I retired from Swansea University as a Senior Lecturer in Sociology and now hold the position of Honorary Research Fellow. I have recently published five articles on philosophical topics and another concerned with the application of the theory of the selfish gene to the human population. Address: Swansea, United Kingdom
There are three main moral theories: virtue ethics, the deontological approach and utilitarianism... more There are three main moral theories: virtue ethics, the deontological approach and utilitarianism. The concern here is how they interrelate, why they come into focus at different times and places, and how they are configured in their application to a modern democratic society. Person-oriented virtue ethics was the dominant understanding in Ancient Greece but within the Western tradition this was later subordinated to the monotheism of Ancient Judaism as modified by Christianity. Of growing importance by the eighteenth century was rights theory which was often still situated religiously. Kant’s principle of the categorical imperative has been highly influential but was challenged by the emerging nature of industrial and capitalist society. Utilitarianism, within which the moral rightness of activity resides in its tendency to promote happiness or unhappiness, represented the decisive move from the transcendental to the immanent approach. Although all three approaches to moral theory continue to be relevant to identifiable situations and aspects of modern society, there has been a substantial turn towards a heavily modified utilitarianism associated with parliamentary democracy and market economies founded on property ownership. The root cause of this is the ability of utilitarianism, as opposed to the other approaches, to handle considerations of number and probability. The concept of utility is fundamental in economics but the idea has evolved away from its origins to mean “preference”. There is a sense in which the straightforward appeal of basic utilitarianism has been “leased out” in modified form to a set of institutional arrangements. Certain “pressure points” in a modern society are noted which pose particular problems pertinent to moral theory. Bernard Williams argues persuasively for an appropriately modified form of virtue ethics.
A perspective in the philosophy of mathematics is developed from a consideration of the strengths... more A perspective in the philosophy of mathematics is developed from a consideration of the strengths and limitations of both logicism and platonism, with an early focus on Frege's work. Importantly, although many set-theoretic structures may be developed each of which offers limited isomorphism with the system of natural numbers, no one of them may be identified with it. Furthermore, the timeless, ever present nature of mathematical concepts and results itself offers direct access, in the face of a platonist account which generates a supposed problem of access. Crucially too, pure mathematics has its own distinctive method of confirming or validating results-mathematical proof-which supplies a higher level of confidence and objectivity than that available elsewhere. The dichotomy of invention and discovery is too jejune a framework for analysing creative mathematical activity. The Gödelian platonist perspective is evaluated and queried through scrutiny of the part played by mathematical resources and constraints in relation to human activity. It appears that there can be non-causal mathematical explanations and mathematical constraint on purely natural processes. Valuable implications of Quine's naturalism are explored, but one must be cautious of his thesis of confirmational holism. The distinction between algebraic and non-algebraic mathematical theories usefully contributes to our understanding of the internally differentiated nature of the subject.
Journal of the Royal Statistical Society, Series A (Statistics in Society) , 2022
Violet Rosina Cane, MA (Cantab), 31.1.1916–27.6.2008, was a Cambridge-educated statistician whose... more Violet Rosina Cane, MA (Cantab), 31.1.1916–27.6.2008, was a Cambridge-educated statistician whose research and consulting centred on the applications of classical statistical theory, as well as on the contemporary theory of stochastic processes, including that being developed by some of her colleagues and former teachers at Cambridge.
This article celebrates the life and work of pioneering statistician, Professor Violet Cane. She... more This article celebrates the life and work of pioneering statistician, Professor Violet Cane. She was the sort of female role model that continues to be needed.
Open Journal of Philosophy, vol. 12, no. 1, 54-68, 2022
The extent of confusion between symbols and that which is symbolised is examined across five inst... more The extent of confusion between symbols and that which is symbolised is examined across five institutional spheres. Religion is the institution most marked by confusion of this type; indeed in some respects the symbolic message of religion may be the extent of the substantive reality. On the other hand, the very existence of the nation state may be judged to depend upon the exercise of the human imagination; hence providing a source of instability which may lead to the excesses of nationalism. In regard to social status, the main problematical element is a certain circularity: it is necessary to get people to exhibit differences in behaviour which are then used to justify or constitute the status differences themselves. In politics, the symbolism of left and right threatens to strangle creative thinking, while in education the tendency on all sides to orient towards public systems of measurement and grading undermines the claim that what is really important is pupil and student learning. A social cost is being paid for the failure to recognise and, where possible, address the issues identified.
Open Journal of Philosophy, vol. 4, no. 11, 482-498, 2021
Progress may be made in resolving the tension between free will and determinism by analysis of th... more Progress may be made in resolving the tension between free will and determinism by analysis of the necessary conditions of freedom. It is of the essence that these conditions include causal and deterministic regularities. Furthermore, the human expression of free will is informed by understanding some of those regularities, and increments in that understanding have served to enhance freedom. When the possible character of a deterministic system based on physical theory is considered, it is judged that, far from implying the elimination of human freedom, such a theory might simply set parameters for it; indeed knowledge of that system could again prove to be in some respects liberating. On the other hand, it is of the essence that the overarching biological framework is not a deterministic system and it foregrounds the behavioural flexibility of humans in being able to choose within a range of options and react to chance occurrences. Furthermore, an issue for determinism flows from the way in which randomness (e.g. using a true random number generator) and chance events could and do enter human life. Once the implications of that issue are fully understood, other elements fit comfortably together in our understanding of freely undertaken action: the contribution of reasons and causes; the fact that reasons are never sufficient to account for outcomes; the rationale for the attribution of praise and blame.
Advances in Anthropology, vol. 11(3), pp. 179-200, 2021
In a study drawing from both evolutionary biology and the social sciences, evidence and argument ... more In a study drawing from both evolutionary biology and the social sciences, evidence and argument is assembled in support of the comprehensive application of selfish gene theory to the human population. With a focus on genes giving rise to characteristically-human cooperation ("cooperative genes") involving language and theory of mind, one may situate a whole range of patterned behaviour-including celibacy and even slavery-otherwise seeming to present insuperable difficulties. Crucially, the behaviour which tends to propagate the cooperative genes may be "at cost" to the genes of some who may be party to the cooperation itself. Explanatory insights are provided by Trivers' parent-offspring conflict theory, Lack's principle, and Hamilton's kin selection mechanism. A primary observation is that cooperation using language and theory of mind is itself interdependent with full human conceptualization of a world of objects and of themselves as embodied beings. Human capacities inhering in, or arising out of, the ability to cooperate are also responsible for a vitally important long-term process, the domestication of animals and plants. The approach illuminates the difference between animal and human sexual behaviour, and the emergence of kinship systems. Again, recent patterns of population growth become much more explicable. It is argued that the gene is the single controlling replicator; the notion of the meme as a second independent replicator is flawed.
