‘The happy thought of a single man’: On the legendary beginnings of a style of reasoning

In this paper I direct attention to one feature of Hacking’s recent work on styles of reasoning and argue that this feature is of far greater philosophical significance than Hacking’s limited discussion of this suggests. The feature in question is his use of ‘legendary beginnings’ in setting out a given style, viz. the method of introducing a style of reasoning by recounting a popular and quasi-mythical narrative that ties the crystallisation of that style to a particular person in a particular place and at a particular time. Whilst Hacking both deploys and discusses this method, his comments suggest that this is primarily a stylistic device employed for reasons of expedience. In contrast, it is argued here that recounting the legendary origins of a style of reasoning affords a distinctive way of vindicating that style, a vindication from within the style itself.     

Maligned for mathematics: Sir Thomas Urquhart and his Trissotetras

Thomas Urquhart (1611–1660), celebrated for his English translation of Rabelais’ Gargantua et Pantagruel, has earned some notoriety for his eccentric, putatively incomprehensible early book on trigonometry The Trissotetras (1645). The Trissotetras was too impractical to succeed in its own day as a textbook, since it lacked both trigonometric tables and sample calculations. But its current bad reputation is based on literary authors’ amplifications of the verdict prefaced to its 19th century reprinting by one mathematician, William Wallace, who lacked the background to appreciate the book’s historical context. Considering that context (including seventeenth century ‘copious’ prose, and medieval logic and ‘art of memory’), the bad reputation is undeserved: the book is mathematically clear, clever (e.g. in superimposing 16 problems into one diagram), and complete. The Trissotetras may thus be viewed as simply one more of Urquhart’s polymathic projects and involvements – which included education, rise of the middle class, religious and class conflicts, development of science and mathematics, search for patronage, universal language construction, and development of English prose – which serve to make him a lively and instructive intellectual Everyman for his time.     

The emergence of objectivity: Fleck,Foucault, Kuhn and Hacking

The analytical notions of ‘thought style’, ‘paradigm’, ‘episteme’ and ‘style of reasoning’ are some of the most popular frameworks in the history and philosophy of science. Although their proponents, Ludwik Fleck, Thomas Kuhn, Michel Foucault, and Ian Hacking, are all part of the same philosophical tradition that closely connects history and philosophy, the extent to which they share similar assumptions and objectives is still under debate. In the first part of the paper, I shall argue that, despite the fact that these four thinkers disagree on certain assumptions, their frameworks have the same explanatory goal – to understand how objectivity is possible. I shall present this goal as a necessary element of a common project -- that of historicising Kant's a priori. In the second part of the paper, I shall make an instrumental use of the insights of these four thinkers to form a new model for studying objectivity. I shall also propose a layered diagram that allows the differences between the frameworks to be mapped, while acknowledging their similarities. This diagram will show that the frameworks of style of reasoning and episteme illuminate conditions of possibility that lie at a deeper level than those considered by thought styles and paradigms.     

What were the genuine Banach spaces in 1922? Reflection on axiomatisation and progression of the mathematical thought

This paper provides an analysis of the use of axioms in Banach’s Ph.D. and their role in the progression of Banach’s mathematical thought. In order to give a precise account of the role of Banach’s axioms, we distinguish two levels of activity. The first one is devoted to the overall process of creating a new theory able to answer some prescribed problems in functional analysis. The second one concentrates on the epistemological role of axioms. In particular, the notion of norm completeness, as it appears in Banach’s text, can be interpreted as an epistemic linchpin between several a priori inhomogeneous domains of mathematical thought.

