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A new logical measure for quantum information
Get PDFStarting at the logical level of the logic of partitions, dual to the usual Boolean logic of subsets, the notion of logical entropy, i.e., information as distinctions, is developed as the quantification of the distinctions of partitions--just as probability theory starts with the quantification of elements of subsets. Logical entropy is compared and contrasted with the usual notion of Shannon entropy. Then a semi-algorithmic procedure (from the mathematical folklore) is used to translate the notion of logical entropy at the set level to the corresponding notion of quantum logical entropy at the (Hilbert) vector space level. Examples and some important propositions relate quantum logical entropy to projective measurement and to the Hilbert-Schmidt distance. Overall, the approach demonstrates the logical basis and naturality of this notion of entropy for quantum mechanics
Where do Adjunctions Come From? Chimera Morphisms and Adjoint Functors in Category Theory
Get PDFCategory theory has foundational importance because it provides conceptual lenses to characterize what is important and universal in mathematics—with adjunction seeming to be the primary lens. Our topic is a theory showing “where adjoints come from”. The theory is based on object-to-object “chimera morphisms”, “heteromorphisms”, or “hets” between the objects of different categories (e.g., the insertion of generators as a set-to-group map). After showing that heteromorphisms can be treated rigorously using the machinery of category theory (bifunctors), we show that all adjunctions between two categories arise (up to an isomorphism) as the representations (i.e., universal models) within each category of the heteromorphisms between the two categories. The conventional treatment of adjunctions eschews the whole concept of a heteromorphism, so our purpose is to shine a new light on this notion by showing its origin as a het between categories being universally represented within each of the two categories. This heteromorphic treatment of
adjunctions shows how they can be split into two separable universal constructions. Such universals can also occur without being part of an adjunction. We conclude with the idea that it is the universal constructions (adjunctions being an important special case) that are really the foundational concepts to pick out what is important in mathematics and perhaps in other sciences, not to mention in philosophy
Quantum Foundations of Consciousness: A Reformulated Framework
Get PDFThis paper proposes a theory-neutral formal framework designed to accommodate data that implicates consciousness in anomalous observer-linked phenomena, including structured accounts sometimes interpreted as involving alleged non-human intelligence.
Motivated by growing empirical reports in which observer phenomenology appears coupled to system behavior, the paper introduces an explanatory workspace that expands the standard quantum state space to include a phenomenal dimension.
Specifically, it augments the conventional Hilbert space Hphysical with an orthogonal tensor factor Hphenomenal, allowing conscious states to be structurally represented without reducing them to conventional observables.
The goal is not to offer a reductive theory of consciousness, but to supply a lawful representational space into which empirically grounded anomalies—such as psi effects, attentional modulation, or UAP-linked phenomenology—might coherently fit.
The framework is grounded in an epistemic tradition articulated by Newton, Eddington, Russell, and Chomsky, all of whom emphasize the distinction between the structural apparatus of science and its ontological reach.
It does not seek to redefine physics, but to expand its structural vocabulary—offering a formal arena in which observer-linked anomalies may become empirically visible and testable
Varieties of Wave Function Realism, or, WTF is WFR?
Get PDFThe phrase “Wave Function Realism” (WFR) has come to be used for a family of views according to which quantum theory motivates us to think that quantum wave functions are fields on a space of extremely high dimension, which is in some sense more fundamental that ordinary three-dimensional space or four-dimensional spacetime.
With an aim at gaining clarity about the nature of the project, I distinguish between varieties of Wave Function Realism that one might hold. I focus on two axes of distinction. One has to do with the nature of the project. Is it an Interpretive project, one of accepting standard quantum theory pretty much as we have it, and exploring its implications for ontology? Or is it a Constructive project, which finds standard quantum theory wanting in crucial aspects, and seeks to construct a new theory that will satisfy some set of metaphysical constraints? The other has to do with how radical the claims are that are made about the nature of spacetime. Does the fundamental space on which the wave functions of WFR are defined have intrinsic structure corresponding to the low-dimensional spacetime structure? I call versions of WFR on which this is so “Mild” versions, as on such a view any sense in which the low-dimensional spatial structure is non-fundamental would be at best a highly attenuated one. A more radical view, which I call “Spicy,” has it that the fundamental space has no intrinsic structure corresponding to our low dimension spacetime, and that such structure is emergent from the structure and evolution of certain sort of wave functions.