Open Journal of Philosophy, vol. 10(3), pp. 346-367, 2020
Religion emerged among early humans because both purposive and non-purposive explanations were be... more Religion emerged among early humans because both purposive and non-purposive explanations were being employed but understanding was lacking of their precise scope and limits. Given also a context of very limited human power, the resultant foregrounding of agency and purposive explanation expressed itself in religion's marked tendency towards anthropomorphism and its key role in legitimizing behaviour. The inevitability of death also structures the religious outlook; with ancestors sometimes assigned a role in relation to the living. Subjective elements such as the experience of dreams and the internalization of moral precepts also play their part. Two important sources of variation among religions concern the adoption of a dualist or non-dualist perspective, and whether or not the religion's early political experience is such as to generate a systematic doctrine subordinating politics to religion. The near ubiquity and endurance of religion are further illuminated by analysis of its functions and ideological role. Religion tends to be socially conservative but has the potential to be revolutionary.
Open Journal of Philosophy, vol. 10(1), pp. 45-65, 2020
Drawing mainly from the Tractatus Logico-Philosophicus and his middle period writings, strategic ... more Drawing mainly from the Tractatus Logico-Philosophicus and his middle period writings, strategic issues and problems arising from Wittgenstein's philosophy of mathematics are discussed. Topics have been so chosen as to assist mediation between the perspective of philosophers and that of mathematicians on their developing discipline. There is consideration of rules within arithmetic and geometry and Wittgenstein's distinctive approach to number systems whether elementary or transfinite. Examples are presented to illuminate the relation between the meaning of an arithmetical generalisation or theorem and its proof. An attempt is made to meet directly some of Witt-genstein's critical comments on the mathematical treatment of infinity and irrational numbers.
Open Journal of Philosophy, vol. 9(4), pp. 452-469, 2019
A framework is developed for understanding what is “taken for granted” both in philosophy and in ... more A framework is developed for understanding what is “taken for granted” both in philosophy and in life generally, which may serve to orient philosophical inquiry and make it more effective. The framework takes in language and its development, as well as mathematics, logic, and the empirical sphere with particular reference to the exigencies of life. It is evaluated through consideration of seven philosophical issues concerned with such topics as solipsism, sense data as the route to knowledge, the possible reduction of geometry to logic, and the existence and status of human rights. Various dichotomies and the notion of continuity are evidently highly strategic.
The notion of the selfish gene has been successfully deployed in the understanding of animal beha... more The notion of the selfish gene has been successfully deployed in the understanding of animal behaviour but is widely felt not to have full application at the human level. A lot of evidence and argument is here assembled in support of the comprehensive application of that theory to the human population. With a focus on genes giving rise to characteristically-human cooperation (‘cooperative genes’) it proves possible to situate a whole range of patterned behaviour and phenomena, even including celibacy, the use of contraception, and war, which at first glance seem to present insuperable difficulties. Crucially, the behaviour which tends to propagate the cooperative genes may be ‘at cost’ to the genes of some who may be party to the cooperation itself.
The account builds on the primary insight that cooperation itself gives rise to full human conceptualization of the external world and their own place in it as embodied beings. Cooperation thereby structures practical action and progressively impacts on fertility, mortality and migration; cooperation therefore furthers the continued existence and transmission of the genes which give rise to it. Human capacities underlying the ability to cooperate are also responsible for a vitally important long-term process - the
ii
domestication of animals and plants; the geographical redistribution of such species means that the Earth is able to sustain a progressively larger human population.
A consideration of the implications of characteristically-human cooperation helps one to understand the difference between animal and human sexual behaviour, and to explain the emergence of kinship systems, involving the social recognition of blood ties: one is thereby enabled to bridge the gap between zoology and social anthropology. Cooperation is also the basic source of morality and hence of stabilizing regulation; at the same time it generates a bifurcation in respect of types of human understanding which explains the origin of religion. Significantly, however, the predominating influence of religions on fertility is such as to incline population firmly on an upward trajectory.
Competition between societies at one level of complexity tends to lead to societies of a greater level of complexity. The broader picture is not that various independent variables simply ‘cause’ growth in population but rather that various distinguishable elements – such as societal complexity, the rate of technological innovation (seen as evolutionary), food production, and population size and density - inter-affect each other. Perhaps the most strategic aspect of all is development or reshaping of the division and specialization of labour; crucially, that development tends to increase product while reducing the tendency for conflict to occur which may lead to violence.
Everywhere humans gain access to the means of their subsistence cooperatively, but how they organize to do so develops in patterned ways. In respect of prehistory and history,
iii
that the same trends – towards food production, social complexity and urbanism – are found as independent developments in different parts of the globe points to the contribution of basic facets of human cooperative behaviour. The historically important phenomenon of empire tended to have positive implications for expansion of population. Larger and more stable political entities tend to emerge over extended time – states, empires, nation states – providing a more predictable and secure context within which populations may grow.
In complex societies, the built environment, writing and money contribute to sustaining and extending orderly cooperation. While rationality is generally exhibited within the range of human behaviour, the systematic adoption of a rational approach to life is grounded in the emergence of institutional forms. In connection with globalization, humans are proceeding to reconfigure the external world so as to maximize the possibilities for their own cooperation within it. Contrary to what might initially be thought, there are reasons for judging that the threat or experience of violence and war has played its part in creating the conditions for population growth. In addition, institutional change overtime has tended increasingly to realize a latent potential for cooperation without recourse to violence and war.
Significantly, the increases in population experienced in differing types of society have sometimes tended to exceed those anticipated from the theory of the demographic transition, but once one foregrounds the impact of cooperative genes, patterns become that much more explicable. The populations of western societies tend to be rising but the
iv
overall demographic pattern can nevertheless be said to be substantially ‘at cost’ to the propagation of the genes of the majority of individuals who choose to limit their own fertility. The use of contraception and abortion in recent centuries is to be viewed as a means towards fertility objectives, but those objectives are substantially independent of the means. The interdependence of generations – notably in the early and later years of life - provides a basic link between mortality and fertility, but the needs of each generation promise to be best served if a (slightly) larger one is following it. The present sometimes ‘unwelcome’ migration into richer nations illustrates the persistent tendency in human experience for there to be re-distribution of the potential for population growth in space and in relation to economic resources which tends to keep overall population numbers on an upward trajectory.
