Pub Date : 2024-11-17DOI: 10.1016/j.shpsa.2024.09.004
Toby Friend
Not all testing interventions that we might want to perform, or need to be performable in principle, fail to cause off-path variables. This is a problem for Woodward’s Orthodox Interventionist Theory of causation, but not the ‘Modified Interventionist Theory’, which I proposed in a previous issue of this journal (Friend, 2021). As I explain here, this is because only the modified theory permits ‘soft control’. I will survey three different kinds of case (beyond the case considered previously) in which soft control is necessary for a reasonable application of interventionism. These include cases where soft control makes intervention more practical, physically possible, and causally probative in the context of mechanisms. I’ll also take the opportunity to remove some of the confusing aspects of my original formulation of the modified theory. The result, I believe, constitutes a strong case for it.
{"title":"Soft control: Furthering the case for Modified Interventionist Theory","authors":"Toby Friend","doi":"10.1016/j.shpsa.2024.09.004","DOIUrl":"10.1016/j.shpsa.2024.09.004","url":null,"abstract":"<div><div>Not all testing interventions that we might want to perform, or need to be performable in principle, fail to cause off-path variables. This is a problem for Woodward’s Orthodox Interventionist Theory of causation, but not the ‘Modified Interventionist Theory’, which I proposed in a previous issue of this journal (<span><span>Friend, 2021</span></span>). As I explain here, this is because only the modified theory permits ‘soft control’. I will survey three different kinds of case (beyond the case considered previously) in which soft control is necessary for a reasonable application of interventionism. These include cases where soft control makes intervention more practical, physically possible, and causally probative in the context of mechanisms. I’ll also take the opportunity to remove some of the confusing aspects of my original formulation of the modified theory. The result, I believe, constitutes a strong case for it.</div></div>","PeriodicalId":49467,"journal":{"name":"Studies in History and Philosophy of Science","volume":"108 ","pages":"Pages 93-100"},"PeriodicalIF":1.4,"publicationDate":"2024-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142652329","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-15DOI: 10.1016/j.shpsa.2024.09.005
Isaac Wilhelm
Roughly put, explanatory circles — if any exist — would be propositions such that (i) each explains the next, and (ii) the last explains the first. In this paper, I give two arguments for the view that there are explanatory circles. The first argument appeals to general relativistic worlds in which time is circular. The second argument appeals to special science theories that describe feedback loops. In addition, I show that three standard arguments against explanatory circles are unsuccessful.
{"title":"Explanatory circles","authors":"Isaac Wilhelm","doi":"10.1016/j.shpsa.2024.09.005","DOIUrl":"10.1016/j.shpsa.2024.09.005","url":null,"abstract":"<div><div>Roughly put, explanatory circles — if any exist — would be propositions such that (i) each explains the next, and (ii) the last explains the first. In this paper, I give two arguments for the view that there are explanatory circles. The first argument appeals to general relativistic worlds in which time is circular. The second argument appeals to special science theories that describe feedback loops. In addition, I show that three standard arguments against explanatory circles are unsuccessful.</div></div>","PeriodicalId":49467,"journal":{"name":"Studies in History and Philosophy of Science","volume":"108 ","pages":"Pages 84-92"},"PeriodicalIF":1.4,"publicationDate":"2024-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142639901","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-04DOI: 10.1016/j.shpsa.2024.09.009
Christopher Stephens
How should we evaluate Darwin and Wallace's arguments for common ancestry over separate ancestry? Elliott Sober defends a likelihood reconstruction of Darwin's reasoning that he dubs modus Darwin: similarity, therefore common ancestry. One assumption of Sober's approach is that separate ancestors have traits that are probabilistically independent. I motivate an objection to this assumption by appeal to 19th century naturalist alternatives such as those of Geoffroy and Owen. On Geoffroy and Owen's separate ancestry models, the ancestors can have traits that are probabilistically dependent. I then prove a generalization of Sober's approach that allows for similarity matching among traits to favour common ancestry over separate ancestry even when the traits of the separate ancestors are probabilistically dependent. I consider Helgeson's recent criticisms of Sober's approach and his alternative interpretation of Darwin's reasoning: more similar, hence, more recent common ancestry. I defend Sober's approach against Helgeson's objections.
