Scientific Language, Misc

I argue that the appropriateness of an assertion is sensitive to context—or, really, the “common ground”—in a way that hasn’t previously been emphasized by philosophers. This kind of context-sensitivity explains why some scientific conclusions seem to be appropriately asserted even though they are not known, believed, or justified on the available evidence. I then consider other recent attempts to account for this phenomenon and argue that if they are to be successful, they need to recognize the kind of context-sensitivity that (...) I argue for. (shrink)

Abstraction and generalization are two processes of reasoning that have a special role in the construction of scientific theories and models. They have been important parts of the scientific method ever since the nineteenth century. A philosophical and historical analysis of scientific practices shows how abstraction and generalization found their way into the theory of the logic of science of the nineteenth-century philosopher Charles S. Peirce. Our case studies include the scientific practices of Francis Galton and John Herschel, who introduced (...) composite photographs and graphical methods, respectively, as technologies of generalization and thereby influenced Peirce’s logic of abstraction. Herschel’s account of generalization is further supported by William Whewell, who was very influential on Peirce. By connecting Herschel’s scientific technology of abstraction to Peirce’s logical technology of abstraction—namely, diagrams—we highlight the role of judgments in scientific observation by hypostatic abstractions. We also relate Herschel’s discovery-driven logic of science and Peirce’s open-ended diagrammatic logic to the use of models in science. Ultimately, Peirce’s theory of abstraction is a case of showing how logic applies to reality. (shrink)

Taking a cue from remarks Thomas Kuhn makes in 1990 about the historical turn in philosophy of science, I examine the history of history and philosophy of science within parts of the British philosophical context in the 1950s and early 1960s. During this time, ordinary language philosophy's influence was at its peak. I argue that the ordinary language philosophers' methodological recommendation to analyze actual linguistic practice influences several prominent criticisms of the deductive-nomological model of scientific explanation and that these criticisms (...) relate to the historical turn in philosophy of science. To show these connections, I primarily examine the work of Stephen Toulmin, who taught at Oxford from 1949 to 1954, and Michael Scriven, who completed a dissertation on explanation under Gilbert Ryle and R.B. Braithwaite in 1956. I also consider Mary Hesse's appeal to an ordinary language-influenced account of meaning in her account of the role of models and analogies in scientific reasoning, and W.H. Watson's Wittgensteinian philosophy of science, an early influence on Toulmin. I think there are two upshots to my historical sketch. First, it fills out details of the move away from logical positivism to more historical- and practice-focused philosophies of science. Second, questions about linguistic meaning and the proper targets and aims of philosophical analysis are part and parcel of the historical turn, as well as its reception. Looking at the philosophical background during which so-called linguistic philosophers also had a hand in bringing these questions to prominence helps us understand why. (shrink)

2020 is the year of the fortieth anniversary of Bas van Fraassen’s seminal book The Scientific Image. It is quite surprising, after such a long time, and considering how much the author’s proposal was debated during the last four decades, to find a new review of it on the March issue of Metascience. In “Concluding Unscientific Image”, Hans Halvorson claims that, in the work of the founder of constructive empiricism, not only is there a defense of an anti-realist perspective on (...) science—and, at the same time, a critique of scientific realism—, but also a revolt against the way of doing philosophy that, since Quine, seemed to be hegemonic in analytical philosophy. The present study focuses on Halvorson’s allegations about what maintaining the empirical adequacy of a theory would encompass—and that, according to him, van Fraassen has in mind—and aims at showing that, perhaps, they do not correspond to what van Fraassen actually defends in his book. (shrink)

Human produce discourses on the world: mythologies, religions, mysticisms, philosophies, science. The majority of those discourses are transcendent in nature. Following a conceptual clarification based on the notions of reflection and general discourse, philosophy appears as a transcendent general discourse among others; hence the failure of the latter to account for the world and science; hence the need for a non-transcendent general discourse, a properly scientific general discourse, a metascience. In light of these redefined boundaries, it will be proposed to (...) base metascience on an interpretation of Mario Bunge’s work. This interpretation is based on a set of general postulates that Mario Bunge adheres to and taken for granted by scientists. It is proposed that supporting such a set of postulates without problematizing them in the manner of the philosophers, makes Bunge’s thinking no longer philosophical. (shrink)