In future the human gene pool will be intentionally reshaped increasing the likelihood of there being a large and growing population with a distribution of qualities which will enable them to cooperate even more effectively. The notion of the meme lacks explanatory power and cannot perform the role so far assigned to it. The position is that cooperative genes give rise to cooperative behaviour which tends to propagate the genes, while memes inter alia inhere in cooperative activity; hence the only satisfactory explanatory framework involves a single replicator. It is equally true to say that ‘humans are sometimes selfish’ and that ‘humans naturally create norms of behaviour tending to restrict or eliminate selfishness’. A whole range of phenomena may be understood as involving the working out of the partial ‘conflict of interest’ between cooperative and other genes e.g. theft by a gang, the U.K. National Health Service, and (even) the world’s
v
(possible) emerging political and economic structural form. The propagation of human cooperative genes is potentially ‘at cost’ to the propagation of any of the other genes of other life forms on this planet (and conceivably also elsewhere). That is the full measure of the extent to which these cooperative genes are selfish.
Sociological Focus, vol.6, no. 2, pp. 107-116, 1983
How is the historical development of mathematics to be understood sociologically? The writings
o... more How is the historical development of mathematics to be understood sociologically? The writings
of Mannheim and Wittgenstein suggest two contrasting approaches which may be evaluated through
a detailed analysis of the development of the number concept. Five main number systems can be
distinguished of which the most basic is the system of whole numbers and, given that importance
attaches to generalizing power, there can be shown to be a tendency for the number concept to be
progressively augmented. This process may be understood by reference to the basic pre-Darwinian
evolutionary idea of "unfolding." Complementing this intrinsic element, in actual historical instances
a variety of extrinsic factors may be seen to be operative, facilitating or retarding development. To
explain historical change fully an elaborate normative structure must be analyzed incorporating a
macro-institutional level, the "rules of the mathematical game", notational considerations, and relations
internal to mathematics itself (e.g., between number and geometry).
International Journal of Sociology and Social Policy, vol. 5, issue 1, pp. 54-67, 1985
Within the literature there is a lack of clarity regarding the place of evolutionary,
critical a... more Within the literature there is a lack of clarity regarding the place of evolutionary,
critical and non-evolutionary structuralist conceptions in a sociological account of
mathematical development. This article provides a unifying perspective through an
analysis of two main lines of historical development: the concept of number and
fundamental geometrical notions. The development of number systems can be
explicated on an internalist basis using the pre-Darwinian evolutionary idea of
"unfolding", together with the associated notion of facilitating and retarding
conditions. On the other hand, some major developments in geometry do not lend
themselves to this interpretation but can be understood as innovations stemming
from various internal and external sources. The account highlights the importance
for mathematics of the formation of means-ends relationships, as well as various
"axes" of critical debate.
International Journal of Sociology and Social Policy, vol. 3, issue 4, pp. 64-73, 1983
The underdeveloped state of this field does no credit to sociology. Some sociologists
are more i... more The underdeveloped state of this field does no credit to sociology. Some sociologists
are more interested in using quantification as a source of legitimation than in
confronting mathematics as a central element of culture. Yet mathematics may be
viewed as an institution with a normative core developing alongside experience of the
physical world, susceptible of both "internalist" and "externalist" programmes of
investigation. There is a need to examine how the symbolic system of mathematics
structures the development of thought and how the acceptance of mathematical ideas
is related to their utility. The use of the evolutionary approach has generated some
distinctive concepts which can assist cross-cultural work. Smaller-scale studies continue
to provide insight into the relation between mathematical theory and social
structure.
Journal of Contemporary Religion, vol. 12, no.2, pp.215-228, 1997
This paper explores the relationship between religious beliefs and secular
attitudes of lay peop... more This paper explores the relationship between religious beliefs and secular
attitudes of lay people within a single church, the Anglican Province of Wales (UK). The
origins of the data are described and findings as to the distinctive social characteristics
of the laity reported. Results of the analysis of the interrelationship between different
dimensions of religious belief are reported and discussed. The secular attitudes of the
laity are compared with those of the British population, and found to be on the whole
more 'liberal'. While some differences between the secular attitudes of the laity and the
general population are clearly related to the distinctive social position of the former,
social location is unable to explain all of these differences. A number of relationships
between belief and secular attitudes are described. Anglicans with more 'catholic' beliefs
seem more concerned in their secular attitudes with issues which they perceive as
involving rule breaking or attitudes to authority, while 'evangelicals' react more
strongly to what can be interpreted as unconscionable behaviour.
There are three main moral theories: virtue ethics, the deontological approach and utilitarianism... more There are three main moral theories: virtue ethics, the deontological approach and utilitarianism. The concern here is how they interrelate, why they come into focus at different times and places, and how they are configured in their application to a modern democratic society. Person-oriented virtue ethics was the dominant understanding in Ancient Greece but within the Western tradition this was later subordinated to the monotheism of Ancient Judaism as modified by Christianity. Of growing importance by the eighteenth century was rights theory which was often still situated religiously. Kant’s principle of the categorical imperative has been highly influential but was challenged by the emerging nature of industrial and capitalist society. Utilitarianism, within which the moral rightness of activity resides in its tendency to promote happiness or unhappiness, represented the decisive move from the transcendental to the immanent approach. Although all three approaches to moral theory continue to be relevant to identifiable situations and aspects of modern society, there has been a substantial turn towards a heavily modified utilitarianism associated with parliamentary democracy and market economies founded on property ownership. The root cause of this is the ability of utilitarianism, as opposed to the other approaches, to handle considerations of number and probability. The concept of utility is fundamental in economics but the idea has evolved away from its origins to mean “preference”. There is a sense in which the straightforward appeal of basic utilitarianism has been “leased out” in modified form to a set of institutional arrangements. Certain “pressure points” in a modern society are noted which pose particular problems pertinent to moral theory. Bernard Williams argues persuasively for an appropriately modified form of virtue ethics.