{"title":"Modus Darwin redux","authors":"Christopher Stephens","doi":"10.1016/j.shpsa.2024.09.009","DOIUrl":"10.1016/j.shpsa.2024.09.009","url":null,"abstract":"<div><div>How should we evaluate Darwin and Wallace's arguments for common ancestry over separate ancestry? Elliott Sober defends a likelihood reconstruction of Darwin's reasoning that he dubs <em>modus Darwin</em>: <em>similarity, therefore common ancestry</em>. One assumption of Sober's approach is that separate ancestors have traits that are probabilistically independent. I motivate an objection to this assumption by appeal to 19th century naturalist alternatives such as those of Geoffroy and Owen. On Geoffroy and Owen's separate ancestry models, the ancestors can have traits that are probabilistically dependent. I then prove a generalization of Sober's approach that allows for similarity matching among traits to favour common ancestry over separate ancestry even when the traits of the separate ancestors are probabilistically dependent. I consider Helgeson's recent criticisms of Sober's approach and his alternative interpretation of Darwin's reasoning: <em>more similar, hence, more recent common ancestry</em>. I defend Sober's approach against Helgeson's objections.</div></div>","PeriodicalId":49467,"journal":{"name":"Studies in History and Philosophy of Science","volume":"108 ","pages":"Pages 73-83"},"PeriodicalIF":1.4,"publicationDate":"2024-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142578939","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-16DOI: 10.1016/j.shpsa.2024.09.007
Marco Giovanelli
Cassirer’s early philosophy of space and time, overshadowed by his later work on relativity, has been scarcely explored in the literature. This paper aims to bridge this gap. It argues that understanding Cassirer’s point of view requires acknowledging the pivotal role he attributed to the work of Leonhard Euler in the philosophical ‘coming of age’ of modern science. Against the Leibniz-Berkeley philosophical plea for the relativity of all motion, Euler objected that if Newton’s absolute space and time did not exist, the principle of inertia would be come meaningless and with it a scientific theory of motion. According to Cassirer, Kant took a step beyond Euler by shifting the focus from the existence of space and time as ‘things’ to their function as necessary ‘conditions’ of the possibility of mechanics. In the nineteenth century, it became clear that Newton’s absolute space and time entail more structure than necessary. Nevertheless, according to Cassirer, the Euler-Kant insight still holds: a geometric structure serving as an inertial structure is the condicio sine qua non of a coherent theory of motion, including general relativity. This paper concludes that Cassirer came close to defending a sort of ‘inertial functionalism’ dressed in neo-Kantian garb.
{"title":"The philosophical coming of age of science. Euler’s role in Cassirer’s early philosophy of space and time","authors":"Marco Giovanelli","doi":"10.1016/j.shpsa.2024.09.007","DOIUrl":"10.1016/j.shpsa.2024.09.007","url":null,"abstract":"<div><div>Cassirer’s early philosophy of space and time, overshadowed by his later work on relativity, has been scarcely explored in the literature. This paper aims to bridge this gap. It argues that understanding Cassirer’s point of view requires acknowledging the pivotal role he attributed to the work of Leonhard Euler in the philosophical ‘coming of age’ of modern science. Against the Leibniz-Berkeley <em>philosophical</em> plea for the relativity of all motion, Euler objected that if Newton’s absolute space and time did not exist, the principle of inertia would be come meaningless and with it a <em>scientific</em> theory of motion. According to Cassirer, Kant took a step beyond Euler by shifting the focus from the <em>existence</em> of space and time as ‘things’ to their <em>function</em> as necessary ‘conditions’ of the possibility of mechanics. In the nineteenth century, it became clear that Newton’s absolute space and time entail more structure than necessary. Nevertheless, according to Cassirer, the Euler-Kant insight still holds: a geometric structure serving as an inertial structure is the <em>condicio sine qua non</em> of a coherent theory of motion, including general relativity. This paper concludes that Cassirer came close to defending a sort of ‘inertial functionalism’ dressed in neo-Kantian garb.</div></div>","PeriodicalId":49467,"journal":{"name":"Studies in History and Philosophy of Science","volume":"108 ","pages":"Pages 55-63"},"PeriodicalIF":1.4,"publicationDate":"2024-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142441593","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-16DOI: 10.1016/j.shpsa.2024.09.003
Michael T. Michael
This paper critically examines the validity of Freudian psychoanalysis within the framework of Moberger's characterisation of pseudoscience as bullshit with scientific pretensions. The central question addressed is whether Freudian psychoanalysis qualifies as “bullshit,” following Moberger's guideline of looking for systematic fallacies. The analysis centres on two fundamental critiques against psychoanalysis: one posited by Popper, contending that psychoanalytic interpretation is excessively flexible, and another by Glymour, asserting that Freud's interpretative method baselessly posits associations as causes. This paper argues that both criticisms rest on misunderstandings and asserts that Freudian psychoanalysis does not commit the alleged fallacies. It also offers positive evidence that Freud was not a bullshitter. The conclusion drawn is that psychoanalysis should not be regarded as bullshit, and hence does not qualify as pseudoscience on Moberger's criteria. Consequently, the paper suggests that Freudian psychoanalysis deserves a fairer hearing then many have given it.