Judging from what they say about the view, it seems that proponents of WFR intend it to be Interpretive and Spicy. I will argue that there can be no such position. Standard quantum mechanics makes such heavy use of low-dimensional spacetime structure that an Interpretive version of WFR must be Extremely Mild. A Spicy but Constructive version has yet to be formulated
Affect And Time: On The Worldly Origins Of Schizophrenic Vulnerability
Get PDFProminent phenomenological accounts of schizophrenia have long implicated disturbances in temporality as a central characteristic of the disorder (Minkowski, 1923; Stanghellini et al., 2016; Martin et al., 2019). Early clinical phenomenologists such as Minkowski posited that schizophrenia is defined by a fundamental alteration to the patient’s temporal experience, describing phenomena such as a “blocked future” and “fragmented time” that disrupts continuity between past, present, and future. Minkowski's notion of trouble générateur highlighted the incapacity to resonate with reality, marking a profound disconnect from shared temporal and existential structures. This view remains influential in contemporary research where scholars continue to explore temporal disintegration as a core feature of schizophrenia (Fuchs, 2010; Stanghellini et al., 2016). However, the more fundamental nature of this temporal disintegration has begun to be reinterpreted in clinical phenomenology.
In this chapter, we briefly assess this ongoing reinterpretation (Section 1), revisit pertinent phenomenological resources provided by Heidegger and Merleau-Ponty on time and affect (Section 2) and apply these ideas to the intersection between affective temporality and schizophrenia in its prodromal stage (Section 3) and bodily (Section 4) and intersubjective dimensions (Section 5). Finally, we examine the paradigm case of ‘mission delusions’, a symptom characterised by an affective-temporal rupture between self and world which incorporates all these themes (Section 6)
Traces of thinking: a stigmergic approach to 4E cognition
Get PDFThis paper outlines an approach to analysing minimal cognition that brings out its social and historical dimensions. It proposes a model, the coordinated systems approach (CSA), which understands cognition as a coordinated coalition of loosely autonomous processes responsible for goal-directedness in a system. On this view, even individual cognition has something of a social flavour to it. The central concept of the paper is stigmergy: a process where the material trace of actions of system elements in their environment is a sign that coordinates a group of semi-autonomous processes in future actions – this is the social dimension. The historical dimension refers to longer term processes which establish the coordinative power of the sign and endow it with normative force. According to this proposal, a full explanation of cognitive capabilities should reference both dimensions. In the second half of the paper the CSA is let loose on some puzzles in 4E cognition. Can the model deal with old problems such as that of cognitive bloat, or new problems such as the supposed external memory of the slime mould Physarum polycephalum? Potentially, the approach could be used to analyse minimal cognitive phenomena over a range of scales from bacteria to human beings
The Inferential-Connection Mediated (ICM) Model: Concept Reference and Evolution
Get PDFDespite decades of research in philosophy and cognitive science, the nature of concepts and the mechanisms underlying their change remain unresolved. Competing frameworks—externalist, inferentialist, embodied, and geometric—offer important insights but lack a unified account of how different types of concepts form, stabilize, and evolve. We propose a Systematic and Dynamic (SD) approach that examines mental content before and after concept formation, leading to the identification of inferential connections as ontologically distinct elements of conceptual architecture. Building on this foundation, we introduce the Inferential-Connection Mediated (ICM) model, which reconceptualizes concepts as dynamically structured entities composed of referential anchors—core subsets of inferential connections that fix reference—and broader networks that support reasoning, explanation, and communication. We distinguish among three types of inferential connections (observational, intentional, indirect) and classify four major concept types (theoretical, observational, subjective, and utilitarian), showing how differences in internal structure predict divergent developmental and evolutionary trajectories. The ICM model resolves long standing theoretical tensions—such as inferentialism vs. externalism, atomism vs. empiricism, and relativism vs. realism—by offering a unified, structurally grounded account of conceptual stability and change. We invite interdisciplinary commentary on the model’s implications for concept acquisition, reference, revision, and conceptual engineering across philosophy, cognitive science, linguistics, and artificial intelligence
