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Jens Mammen

Aalborg University, Department of Communication & Psychology, Honorary Professor

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Akihiro Kanamori

Boston University

University of Hamburg

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Marquette University

Dortmund University of Technology - Technische Universität Dortmund

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Papers by Jens Mammen

Set Theory and a Model of the Mind in Psychology

Review of Symbolic Logic, Mar 14, 2022

We investigate the mathematics of a model of the human mind which has been proposed by the psycho... more We investigate the mathematics of a model of the human mind which has been proposed by the psychologist Jens Mammen. Mathematical realizations of this model consist of so-called Mammen spaces, where a Mammen space is a triple (U, S, C), where U is a non-empty set ("the universe"), S is a perfect Hausdorff topology on U , and C ⊆ P(U) together with S satisfy certain axioms. We refute a conjecture put forward by J. Hoffmann-Jørgensen, who conjectured that the existence of a "complete" Mammen space implies the Axiom of Choice, by showing that in the first Cohen model, in which ZF holds but AC fails, there is a complete Mammen space. We obtain this by proving that in the first Cohen model, every perfect topology can be extended to a maximal perfect topology. On the other hand, we also show that if all sets are Lebesgue measurable, or all sets are Baire measurable, then there are no complete Mammen spaces with a countable universe. Finally, we investigate two new cardinal invariants uM and uT associated with complete Mammen spaces and maximal perfect topologies, and establish some basic inequalities that are provable in ZFC. Further, we show uM = uT = 2 ℵ 0 follows from Martin's Axiom, and, contrastingly, we show that ℵ1 = uM = uT < 2 ℵ 0 = ℵ2 in the Baumgartner-Laver model.

Bridging: Some Personal Reflections

Springer eBooks, 2021

Postscript by Jens Mammen (2018): A Science Thriller

Til forsvar for den sunde fornuft. Kan psykologien blive en videnskab uden at fjerne sig fra virkeligheden?: Tiltrædelsesforelæsning den 24. april 2009 som adjungeret professor ved Aalborg Universitet

A New Logical Foundation for Psychology

SpringerBriefs in psychology, 2017

The use of general descriptive names, registered names, trademarks, service marks, etc. in this p... more The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Using a Topological Model in Psychology: Developing Sense and Choice Categories

Integrative Psychological and Behavioral Science, Mar 1, 2016

A duality of sense categories and choice categories is introduced to map two distinct but coopera... more A duality of sense categories and choice categories is introduced to map two distinct but cooperating ways in which we as humans are relating actively to the world. We are sensing similarities and differences in our world of objects and persons, but we are also as bodies moving around in this world encountering, selecting, and attaching to objects beyond our sensory interactions and in this way also relating to the individual objects' history. This duality is necessary if we shall understand man as relating to the historical depth of our natural and cultural world, and to understand our cognitions and affections. Our personal affections and attachments, as well as our shared cultural values are centered around objects and persons chosen as reference points and landmarks in our lives, uniting and separating, not to be understood only in terms of sensory selections. The ambition is to bridge the gap between psychology as part of Naturwissenschaft and of Geisteswissenschaft, and at the same time establish a common frame for understanding cognition and affection, and our practical and cultural life (Mammen and Mironenko 2015). The duality of sense and choice categories can be described formally using concepts from modern mathematics, primarily topology, surmounting the reductions rooted in the mechanistic concepts from Renaissance science and mathematics. The formal description is based on 11 short and simple axioms held in ordinary language and visualized with instructive figures. The axioms are bridging psychology and mathematics and not only enriching psychology but also opening for a new interpretation of parts of the foundation of mathematics and logic.

Consequences of the Duality in Humans’ Relations to the World of Objects

SpringerBriefs in psychology, 2017

The duality of humans’ relations to objects’ form and features and to their existence as matter a... more The duality of humans’ relations to objects’ form and features and to their existence as matter and continuous threads in time and space has far-reaching consequences for our capacity to accumulate and communicate empirical knowledge, for our knowledge of laws of nature, for our framing of sensory perception, and for emotions, affections, sentiments, motivation, love and solidarity, meaning and culture rooted in significant places, objects, and persons.

Sense and Choice Categories

SpringerBriefs in psychology, 2017

The duality in humans’ asymmetric subject-object relations to the world can be described as two d... more The duality in humans’ asymmetric subject-object relations to the world can be described as two different ways of selecting, differentiating, and combining categories of objects in the world, sense categories based on objects’ form or features and choice categories based on objects’ existence as matter distributed and moving in space and time. The joint structure of these categories can be described in a simple and elegant axiomatic system using modern mathematical logic and topology, but expressed in terms of ordinary language, and with far-reaching consequences.