{"title":"Freud, bullshit, and pseudoscience","authors":"Michael T. Michael","doi":"10.1016/j.shpsa.2024.09.003","DOIUrl":"10.1016/j.shpsa.2024.09.003","url":null,"abstract":"<div><div>This paper critically examines the validity of Freudian psychoanalysis within the framework of Moberger's characterisation of pseudoscience as bullshit with scientific pretensions. The central question addressed is whether Freudian psychoanalysis qualifies as “bullshit,” following Moberger's guideline of looking for systematic fallacies. The analysis centres on two fundamental critiques against psychoanalysis: one posited by Popper, contending that psychoanalytic interpretation is excessively flexible, and another by Glymour, asserting that Freud's interpretative method baselessly posits associations as causes. This paper argues that both criticisms rest on misunderstandings and asserts that Freudian psychoanalysis does not commit the alleged fallacies. It also offers positive evidence that Freud was not a bullshitter. The conclusion drawn is that psychoanalysis should not be regarded as bullshit, and hence does not qualify as pseudoscience on Moberger's criteria. Consequently, the paper suggests that Freudian psychoanalysis deserves a fairer hearing then many have given it.</div></div>","PeriodicalId":49467,"journal":{"name":"Studies in History and Philosophy of Science","volume":"108 ","pages":"Pages 64-72"},"PeriodicalIF":1.4,"publicationDate":"2024-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142445871","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-12DOI: 10.1016/j.shpsa.2024.09.006
Thomas Marré
{"title":"Kant on the logical form of organized being","authors":"Thomas Marré","doi":"10.1016/j.shpsa.2024.09.006","DOIUrl":"10.1016/j.shpsa.2024.09.006","url":null,"abstract":"","PeriodicalId":49467,"journal":{"name":"Studies in History and Philosophy of Science","volume":"108 ","pages":"Pages 46-54"},"PeriodicalIF":1.4,"publicationDate":"2024-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142424636","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-07DOI: 10.1016/j.shpsa.2024.09.002
David Wallace
Phenomena in gauge theory are often described in the physics literature via a specific choice of gauge. In foundational and philosophical discussions this is often criticized as introducing gauge dependence, and contrasted against (often aspirational) “gauge-invariant” descriptions of the physics. I argue, largely in the context of scalar electrodynamics, that this is misguided, and that descriptions of a physical process within a specific gauge are in fact gauge-invariant descriptions. However, most of them are non-local descriptions of that physics, and I suggest that this ought to be the real objection to such descriptions. I explore the unitary gauge as the exception to this nonlocality and consider its strengths and limitations, as well as (more briefly) its extension beyond scalar electrodynamics.
{"title":"Gauge invariance through gauge fixing","authors":"David Wallace","doi":"10.1016/j.shpsa.2024.09.002","DOIUrl":"10.1016/j.shpsa.2024.09.002","url":null,"abstract":"<div><div>Phenomena in gauge theory are often described in the physics literature via a specific choice of gauge. In foundational and philosophical discussions this is often criticized as introducing gauge dependence, and contrasted against (often aspirational) “gauge-invariant” descriptions of the physics. I argue, largely in the context of scalar electrodynamics, that this is misguided, and that descriptions of a physical process within a specific gauge are in fact gauge-invariant descriptions. However, most of them are <em>non-local</em> descriptions of that physics, and I suggest that this ought to be the real objection to such descriptions. I explore the unitary gauge as the exception to this nonlocality and consider its strengths and limitations, as well as (more briefly) its extension beyond scalar electrodynamics.</div></div>","PeriodicalId":49467,"journal":{"name":"Studies in History and Philosophy of Science","volume":"108 ","pages":"Pages 38-45"},"PeriodicalIF":1.4,"publicationDate":"2024-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142394692","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-07DOI: 10.1016/j.shpsa.2024.09.008
Kati Kish Bar-On
Brouwer's philosophy of mathematics is usually regarded as an intra-subjective, even solipsistic approach, an approach that also underlies his mathematical intuitionism, as he strived to create a mathematics that develops out of something inner and a-linguistic. Thus, points of connection between Brouwer's mathematical views and his views about and the social world seem improbable and are rarely mentioned in the literature. The current paper aims to challenge and change that. The paper employs a socially oriented prism to examine Brouwer's views on the construction, use, and practice of mathematics. It focuses on Brouwer's views on language, his social interactions, and the importance of group context as they appear in the significs dialogues. It does so by exploring the establishment and dissolution of the significs movement, focusing on Gerrit Mannoury's influence and relationship with Brouwer and analyzing several fragments from the significs dialogues while emphasizing the role Brouwer ascribed to groups in forming and sharing new ideas. The paper concludes by raising two questions that challenge common historical and philosophical readings of intuitionism.