     

Grasping the spirit in nature: Anschauung in Ørsted's epistemology of science and beauty

The intersection between art, poetry, philosophy and science was the leitmotif which guided the lives and careers of romantic natural philosophers including that of the Danish natural philosopher, H. C. Ørsted. A simple model of Ørsted’s career would be one in which it was framed by two periods of philosophical speculation: the youth’s curious and idealistic interest in new attractive thoughts and the experienced man’s mature reflections at the end of his life. We suggest that a closer look at the epistemological aspects of his works on the theory of beauty reveals a connection between this late work and his early philosophical work including experimental philosophy, but also with the work in teaching and textbook writing, that lies in between. The latter includes Ørsted’s view on the application of mathematics in natural philosophy as well as his failed attempt at a genetic presentation of elementary geometry.     

Isaac Newton and Augustan Anglo-Latin poetry

Although many historians of science acknowledge the extent to which Greek and Roman ideals framed eighteenth-century thought, many classical references in the texts they study remain obscure. Poems played an important role not only in spreading ideas about natural philosophy, but also in changing people’s perceptions of its value; they contributed to Newton’s swelling reputation as an English hero. By writing about Latin poetry, we focus on the intersection of two literary genres that were significant for eighteenth-century natural philosophy, but seem alien to modern science. We classify Augustan Latinate scientific poetry by considering the audiences for whom the poems were intended. We distinguish three broad categories. One type of poetry was circulated amongst gentlemanly scholars (we look particularly at Tripos verses, and laments for Queen Caroline). A second group comprised poetry written specifically to promote or criticise Newton and his books, particularly the Principia (we look at versions of Pope’s epitaph, and Halley’s Lucretian poem). After Newton’s death, a third type of poetry became increasingly significant, included in collections of poems rather than in texts of natural philosophy. Overall, we show how the classical past was vital for creating the scientific future.     

Thought styles and paradigms—a comparative study of Ludwik Fleck and Thomas S. Kuhn

At first glance there seem to be many similarities between Thomas S. Kuhn’s and Ludwik Fleck’s accounts of the development of scientific knowledge. Notably, both pay attention to the role played by the scientific community in the development of scientific knowledge. But putting first impressions aside, one can criticise some philosophers for being too hasty in their attempt to find supposed similarities in the works of the two men. Having acknowledged that Fleck anticipated some of Kuhn’s later theses, there seems to be a temptation in more recent research to equate both theories in important respects. Because of this approach, one has to deal with the problem of comparing the most notable technical terms of both philosophers, namely “thought style” and “paradigm”.This paper aims at a more thorough comparison between Ludwik Fleck’s concept of thought style and Thomas Kuhn’s concept of paradigm. Although some philosophers suggest that these two concepts are essentially equal in content, a closer examination reveals that this is not the case. This thesis of inequality will be defended in detail, also taking into account some of the alleged similarities which may be responsible for losing sight of the differences between these theories.     

Kuhn on incommensurability and theory choice

The incommensurability of two theories seems to problematize theory comparisons, which allow for the selection of the better of the two theories. If so, it becomes puzzling how the quality of theories can improve with time, i.e. how science can progress across changes in incommensurable theories. I argue that in papers published in the 1990s, Kuhn provided a novel way to resolve this apparent tension between incommensurability and scientific progress. He put forward an account of their compatibility which worked not by downplaying the negative consequences of incommensurability but instead by allowing them to reach their natural end: a process of specialisation. This development in Kuhn’s thought has yet to be properly recorded but it is also interesting in its own right. It shows how a robust version of incommensurability—one which really does have severe negative consequences for scientists’ capacity to perform comparative evaluations of incommensurable theories—need make no puzzle of the progress of science.     

