Completing bases in four dimensions

Criteria for the completion of an incomplete basis of, or context in, a four-dimensional Hilbert space by (in)decomposable vectors are given. This, in particular, has consequences for the task of ``completing'' one or more bases or contexts of a (hyper)graph: find a complete faithful orthogonal representation (aka coordinatization) of a hypergraph when only a coordinatization of the intertwining observables is known. In general indecomposability and thus physical entanglement and the encoding of relational properties by quantum states ``prevails'' and occurs more often than separability associated with well defined individual, separable states.

Mutability and Relationality: Towards an African Four-Dimensionalist Pan-Psychism

This article challenges a certain Theist conception of God as immutable. I argue that the idea that God is immutable can be challenged on the grounds of its metaphysical groundwork. More precisely, I contend that the idea that God is immutable entails endurantism, which I demonstrate to be mistaken. This view cannot be right because it potentially involves three absurd implications: (a) a violation of the principle of the Indiscernibility of Identicals (b) the idea that God becomes a different God with any change that occurs (c) the view that only the present is real and there is no future and past. As these solutions are absurd, the endurantist view ought to be abandoned. I then suggest an alternative theory that does not meet the same problems, which I call African four-dimensionalist Pan-Psychism. This theory I advance maintains that God is the sum of His spatial and temporal parts, is mutable and has relational properties (e.g., He changes with the occurrence of evil or good in the world). I uphold that this view does not have the absurd implications of its competitors.

Intersectionality at the Macro Level: Social Theory as Practice (Chapter prepared for Routledge Handbook of Intersectionality, Kathy Davis and Helma Lutz, editors).

The macro-level of society consists of the relationships among its institutional structures and how such patterned relations change in systematic ways over time. Considering intersectionality at this level implies asking how global systems that produce inequality operate together. The challenge for macro-level thinking about intersectionality is to resist the long history of treating capitalism, class relations and the global economy as the most fundamental set of global relations. Intersectional theorizing at this level combines analysis of the emergent and relational properties of inequality-producing systems with an equally critical attitude to all of these structural inequalities. However, in contrast to top-down theorizing about abstract systems, intersectional macro-theorizing incorporates a focus on experience that enlarges the meaning of developing critique. This chapter situates the development of intersectional theory at the macro-level and highlights its contributions.

Recent Advances in Heterogeneous Relation Learning for Recommendation

Recommender systems have played a critical role in many web applications to meet user's personalized interests and alleviate the information overload. In this survey, we review the development of recommendation frameworks with the focus on heterogeneous relational learning, which consists of different types of dependencies among users and items. The objective of this task is to map heterogeneous relational data into latent representation space, such that the structural and relational properties from both user and item domain can be well preserved. To address this problem, recent research developments can fall into three major categories: social recommendation, knowledge graph-enhanced recommender system, and multi-behavior recommendation. We discuss the learning approaches in each category, such as matrix factorization, attention mechanism and graph neural networks, for effectively distilling heterogeneous contextual information. Finally, we present exploratory outlook to highlight several promising directions and opportunities in heterogeneous relational learning frameworks for recommendation.

The Case against Powers

Walter Ott argues that there is a central, underlying metaphysical worry that animated early modern thinking against causal powers that is still unresolved. He emphasizes that there is a spectre of power holism embedded in the Aristotelian’s commitment to intrinsicality. Ott sees this as the worry expressed in Descartes’s ‘little souls’ argument against powers, which he sees as an important precursor to Neil Williams’s recent ‘problem of fit’ objection to neo-Aristotelian causal powers. And it is this ‘problem of fit’ that highlights the connection between intrinsicality and powers holism. According to Ott, however, the lesson to take from the ‘problem of fit’ is not that Humeanism is the proper position. He suggests instead that we return to a mitigate powers ontology like that found in Boyle and Locke. The idea here is that powers are really relational properties that cannot be reduced to any one of their relata; they simply ‘are internal relations among the intrinsic properties of things’.

A language for qualia: on verbal influence of the phenomenal

Despite several decades of intense scrutiny, the problem of the “explanatory gap” remains one of the most topical issues in today’s cognitive sciences. This paper argues that, if re-articulated as the (relative) ineffability of phenomenal properties of sensory experiences, it can become an object of linguistic treatment to a sensible effect. The paper proceeds from discussing the problem of ineffability at large to a brief analysis of the current accounts of phenomenal mental states. It then proposes a tentative descriptive framework for phenomenal judgments, i.e. statements involving reference to the speaker’s qualia. The main argument of the paper consists in relativization of the ineffability thesis and in establishing that phenomenal contents can be communicated verbally via a special type of discursive units––phenomemes––by way of referencing relational properties of the sensory experiences in question. In the concluding section, the paper suggests that phenomemes constitute a narrative dimension and highlights the potential of further research on the subject for the pragmatics of communication, cognitive stylistics, and other areas of the language-related scholarship.

