We discuss the paradox with a focus on scientific models and argue that there is another resolution available which is compatible with retaining veritism: rejecting the idea that scientific models should be interpreted literally. (shrink)

It has been suggested that quantum particles are genuinelyvague objects (Lowe 1994a). The present work explores thissuggestion in terms of the various metaphysical packages that areavailable for describing such particles. The formal frameworksunderpinning such packages are outlined and issues of identityand reference are considered from this overall perspective. Indoing so we hope to illuminate the diverse ways in whichvagueness can arise in the quantum context.

Analogies between classical statistical mechanics and quantum field theory played a pivotal role in the development of renormalization group methods for application in the two theories. This paper focuses on the analogies that informed the application of RG methods in QFT by Kenneth Wilson and collaborators in the early 1970's. The central task that is accomplished is the identification and analysis of the analogical mappings employed. The conclusion is that the analogies in this case study are formal analogies, and not (...) physical analogies. That is, the analogical mappings relate elements of the models that play formally analogous roles and that have substantially different physical interpretations. Unlike other cases of the use of analogies in physics, the analogical mappings do not preserve causal structure. The conclusion that the analogies in this case are purely formal carries important implications for the interpretation of QFT, and poses challenges for philosophical accounts of analogical reasoning and arguments in defence of scientific realism. Analysis of the interpretation of the cutoffs is presented as an illustrative example of how physical disanalogies block the exportation of physical interpretations from from statistical mechanics to QFT. A final implication is that the application of RG methods in QFT supports non-causal explanations, but in a different manner than in statistical mechanics. (shrink)

: Psychological explanations of philosophical intuitions can help us assess their evidentiary value, and our warrant for accepting them. To explain and assess conceptual or classificatory intuitions about specific situations, some philosophers have suggested explanations which invoke heuristic rules proposed by cognitive psychologists. The present paper extends this approach of intuition assessment by heuristics-based explanation, in two ways: It motivates the proposal of a new heuristic, and shows that this metaphor heuristic helps explain important but neglected intuitions: general factual intuitions (...) which have been highly influential in the philosophies of mind and perception but neglected in on-going debates in the epistemology of philosophy. To do so, the paper integrates results from three philosophically pertinent but hitherto largely unconnected strands of psychological research: research on intuitive judgement, analogy and metaphor, and memory-based processing, respectively. The paper shows that the heuristics-based explanation thus obtained satisfies the key requirements cognitive psychologists impose on such explanations, that it can explain the philosophical intuitions targeted, and that this explanation supports normative assessment of the intuitions' evidentiary value: It reveals whether particular intuitions are due to proper exercise of cognitive competencies or constitute cognitive illusions. (shrink)

Everyday memory tasks often require that researchers focus on output-bound measures of memory. As a result, nonmemorial processes (e.g., report option and grain size) may influence recall accuracy. These nonmemorial processes, usually eliminated by laboratory researchers, have the potential to explain some anomalous results and may even be useful to enhance everyday recollection.

This article looks at how fisheries biologists of the early twentieth century conceptualized and measured overfishing and attempted to make it a scientific object. Considering both theorizing and physical practices, the essay shows that categories and understandings of both the fishing industry and fisheries science were deeply and, at times, inextricably interwoven. Fish were both scientific and economic objects. The various models fisheries science used to understand the world reflected amalgamations of biological, physical, economic, and political factors. As a result, (...) scientists had great difficulty stabilizing the concept of overfishing and many influential scholars into the 1930s even doubted the coherence of the concept. In light of recent literature in history of fisheries and environmental social sciences that critiques the infiltration of political and economic imperatives into fisheries and environmental sciences more generally, this essay highlights both how early fisheries scientists understood their field of study as the entire combination of interactions between political, economic, biological and physical factors and the work that was necessary to separate them. (shrink)

Mathematicians and physical scientists depend heavily on the formal symbolism of mathematics in order to express and develop their theories. For this and other reasons the last hundred years has seen a growing interest in the nature of formal language and the way it expresses meaning; particularly the objective, shared aspect of meaning as opposed to subjective, personal aspects. This dichotomy suggests the question: do the objective philosophical theories of meaning offer concepts which can be applied in psychological theories of (...) meaning? In recent years cognitive scientists such as Chomsky [1980], Fodor [1981] and MacNamara [1982] have used philosophical approaches to the meaning of formal language expressions as the basis for their psychological theories. Following this lead it seems appropriate to review some of the main treatments of meaning with a view to their transferability. (shrink)

Parallel to Koriat & Goldsmith's accounting of human memory, there are two distinct approaches in animal learning. Behaviorist approaches focus on quantitative aspects of conditioned response probability, whereas cognitive and ethological approaches focus on qualitative aspects of how memory is used in real life. Moreover, in animal research these distinguishable measures of memory are dissociated in experimental amnesia.