Thought styles and paradigms: A comparative study of Ludwik Fleck and Thomas S. Kuhn

At first glance there seem to be many similarities between Thomas S. Kuhn’s and Ludwik Fleck’s accounts of the development of scientific knowledge. Notably, both pay attention to the role played by the scientific community in the development of scientific knowledge. But putting first impressions aside, one can criticise some philosophers for being too hasty in their attempt to find supposed similarities in the works of the two men. Having acknowledged that Fleck anticipated some of Kuhn’s later theses, there seems to be a temptation in more recent research to equate both theories in important respects. Because of this approach, one has to deal with the problem of comparing the most notable technical terms of both philosophers, namely “thought style” and “paradigm”.This paper aims at a more thorough comparison between Ludwik Fleck’s concept of thought style and Thomas Kuhn’s concept of paradigm. Although some philosophers suggest that these two concepts are essentially equal in content, a closer examination reveals that this is not the case. This thesis of inequality will be defended in detail, also taking into account some of the alleged similarities which may be responsible for losing sight of the differences between these theories.     

Knowing what would happen: The epistemic strategies in Galileo's thought experiments

While philosophers have subjected Galileo's classic thought experiments to critical analysis, they have tended to largely ignored the historical and intellectual context in which they were deployed, and the specific role they played in Galileo's overall vision of science. In this paper I investigate Galileo's use of thought experiments, by focusing on the epistemic and rhetorical strategies that he employed in attempting to answer the question of how one can know what would happen in an imaginary scenario. Here I argue we can find three different answers to this question in Galileo later dialogues, which reflect the changing meanings of ‘experience’ and ‘knowledge’ (scientia) in the early modern period. Once we recognise that Galileo's thought experiments sometimes drew on the power of memory and the explicit appeal to ‘common experience’, while at other times, they took the form of demonstrative arguments intended to have the status of necessary truths; and on still other occasions, they were extrapolations, or probable guesses, drawn from a carefully planned series of controlled experiments, it becomes evident that no single account of the epistemological relationship between thought experiment, experience and experiment can adequately capture the epistemic variety we find Galileo's use of imaginary scenarios. To this extent, we cannot neatly classify Galileo's use of thought experiments as either ‘medieval’ or ‘early modern’, but we should see them as indicative of the complex epistemological transformations of the early seventeenth century.     

Structures and strategies in ancient Greek and Roman technical writing: An Introduction

Most of our knowledge of Greek and Roman scientific practice and its place in ancient culture is derived from our study of ancient texts. In the last few decades, this written evidence—ancient technical or specialist literature—has begun to be studied using tools of literary analysis to help answer questions about, for instance, how these works were composed, their authors’ intentions and the expectations of their readers.This introduction to Structures and strategies in ancient Greek and Roman technical writing provides an overview of recent scholarship in the area, and the difficulty in pinning down what ‘technical/specialist literature’ might mean in an ancient context, since Greek and Roman authors communicated scientific knowledge using a wide variety of styles and forms of text (e.g. poetry, dialogues, letters).An outline of the three sections is provided: Form as a mirror of method, in which Sabine Föllinger and Alexander Mueller explore ways in which the structures of texts by Aristotle and Plutarch may reflect methodological concerns; Authors and their implied readers, with contributions by Oliver Stoll, David Creese, Boris Dunsch and Paula Olmos, which examines what ancient texts can tell us about the place of technical knowledge in antiquity; Science and the uses of poetry, with articles by Jochen Althoff, Michael Coxhead and Laurence Totelin, and a new English translation of the Aetna poem by Harry Hine, which explores the (to us) unexpected roles of poetry in ancient scientific culture.     

The metabotropic GABA receptor: molecular insights and their functional consequences

