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Duality, Intensionality, and Contextuality: Philosophy of Category Theory and the Categorical Unity of Science in Samson Abramsky

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Samson Abramsky on Logic and Structure in Computer Science and Beyond

Part of the book series: Outstanding Contributions to Logic ((OCTR,volume 25))

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Abstract

Science does not exist in vacuum; it arises and works in context. Ground-breaking achievements transforming the scientific landscape often stem from philosophical thought, just as symbolic logic and computer science were born from the early analytic philosophy, and for the very reason they impact our global worldview as a coherent whole as well as local knowledge production in different specialised domains. Here we take first steps in elucidating rich philosophical contexts in which Samson Abramsky’s far-reaching work centring around categorical science as a new kind of science may be placed, explicated, and articulated. We argue, inter alia, that Abramsky’s work, as a whole, may be construed as demonstrating the categorical unity of science, or rather the sciences, in a mathematically rigorous, down-to-earth manner, which has been a salient feature of his work. At the same time we trace his intellectual history, leading from duality, to intensionality, and to contextuality, and place it in a broader context of philosophy beyond the analytic-continental divide, namely towards the reintegration of them as in the post-analytic tradition. Besides, we address issues in philosophy of category theory, such as the foundational autonomy of category theory and the (presumably two) dogmas of set-theoretical foundationalism, which Abramsky actually touch upon in one of his few philosophically inclined works. As to philosophy of category theory, we also address categorical structuralism as higher-order structuralism, categorical epistemology as elucidating higher-order meta-laws, and categorical ontology as allowing for reduction of ontological commitment via structural realism, the structuralist resolution of Benaceraff’s dilemma, and the pluralistic multiverse view of science as opposed to the set-theoretical reductionist ‘universe’ view. We conclude by speculating about the existence of the Oxford School of (Pluralistic) Unified Science as opposed to the Vienna Circle of (Monistic) Unified Science and to the Stanford School of (Pluralistic) Disunified Science; Categorical Unified Science may potentially allow us to reconcile the two camps on the unity and disunity of science whilst doing justice to both of them. Categorical unity arguably allows for unification via epistemological and ontological networking, and via knowledge transfer thus enabled, rather than unification via the reduction of everything and every truth to a single foundationalist framework, whilst taking at face value disunity, plurality, and diversity, and their significance in science and in human civilisation as a whole.

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Acknowledgements

I would like to express my deepest gratitude to Samson Abramsky for his robust continual support and encouragements, without which my life might have been different from what it is currently. At the same time, I would like to dedicate this article to the memory of our wonderful friend and colleague Klaus Keimel, who is one of the founders of domain theory as a theory in pure mathematics rather than computer science, and according to what Bob Coecke told me, wrote a strong letter of recommendation for me, thus having allowed me to do a PhD with Samson and Bob in Oxford, without which this article would have never come into existence in the first place. I can however tell for sure that Klaus would nevertheless dislike this article, especially in light of his nature as a hardcore mathematician, and yet despite many such disagreements, we were actually good friends of each other. The same would apply to Samson, who would disagree with some aspects of this work, and we are nonetheless good friends of each other. As you may have noticed already, I am going to argue that these are indeed cases of the unity (of humans rather than science) that is coherent with plurality and diversity, which has been the subject matter of the present article. I would like to note that this work largely stemmed from the Symposium on the Categorical Unity of the Sciences (Kyoto, 22–23 March 2019), which I held in the precious occasion of Samson’s visit in Kyoto, where I worked then as Hakubi Assistant Professor (since my DPhil study in Oxford), but soon after which I have got an opportunity to move to Australia as a Lecturer at ANU with the great help of Samson, Bob, and Jamie Vicary, to all of whom I am truly grateful for their gentle assistance. I hereby acknowledge that the present work was financially supported by JST PRESTO (grant code: JPMJPR17G9) and JSPS KAKENHI (grant code: 17K14231).

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  1. School of Computing, Australian National University, Canberra, Australia

    Yoshihiro Maruyama

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  1. Department of Ethics, Governance and Society, Vrije Universiteit Amsterdam, Amsterdam, The Netherlands

    Alessandra Palmigiano

  2. Department of Computer Science, University College London, London, UK

    Mehrnoosh Sadrzadeh

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Maruyama, Y. (2023). Duality, Intensionality, and Contextuality: Philosophy of Category Theory and the Categorical Unity of Science in Samson Abramsky. In: Palmigiano, A., Sadrzadeh, M. (eds) Samson Abramsky on Logic and Structure in Computer Science and Beyond. Outstanding Contributions to Logic, vol 25. Springer, Cham. https://doi.org/10.1007/978-3-031-24117-8_2

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