A perspective in the philosophy of mathematics is developed from a consideration of the strengths... more A perspective in the philosophy of mathematics is developed from a consideration of the strengths and limitations of both logicism and platonism, with an early focus on Frege's work. Importantly, although many set-theoretic structures may be developed each of which offers limited isomorphism with the system of natural numbers, no one of them may be identified with it. Furthermore, the timeless, ever present nature of mathematical concepts and results itself offers direct access, in the face of a platonist account which generates a supposed problem of access. Crucially too, pure mathematics has its own distinctive method of confirming or validating results-mathematical proof-which supplies a higher level of confidence and objectivity than that available elsewhere. The dichotomy of invention and discovery is too jejune a framework for analysing creative mathematical activity. The Gödelian platonist perspective is evaluated and queried through scrutiny of the part played by mathematical resources and constraints in relation to human activity. It appears that there can be non-causal mathematical explanations and mathematical constraint on purely natural processes. Valuable implications of Quine's naturalism are explored, but one must be cautious of his thesis of confirmational holism. The distinction between algebraic and non-algebraic mathematical theories usefully contributes to our understanding of the internally differentiated nature of the subject.
Journal of the Royal Statistical Society, Series A (Statistics in Society) , 2022
Violet Rosina Cane, MA (Cantab), 31.1.1916–27.6.2008, was a Cambridge-educated statistician whose... more Violet Rosina Cane, MA (Cantab), 31.1.1916–27.6.2008, was a Cambridge-educated statistician whose research and consulting centred on the applications of classical statistical theory, as well as on the contemporary theory of stochastic processes, including that being developed by some of her colleagues and former teachers at Cambridge.
This article celebrates the life and work of pioneering statistician, Professor Violet Cane. She... more This article celebrates the life and work of pioneering statistician, Professor Violet Cane. She was the sort of female role model that continues to be needed.
Open Journal of Philosophy, vol. 12, no. 1, 54-68, 2022
The extent of confusion between symbols and that which is symbolised is examined across five inst... more The extent of confusion between symbols and that which is symbolised is examined across five institutional spheres. Religion is the institution most marked by confusion of this type; indeed in some respects the symbolic message of religion may be the extent of the substantive reality. On the other hand, the very existence of the nation state may be judged to depend upon the exercise of the human imagination; hence providing a source of instability which may lead to the excesses of nationalism. In regard to social status, the main problematical element is a certain circularity: it is necessary to get people to exhibit differences in behaviour which are then used to justify or constitute the status differences themselves. In politics, the symbolism of left and right threatens to strangle creative thinking, while in education the tendency on all sides to orient towards public systems of measurement and grading undermines the claim that what is really important is pupil and student learning. A social cost is being paid for the failure to recognise and, where possible, address the issues identified.
Open Journal of Philosophy, vol. 4, no. 11, 482-498, 2021
Progress may be made in resolving the tension between free will and determinism by analysis of th... more Progress may be made in resolving the tension between free will and determinism by analysis of the necessary conditions of freedom. It is of the essence that these conditions include causal and deterministic regularities. Furthermore, the human expression of free will is informed by understanding some of those regularities, and increments in that understanding have served to enhance freedom. When the possible character of a deterministic system based on physical theory is considered, it is judged that, far from implying the elimination of human freedom, such a theory might simply set parameters for it; indeed knowledge of that system could again prove to be in some respects liberating. On the other hand, it is of the essence that the overarching biological framework is not a deterministic system and it foregrounds the behavioural flexibility of humans in being able to choose within a range of options and react to chance occurrences. Furthermore, an issue for determinism flows from the way in which randomness (e.g. using a true random number generator) and chance events could and do enter human life. Once the implications of that issue are fully understood, other elements fit comfortably together in our understanding of freely undertaken action: the contribution of reasons and causes; the fact that reasons are never sufficient to account for outcomes; the rationale for the attribution of praise and blame.
Advances in Anthropology, vol. 11(3), pp. 179-200, 2021
In a study drawing from both evolutionary biology and the social sciences, evidence and argument ... more In a study drawing from both evolutionary biology and the social sciences, evidence and argument is assembled in support of the comprehensive application of selfish gene theory to the human population. With a focus on genes giving rise to characteristically-human cooperation ("cooperative genes") involving language and theory of mind, one may situate a whole range of patterned behaviour-including celibacy and even slavery-otherwise seeming to present insuperable difficulties. Crucially, the behaviour which tends to propagate the cooperative genes may be "at cost" to the genes of some who may be party to the cooperation itself. Explanatory insights are provided by Trivers' parent-offspring conflict theory, Lack's principle, and Hamilton's kin selection mechanism. A primary observation is that cooperation using language and theory of mind is itself interdependent with full human conceptualization of a world of objects and of themselves as embodied beings. Human capacities inhering in, or arising out of, the ability to cooperate are also responsible for a vitally important long-term process, the domestication of animals and plants. The approach illuminates the difference between animal and human sexual behaviour, and the emergence of kinship systems. Again, recent patterns of population growth become much more explicable. It is argued that the gene is the single controlling replicator; the notion of the meme as a second independent replicator is flawed.
Open Journal of Philosophy, vol. 10(3), pp. 346-367, 2020
Religion emerged among early humans because both purposive and non-purposive explanations were be... more Religion emerged among early humans because both purposive and non-purposive explanations were being employed but understanding was lacking of their precise scope and limits. Given also a context of very limited human power, the resultant foregrounding of agency and purposive explanation expressed itself in religion's marked tendency towards anthropomorphism and its key role in legitimizing behaviour. The inevitability of death also structures the religious outlook; with ancestors sometimes assigned a role in relation to the living. Subjective elements such as the experience of dreams and the internalization of moral precepts also play their part. Two important sources of variation among religions concern the adoption of a dualist or non-dualist perspective, and whether or not the religion's early political experience is such as to generate a systematic doctrine subordinating politics to religion. The near ubiquity and endurance of religion are further illuminated by analysis of its functions and ideological role. Religion tends to be socially conservative but has the potential to be revolutionary.