This article explores the history of British Mensa to examine the contested status of high intelligence in Great Britain between the late 1940s and the late 1980s. Based on journals and leaflets from the association and newspaper articles about it, the article shows how protagonists from the high IQ society campaigned for intelligence and its testing among the British public. Yet scathing reactions to the group in newspapers suggest that journalists considered it socially provocative to stress one’s own brainpower as (...) extraordinarily high. To better understand such disagreements, the article analyses communicative patterns that were used to make judgements about intelligence. This case study sheds light on how aspects of difference and the ascription of social positions are negotiated in public understandings of intelligence. (shrink)

In recent years, the opioid crisis in the United States has sparked significant discussion on doctor–patient interactions concerning chronic pain treatments, but little to no attention has been given to investigating the vocal aspects of patient talk. This exploratory sociolinguistic study intends to fill this knowledge gap by employing prosodic discourse analysis to examine context-specific linguistic features used by the interlocutors of two distinct medical interactions. We found that patients employed both low pitch and creak as linguistic resources when describing (...) chronic pain, narrating symptoms and requesting opioids. The situational use of both features informs us about the linguistic ways in which patients frame fraught issues like chronic pain in light of the current opioid crisis. This study expands the breadth of phonetic analysis within the domain of discourse analysis, serving to illuminate discussions surrounding the illocutionary role of the lower vocal tract in expressing emotions. (shrink)

This article intends to contribute to the science–religion historiography with two topics—philology and the construction of national identities—that can help provide a more complex picture of the relations between science and religion. We use the life and work of the Mallorcan Catholic priest Antoni Maria Alcover (1862–1932) as a case study that puts language, linguistics, and nationalism on the board of science and religion studies. Alcover was the main driving force of the Catalan Dictionary, a collective enterprise that set out (...) to inventory the complete oral and literary lexicon of this language, and which mobilized thousands of people, many of which were clergymen, from all over the Catalan‐speaking territories. In the article, we will explore Alcover's education; the way he established a link between language, religion, and fatherland; the shaping of his identity as a philologist in the image mainly of new German notions and practices; as well as his role in the institutionalization process of the Catalan language as a scientific language, as a language for science and for religion. (shrink)

I draw upon speech act theory to understand the speech acts appropriate to the multiple aims of scientific practice and the role of nonepistemic values in evaluating speech acts made relative to those aims. First, I look at work that distinguishes explaining from describing within scientific practices. I then argue speech act theory provides a framework to make sense of how explaining, describing, and other acts have different felicity conditions. Finally, I argue that if explaining aims to convey understanding to (...) particular audiences rather than describe literally across all contexts, then evaluating explanatory acts directed to the public or policymakers involves asking nonepistemic questions. (shrink)

