We contend that lockdown restrictions to prevent the spread of Covid-19 in South Africa have exposed deep divisions between citizens and the state, due in part to the neglect of citizenship education and to the neglect of our historical citizenship heritage. We propose in this paper two sources of appropriate normative guidelines, rooted in our common, collective history and ethics, which we ought to promote among citizens to reunite our people. We argue that citizenship education ought not only to be promoted actively in schools but that it must be reformed on the basis of two sets of foundational principles: a) Ubuntu; and b) the Freedom Charter. These encourage integration between citizens and subjects, and between citizens and the state; not to impose false universality from above, nor incoherent heteronomy from below, but to regulate these with cultural and historical continuity in transformation.
{"title":"Restorative Transformation after Lockdown: Freedom and Ubuntu in Civic Education","authors":"C. Allsobrook, Gugu Ndlazi","doi":"10.25159/2413-3086/8516","DOIUrl":"https://doi.org/10.25159/2413-3086/8516","url":null,"abstract":"We contend that lockdown restrictions to prevent the spread of Covid-19 in South Africa have exposed deep divisions between citizens and the state, due in part to the neglect of citizenship education and to the neglect of our historical citizenship heritage. We propose in this paper two sources of appropriate normative guidelines, rooted in our common, collective history and ethics, which we ought to promote among citizens to reunite our people. We argue that citizenship education ought not only to be promoted actively in schools but that it must be reformed on the basis of two sets of foundational principles: a) Ubuntu; and b) the Freedom Charter. These encourage integration between citizens and subjects, and between citizens and the state; not to impose false universality from above, nor incoherent heteronomy from below, but to regulate these with cultural and historical continuity in transformation.","PeriodicalId":42048,"journal":{"name":"Phronimon","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69125316","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A global pandemic such as that of the 2020 Covid-19 corona virus, causing great suffering and loss of life, brings home the difficult conditions that make for our fragile human life. But the question that religious belief poses, about “natural evil” in a world created by a loving God, satirised by Voltaire in the 18th century, masks the more existential problem, the possibility of greater human solidarity. In the background is the Deist view of God complementing the “polite society” of mutual benefit and guaranteeing the latter’s benevolent outcome. It is a worldview, as Charles Taylor (2007) explains, that has put aside the premodern idea of human transformation, that was symbolised by religious virtuosi, saints, theophanies, and so on, now looked upon with suspicion by modernity. But the possibility of transformation, of a generous human response to suffering, is what is called for in a pandemic. In Camus’ novel, The Plague, we see the more authentic response that resists being boxed in by religious enthusiasts to a constricted and ideological affirmation of a cosmic picture that obscures the fault-lines of bourgeois society.
{"title":"Solidarity at Issue: Pandemics and Religious Belief","authors":"J. Giddy","doi":"10.25159/2413-3086/8568","DOIUrl":"https://doi.org/10.25159/2413-3086/8568","url":null,"abstract":"A global pandemic such as that of the 2020 Covid-19 corona virus, causing great suffering and loss of life, brings home the difficult conditions that make for our fragile human life. But the question that religious belief poses, about “natural evil” in a world created by a loving God, satirised by Voltaire in the 18th century, masks the more existential problem, the possibility of greater human solidarity. In the background is the Deist view of God complementing the “polite society” of mutual benefit and guaranteeing the latter’s benevolent outcome. It is a worldview, as Charles Taylor (2007) explains, that has put aside the premodern idea of human transformation, that was symbolised by religious virtuosi, saints, theophanies, and so on, now looked upon with suspicion by modernity. But the possibility of transformation, of a generous human response to suffering, is what is called for in a pandemic. In Camus’ novel, The Plague, we see the more authentic response that resists being boxed in by religious enthusiasts to a constricted and ideological affirmation of a cosmic picture that obscures the fault-lines of bourgeois society.","PeriodicalId":42048,"journal":{"name":"Phronimon","volume":"15 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69124904","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Plato constructs the philosopher in contrast to the sophist. Both sophistical and rhetorical logos, in their epistemic closeness to philosophical logos, require a constant act of demarcation throughout Plato’s works. The challenge posed by the sophists creates a constant, instable tension in several Platonic dialogues. Why is the Athenian philosopher obsessed by a different yet comparable approach to virtue, knowledge and social order? Why does the Athenian philosopher need and, at the same time, reject the sophist when it comes to shaping his own self-image? To try to answer these questions, I will go back to a foundational moment where the Platonic philosopher is theoretically constructed and conceptually produced against the sophist, namely, Plato’s Sophist, Statesman, Protagoras, Gorgias and Phaedrus. The aim of the article is to show how the Platonic philosopher is conveniently defined through a series of partisan demarcations grounded on ontological privilege, epistemic exclusion, ethical circularity and, ultimately, political delegitimation.