{"title":"Mathematics and society reunited: The social aspects of Brouwer's intuitionism","authors":"Kati Kish Bar-On","doi":"10.1016/j.shpsa.2024.09.008","DOIUrl":"10.1016/j.shpsa.2024.09.008","url":null,"abstract":"<div><div>Brouwer's philosophy of mathematics is usually regarded as an intra-subjective, even solipsistic approach, an approach that also underlies his mathematical intuitionism, as he strived to create a mathematics that develops out of something inner and a-linguistic. Thus, points of connection between Brouwer's mathematical views and his views about and the social world seem improbable and are rarely mentioned in the literature. The current paper aims to challenge and change that. The paper employs a socially oriented prism to examine Brouwer's views on the construction, use, and practice of mathematics. It focuses on Brouwer's views on language, his social interactions, and the importance of group context as they appear in the <em>significs dialogues</em>. It does so by exploring the establishment and dissolution of the significs movement, focusing on Gerrit Mannoury's influence and relationship with Brouwer and analyzing several fragments from the significs dialogues while emphasizing the role Brouwer ascribed to groups in forming and sharing new ideas. The paper concludes by raising two questions that challenge common historical and philosophical readings of intuitionism.</div></div>","PeriodicalId":49467,"journal":{"name":"Studies in History and Philosophy of Science","volume":"108 ","pages":"Pages 28-37"},"PeriodicalIF":1.4,"publicationDate":"2024-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142394693","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-01DOI: 10.1016/j.shpsa.2024.09.001
Johannes Fankhauser , James Read
Gravitational redshift effects undoubtedly exist; moreover, the experimental setups which confirm the existence of these effects—the most famous of which being the Pound–Rebka experiment—are extremely well-known. Nonetheless—and perhaps surprisingly—there remains a great deal of confusion in the literature regarding what these experiments really establish. Our goal in the present article is to clarify these issues, in three concrete ways. First, although (i) Brown and Read (2016) are correct to point out that, given their sensitivity, the outcomes of experimental setups such as the original Pound–Rebka configuration can be accounted for using solely the machinery of accelerating frames in special relativity (barring some subtleties due to the Rindler spacetime necessary to model the effects rigorously), nevertheless (ii) an explanation of the results of more sensitive gravitational redshift outcomes does in fact require more. Second, although typically this ‘more’ is understood as the invocation of spacetime curvature within the framework of general relativity, in light of the so-called ‘geometric trinity’ of gravitational theories, in fact curvature is not necessary to explain even these results. Thus (a) one can often explain the results of these experiments using only the resources of special relativity, and (b) even when one cannot, one need not invoke spacetime curvature. And third: while one might think that the absence of gravitational redshift effects would imply that spacetime is flat (indeed, Minkowskian), this can be called into question given the possibility of the cancelling of gravitational redshift effects by charge in the context of the Reissner–Nordström metric. This argument is shown to be valid and both attractive forces as well as redshift effects can be effectively shielded (and even be repulsive or blueshifted, respectively) in the charged setting. Thus, it is not the case that the absence of gravitational effects implies a Minkowskian spacetime setting.