Til Forsvar for Den Sunde Fornuft. Kan Psykologien Blive en Videnskab Uden at Fjerne Sig Fra Virkeligheden?

Psyke and Logos, Dec 31, 2009

Rebellion, Theory, and Dialogue: an Interview with Jens Mammen

Human Arenas, Dec 19, 2018

The conversation begins with a reflection on the 1968 student rebellion in Copenhagen University,... more The conversation begins with a reflection on the 1968 student rebellion in Copenhagen University, and its implications for Psychology in Denmark and internationally. Against this historical background, Jens Mammen's own theoretical works and his approach to teaching are discussed. Also included, are reflections on scientific progress, the current academic conditions, the relationship between theories and theorists, and interdisciplinary thinking.

A Commentary by Jens Mammen (1986): Or Notes on Mathematics, Intuition and Reality (inter alia Sticklebacks)

Onset of meditation explored with fMRI

NeuroImage, Jun 1, 2001

Set theory and a model of the mind in psychology

arXiv (Cornell University), Sep 14, 2021

We investigate the mathematics of a model of the human mind which has been proposed by the psycho... more We investigate the mathematics of a model of the human mind which has been proposed by the psychologist Jens Mammen. Mathematical realizations of this model consist of so-called Mammen spaces, where a Mammen space is a triple (U, S, C), where U is a non-empty set ("the universe"), S is a perfect Hausdorff topology on U , and C ⊆ P(U) together with S satisfy certain axioms. We refute a conjecture put forward by J. Hoffmann-Jørgensen, who conjectured that the existence of a "complete" Mammen space implies the Axiom of Choice, by showing that in the first Cohen model, in which ZF holds but AC fails, there is a complete Mammen space. We obtain this by proving that in the first Cohen model, every perfect topology can be extended to a maximal perfect topology. On the other hand, we also show that if all sets are Lebesgue measurable, or all sets are Baire measurable, then there are no complete Mammen spaces with a countable universe. Finally, we investigate two new cardinal invariants uM and uT associated with complete Mammen spaces and maximal perfect topologies, and establish some basic inequalities that are provable in ZFC. Further, we show uM = uT = 2 ℵ 0 follows from Martin's Axiom, and, contrastingly, we show that ℵ1 = uM = uT < 2 ℵ 0 = ℵ2 in the Baumgartner-Laver model.

Mere om handling og rationalitet

A Grammar of Praxis: an Exposé of “A New Logical Foundation for Psychology”, a Few Additions, and Replies to Alaric Kohler and Alexander Poddiakov

Integrative Psychological and Behavioral Science, Mar 20, 2019

A Plea for Scientific Ambitions: Reply to Commentaries from Martin Wieser, Nikolai Veresov, Asger Neumann, and Peter Krøjgaard

Integrative Psychological and Behavioral Science, Jun 1, 2016

The paper is a reply to commentaries to &amp;amp;amp;amp;quot;Activity theories and the Ontol... more The paper is a reply to commentaries to &amp;amp;amp;amp;quot;Activity theories and the Ontology of Psychology: Learning from Danish and Russian Experiences&amp;amp;amp;amp;quot; (Mammen and Mironenko 2015). At the same time it is an attempt to reply to more general issues raised by the commentators and an attempt to further develop some general ideas from our paper with a focus on the introduction of the new analytical concepts sense and choice categories. These concepts have been elaborated in an axiomatic frame in (Mammen 2016) and the present paper is thus also pointing forwards to that and supporting it with examples from research on adult human relations of love and affection and on infant cognitive development. A few examples from myth and literature are referred to also. The ambition is to introduce new analytical tools across schools and domains of psychology which open for theoretical inclusion of new phenomena and re-structuring of well-known ones. The hope is to surmount some problems, as e.g. the dilemma between dualism and reductionism, which have been obstacles in the search for conceptual and methodological coherence in psychology. In the first place the hope is also to sharpen the analytical, critical and practical potential of psychology as a science. The ambition is not, here and now, to develop a comprehensive general theory as a container for the huge amount of empirical results collected using very heterogeneous criteria for what belongs to the domain of psychology and very heterogeneous conceptual frames. Here we still need some patience following the lesson from natural science, step by step including new domains as the conceptual and practical frames are expanding, but on the other hand not excluding anything apriori.

A New Beginning

SpringerBriefs in psychology, 2017

Methodological Envoi: A Few Guide-Lines (2018)

Virksomhed, viden, læring

“The Two Cultures” and the Place of Psychology

SpringerBriefs in psychology, 2017

Psychology has been caught between two opposing allies, natural science and human or social scien... more Psychology has been caught between two opposing allies, natural science and human or social science, but mostly in reduced versions as mechanicism and hermeneutics, respectively. A new understanding of human life as described here could, however, open for a unified field of study, including psychology.

