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The Contextuality-by-Default View of the Sheaf-Theoretic Approach to Contextuality
The Sheaf-Theoretic Contextuality (STC) theory developed by Abramsky and colleagues is a very general account of whether multiply overlap** subsets...
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Sheaf Representations and Duality in Logic
The fundamental duality theories relating algebra and geometry that were discovered in the mid-twentieth century can also be applied to logic via its...
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Logical Journeys: A Scientific Autobiography
A short scientific biography emphasising the main phases of Abramsky’s research: duality theory and domains in logical form, game semantics,...
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Closing Bell Boxing Black Box Simulations in the Resource Theory of Contextuality
This chapter contains an exposition of the sheaf-theoretic framework for contextuality emphasising resource-theoretic aspects, as well as some...
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Local causation
The counterfactual and regularity theories are universal accounts of causation. I argue that these should be generalized to produce local accounts of...
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Intuitionistic Modal Algebras
Recent research on algebraic models of quasi-Nelson logic has brought new attention to a number of classes of algebras which result from enriching...
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Plurivaluationism, Semantic Nondeterminism and Communication
Broadly, this paper is about how communication—the exchange of information—is possible when the words used are not known to have particular meanings....
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Grothendieck’s theory of schemes and the algebra–geometry duality
We shall address from a conceptual perspective the duality between algebra and geometry in the framework of the refoundation of algebraic geometry...
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Metaphysics and Magic: Echoes of the Tractatus in Wittgenstein’s ‘Remarks on Frazer’
In this chapter I trace a number of thematic connections between Wittgenstein’s Tractatus and Notebooks on the one hand, and his ‘Remarks on Frazer’s...
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‘I Don’t Know Why We Take so Much Pleasure in Thinking That People Are Damned’: Leibniz and the Question of the Salvation of Pagans
Leibniz believed that amor Dei super omnia – a love for God above all things – is sufficient for salvation. He commends intellectual enlightenment as...
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Gödel, Escher, Bell: Contextual Semantics of Logical Paradoxes
Quantum physics exhibits various non-classical and paradoxical features. Among them are non-locality and contextuality (e.g. Bell’s theorem or the...
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Smooth Infinitesimals in the Metaphysical Foundation of Spacetime Theories
I propose a theory of space with infinitesimal regions called smooth infinitesimal geometry (SIG) based on certain algebraic objects (i.e., rings),...
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A Bergsonian Perspective on Causality and Evolution
Bergsonian philosophy is not generally regarded as a true philosophy of biology. Bergson’s rejection of Darwinism, his silence on incipient genetics,...
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Categorical Proof-theoretic Semantics
In proof-theoretic semantics, model-theoretic validity is replaced by proof-theoretic validity. Validity of formulae is defined inductively from a...
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Grothendieck Toposes as Unifying ‘Bridges’: A Mathematical Morphogenesis
We present some philosophical principles underlying the theory of topos-theoretic ‘bridges’, introduced by the author in 2010 and further developed...
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Exploring Mathematical Objects from Custom-Tailored Mathematical Universes
Toposes can be pictured as mathematical universes. Besides the standard topos, in which most of mathematics unfolds, there is a colorful host of...
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Mathematical Practice, Fictionalism and Social Ontology
From the perspective of mathematical practice, I examine positions claiming that mathematical objects are introduced by human agents. I consider in...
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Duality, Intensionality, and Contextuality: Philosophy of Category Theory and the Categorical Unity of Science in Samson Abramsky
Science does not exist in vacuum; it arises and works in context. Ground-breaking achievements transforming the scientific landscape often stem from...