人们普遍认为，不可能性、不完整性、不一致性、不可度、随机性、可预见性、悖论、不确定性和理性极限是完全不同的科学物理或数学问题，在常见。我认为，它们主要是标准的哲学问题（即语言游戏），这些问题大多在80 多年前由维特根斯坦解决。 -/- "在这种情况下，我们'想说'当然不是哲学，而是它的原材料。因此，例如，数学家倾向于对数学事实的客观性和现实性说的，不是数学哲学，而是哲学处理的东西。维特根斯坦 PI 234 -/- "哲学家们经常看到科学的方法，他们不可抗拒地试图以科学的方式提问和回答问题。这种倾向是形而上学的真正源泉，将哲学家带入完全的黑暗之中。 维特根斯坦 -/- 我简要地总结了现代两位最杰出的学生路德维希·维特根斯坦和约翰·西尔关于故意的逻辑结构（思想、语言、行为）的一些主要发现，作为我的起点Wittgenstein 的基本发现——所有真正的"哲学"问题都是相同的——关于在特定上下文中如何使用语言的困惑，因此所有解决方案都是一样的——研究如何在相关上下文中使用语言，使其真实性条件（满意度或 COS 条件）是明确的。基本问题是，人们可以说什么，但一个人不能意味着（状态明确COS）任何任意的话语和意义只有在非常具体的上下文中才可能。 -/- 在两种思想体系的现代视角（被推广为"思维快，思维慢"）的框架内，我从维特根斯坦人的角度剖析了一些主要评论员关于这些问题的一些著作，并采用了一个新的表意向性和新的双系统命名法。 我表明，这是一个强大的启发式描述这些假定的科学，物理或数学问题的真实性质，这是真正最好的处理作为标准哲学问题，如何使用语言（语言游戏在维特根斯坦的术语）。 -/- 我的论点是，这里突出特征的意向表（理性、思想、思想、语言、个性等）或多或少地准确地描述了，或者至少作为启发式，我们思考和行为的方式，所以它包含不只是哲学和心理学，但其他一切（历史，文学，数学，政治等） 。特别要注意，我（以及西尔、维特根斯坦和其他人）认为，故意和理性包括有意识的审议语言系统2和无意识的自动预语言系统1行为或反射。 .

Science has uncovered many mistakes that had been hidden for centuries among implicit everyday assumptions. When we make explicit what lies implicit within language, there is no guarantee that we will arrive at truth about the world. Many therefore assume that only science delivers truth. Recent debates on this issue often refer to Wilfred Sellars’s arguments against the pre-conceptual given but conclude that his additional insistence on the exclusivity of the scientific image of the world is unfounded. In this paper (...) I resort to Robert Brandom’s development of these arguments to show that saying a word, understanding a concept and engaging in some practices go together. Both laws of nature and social norms regulate these practices and determine the identity conditions of objects. I argue therefore that the conceptual scheme indeed reflects the nature of things because it results from our successful engagement with the world during the long sweep of evolutionary time. (shrink)

Reports of the Intergovernmental Panel on Climate Change (IPCC) employ an evolving framework of calibrated language for assessing and communicating degrees of certainty in findings. A persistent challenge for this framework has been ambiguity in the relationship between multiple degree-of-certainty metrics. We aim to clarify the relationship between the likelihood and confidence metrics used in the Fifth Assessment Report (2013), with benefits for mathematical consistency among multiple findings and for usability in downstream modeling and decision analysis. We discuss how our (...) proposal meshes with current and proposed practice in IPCC uncertainty assessment. (shrink)

Comparative philosophy between two disparate cultural-philosophic traditions, such as Western and Chinese philosophy, has become a new trend of philosophical fashion in the late twentieth and early twenty-first centuries. Having learned from the past, contemporary comparative philosophers cautiously safeguard their comparative studies against two potential pitfalls, namely cultural universalism and cultural relativism. The Orientalism that assumed the superiority of the Occidental has become a memory of the past. The historical pendulum has apparently swung to the other extreme. The more recent (...) "reverse Orientalism" has started to reclaim the superiority of the Oriental. We have even been told that the twenty-first... (shrink)

Recent philosophical analyses of the epistemic dimension of images in the sciences show a certain trend in acknowledging potential roles of these images beyond their merely decorative or pedagogical functions. We argue, however, that this new debate has yet paid little attention to a special type of pictures, we call ‘visual metaphor’, and its versatile heuristic potential in organizing data, supporting communication, and guiding research, modeling, and theory formation. Based on a case study of Conrad Hal Waddington’s epigenetic landscape images (...) in biology, we develop a descriptive framework applicable to heuristic roles of various visual metaphors in the sciences. (shrink)

This article motivates a shift in certain strands of the debate over legitimate roles for nonepistemic values in scientific practice from investigating what is involved in taking cognitive attitudes like acceptance toward an empirical hypothesis to looking at a social understanding of assertion, the act of communicating that hypothesis. I argue that speech act theory’s account of assertion as a type of doing makes salient legitimate roles nonepistemic values can play in scientific practice. The article also shows how speech act (...) theory might provide a framework for fruitfully extending aspects of the social and pragmatic turns in the philosophy of science. (shrink)