Recent years have seen rapid and significant advances in our understanding of the G-protein-coupled gamma-amino butyric acid, B-type (GABA(B)) receptor, which could be a therapeutic target in conditions as diverse as epilepsy and hypertension. This progress originated with the ground-breaking work of Bernhard Bettler's team at Novartis who cloned the DNA encoding a GABA(B) receptor in 1997. Currently, the receptor is thought to be an unusual, possibly unique, example of a heterodimer composed of homologous, seven-transmembrane-domain (7TMD) subunits (named GABA(B) R1 and GABA(B) R2), neither of which is fully functional when expressed alone. The large N-terminal domain of the GABA(B) R1 subunit projects extracellularly and contains a ligand binding site. The similarity of the amino acid sequence of this region to some bacterial periplasmic amino acid-binding proteins of known structure has enabled structural and functional modelling of the N-terminal domain, and the identification of residues whose substitution modulates agonist/antagonist binding affinities. The intracellular C-terminal domains of the R1 and R2 subunits appear to constitute an important means of contact between the two subunits. Alternative splice variants, a common and functionally important feature of 7TMD proteins, have been demonstrated for the R1 subunit. Notably GABA(B) R1a differs from GABA(B) R1b by the possession of an N-terminal extension containing two complement protein modules (also called SCRs, or sushi domains) of unknown function. The levels at which each of the respective variants is expressed are not equal to one another, with variations occurring over the course of development and throughout the central nervous system. It is not yet clear, however, whether one variant is predominantly presynaptically located and the other postsynaptically located. The existence of as yet unidentified splice variants, additional receptor subtypes and alternative quaternary composition has not been ruled out as a source of receptor heterogeneity.     

Comparing dualities and gauge symmetries

We discuss some aspects of the relation between dualities and gauge symmetries. Both of these ideas are of course multi-faceted, and we confine ourselves to making two points. Both points are about dualities in string theory, and both have the ‘flavour’ that two dual theories are ‘closer in content’ than you might think. For both points, we adopt a simple conception of a duality as an ‘isomorphism’ between theories: more precisely, as appropriate bijections between the two theories’ sets of states and sets of quantities.The first point (Section 3) is that this conception of duality meshes with two dual theories being ‘gauge related’ in the general philosophical sense of being physically equivalent. For a string duality, such as T-duality and gauge/gravity duality, this means taking such features as the radius of a compact dimension, and the dimensionality of spacetime, to be ‘gauge’.The second point (4 Gauge/gravity duality, 5 Some complications for gauge invariance, 6 Galileo׳s ship, (Local)) is much more specific. We give a result about gauge/gravity duality that shows its relation to gauge symmetries (in the physical sense of symmetry transformations that are spacetime-dependent) to be subtler than you might expect. For gauge theories, you might expect that the duality bijections relate only gauge-invariant quantities and states, in the sense that gauge symmetries in one theory will be unrelated to any symmetries in the other theory. This may be so in general; and indeed, it is suggested by discussions of Polchinski and Horowitz. But we show that in gauge/gravity duality, each of a certain class of gauge symmetries in the gravity/bulk theory, viz. diffeomorphisms, is related by the duality to a position-dependent symmetry of the gauge/boundary theory.     

Taming theory with thought experiments: Understanding and scientific progress

I claim that one way thought experiments contribute to scientific progress is by increasing scientific understanding. Understanding does not have a currently accepted characterization in the philosophical literature, but I argue that we already have ways to test for it. For instance, current pedagogical practice often requires that students demonstrate being in either or both of the following two states: 1) Having grasped the meaning of some relevant theory, concept, law or model, 2) Being able to apply that theory, concept, law or model fruitfully to new instances. Three thought experiments are presented which have been important historically in helping us pass these tests, and two others that cause us to fail. Then I use this operationalization of understanding to clarify the relationships between scientific thought experiments, the understanding they produce, and the progress they enable. I conclude that while no specific instance of understanding (thus conceived) is necessary for scientific progress, understanding in general is.     

Kant and the scope of the analytic method

The paper investigates Kant's pre-critical views on the use of analytic and synthetic methods in Newtonian science and in philosophical reasoning. In his 1755/56 writings, Kant made use of two variants of the analytic method, i.e., conceptual analysis in a Cartesian (or Leibnizean) sense, and analysis of the phenomena in a Newtonian sense. His Prize Essay (1764) defends Newton's analytic method of physics as appropriate for philosophy, in contradistinction to the synthetic method of mathematics. A closer look, however, shows that Kant does not identify Newton's method with conceptual analysis, but just suggests a methodological analogy between both methods. Kant’s 1768 paper on incongruent counterparts also fits in with his pre-critical use of conceptual analysis. Here, Kant criticizes Leibniz’ relational concept of space, arguing that it is incompatible with the phenomenon of chiral objects. Since this result was in conflict with his pre-critical views about space, Kant abandoned the analytic method of philosophy in favour of his critical method. The paper closes by comparing Kant's pre-critical analytic method and the way in which he once again took up the methodological analogy between Newtonian science and metaphysics, in the preface B to the Critique of Pure Reason, in the context of his thought experiment of pure reason.     