Open Journal of Philosophy, vol. 10(1), pp. 45-65, 2020
Drawing mainly from the Tractatus Logico-Philosophicus and his middle period writings, strategic ... more Drawing mainly from the Tractatus Logico-Philosophicus and his middle period writings, strategic issues and problems arising from Wittgenstein's philosophy of mathematics are discussed. Topics have been so chosen as to assist mediation between the perspective of philosophers and that of mathematicians on their developing discipline. There is consideration of rules within arithmetic and geometry and Wittgenstein's distinctive approach to number systems whether elementary or transfinite. Examples are presented to illuminate the relation between the meaning of an arithmetical generalisation or theorem and its proof. An attempt is made to meet directly some of Witt-genstein's critical comments on the mathematical treatment of infinity and irrational numbers.
Open Journal of Philosophy, vol. 9(4), pp. 452-469, 2019
A framework is developed for understanding what is “taken for granted” both in philosophy and in ... more A framework is developed for understanding what is “taken for granted” both in philosophy and in life generally, which may serve to orient philosophical inquiry and make it more effective. The framework takes in language and its development, as well as mathematics, logic, and the empirical sphere with particular reference to the exigencies of life. It is evaluated through consideration of seven philosophical issues concerned with such topics as solipsism, sense data as the route to knowledge, the possible reduction of geometry to logic, and the existence and status of human rights. Various dichotomies and the notion of continuity are evidently highly strategic.
The notion of the selfish gene has been successfully deployed in the understanding of animal beha... more The notion of the selfish gene has been successfully deployed in the understanding of animal behaviour but is widely felt not to have full application at the human level. A lot of evidence and argument is here assembled in support of the comprehensive application of that theory to the human population. With a focus on genes giving rise to characteristically-human cooperation (‘cooperative genes’) it proves possible to situate a whole range of patterned behaviour and phenomena, even including celibacy, the use of contraception, and war, which at first glance seem to present insuperable difficulties. Crucially, the behaviour which tends to propagate the cooperative genes may be ‘at cost’ to the genes of some who may be party to the cooperation itself.
The account builds on the primary insight that cooperation itself gives rise to full human conceptualization of the external world and their own place in it as embodied beings. Cooperation thereby structures practical action and progressively impacts on fertility, mortality and migration; cooperation therefore furthers the continued existence and transmission of the genes which give rise to it. Human capacities underlying the ability to cooperate are also responsible for a vitally important long-term process - the
ii
domestication of animals and plants; the geographical redistribution of such species means that the Earth is able to sustain a progressively larger human population.
A consideration of the implications of characteristically-human cooperation helps one to understand the difference between animal and human sexual behaviour, and to explain the emergence of kinship systems, involving the social recognition of blood ties: one is thereby enabled to bridge the gap between zoology and social anthropology. Cooperation is also the basic source of morality and hence of stabilizing regulation; at the same time it generates a bifurcation in respect of types of human understanding which explains the origin of religion. Significantly, however, the predominating influence of religions on fertility is such as to incline population firmly on an upward trajectory.
Competition between societies at one level of complexity tends to lead to societies of a greater level of complexity. The broader picture is not that various independent variables simply ‘cause’ growth in population but rather that various distinguishable elements – such as societal complexity, the rate of technological innovation (seen as evolutionary), food production, and population size and density - inter-affect each other. Perhaps the most strategic aspect of all is development or reshaping of the division and specialization of labour; crucially, that development tends to increase product while reducing the tendency for conflict to occur which may lead to violence.
Everywhere humans gain access to the means of their subsistence cooperatively, but how they organize to do so develops in patterned ways. In respect of prehistory and history,
iii
that the same trends – towards food production, social complexity and urbanism – are found as independent developments in different parts of the globe points to the contribution of basic facets of human cooperative behaviour. The historically important phenomenon of empire tended to have positive implications for expansion of population. Larger and more stable political entities tend to emerge over extended time – states, empires, nation states – providing a more predictable and secure context within which populations may grow.
In complex societies, the built environment, writing and money contribute to sustaining and extending orderly cooperation. While rationality is generally exhibited within the range of human behaviour, the systematic adoption of a rational approach to life is grounded in the emergence of institutional forms. In connection with globalization, humans are proceeding to reconfigure the external world so as to maximize the possibilities for their own cooperation within it. Contrary to what might initially be thought, there are reasons for judging that the threat or experience of violence and war has played its part in creating the conditions for population growth. In addition, institutional change overtime has tended increasingly to realize a latent potential for cooperation without recourse to violence and war.
Significantly, the increases in population experienced in differing types of society have sometimes tended to exceed those anticipated from the theory of the demographic transition, but once one foregrounds the impact of cooperative genes, patterns become that much more explicable. The populations of western societies tend to be rising but the
iv
overall demographic pattern can nevertheless be said to be substantially ‘at cost’ to the propagation of the genes of the majority of individuals who choose to limit their own fertility. The use of contraception and abortion in recent centuries is to be viewed as a means towards fertility objectives, but those objectives are substantially independent of the means. The interdependence of generations – notably in the early and later years of life - provides a basic link between mortality and fertility, but the needs of each generation promise to be best served if a (slightly) larger one is following it. The present sometimes ‘unwelcome’ migration into richer nations illustrates the persistent tendency in human experience for there to be re-distribution of the potential for population growth in space and in relation to economic resources which tends to keep overall population numbers on an upward trajectory.
In future the human gene pool will be intentionally reshaped increasing the likelihood of there being a large and growing population with a distribution of qualities which will enable them to cooperate even more effectively. The notion of the meme lacks explanatory power and cannot perform the role so far assigned to it. The position is that cooperative genes give rise to cooperative behaviour which tends to propagate the genes, while memes inter alia inhere in cooperative activity; hence the only satisfactory explanatory framework involves a single replicator. It is equally true to say that ‘humans are sometimes selfish’ and that ‘humans naturally create norms of behaviour tending to restrict or eliminate selfishness’. A whole range of phenomena may be understood as involving the working out of the partial ‘conflict of interest’ between cooperative and other genes e.g. theft by a gang, the U.K. National Health Service, and (even) the world’s
v
(possible) emerging political and economic structural form. The propagation of human cooperative genes is potentially ‘at cost’ to the propagation of any of the other genes of other life forms on this planet (and conceivably also elsewhere). That is the full measure of the extent to which these cooperative genes are selfish.