Counterfactual reasoning has been used to account for many aspects of scientific reasoning. More recently, it has also been used to account for the scientific practice of modeling. Truth in a model is truth in a situation considered as counterfactual. When we reason with models, we reason with counterfactuals. Focusing on selected models like Bohr’s atom model or models of population dynamics, I present an account of how the imaginative development of a counterfactual supposition leads us from reality to interesting (...) model assumptions; how it guides our reasoning from these assumptions to interesting consequences for the model scenario via counterfactual entailment; and how it leads us back to conclusions on real target phenomena. (shrink)

Ist der Unterschied zwischen wissenschaftlichen Gesetzen und Theorien ein qualitativer oder lediglich von quantitativer Art? Der Autor versucht zu zeigen, daß Gesetze und Theorien fundamental verschieden sind und daß die Kenntnis ihrer verschiedenen Natur notwendig für ein richtiges Wissenschaftsverständnis ist. Aus seiner Sicht sind Theorien geistige Konstruktionen mit dem Ziel, kausale Erklärungen von empirischen Gesetzen zu geben, während diese Gesetze auf der Grundlage von Messungen entdeckt werden und die Tatsachen der Wissenschaft konstituieren. Erkenntnistheoretisch sind daher Theorien und Gesetze auf verschiedenen (...) Ebenen anzusiedeln: während Gesetze Wissen liefern, liefern Theorien Verstehen. Der Kern der Theorien besteht aus Modellen, die idealisierte Abstraktionen aus Zustandsarten darstellen. Theoretische Modelle konstituieren Ontologien, die kausale Mechanismen aufzeigen. Solche Ontologien betreffen den Bedeutungsaspekt des Gegenstandsbereichs, auf den die Theorie angewendet wird, während empirische Gesetze den Ausdrucksaspekt des gleichen Gegenstandsbereichs betreffen. Theorien erklären Gesetze, indem sie zeigen, wie der Ausdrucksaspekt lediglich der natürliche Ausdruck der Auswirkungen der Kausalmechanismen in Bedeutungsaspekt sind. (shrink)

Sociologists are fond of game metaphors. However, such metaphors rarely go beyond casual references to generic games. Yet games are little social systems, and each game offers a distinctive perspective on the relationship between rules and constraints, on the one side, and emergent order, on the other. In this article, we examine three games—chess, go, and poker—for sociological insights into contested social arenas such as markets, warfare, politics, and the professions. We describe each game's rules and emergent properties, and then (...) offer a brief theorization of the social world through the "lens" of that game. Then we show how a study of the three games advances the sociology of strategy by enriching ideas about skill, position, and strategic dilemma. (shrink)

Discusses philosophy and the science of its lesson. Observation of the perspective that laws of nature exist in theories thereby quantifying statements capable of sustaining counterfactuals; Belief on the confirmation or falsification of theories by treating putative laws as premises of hypothetical argument; Aim of science to use fewer laws to explain greater facts; Similarity between prediction and explanation.

I argue that Darwinian evolutionary theory has a rhetorical dimension and that rhetorical criticism plays a role in how evolutionary science acquires knowledge. I define what I mean by rhetoric by considering Darwin’s Origin. I use the Modern Evolutionary Synthesis to show how rhetoric conceived as situated and addressed argumentation enters into evolutionary theorizing. Finally, I argue that rhetorical criticism helps judge the success, limits, and failures of these theories.

In the twentieth century, no person epitomized more dramatically the “Renaissance mind” than Herbert A. Simon (1916–2001). In aworking life spanning over 60 years, Simon made seminal contributions to administrative theory, axiomatic foundations of physics, economics, sociology, econometrics, cognitive psychology, logic of scientific discovery, and artificial intelligence. Simon's life of the mind, thus, affords nothing less than a “laboratory” in which to observe and examine at close quarters the phenomenon ofmultidisciplinary creativity. In this paper, we attempt to shed some light (...) on the nature of Simon's creativity and the nature of his particular Renaissance mind. In particular, we have attempted here to articulate thecognitive styleunderlying Simon's multidisciplinary creativity. (shrink)