{"title":"Hic Sunt Leones: Mythologies and Partisan Constructions of the Good Philosopher in Plato","authors":"Sergio Alloggio","doi":"10.25159/2413-3086/6741","DOIUrl":"https://doi.org/10.25159/2413-3086/6741","url":null,"abstract":"Plato constructs the philosopher in contrast to the sophist. Both sophistical and rhetorical logos, in their epistemic closeness to philosophical logos, require a constant act of demarcation throughout Plato’s works. The challenge posed by the sophists creates a constant, instable tension in several Platonic dialogues. Why is the Athenian philosopher obsessed by a different yet comparable approach to virtue, knowledge and social order? Why does the Athenian philosopher need and, at the same time, reject the sophist when it comes to shaping his own self-image? To try to answer these questions, I will go back to a foundational moment where the Platonic philosopher is theoretically constructed and conceptually produced against the sophist, namely, Plato’s Sophist, Statesman, Protagoras, Gorgias and Phaedrus. The aim of the article is to show how the Platonic philosopher is conveniently defined through a series of partisan demarcations grounded on ontological privilege, epistemic exclusion, ethical circularity and, ultimately, political delegitimation.","PeriodicalId":42048,"journal":{"name":"Phronimon","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2019-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49425632","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The Information Systems discipline (IS) is usually regarded as a social science because it includes research on human-related aspects of these systems. However, a limited number of IS research outputs use approaches that are typical of the traditional arts and humanities. Little recognition has been given to the arts and humanities-informed stream of the IS discipline. This article aims to clarify the subtle distinctions between these scientific constellations and IS’s place in it. It highlights the cluster of arts, humanities and IS in the inter-linked world of scientific disciplines and makes some recommendations to build further on these accomplishments.
{"title":"Is the Philosophy of the Information Systems Discipline Informed by the Arts and Humanities?","authors":"Jan Hendrik Kroeze","doi":"10.25159/2413-3086/4898","DOIUrl":"https://doi.org/10.25159/2413-3086/4898","url":null,"abstract":"The Information Systems discipline (IS) is usually regarded as a social science because it includes research on human-related aspects of these systems. However, a limited number of IS research outputs use approaches that are typical of the traditional arts and humanities. Little recognition has been given to the arts and humanities-informed stream of the IS discipline. This article aims to clarify the subtle distinctions between these scientific constellations and IS’s place in it. It highlights the cluster of arts, humanities and IS in the inter-linked world of scientific disciplines and makes some recommendations to build further on these accomplishments.","PeriodicalId":42048,"journal":{"name":"Phronimon","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2019-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49658131","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Ethno-philosophy, as a philosophical project, has had its fair share of criticism from some professional African philosophers, with Paulin Hountondji as an outstanding critic. Ethno-philosophy is believed to be deficient in criticality and analyticity, which are considered hallmarks of good philosophy anywhere. In this paper I engage Fainos Mangena, a tireless defender of ethno-philosophy, in a critical conversation. In making a case for the continuing relevance of ethno-philosophy, while acknowledging its shortcomings, I argue that the universalist critique of ethno-philosophy has exposed the philosophical poverty of this specific form of thought. I assert that the equation of ethno-philosophy with substantive African philosophy will lead to the emergence of an impoverished African philosophical tradition, notwithstanding the desirability of a unique African philosophy distinguishable from non-African philosophical traditions—in particular the Western philosophical tradition. I point out that Innocent Asouzu and J.O. Chimakonam’s Ibuanyidanda ontology and Ezumezu logical system demonstrate the viability of a philosophical programme that seeks to transcend ethno-philosophy by enriching it with concepts that promote the criticality and analyticity demanded by critics of ethno-philosophy, in a manner conducive to system-building.