As the digitization of information accelerates, the push to encode our surrounding numerically instead of linguistically increases. The role that language has traditionally played in the nomenclature of an integrative taxonomy is being replaced by the numeric identification of one or few quantitative characteristics. Nineteenth-century scientific systems of color identification divided, grouped, and named colors according to multiple characteristics. Now color identification relies on numeric values applied to spectrographic readings. This means of identification of color lacks the taxonomic rigor of (...) nineteenth century systems. Identifying color by numeric value instead of by grouping and naming them, strips color taxonomy of all but one quantitative aspect of a color. I use the case of color taxonomy to argue against a similar trend of numeric identification in the biological sciences. Unlike historically more integrative approaches to taxonomy in biology, genomic sequencing identifies one or few quantitative characteristics to encode an organism. If genomic sequencing becomes the primary means of identification in the biological sciences, just as in numeric systems of color identification, scientific taxonomy would suffer. Basing my analysis on theories of perception of division and on theories of language, I use the cases of color and species to argue for the advantages of an integrative taxonomic system of naming and categorizing over a method of identification, which encodes limited characteristics numerically. I hold that language is the most sophisticated tool for systematic taxonomy and that taxonomic nomenclature should be retained. (shrink)

У статті описано підходи до написання словників у перші десятиліття ХХ ст. Розглянуто концепцію і принципи укладання російсько-українського академічного словника. Проаналізовано реалізацію концепції російсько-українського академічного словника як лексикографічної праці, що поєднує риси перекладного, тлумачного, синонімічного та фразеологічного словників.

Статтю присвячено синтаксичній репрезентації мовної особистості в лінгвістичному дискурсі. Об’єктом дослідження стали окличні та інтонаційно незакінчені речення. Їх розглянуто як синтаксичні засоби вираження експресивності в різножанрових працях українських учених – О. І. Бондаря, П. Ю. Гриценка, С. Я. Єрмоленко, Ю. О. Карпенка. Акцентовано увагу на типах, семантиці аналізованих висловлювань та їхньому прагматичному потенціалі.

Criticism of big data has focused on showing that more is not necessarily better, in the sense that data may lose their value when taken out of context and aggregated together. The next step is to incorporate an awareness of pitfalls for aggregation into the design of data infrastructure and institutions. A common strategy minimizes aggregation errors by increasing the precision of our conventions for identifying and classifying data. As a counterpoint, we argue that there are pragmatic trade-offs between precision (...) and ambiguity that are key to designing effective solutions for generating big data about biodiversity. We focus on the importance of theory-dependence as a source of ambiguity in taxonomic nomenclature and hence a persistent challenge for implementing a single, long-term solution to storing and accessing meaningful sets of biological specimens. We argue that ambiguity does have a positive role to play in scientific progress as a tool for efficiently symbolizing multiple aspects of taxa and mediating between conflicting hypotheses about their nature. Pursuing a deeper understanding of the trade-offs and synthesis of precision and ambiguity as virtues of scientific language and communication systems then offers a productive next step for realizing sound, big biodiversity data services. (shrink)

Taking Carnap’s classic exposition as a starting point, this paper develops a pragmatic account of the method of explication, defends it against a range of challenges and proposes a detailed recipe for the practice of explicating. It is then argued that confusions are involved in characterizing explications as definitions, and in advocating precising definitions as an alternative to explications. Explication is better characterized as conceptual re-engineering for theoretical purposes, in contrast to conceptual re-engineering for other purposes and improving exactness for (...) purely practical reasons. Finally, three limitations which call for further development of the method of explication are discussed. (shrink)