Sociological Focus, vol.6, no. 2, pp. 107-116, 1983
How is the historical development of mathematics to be understood sociologically? The writings
o... more How is the historical development of mathematics to be understood sociologically? The writings
of Mannheim and Wittgenstein suggest two contrasting approaches which may be evaluated through
a detailed analysis of the development of the number concept. Five main number systems can be
distinguished of which the most basic is the system of whole numbers and, given that importance
attaches to generalizing power, there can be shown to be a tendency for the number concept to be
progressively augmented. This process may be understood by reference to the basic pre-Darwinian
evolutionary idea of "unfolding." Complementing this intrinsic element, in actual historical instances
a variety of extrinsic factors may be seen to be operative, facilitating or retarding development. To
explain historical change fully an elaborate normative structure must be analyzed incorporating a
macro-institutional level, the "rules of the mathematical game", notational considerations, and relations
internal to mathematics itself (e.g., between number and geometry).
International Journal of Sociology and Social Policy, vol. 5, issue 1, pp. 54-67, 1985
Within the literature there is a lack of clarity regarding the place of evolutionary,
critical a... more Within the literature there is a lack of clarity regarding the place of evolutionary,
critical and non-evolutionary structuralist conceptions in a sociological account of
mathematical development. This article provides a unifying perspective through an
analysis of two main lines of historical development: the concept of number and
fundamental geometrical notions. The development of number systems can be
explicated on an internalist basis using the pre-Darwinian evolutionary idea of
"unfolding", together with the associated notion of facilitating and retarding
conditions. On the other hand, some major developments in geometry do not lend
themselves to this interpretation but can be understood as innovations stemming
from various internal and external sources. The account highlights the importance
for mathematics of the formation of means-ends relationships, as well as various
"axes" of critical debate.
International Journal of Sociology and Social Policy, vol. 3, issue 4, pp. 64-73, 1983
The underdeveloped state of this field does no credit to sociology. Some sociologists
are more i... more The underdeveloped state of this field does no credit to sociology. Some sociologists
are more interested in using quantification as a source of legitimation than in
confronting mathematics as a central element of culture. Yet mathematics may be
viewed as an institution with a normative core developing alongside experience of the
physical world, susceptible of both "internalist" and "externalist" programmes of
investigation. There is a need to examine how the symbolic system of mathematics
structures the development of thought and how the acceptance of mathematical ideas
is related to their utility. The use of the evolutionary approach has generated some
distinctive concepts which can assist cross-cultural work. Smaller-scale studies continue
to provide insight into the relation between mathematical theory and social
structure.
Journal of Contemporary Religion, vol. 12, no.2, pp.215-228, 1997
This paper explores the relationship between religious beliefs and secular
attitudes of lay peop... more This paper explores the relationship between religious beliefs and secular
attitudes of lay people within a single church, the Anglican Province of Wales (UK). The
origins of the data are described and findings as to the distinctive social characteristics
of the laity reported. Results of the analysis of the interrelationship between different
dimensions of religious belief are reported and discussed. The secular attitudes of the
laity are compared with those of the British population, and found to be on the whole
more 'liberal'. While some differences between the secular attitudes of the laity and the
general population are clearly related to the distinctive social position of the former,
social location is unable to explain all of these differences. A number of relationships
between belief and secular attitudes are described. Anglicans with more 'catholic' beliefs
seem more concerned in their secular attitudes with issues which they perceive as
involving rule breaking or attitudes to authority, while 'evangelicals' react more
strongly to what can be interpreted as unconscionable behaviour.
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Papers by Richard Startup
modified by Christianity. Of growing importance by the eighteenth century was rights theory which was often still situated religiously. Kant’s principle of the categorical imperative has been highly influential but was challenged by the emerging nature of industrial and capitalist society. Utilitarianism, within which the moral rightness of activity resides in its tendency to promote happiness or unhappiness, represented the decisive move from the transcendental to
the immanent approach. Although all three approaches to moral theory continue to be relevant to identifiable situations and aspects of modern society, there has been a substantial turn towards a heavily modified utilitarianism associated with parliamentary democracy and market economies founded on property ownership. The root cause of this is the ability of utilitarianism, as opposed to the other approaches, to handle considerations of number and probability. The concept of utility is fundamental in economics but the idea has evolved away from its origins to mean “preference”. There is a sense in which the straightforward appeal of basic utilitarianism has been “leased out”
in modified form to a set of institutional arrangements. Certain “pressure points” in a modern society are noted which pose particular problems pertinent to moral theory. Bernard Williams argues persuasively for an appropriately modified form of virtue ethics.
The account builds on the primary insight that cooperation itself gives rise to full human conceptualization of the external world and their own place in it as embodied beings. Cooperation thereby structures practical action and progressively impacts on fertility, mortality and migration; cooperation therefore furthers the continued existence and transmission of the genes which give rise to it. Human capacities underlying the ability to cooperate are also responsible for a vitally important long-term process - the
ii
domestication of animals and plants; the geographical redistribution of such species means that the Earth is able to sustain a progressively larger human population.
A consideration of the implications of characteristically-human cooperation helps one to understand the difference between animal and human sexual behaviour, and to explain the emergence of kinship systems, involving the social recognition of blood ties: one is thereby enabled to bridge the gap between zoology and social anthropology. Cooperation is also the basic source of morality and hence of stabilizing regulation; at the same time it generates a bifurcation in respect of types of human understanding which explains the origin of religion. Significantly, however, the predominating influence of religions on fertility is such as to incline population firmly on an upward trajectory.
Competition between societies at one level of complexity tends to lead to societies of a greater level of complexity. The broader picture is not that various independent variables simply ‘cause’ growth in population but rather that various distinguishable elements – such as societal complexity, the rate of technological innovation (seen as evolutionary), food production, and population size and density - inter-affect each other. Perhaps the most strategic aspect of all is development or reshaping of the division and specialization of labour; crucially, that development tends to increase product while reducing the tendency for conflict to occur which may lead to violence.
Everywhere humans gain access to the means of their subsistence cooperatively, but how they organize to do so develops in patterned ways. In respect of prehistory and history,
iii
that the same trends – towards food production, social complexity and urbanism – are found as independent developments in different parts of the globe points to the contribution of basic facets of human cooperative behaviour. The historically important phenomenon of empire tended to have positive implications for expansion of population. Larger and more stable political entities tend to emerge over extended time – states, empires, nation states – providing a more predictable and secure context within which populations may grow.