Set Theory and a Model of the Mind in Psychology

Review of Symbolic Logic, Mar 14, 2022

We investigate the mathematics of a model of the human mind which has been proposed by the psycho... more We investigate the mathematics of a model of the human mind which has been proposed by the psychologist Jens Mammen. Mathematical realizations of this model consist of so-called Mammen spaces, where a Mammen space is a triple (U, S, C), where U is a non-empty set ("the universe"), S is a perfect Hausdorff topology on U , and C ⊆ P(U) together with S satisfy certain axioms. We refute a conjecture put forward by J. Hoffmann-Jørgensen, who conjectured that the existence of a "complete" Mammen space implies the Axiom of Choice, by showing that in the first Cohen model, in which ZF holds but AC fails, there is a complete Mammen space. We obtain this by proving that in the first Cohen model, every perfect topology can be extended to a maximal perfect topology. On the other hand, we also show that if all sets are Lebesgue measurable, or all sets are Baire measurable, then there are no complete Mammen spaces with a countable universe. Finally, we investigate two new cardinal invariants uM and uT associated with complete Mammen spaces and maximal perfect topologies, and establish some basic inequalities that are provable in ZFC. Further, we show uM = uT = 2 ℵ 0 follows from Martin's Axiom, and, contrastingly, we show that ℵ1 = uM = uT < 2 ℵ 0 = ℵ2 in the Baumgartner-Laver model.

Bridging: Some Personal Reflections

Springer eBooks, 2021

Postscript by Jens Mammen (2018): A Science Thriller

Til forsvar for den sunde fornuft. Kan psykologien blive en videnskab uden at fjerne sig fra virkeligheden?: Tiltrædelsesforelæsning den 24. april 2009 som adjungeret professor ved Aalborg Universitet

A New Logical Foundation for Psychology

SpringerBriefs in psychology, 2017

The use of general descriptive names, registered names, trademarks, service marks, etc. in this p... more The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Using a Topological Model in Psychology: Developing Sense and Choice Categories

Integrative Psychological and Behavioral Science, Mar 1, 2016

A duality of sense categories and choice categories is introduced to map two distinct but coopera... more A duality of sense categories and choice categories is introduced to map two distinct but cooperating ways in which we as humans are relating actively to the world. We are sensing similarities and differences in our world of objects and persons, but we are also as bodies moving around in this world encountering, selecting, and attaching to objects beyond our sensory interactions and in this way also relating to the individual objects' history. This duality is necessary if we shall understand man as relating to the historical depth of our natural and cultural world, and to understand our cognitions and affections. Our personal affections and attachments, as well as our shared cultural values are centered around objects and persons chosen as reference points and landmarks in our lives, uniting and separating, not to be understood only in terms of sensory selections. The ambition is to bridge the gap between psychology as part of Naturwissenschaft and of Geisteswissenschaft, and at the same time establish a common frame for understanding cognition and affection, and our practical and cultural life (Mammen and Mironenko 2015). The duality of sense and choice categories can be described formally using concepts from modern mathematics, primarily topology, surmounting the reductions rooted in the mechanistic concepts from Renaissance science and mathematics. The formal description is based on 11 short and simple axioms held in ordinary language and visualized with instructive figures. The axioms are bridging psychology and mathematics and not only enriching psychology but also opening for a new interpretation of parts of the foundation of mathematics and logic.

Consequences of the Duality in Humans’ Relations to the World of Objects

SpringerBriefs in psychology, 2017

The duality of humans’ relations to objects’ form and features and to their existence as matter a... more The duality of humans’ relations to objects’ form and features and to their existence as matter and continuous threads in time and space has far-reaching consequences for our capacity to accumulate and communicate empirical knowledge, for our knowledge of laws of nature, for our framing of sensory perception, and for emotions, affections, sentiments, motivation, love and solidarity, meaning and culture rooted in significant places, objects, and persons.

Sense and Choice Categories

SpringerBriefs in psychology, 2017

The duality in humans’ asymmetric subject-object relations to the world can be described as two d... more The duality in humans’ asymmetric subject-object relations to the world can be described as two different ways of selecting, differentiating, and combining categories of objects in the world, sense categories based on objects’ form or features and choice categories based on objects’ existence as matter distributed and moving in space and time. The joint structure of these categories can be described in a simple and elegant axiomatic system using modern mathematical logic and topology, but expressed in terms of ordinary language, and with far-reaching consequences.

Til Forsvar for Den Sunde Fornuft. Kan Psykologien Blive en Videnskab Uden at Fjerne Sig Fra Virkeligheden?