This paper argues that challenges that are grand in scope such as "lifelong health and wellbeing", "climate action", or "food security" cannot be addressed through scientific research only. Indeed scientific research could inhibit addressing such challenges if scientific analysis constrains the multiple possible understandings of these challenges into already available scientific categories and concepts without translating between these and everyday concerns. This argument builds on work in philosophy of science and race to postulate a process through which non-scientific notions become (...) part of science. My aim is to make this process available to scrutiny: what I call founding everyday ideas in science is both culturally and epistemologically conditioned. Founding transforms a common idea into one or more scientifically relevant ones, which can be articulated into descriptively thicker and evaluatively deflated terms and enable operationalisation and measurement. The risk of founding however is that it can invisibilise or exclude from realms of scientific scrutiny interpretations that are deemed irrelevant, uninteresting or nonsensical in the domain in question-but which may remain salient for addressing grand-in-scope challenges. The paper considers concepts of "wellbeing" in development economics versus in gerontology to illustrate this process. (shrink)

This is a brief review of the significance of Martin Rudwick’s article, ‘The Emergence of a Visual Language for Geological Science 1760–1840’, published in this journal 40 years ago.

Scientific realists believe both what a scientific theory says about observables and unobservables. In contrast, scientific antirealists believe what a scientific theory says about observables, but not about unobservables. I argue that scientific realism is a more useful doctrine than scientific antirealism in science classrooms. If science teachers are antirealists, they are caught in Moore’s paradox when they help their students grasp the content of a scientific theory, and when they explain a phenomenon in terms of a scientific theory. Teachers (...) ask questions to their students to check whether they have grasped the content of a scientific theory. If the students are antirealists, they are also caught in Moore’s paradox when they respond positively to their teachers’ questions, and when they explain a phenomenon in terms of a scientific theory. Finally, neither teachers nor students can understand phenomena in terms of scientific theories, if they are antirealists. (shrink)

Conceptual metaphors facilitate both productive and pernicious analogical reasoning. This article addresses the question: When and why does the frequently helpful use of metaphor become pernicious? By applying the most influential theoretical framework from cognitive psychology in analysing the philosophically most prominent example of pernicious metaphorical reasoning, we identify a philosophically relevant but previously undescribed fallacy in analogical reasoning with metaphors. We then outline an explanation of why even competent thinkers commit this fallacy and obtain a psychologically informed ‘debunking’ explanation (...) of the kind experimental philosophy’s ‘sources project’ seeks. (shrink)

Ernst Cassirer’s focus on the expressive function of language should be read, not in the context of Carnap’s debate with Heidegger, but in the context of the earlier work of Chajim (Heymann) Steinthal. Steinthal distinguishes the expressive form of language, when language is studied as a natural phenomenon, from language as a logical, inferential system. Steinthal argues that language always can be expressed in terms of logical inference. Thus, he would disagree with Heidegger, just as Carnap does. But, Steinthal insists, (...) that is not to say that language, as a natural phenomenon, is exhausted by logic or by the place of terms or relations in inferential structures. Steinthal’s “form” of linguistic “expression” is an early version of Cassirer’s “expressive function” for language. The expressive function, then, should not be seen to place a barrier between Carnap and Cassirer. Rather, Steinthal and Cassirer deal with a question that, as far as I know, Carnap does not address directly: how should philosophers analyze human language as a natural phenomenon, as a part of our expression as animals? And how does that expression determine the semantic categories, kind terms, and other structures that develop within, and characterize, human language itself? (shrink)

In recent decades, English has become the uncontestable lingua franca of philosophy of science and of most other areas of philosophy and of the humanities. To have a lingua franca produces enormous benefits for the entire scientific community. The price for those benefits, however, is paid almost exclusively by non-native speakers of English. Section 1 identifies three asymmetries that individual NoNES researchers encounter: ‘publication asymmetry’, ‘resources asymmetry’, and ‘team asymmetry’. Section 2 deals with ‘globalized parochialism asymmetry’: thanks to English being (...) a lingua franca, a special perspective, mostly US and British, is being globalized and is replacing European topics and approaches. This has serious consequences for history of philosophy as well as for philosophical theory: thinkers of the past tend to be dealt with on the global level at best only if and insofar they are translated into English. Similarly, the theoretical agenda of globalized philosophy of scien... (shrink)

These last decades have seen many publications dealing with science and religion. The overall debate seems to have settled on the idea that dialogue between these disciplines is of utmost importance. Bolger’s book, therefore, comes as a surprise because he seems to take issue with this consensus. Is it the case that a subtle form of scientism is infecting large areas of theological discourse, with the result that the dialogue between these two disciplines is often seriously misguided?