In complex societies, the built environment, writing and money contribute to sustaining and extending orderly cooperation. While rationality is generally exhibited within the range of human behaviour, the systematic adoption of a rational approach to life is grounded in the emergence of institutional forms. In connection with globalization, humans are proceeding to reconfigure the external world so as to maximize the possibilities for their own cooperation within it. Contrary to what might initially be thought, there are reasons for judging that the threat or experience of violence and war has played its part in creating the conditions for population growth. In addition, institutional change overtime has tended increasingly to realize a latent potential for cooperation without recourse to violence and war.
Significantly, the increases in population experienced in differing types of society have sometimes tended to exceed those anticipated from the theory of the demographic transition, but once one foregrounds the impact of cooperative genes, patterns become that much more explicable. The populations of western societies tend to be rising but the
iv
overall demographic pattern can nevertheless be said to be substantially ‘at cost’ to the propagation of the genes of the majority of individuals who choose to limit their own fertility. The use of contraception and abortion in recent centuries is to be viewed as a means towards fertility objectives, but those objectives are substantially independent of the means. The interdependence of generations – notably in the early and later years of life - provides a basic link between mortality and fertility, but the needs of each generation promise to be best served if a (slightly) larger one is following it. The present sometimes ‘unwelcome’ migration into richer nations illustrates the persistent tendency in human experience for there to be re-distribution of the potential for population growth in space and in relation to economic resources which tends to keep overall population numbers on an upward trajectory.
In future the human gene pool will be intentionally reshaped increasing the likelihood of there being a large and growing population with a distribution of qualities which will enable them to cooperate even more effectively. The notion of the meme lacks explanatory power and cannot perform the role so far assigned to it. The position is that cooperative genes give rise to cooperative behaviour which tends to propagate the genes, while memes inter alia inhere in cooperative activity; hence the only satisfactory explanatory framework involves a single replicator. It is equally true to say that ‘humans are sometimes selfish’ and that ‘humans naturally create norms of behaviour tending to restrict or eliminate selfishness’. A whole range of phenomena may be understood as involving the working out of the partial ‘conflict of interest’ between cooperative and other genes e.g. theft by a gang, the U.K. National Health Service, and (even) the world’s
v
(possible) emerging political and economic structural form. The propagation of human cooperative genes is potentially ‘at cost’ to the propagation of any of the other genes of other life forms on this planet (and conceivably also elsewhere). That is the full measure of the extent to which these cooperative genes are selfish.
of Mannheim and Wittgenstein suggest two contrasting approaches which may be evaluated through
a detailed analysis of the development of the number concept. Five main number systems can be
distinguished of which the most basic is the system of whole numbers and, given that importance
attaches to generalizing power, there can be shown to be a tendency for the number concept to be
progressively augmented. This process may be understood by reference to the basic pre-Darwinian
evolutionary idea of "unfolding." Complementing this intrinsic element, in actual historical instances
a variety of extrinsic factors may be seen to be operative, facilitating or retarding development. To
explain historical change fully an elaborate normative structure must be analyzed incorporating a
macro-institutional level, the "rules of the mathematical game", notational considerations, and relations
internal to mathematics itself (e.g., between number and geometry).
critical and non-evolutionary structuralist conceptions in a sociological account of
mathematical development. This article provides a unifying perspective through an
analysis of two main lines of historical development: the concept of number and
fundamental geometrical notions. The development of number systems can be
explicated on an internalist basis using the pre-Darwinian evolutionary idea of
"unfolding", together with the associated notion of facilitating and retarding
conditions. On the other hand, some major developments in geometry do not lend
themselves to this interpretation but can be understood as innovations stemming
from various internal and external sources. The account highlights the importance
for mathematics of the formation of means-ends relationships, as well as various
"axes" of critical debate.
are more interested in using quantification as a source of legitimation than in
confronting mathematics as a central element of culture. Yet mathematics may be
viewed as an institution with a normative core developing alongside experience of the
physical world, susceptible of both "internalist" and "externalist" programmes of
investigation. There is a need to examine how the symbolic system of mathematics
structures the development of thought and how the acceptance of mathematical ideas
is related to their utility. The use of the evolutionary approach has generated some
distinctive concepts which can assist cross-cultural work. Smaller-scale studies continue
to provide insight into the relation between mathematical theory and social
structure.
attitudes of lay people within a single church, the Anglican Province of Wales (UK). The
origins of the data are described and findings as to the distinctive social characteristics
of the laity reported. Results of the analysis of the interrelationship between different
dimensions of religious belief are reported and discussed. The secular attitudes of the
laity are compared with those of the British population, and found to be on the whole
more 'liberal'. While some differences between the secular attitudes of the laity and the
general population are clearly related to the distinctive social position of the former,
social location is unable to explain all of these differences. A number of relationships
between belief and secular attitudes are described. Anglicans with more 'catholic' beliefs
seem more concerned in their secular attitudes with issues which they perceive as
involving rule breaking or attitudes to authority, while 'evangelicals' react more
strongly to what can be interpreted as unconscionable behaviour.
modified by Christianity. Of growing importance by the eighteenth century was rights theory which was often still situated religiously. Kant’s principle of the categorical imperative has been highly influential but was challenged by the emerging nature of industrial and capitalist society. Utilitarianism, within which the moral rightness of activity resides in its tendency to promote happiness or unhappiness, represented the decisive move from the transcendental to
the immanent approach. Although all three approaches to moral theory continue to be relevant to identifiable situations and aspects of modern society, there has been a substantial turn towards a heavily modified utilitarianism associated with parliamentary democracy and market economies founded on property ownership. The root cause of this is the ability of utilitarianism, as opposed to the other approaches, to handle considerations of number and probability. The concept of utility is fundamental in economics but the idea has evolved away from its origins to mean “preference”. There is a sense in which the straightforward appeal of basic utilitarianism has been “leased out”
in modified form to a set of institutional arrangements. Certain “pressure points” in a modern society are noted which pose particular problems pertinent to moral theory. Bernard Williams argues persuasively for an appropriately modified form of virtue ethics.
The account builds on the primary insight that cooperation itself gives rise to full human conceptualization of the external world and their own place in it as embodied beings. Cooperation thereby structures practical action and progressively impacts on fertility, mortality and migration; cooperation therefore furthers the continued existence and transmission of the genes which give rise to it. Human capacities underlying the ability to cooperate are also responsible for a vitally important long-term process - the
ii
domestication of animals and plants; the geographical redistribution of such species means that the Earth is able to sustain a progressively larger human population.