Psyke and Logos, Dec 31, 2009

Rebellion, Theory, and Dialogue: an Interview with Jens Mammen

Human Arenas, Dec 19, 2018

The conversation begins with a reflection on the 1968 student rebellion in Copenhagen University,... more The conversation begins with a reflection on the 1968 student rebellion in Copenhagen University, and its implications for Psychology in Denmark and internationally. Against this historical background, Jens Mammen's own theoretical works and his approach to teaching are discussed. Also included, are reflections on scientific progress, the current academic conditions, the relationship between theories and theorists, and interdisciplinary thinking.

A Commentary by Jens Mammen (1986): Or Notes on Mathematics, Intuition and Reality (inter alia Sticklebacks)

Onset of meditation explored with fMRI

NeuroImage, Jun 1, 2001

Set theory and a model of the mind in psychology

arXiv (Cornell University), Sep 14, 2021

We investigate the mathematics of a model of the human mind which has been proposed by the psycho... more We investigate the mathematics of a model of the human mind which has been proposed by the psychologist Jens Mammen. Mathematical realizations of this model consist of so-called Mammen spaces, where a Mammen space is a triple (U, S, C), where U is a non-empty set ("the universe"), S is a perfect Hausdorff topology on U , and C ⊆ P(U) together with S satisfy certain axioms. We refute a conjecture put forward by J. Hoffmann-Jørgensen, who conjectured that the existence of a "complete" Mammen space implies the Axiom of Choice, by showing that in the first Cohen model, in which ZF holds but AC fails, there is a complete Mammen space. We obtain this by proving that in the first Cohen model, every perfect topology can be extended to a maximal perfect topology. On the other hand, we also show that if all sets are Lebesgue measurable, or all sets are Baire measurable, then there are no complete Mammen spaces with a countable universe. Finally, we investigate two new cardinal invariants uM and uT associated with complete Mammen spaces and maximal perfect topologies, and establish some basic inequalities that are provable in ZFC. Further, we show uM = uT = 2 ℵ 0 follows from Martin's Axiom, and, contrastingly, we show that ℵ1 = uM = uT < 2 ℵ 0 = ℵ2 in the Baumgartner-Laver model.

Mere om handling og rationalitet

A Grammar of Praxis: an Exposé of “A New Logical Foundation for Psychology”, a Few Additions, and Replies to Alaric Kohler and Alexander Poddiakov

Integrative Psychological and Behavioral Science, Mar 20, 2019

A Plea for Scientific Ambitions: Reply to Commentaries from Martin Wieser, Nikolai Veresov, Asger Neumann, and Peter Krøjgaard

Integrative Psychological and Behavioral Science, Jun 1, 2016

The paper is a reply to commentaries to &amp;amp;amp;amp;quot;Activity theories and the Ontol... more The paper is a reply to commentaries to &amp;amp;amp;amp;quot;Activity theories and the Ontology of Psychology: Learning from Danish and Russian Experiences&amp;amp;amp;amp;quot; (Mammen and Mironenko 2015). At the same time it is an attempt to reply to more general issues raised by the commentators and an attempt to further develop some general ideas from our paper with a focus on the introduction of the new analytical concepts sense and choice categories. These concepts have been elaborated in an axiomatic frame in (Mammen 2016) and the present paper is thus also pointing forwards to that and supporting it with examples from research on adult human relations of love and affection and on infant cognitive development. A few examples from myth and literature are referred to also. The ambition is to introduce new analytical tools across schools and domains of psychology which open for theoretical inclusion of new phenomena and re-structuring of well-known ones. The hope is to surmount some problems, as e.g. the dilemma between dualism and reductionism, which have been obstacles in the search for conceptual and methodological coherence in psychology. In the first place the hope is also to sharpen the analytical, critical and practical potential of psychology as a science. The ambition is not, here and now, to develop a comprehensive general theory as a container for the huge amount of empirical results collected using very heterogeneous criteria for what belongs to the domain of psychology and very heterogeneous conceptual frames. Here we still need some patience following the lesson from natural science, step by step including new domains as the conceptual and practical frames are expanding, but on the other hand not excluding anything apriori.

A New Beginning

SpringerBriefs in psychology, 2017

Methodological Envoi: A Few Guide-Lines (2018)

Virksomhed, viden, læring

“The Two Cultures” and the Place of Psychology

SpringerBriefs in psychology, 2017

Psychology has been caught between two opposing allies, natural science and human or social scien... more Psychology has been caught between two opposing allies, natural science and human or social science, but mostly in reduced versions as mechanicism and hermeneutics, respectively. A new understanding of human life as described here could, however, open for a unified field of study, including psychology.