{"title":"The Sense in which Ethno-philosophy can Remain Relevant in 21st Century African Philosophy","authors":"A. Agadá","doi":"10.25159/2413-3086/4158","DOIUrl":"https://doi.org/10.25159/2413-3086/4158","url":null,"abstract":"Ethno-philosophy, as a philosophical project, has had its fair share of criticism from some professional African philosophers, with Paulin Hountondji as an outstanding critic. Ethno-philosophy is believed to be deficient in criticality and analyticity, which are considered hallmarks of good philosophy anywhere. In this paper I engage Fainos Mangena, a tireless defender of ethno-philosophy, in a critical conversation. In making a case for the continuing relevance of ethno-philosophy, while acknowledging its shortcomings, I argue that the universalist critique of ethno-philosophy has exposed the philosophical poverty of this specific form of thought. I assert that the equation of ethno-philosophy with substantive African philosophy will lead to the emergence of an impoverished African philosophical tradition, notwithstanding the desirability of a unique African philosophy distinguishable from non-African philosophical traditions—in particular the Western philosophical tradition. I point out that Innocent Asouzu and J.O. Chimakonam’s Ibuanyidanda ontology and Ezumezu logical system demonstrate the viability of a philosophical programme that seeks to transcend ethno-philosophy by enriching it with concepts that promote the criticality and analyticity demanded by critics of ethno-philosophy, in a manner conducive to system-building.","PeriodicalId":42048,"journal":{"name":"Phronimon","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2019-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49280998","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The controversies in contemporary truth discourses can be traced directly or indirectly to the Fregean choice of “thought” as the truth bearer, Ramsey’s redundancy thesis, Tarskian semantic conception, and Davidson’s defence of the indefinability of truth. The common feature of these four positions is an inadequate treatment of the “what is” question. Because of the neglect of this kind of question, the consequence is that truth has been reduced to a thin concept (that is a reduction of truth to logical, semantic or linguistic analysis of the truth predicate, or analysis of intentional signs at the expense of intentional acts) and subsequent quest for the deflation of truth. I argue that such an approach to the philosophical investigation of truth is at best inadequate and at worst bound to fail. Hence, I propose that an adequate exploration of truth must first address the “what is” question, rather than just assuming it. Further, I argue that to realise this, it is vital to take into consideration the wider context in which the truth question arises, that is, the human quest for knowledge and self-transcendence; and it is the conception of truth as critical correspondence that is capable of sufficiently answering the question.
{"title":"Truth and the Quest for Definition","authors":"P. Aleke","doi":"10.25159/2413-3086/4421","DOIUrl":"https://doi.org/10.25159/2413-3086/4421","url":null,"abstract":"The controversies in contemporary truth discourses can be traced directly or indirectly to the Fregean choice of “thought” as the truth bearer, Ramsey’s redundancy thesis, Tarskian semantic conception, and Davidson’s defence of the indefinability of truth. The common feature of these four positions is an inadequate treatment of the “what is” question. Because of the neglect of this kind of question, the consequence is that truth has been reduced to a thin concept (that is a reduction of truth to logical, semantic or linguistic analysis of the truth predicate, or analysis of intentional signs at the expense of intentional acts) and subsequent quest for the deflation of truth. I argue that such an approach to the philosophical investigation of truth is at best inadequate and at worst bound to fail. Hence, I propose that an adequate exploration of truth must first address the “what is” question, rather than just assuming it. Further, I argue that to realise this, it is vital to take into consideration the wider context in which the truth question arises, that is, the human quest for knowledge and self-transcendence; and it is the conception of truth as critical correspondence that is capable of sufficiently answering the question.","PeriodicalId":42048,"journal":{"name":"Phronimon","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2019-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46232003","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper explores the implications of “decolonisation,†first by focusing on the work of African thinker, Frantz Fanon’s work in this regard, particularly his insistence that decolonisation entails the creation of “new†people, before moving on to the related question of “identity.†Here the emphasis is on the work of Manuel Castells, specifically his examination of three kinds of identity-construction, the third of which he regards as being the most important category for understanding this process in the 21st century, namely “resistance identity.†It is argued that this casts the decolonisation debate in South Africa in an intelligible light. An interpretation of E.M. Forster’s paradigmatically “decolonising†novel, A Passage to India, is offered to unpack the meaning of the concept further, before switching the terrain to the question of the urgent need for a different kind of decolonisation, today, pertaining to the economic neo-colonisation of the world by neoliberal capitalism. The work of Hardt and Negri on the emerging world order under what they call “Empire†is indispensable in this regard, and their characterisation of the subject under neoliberal Empire in terms of the figures of the indebted, securitised, mediatised and represented, stresses the need for global decolonisation in the name of democracy. This part of the paper is concluded with a consideration of what decolonisation is really “all about,†namely power.