Generalizing While Embracing Differences: Configurations of Representations and Cross- Fertilization
Get PDFHow do biologists pursue generalizations given the heterogeneity of biological systems? This paper addresses this question by examining an aspect of scientific generalization that has received little philosophical attention: how scientists express generalizations. Although it is commonly assumed that a scientific generalization takes the form of a representation referring to a property that is shared across a range of things, scientists sometimes express their ideas about generality by displaying multiple representations in certain configurations. Such configurations highlight commonalities between different target systems without eliminating system-specific differences. I analyze visual representations in review articles about collective cell migration as a case study. This illustrates that different types of visualizations, including single diagrams and configurations of multiple representations, function in a complementary way to promote understanding of, and reasoning about, generality, specificity, and diversity of biological mechanisms. I also discuss roles of generalizations in scientific investigations more broadly. I argue that an important role of generalizations in scientific research is to mediate and facilitate cross-fertilization among studies of different target systems. Multiple generalizations in research on collective cell migration together provide perspectives from which different biological systems are characterized and compared. They also provide heuristic hypotheses for studying less-explored systems as well as a basis for comparing developmental, pathological, and regenerative processes. This study sheds new light on how scientists pursue generalizations while embracing system-specific details. It also suggests that philosophical discussions should pay more attention to not only what representations scientists construct, but also how they present such representations
Applied Set Theory and Logic
Get PDFThis volume presents a comprehensive introduction to set theory and mathematical logic with a distinctive emphasis on practical application across disciplines such as computer science, electrical engineering, and database systems. Core logical operations—conjunction, disjunction, negation, implication—are defined and explored through real-world examples and truth-table analysis. Foundational theorems like the Law of the Excluded Middle, Non-Contradiction, and Modus Ponens are rigorously examined with formal proofs and applied exercises. The text extends into predicate calculus and advanced set-theoretic constructs, including the Von Neumann ordinal framework and modal logic, illuminating their significance in formal verification, algorithm design, and hardware analysis. Each chapter blends theoretical rigor with accessible explanations and problem-based learning to develop both conceptual understanding and practical reasoning skills. This makes the book an ideal resource for students and professionals seeking to bridge formal logic with computational and engineering domains
Resolution Matrix Semantics for Modal Logic: Philosophical Implications of Indeterminacy and Poly-Logic Thinking
Get PDFThis paper explores the philosophical implications of Resolution Matrix Semantics (RMS) as an alternative foundation for modal logic. Unlike traditional Kripkean models, which interpret modality through relations between multiple possible worlds governed by classical logic, RMS treats indeterminate truth values as fundamental, operating within a single world. RMS introduces "blinking" truth assignments and sub-interpretations to resolve uncertainty, capturing the inherently poly-logical nature of human thought. Drawing a parallel to quantum physics, we argue that Kripke models resemble Everett’s Many-Worlds interpretation, while RMS aligns with the Copenhagen interpretation’s emphasis on intrinsic uncertainty. RMS offers a new view of modal reasoning—not as a proliferation of worlds, but as a diversification of perspectives within one world. The framework’s philosophical significance is examined through connections to poly-logic thinking, quantum cognitive models, and potential applications in artificial intelligence and parallel computing. RMS ultimately provides a dynamic, pluralistic model for rationality that better reflects the complexity of human cognition and decision-making under uncertainty