A language for qualia: on verbal influence of the phenomenal

Despite several decades of intense scrutiny, the problem of the “explanatory gap” remains one of the most topical issues in today’s cognitive sciences. This paper argues that, if re-articulated as the (relative) ineffability of phenomenal properties of sensory experiences, it can become an object of linguistic treatment to a sensible effect. The paper proceeds from discussing the problem of ineffability at large to a brief analysis of the current accounts of phenomenal mental states. It then proposes a tentative descriptive framework for phenomenal judgments, i.e. statements involving reference to the speaker’s qualia. The main argument of the paper consists in relativization of the ineffability thesis and in establishing that phenomenal contents can be communicated verbally via a special type of discursive units––phenomemes––by way of referencing relational properties of the sensory experiences in question. In the concluding section, the paper suggests that phenomemes constitute a narrative dimension and highlights the potential of further research on the subject for the pragmatics of communication, cognitive stylistics, and other areas of the language-related scholarship.

Response to Christopher Peacocke: Perception

Aestheticians set out principled ways of thinking about music, but usually at the expense of the inclusive approach demanded by today’s pluralistic musical culture. In this response I welcome the openness of Peacocke’s approach, suggesting some relational properties of music additional to those he discusses: the “topics” of eighteenth-century music, which condense metaphorical “hearing-as” into historical stereotypes; performance style, which always involves reference to or play with other styles; the constructions of social relationship that music affords, whether real or imagined; and history, which raises the issue of the relationship between aesthetics and the historical other. When Peacocke, like other aestheticians, says “we hear structure”, who are “we”? And who does “we” exclude? If we define music as “ours” in relation to historical or cultural others, can there actually be an aesthetics that is both principled and inclusive?

Perception

This chapter argues that the perception of music involves more than the syntactic and other relations recognized in most music theory. More precisely, the perception of music involves hearing features of the music metaphorically-as mental states and other states of affairs. It also involves hearing the musical event as an action. There are many examples of the aesthetic exploitation by composers of the capacity for perception of various relational properties of these general kinds. There are also differences and similarities between music and poetry, for which there is an account in the presented framework. The account also explains the possibility of music communicating new and unnamed emotions. The perception of relational properties is equally crucial in articulating the distinctive features of live performance. Music also contrasts with other art forms, in that the perception of relational properties, unlike literature, depiction or dance, is almost the only resource available to the composer. This makes the perception of relational properties of music uniquely significant for this art form.

On the Classification Between $$\psi$$-Ontic and $$\psi$$-Epistemic Ontological Models

Harrigan and Spekkens (Found Phys 40:125–157, 2010) provided a categorization of quantum ontological models classifying them as $$\psi$$ ψ -ontic or $$\psi$$ ψ -epistemic if the quantum state $$\psi$$ ψ describes respectively either a physical reality or mere observers’ knowledge. Moreover, they claimed that Einstein—who was a supporter of the statistical interpretation of quantum mechanics—endorsed an epistemic view of $$\psi .$$ ψ . In this essay we critically assess such a classification and some of its consequences by proposing a twofold argumentation. Firstly, we show that Harrigan and Spekkens’ categorization implicitly assumes that a complete description of a quantum system (its ontic state, $$\lambda$$ λ ) only concerns single, individual systems instantiating absolute, intrinsic properties. Secondly, we argue that such assumptions conflict with some current interpretations of quantum mechanics, which employ different ontic states as a complete description of quantum systems. In particular, we will show that, since in the statistical interpretation ontic states describe ensembles rather than individuals, such a view cannot be considered $$\psi$$ ψ -epistemic. As a consequence, the authors misinterpreted Einstein’s view concerning the nature of the quantum state. Next, we will focus on relational quantum mechanics and perspectival quantum mechanics, which in virtue of their relational and perspectival metaphysics employ ontic states $$\lambda$$ λ dealing with relational properties. We conclude that Harrigan and Spekkens’ categorization is too narrow and entails an inadequate classification of the mentioned interpretations of quantum theory. Hence, any satisfactory classification of quantum ontological models ought to take into account the variations of $$\lambda$$ λ across different interpretations of quantum mechanics.