{"title":"Decolonisation, Identity, Neo-Colonialism and Power","authors":"B. Olivier","doi":"10.25159/2413-3086/3065","DOIUrl":"https://doi.org/10.25159/2413-3086/3065","url":null,"abstract":"This paper explores the implications of “decolonisation,†first by focusing on the work of African thinker, Frantz Fanon’s work in this regard, particularly his insistence that decolonisation entails the creation of “new†people, before moving on to the related question of “identity.†Here the emphasis is on the work of Manuel Castells, specifically his examination of three kinds of identity-construction, the third of which he regards as being the most important category for understanding this process in the 21st century, namely “resistance identity.†It is argued that this casts the decolonisation debate in South Africa in an intelligible light. An interpretation of E.M. Forster’s paradigmatically “decolonising†novel, A Passage to India, is offered to unpack the meaning of the concept further, before switching the terrain to the question of the urgent need for a different kind of decolonisation, today, pertaining to the economic neo-colonisation of the world by neoliberal capitalism. The work of Hardt and Negri on the emerging world order under what they call “Empire†is indispensable in this regard, and their characterisation of the subject under neoliberal Empire in terms of the figures of the indebted, securitised, mediatised and represented, stresses the need for global decolonisation in the name of democracy. This part of the paper is concluded with a consideration of what decolonisation is really “all about,†namely power.","PeriodicalId":42048,"journal":{"name":"Phronimon","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2019-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44774723","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
It requires no measure of razor-sharp analysis or prophecy to observe that, 25 years into a hard-won democracy, millions of South Africans have not yet obtained the freedom that would enable them to collaborate in creating a qualitative, new society. Part of the problem seems to be the dichotomisation of a number of unavoidable questions resulting from freedom. In this article, some of these issues—like the notion of the born free, liberation, corruption, truth and freedom as a gift—are brought into discourse with the matter of freedom. Particular reference is made to the philosopher, Hanna Arendt, as well as the apostle Paul, in their respective interpretations of freedom. The article concludes with some broad strokes on the implications for South Africa of Paul’s understanding of freedom. The basic thesis of the article is that, unless freedom is brought into a critical conversation with philosophical and theological interpretations of freedom, it will not deliver to millions of South Africans trapped in inequality, unemployment and poverty.
{"title":"“We Are Free only when Others Are Freeâ€: Reflections on Freedom from Philosophical and Theological Perspectives","authors":"N. Botha","doi":"10.25159/2413-3086/1963","DOIUrl":"https://doi.org/10.25159/2413-3086/1963","url":null,"abstract":"It requires no measure of razor-sharp analysis or prophecy to observe that, 25 years into a hard-won democracy, millions of South Africans have not yet obtained the freedom that would enable them to collaborate in creating a qualitative, new society. Part of the problem seems to be the dichotomisation of a number of unavoidable questions resulting from freedom. In this article, some of these issues—like the notion of the born free, liberation, corruption, truth and freedom as a gift—are brought into discourse with the matter of freedom. Particular reference is made to the philosopher, Hanna Arendt, as well as the apostle Paul, in their respective interpretations of freedom. The article concludes with some broad strokes on the implications for South Africa of Paul’s understanding of freedom. The basic thesis of the article is that, unless freedom is brought into a critical conversation with philosophical and theological interpretations of freedom, it will not deliver to millions of South Africans trapped in inequality, unemployment and poverty.","PeriodicalId":42048,"journal":{"name":"Phronimon","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2019-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48584508","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper reflects on the foundational principles and strategies for tertiary education in Africa. Since the early 1940s, Ghanaian philosophers have advanced unambiguous perspectives on education policy in Africa. Although the integrity and cogency of these perspectives have remained intact for over 60 years, they have not yet found expression in public policy formulation. Available evidence suggests that Africa has so far remained impervious to the perspectives and strategies for education outlined by Ghanaian philosophers since Nkrumah’s overthrow from the presidency in Ghana. Current African Union strategies on education, articulated in Agenda 2063, seem to validate the resistance by national governments to these philosophical perspectives. This paper seeks to argue that what these philosophers espouse are excellent conceptual models worthy of development and implementation in Africa; and that in service of a sounder educational future for Ghana and Africa than that which currently prevails, a sankofa approach to the conceptualisation of education, which incorporates these Ghanaian philosophical perspectives, is desirable.