The evidential significance of thought experiment in science

The most promising way to regard thought experiment is as a species of experiment, alongside concrete experiment. Of the authors who take this view, many portray thought experiment as possessing evidential significance intrinsically. In contrast, concrete experiment is nowadays most convincingly portrayed as acquiring evidential significance in a particular area of science at a particular time in consequence of the persuasive efforts of scientists. I argue that the claim that thought experiment possesses evidential significance intrinsically is contradicted by the history of science. Thought experiment, like concrete experiment, has evidential significance only where particular assumptions—such as the Galilean doctrine of phenomena—are taken to hold; under alternative premises, in themselves equally defensible, thought experiment is evidentially inert.     

The consistency,coherence and calibration of holistic,decomposed and recomposed judgemental probability forecasts

In this paper we make an empirical investigation of the relationship between the consistency, coherence and validity of probability judgements in a real-world forecasting context. Our results indicate that these measures of the adequacy of an individual's probability assessments are not closely related as we anticipated. Twenty-nine of our thirty-six subjects were better calibrated in point probabilities than in odds and our subjects were, in general more coherent using point probabilities than odds forecasts. Contrary to our expectations we found very little difference in forecasting response and performance between simple and compound holistic forecasts. This result is evidence against the ‘divide-and-conquer’ rationale underlying most applications of normative decision theory. In addition, our recompositions of marginal and conditional assessments into compound forecasts were no better calibrated or resolved than their holistic counterparts. These findings convey two implications for forecasting. First, untrained judgemental forecasters should use point probabilities in preference to odds. Second, judgemental forecasts of complex compound probabilities may be as well assessed holistically as they are using methods of decomposition and recomposition. In addition, our study provides a paradigm for further studies of the relationship between consistency, coherence and validity in judgemental probability forecasting.     

Time-Symmetrised Quantum Theory,Counterfactuals and ‘Advanced Action’

Recent authors have raised objections to the counterfactual interpretation of the Aharonov–Bergmann–Lebowitz (ABL) rule of time-symmetrised quantum theory (TSQT). I distinguish between two different readings of the ABL rule, counterfactual and non-counterfactual, and confirm that TSQT advocate L. Vaidman is employing the counterfactual reading to which these authors object. Vaidman has responded to the objections by proposing a new kind of time-symmetrised counterfactual, which he has defined in two different ways. It is argued that neither definition succeeds in overcoming the objections, except in a limited special case previously noted by Cohen and Hiley. In addition, a connection is made between TSQT and Price’s concept of ‘advanced action’, which further supports the special case discussed.     

Galileo and the problem of infinity

During the period before the Greek revolution of 1821, and especially during the years between 1750 and 1821, there were two ways in which European scientific thought was propagated in Greece. The first is traditional. It comes from ancient Greece and, through Byzantium, reaches the period before the Greek revolution. It makes known the thought of Aristotle, Democrititus, and others on ‘natural philosophy’. The second way comes from Europe. The Greek scholars of the period before the Greek revolution, and especially at the end of the eighteenth century, tried to bring to and propagate in Greece the spirit ofthe European Enlightenment, They tried to make known to the Greek people the scientific achievements of Newton, Descartes, Lavoisier, and Laplace. Scientific knowledge is an important weapon against superstition, and Greek students had to learn about science to become free persons in an independent Greek state.