{"title":"Gravitational redshift revisited: Inertia, geometry, and charge","authors":"Johannes Fankhauser , James Read","doi":"10.1016/j.shpsa.2024.09.001","DOIUrl":"10.1016/j.shpsa.2024.09.001","url":null,"abstract":"<div><div>Gravitational redshift effects undoubtedly exist; moreover, the experimental setups which confirm the existence of these effects—the most famous of which being the Pound–Rebka experiment—are extremely well-known. Nonetheless—and perhaps surprisingly—there remains a great deal of confusion in the literature regarding what these experiments really establish. Our goal in the present article is to clarify these issues, in three concrete ways. First, although (i) Brown and Read (2016) are correct to point out that, given their sensitivity, the outcomes of experimental setups such as the original Pound–Rebka configuration can be accounted for using solely the machinery of accelerating frames in special relativity (barring some subtleties due to the Rindler spacetime necessary to model the effects rigorously), nevertheless (ii) an explanation of the results of more sensitive gravitational redshift outcomes <em>does</em> in fact require more. Second, although typically this ‘more’ is understood as the invocation of spacetime curvature within the framework of general relativity, in light of the so-called ‘geometric trinity’ of gravitational theories, in fact curvature is not <em>necessary</em> to explain even these results. Thus (a) one can often explain the results of these experiments using only the resources of special relativity, and (b) even when one cannot, one need not invoke spacetime curvature. And third: while one might think that the absence of gravitational redshift effects would imply that spacetime is flat (indeed, Minkowskian), this can be called into question given the possibility of the cancelling of gravitational redshift effects by charge in the context of the Reissner–Nordström metric. This argument is shown to be valid and both attractive forces as well as redshift effects can be effectively shielded (and even be repulsive or blueshifted, respectively) in the charged setting. Thus, it is not the case that the absence of gravitational effects implies a Minkowskian spacetime setting.</div></div>","PeriodicalId":49467,"journal":{"name":"Studies in History and Philosophy of Science","volume":"108 ","pages":"Pages 19-27"},"PeriodicalIF":1.4,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142367191","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-24DOI: 10.1016/j.shpsa.2024.08.002
Anand Ekbote
I examine a known case of undergeneralization in Euclid's Elements arising from Euclid's non-cognizance of the reflex angle. Sir Thomas Heath (1956) attributed the undergeneralization to Euclid's lack of awareness, an assessment that I dispute. Non-recognition of reflex angles also leads to Proclus' four-sided triangles which violate an essential property of triangles. I show that these issues are resolvable. However, the question as to why Euclid did not acknowledge the reflex angle remains. I claim that the best explanation is that Euclid was guided by reasons of rigor. I argue that the propositional role of diagrammata in Greek mathematics as expounded by Netz (1998,2003) and Euclid's view of the reliability of sense perception impose a crucial representational constraint that governs how diagrams could be used in the Elements. I show that the missing reflex angle, and the careful crafting of definitions in the Elements are evidence that the representation constraint was indeed meticulously followed, even at apparent cost. I argue that alternative explanations for the missing reflex angle are not tenable. In sum, Euclid was aware of the limitations of diagrams, and worked assiduously within their limitations to preserve rigor.
{"title":"Euclidean rigor and the curious case of the (missing) reflex angle","authors":"Anand Ekbote","doi":"10.1016/j.shpsa.2024.08.002","DOIUrl":"10.1016/j.shpsa.2024.08.002","url":null,"abstract":"<div><div>I examine a known case of undergeneralization in Euclid's <span><em>Elements</em></span> arising from Euclid's non-cognizance of the reflex angle. Sir Thomas Heath (1956) attributed the undergeneralization to Euclid's lack of awareness, an assessment that I dispute. Non-recognition of reflex angles also leads to Proclus' four-sided triangles which violate an essential property of triangles. I show that these issues are resolvable. However, the question as to why Euclid did not acknowledge the reflex angle remains. I claim that the best explanation is that Euclid was guided by reasons of rigor. I argue that the propositional role of <span><em>diagrammata</em></span> in Greek mathematics as expounded by Netz (1998,2003) and Euclid's view of the reliability of sense perception impose a crucial representational constraint that governs how diagrams could be used in the <span><em>Elements.</em></span> I show that the missing reflex angle, and the careful crafting of definitions in the <span><em>Elements</em></span> are evidence that the representation constraint was indeed meticulously followed, even at apparent cost. I argue that alternative explanations for the missing reflex angle are not tenable. In sum, Euclid was aware of the limitations of diagrams, and worked assiduously within their limitations to preserve rigor.</div></div>","PeriodicalId":49467,"journal":{"name":"Studies in History and Philosophy of Science","volume":"108 ","pages":"Pages 10-18"},"PeriodicalIF":1.4,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142314738","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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