This contribution examines the role of diagrams in early modern pedagogy. It begins with an analysis of images from the 1632 Dialogo and 1638 Discorsi. I claim that Galileo often employed images in a pedagogical context, illustrating to readers through his dialogue how he may have used images in his own teaching. Building on the work of previous historians, I argue that a classification of Galileo’s images should include not only heuristic images and images used for virtual witnessing, but also (...) pedagogical images designed to illustrate to the reader (or student) how to reach conclusions about a given question. I then turn to the way Galileo’s readers at the University of Pisa employed Galileo’s images in their own teaching. I argue that Galileo’s readers employed his images in their own works in ways which reflected their training and the genre in which they wrote and taught. (shrink)

Fundamental problems of the uses of formal techniques and of natural and instrumental practices have been raised again and again these past two decades, in many quarters and from varying viewpoints. We have brought a number of quite basic studies of these issues together in this volume, not linked con ceptually nor by any rigorously defined problematic, but rather simply some of the most interesting and even provocative of recent research accomplish ments. Most of these papers are derived from the (...) Boston Colloquium for the Philosophy of Science during 1973-80, the two exceptions being those of Karel Berka (on scales of measurement) and A. A. Zinov'ev (on a non-tradi tional theory of quantifiers). Just how intriguing these results (or conjectures?) seem to us may be seen from some brief quotations: (1) Judson Webb: ".... the abstract machine concept has many of the appropriate kinds of properties for modelling living, reproducing, rule following, self-reflecting, accident-prone, and lucky creatures... the a priori logical results relevant to the abstract machine concept, above all Godel's, could not conceivably have turned out any better for the mechanist. " (2) M. L. Dalla Chiara: "... modal interpretation (of quantum logic) shows clearly that it possesses a logical meaning which is quite independent of quantum mechanics. " (3) Isaac Levi: (as against Peirce and Popper) "... infallibilism is con sistent with corrigibilism, and a view which respects avoidance of error is an important desideratum for science. (shrink)

Claims are universal when they are not dependent on when and where they are made. Mathematics and the natural sciences are the typical disciplines that allow such claims to be made. Is the striving for universal claims in other disciplines justified? Those who attempt to answer this question in the affirmative often argue that it is justified when mathematics and the natural sciences are taken as the model for other disciplines. In this paper I challenge this position and analyze the (...) issue by looking at it from a new angle, a perspective that involves two key concepts: violence and loyalty. The result of this analysis throws light on the broader question concerning what the search for truth might mean in a pluralistic world. (shrink)

This paper consists of three sections. In the first one, some of the main developments in the philosophy of science through the xx century up to the present will be pointed out, and inserted them in the frame of some more general philosophical transformations, such as the so-called “linguistic turn” and “pragmatic turn”, respectively. In the second one, the established connection will be nuanced, from a revision of the work of a “classical” author such as Carnap. Finally, it will be (...) intended a kind of “balance and future perspectives”. (shrink)

In this paper, a new account of empirical claims in structuralism is developed. Its novelty derives from the use that is made of the linguistic approach to scientific theories despite the presumed incompatibility of structuralism with that approach. It is shown how the linguistic approach can be applied to the framework of structuralism if the semantic foundations of that approach are refined to do justice to the doctrine of indirect interpretation of theoretical terms. This doctrine goes back to Carnap but (...) has been advanced until the present day without a proper semantic explanation. (shrink)