A consideration of the implications of characteristically-human cooperation helps one to understand the difference between animal and human sexual behaviour, and to explain the emergence of kinship systems, involving the social recognition of blood ties: one is thereby enabled to bridge the gap between zoology and social anthropology. Cooperation is also the basic source of morality and hence of stabilizing regulation; at the same time it generates a bifurcation in respect of types of human understanding which explains the origin of religion. Significantly, however, the predominating influence of religions on fertility is such as to incline population firmly on an upward trajectory.
Competition between societies at one level of complexity tends to lead to societies of a greater level of complexity. The broader picture is not that various independent variables simply ‘cause’ growth in population but rather that various distinguishable elements – such as societal complexity, the rate of technological innovation (seen as evolutionary), food production, and population size and density - inter-affect each other. Perhaps the most strategic aspect of all is development or reshaping of the division and specialization of labour; crucially, that development tends to increase product while reducing the tendency for conflict to occur which may lead to violence.
Everywhere humans gain access to the means of their subsistence cooperatively, but how they organize to do so develops in patterned ways. In respect of prehistory and history,
iii
that the same trends – towards food production, social complexity and urbanism – are found as independent developments in different parts of the globe points to the contribution of basic facets of human cooperative behaviour. The historically important phenomenon of empire tended to have positive implications for expansion of population. Larger and more stable political entities tend to emerge over extended time – states, empires, nation states – providing a more predictable and secure context within which populations may grow.
In complex societies, the built environment, writing and money contribute to sustaining and extending orderly cooperation. While rationality is generally exhibited within the range of human behaviour, the systematic adoption of a rational approach to life is grounded in the emergence of institutional forms. In connection with globalization, humans are proceeding to reconfigure the external world so as to maximize the possibilities for their own cooperation within it. Contrary to what might initially be thought, there are reasons for judging that the threat or experience of violence and war has played its part in creating the conditions for population growth. In addition, institutional change overtime has tended increasingly to realize a latent potential for cooperation without recourse to violence and war.
Significantly, the increases in population experienced in differing types of society have sometimes tended to exceed those anticipated from the theory of the demographic transition, but once one foregrounds the impact of cooperative genes, patterns become that much more explicable. The populations of western societies tend to be rising but the
iv
overall demographic pattern can nevertheless be said to be substantially ‘at cost’ to the propagation of the genes of the majority of individuals who choose to limit their own fertility. The use of contraception and abortion in recent centuries is to be viewed as a means towards fertility objectives, but those objectives are substantially independent of the means. The interdependence of generations – notably in the early and later years of life - provides a basic link between mortality and fertility, but the needs of each generation promise to be best served if a (slightly) larger one is following it. The present sometimes ‘unwelcome’ migration into richer nations illustrates the persistent tendency in human experience for there to be re-distribution of the potential for population growth in space and in relation to economic resources which tends to keep overall population numbers on an upward trajectory.
In future the human gene pool will be intentionally reshaped increasing the likelihood of there being a large and growing population with a distribution of qualities which will enable them to cooperate even more effectively. The notion of the meme lacks explanatory power and cannot perform the role so far assigned to it. The position is that cooperative genes give rise to cooperative behaviour which tends to propagate the genes, while memes inter alia inhere in cooperative activity; hence the only satisfactory explanatory framework involves a single replicator. It is equally true to say that ‘humans are sometimes selfish’ and that ‘humans naturally create norms of behaviour tending to restrict or eliminate selfishness’. A whole range of phenomena may be understood as involving the working out of the partial ‘conflict of interest’ between cooperative and other genes e.g. theft by a gang, the U.K. National Health Service, and (even) the world’s
v
(possible) emerging political and economic structural form. The propagation of human cooperative genes is potentially ‘at cost’ to the propagation of any of the other genes of other life forms on this planet (and conceivably also elsewhere). That is the full measure of the extent to which these cooperative genes are selfish.
of Mannheim and Wittgenstein suggest two contrasting approaches which may be evaluated through
a detailed analysis of the development of the number concept. Five main number systems can be
distinguished of which the most basic is the system of whole numbers and, given that importance
attaches to generalizing power, there can be shown to be a tendency for the number concept to be
progressively augmented. This process may be understood by reference to the basic pre-Darwinian
evolutionary idea of "unfolding." Complementing this intrinsic element, in actual historical instances
a variety of extrinsic factors may be seen to be operative, facilitating or retarding development. To
explain historical change fully an elaborate normative structure must be analyzed incorporating a
macro-institutional level, the "rules of the mathematical game", notational considerations, and relations
internal to mathematics itself (e.g., between number and geometry).
critical and non-evolutionary structuralist conceptions in a sociological account of
mathematical development. This article provides a unifying perspective through an
analysis of two main lines of historical development: the concept of number and
fundamental geometrical notions. The development of number systems can be
explicated on an internalist basis using the pre-Darwinian evolutionary idea of
"unfolding", together with the associated notion of facilitating and retarding
conditions. On the other hand, some major developments in geometry do not lend
themselves to this interpretation but can be understood as innovations stemming
from various internal and external sources. The account highlights the importance
for mathematics of the formation of means-ends relationships, as well as various
"axes" of critical debate.
are more interested in using quantification as a source of legitimation than in
confronting mathematics as a central element of culture. Yet mathematics may be
viewed as an institution with a normative core developing alongside experience of the
physical world, susceptible of both "internalist" and "externalist" programmes of
investigation. There is a need to examine how the symbolic system of mathematics
structures the development of thought and how the acceptance of mathematical ideas
is related to their utility. The use of the evolutionary approach has generated some
distinctive concepts which can assist cross-cultural work. Smaller-scale studies continue
to provide insight into the relation between mathematical theory and social
structure.
attitudes of lay people within a single church, the Anglican Province of Wales (UK). The
origins of the data are described and findings as to the distinctive social characteristics
of the laity reported. Results of the analysis of the interrelationship between different
dimensions of religious belief are reported and discussed. The secular attitudes of the
laity are compared with those of the British population, and found to be on the whole
more 'liberal'. While some differences between the secular attitudes of the laity and the
general population are clearly related to the distinctive social position of the former,
social location is unable to explain all of these differences. A number of relationships
between belief and secular attitudes are described. Anglicans with more 'catholic' beliefs
seem more concerned in their secular attitudes with issues which they perceive as
involving rule breaking or attitudes to authority, while 'evangelicals' react more
strongly to what can be interpreted as unconscionable behaviour.