{"title":"Educating Africans: Perspectives of Ghanaian Philosophers","authors":"M. Ajei","doi":"10.25159/2413-3086/5277","DOIUrl":"https://doi.org/10.25159/2413-3086/5277","url":null,"abstract":"This paper reflects on the foundational principles and strategies for tertiary education in Africa. Since the early 1940s, Ghanaian philosophers have advanced unambiguous perspectives on education policy in Africa. Although the integrity and cogency of these perspectives have remained intact for over 60 years, they have not yet found expression in public policy formulation. Available evidence suggests that Africa has so far remained impervious to the perspectives and strategies for education outlined by Ghanaian philosophers since Nkrumah’s overthrow from the presidency in Ghana. Current African Union strategies on education, articulated in Agenda 2063, seem to validate the resistance by national governments to these philosophical perspectives. This paper seeks to argue that what these philosophers espouse are excellent conceptual models worthy of development and implementation in Africa; and that in service of a sounder educational future for Ghana and Africa than that which currently prevails, a sankofa approach to the conceptualisation of education, which incorporates these Ghanaian philosophical perspectives, is desirable.","PeriodicalId":42048,"journal":{"name":"Phronimon","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2019-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48823727","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Hermann Weyl published a brief survey as preface to a review of The Philosophy of Bertrand Russell in 1946. In this survey he used the phrase, “The Fall and Original Sin of Set Theory.†Investigating the background of this remark will require that we pay attention to a number of issues within the foundations of mathematics. For example: Did God make the integers—as Kronecker alleged? Is mathematics set theory? Attention will also be given to axiomatic set theory and relevant ontic pre-conditions, such as the difference between number and number symbols, to number as “an aspect of objective reality†(Gödel), integers and induction (Skolem) as well as to the question if infinity—as endlessness—could be completed. In 1831 Gauss objected to viewing the infinite as something completed, which is not allowed in mathematics. It will be argued that the actual infinite is rather connected to what is present “at once,†as an infinite totality. By the year 1900 mathematicians believed that mathematics had reached absolute rigour, but unfortunately the rest of the twentieth century witnessed the opposite. The axiom of infinity ruined the expectations of logicism—mathematics cannot be reduced to logic. The intuitionism of Brouwer, Weyl and others launched a devastating attack on classical analysis, further inspired by the outcome of Gödel’s famous proof of 1931, in which he has shown that a formal mathematical system is inconsistent or incomplete. Intuitionism created a whole new mathematics, which finds no counter-part in classical mathematics. Slater remarked that within this logical paradise of Russell lurked a serpent, hidden behind the unjustified employment of the at once infinite. According to Weyl, “This is the Fall and original sin of set theory for which it is justly punished by the antinomies.†In conclusion, a few systematic distinctions are introduced.
{"title":"The Fall and Original Sin of Set Theory","authors":"D. Strauss","doi":"10.25159/2413-3086/4983","DOIUrl":"https://doi.org/10.25159/2413-3086/4983","url":null,"abstract":"Hermann Weyl published a brief survey as preface to a review of The Philosophy of Bertrand Russell in 1946. In this survey he used the phrase, “The Fall and Original Sin of Set Theory.†Investigating the background of this remark will require that we pay attention to a number of issues within the foundations of mathematics. For example: Did God make the integers—as Kronecker alleged? Is mathematics set theory? Attention will also be given to axiomatic set theory and relevant ontic pre-conditions, such as the difference between number and number symbols, to number as “an aspect of objective reality†(Gödel), integers and induction (Skolem) as well as to the question if infinity—as endlessness—could be completed. In 1831 Gauss objected to viewing the infinite as something completed, which is not allowed in mathematics. It will be argued that the actual infinite is rather connected to what is present “at once,†as an infinite totality. By the year 1900 mathematicians believed that mathematics had reached absolute rigour, but unfortunately the rest of the twentieth century witnessed the opposite. The axiom of infinity ruined the expectations of logicism—mathematics cannot be reduced to logic. The intuitionism of Brouwer, Weyl and others launched a devastating attack on classical analysis, further inspired by the outcome of Gödel’s famous proof of 1931, in which he has shown that a formal mathematical system is inconsistent or incomplete. Intuitionism created a whole new mathematics, which finds no counter-part in classical mathematics. Slater remarked that within this logical paradise of Russell lurked a serpent, hidden behind the unjustified employment of the at once infinite. According to Weyl, “This is the Fall and original sin of set theory for which it is justly punished by the antinomies.†In conclusion, a few systematic distinctions are introduced.","PeriodicalId":42048,"journal":{"name":"Phronimon","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2019-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47782625","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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