Whether meaning is compositional has been a major issue in linguistics and formal philosophy of language for the last 2 decades. Semantic holism is widely and plausibly considered as an objection to the principle of semantic compositionality therein. It comes as a surprise that the holistic peculiarities of scientific language have been rarely addressed in formal accounts so far, given that semantic holism has its roots in the philosophy of science. For this reason, a model-theoretic approach to semantic holism in (...) the language of science is presented here. This approach preserves compositionality to a large extent. *Received September 2009; revised February 2010. †To contact the author, please write to: Seminar for Philosophy, Logic, and Theory of Science, Hauspostfach 49, Ludwig-Maximilians-Universität, Munich 80539, Germany; e-mail: [email protected] (shrink)

The theses in this book are: 1) the tension between the Leibnizian theory of the tropes and their use is resolved in a "pragmatic of discourse" that gives the metaphor a richer dimension than the theorized one, that is, that of "a mechanism capable of combining elements coming from different conceptual spaces into a new metaphorical conceptual space, 'shapeless' to which the metaphor itself provides an adequate language to describe and structure it"; 2) the role of metaphors is placed for (...) Leibniz in the context of a 'multi-method' idea that combines the inventive and the formalizing moment and allows for a multiplicity of directions; 3) the Leibniz system is organized according to a 'logic' that is not deductive but analogical; 4) the valid relations in the system are not only connections of a logical nature; on the contrary, the organization is 'reticular', and the primacy of a relation depends from time to time on the prevalence assigned to a metaphor according to the problem being faced; 5) Leibniz's central metaphors are "emerging parts of a wider submerged translation", i.e. they are both expression and conceptualizing vehicle of a cognitive strategy that wants to govern the complexity of knowledge by organizing it around themes; this strategy is alternative to the Cartesian formulation of "Method" based on the disjunction of objects and notions and instead gives philosophical expression to the Baroque sense of the constant mutability that rules the world. (shrink)

Interpretation in science has gained little attention in the past because philosophers of science believed that interpretation belongs to the context of discovery or must be associated with meaning. But scientists often speak about interpretation when they report their findings. Elsewhere I have argue in favour of a pragmatic-rhetorical theory of explanation, and it is in light of this theory that I suggest we can understand interpretation in the natural sciences.

This article analyzes Galileo's mathematization of motion, focusing in particular on his use of geometrical diagrams. It argues that Galileo regarded his diagrams of acceleration not just as a complement to his mathematical demonstrations, but as a powerful heuristic tool. Galileo probably abandoned the wrong assumption of the proportionality between the degree of velocity and the space traversed in accelerated motion when he realized that it was impossible, on the basis of that hypothesis, to build a diagram of the law (...) of fall. The article also shows how Galileo's discussion of the paradoxes of infinity in the First Day of the Two New Sciences is meant to provide a visual solution to problems linked to the theory of acceleration presented in Day Three of the work. Finally, it explores the reasons why Cavalieri and Gassendi, although endorsing Galileo's law of free fall, replaced Galileo's diagrams of acceleration with alternative ones. (shrink)

According to a grand narrative that long ago ceased to be told, there was a seventeenth century Scientific Revolution, during which a few heroes conquered nature thanks to mathematics. When this grand narrative was brought into question, our perspectives on the question of mathematization should have changed. It seems, however, that they were instead set aside, both because of a general distrust towards sweeping narratives that are always subject to the suspicion that they overlook the unyielding complexity of real history, (...) and because of a shift in our interests. The more obscure and idiosyncratic they are, an alchemist, a patron of the sciences or a lunatic collector is nowadays honored in journals of the history of sciences. As for the general issues involved in the question of mathematization, they are rejected as obsolete, or reserved for specialized journals in the history of mathematics. The article « Forms of mathematization » examines in general the notion of mathematization, distinguishes different forms of mathematization and defends a renewed study of the forms of mathematization in the history of the early sciences. (shrink)

The First Hilbert problem is studied in this paper by applying two instruments: a new methodology distinguishing between mathematical objects and mathematical languages used to describe these objects; and a new numeral system allowing one to express different infinite numbers and to use these numbers for measuring infinite sets. Several counting systems are taken into consideration. It is emphasized in the paper that different mathematical languages can describe mathematical objects (in particular, sets and the number of their elements) with different (...) accuracies. The traditional and the new approaches are compared and discussed. (shrink)