Taking the lead from orthodox quantum theory, I will introduce a handy generalization of the Boolean approach to propositions and questions: the orthoalgebraic framework. I will demonstrate that this formalism relates to a formal theory of questions (or ‘observables’ in the physicist’s jargon). This theory allows formulating attitude questions, which normally are non-commuting, i.e., the ordering of the questions affects the answer behavior of attitude questions. Further, it allows the expression of conditional questions such as “If Mary reads the book, (...) will she recommend it to Peter?”, and thus gives the framework the semantic power of raising issues and being informative at the same time. In the case of commuting observables, there are close similarities between the orthoalgebraic approach to questions and the Jäger/Hulstijn approach to question semantics. However, there are also differences between the two approaches even in case of commuting observables. The main difference is that the Jäger/Hulstijn approach relates to a partition theory of questions whereas the orthoalgebraic approach relates to a ‘decorated’ partition theory (i.e. the elements of the partition are decorated by certain semantic values). Surprisingly, the orthoalgebraic approach is able to overcome most of the difficulties of the Jäger/Hulstijn approach. Furthermore, the general approach is suitable to describe the different types of (non-commutative) attitude questions as investigated in modern survey research. Concluding, I will suggest that an active dialogue between the traditional model-theoretic approaches to semantics and the orthoalgebraic paradigm is mandatory. (shrink)

The role of contingent contexts in formulating relations between properties of systems at different descriptive levels is addressed. Based on the distinction between necessary and sufficient conditions for interlevel relations, a comprehensive classification of such relations is proposed, providing a transparent conceptual framework for discussing particular versions of reduction, emergence, and supervenience. One of these versions, contextual emergence, is demonstrated using two physical examples: molecular structure and chirality, and thermal equilibrium and temperature. The concept of stability is emphasized as a (...) basic guiding principle of contextual property emergence. (shrink)

This paper aims to show that properties of cognitive/conceptual representations and formal‐logical structures of linguistic meaning can be inter‐translated, recast, transformed into one another, and so united together, even though cognitive/conceptual representations and formal‐logical structures of linguistic meaning are apparently distinct in ontology and divergent in their form or character. While cognitive/conceptual representations are ultimately rooted in sensory‐motor systems, formal‐logical structures of linguistic meaning are abstractions detached from and independent of the actualized world. This paper sketches out the foundations of (...) how representations of linguistic meaning in terms of cognitive/conceptual structures in Cognitive/Conceptual Semantics can be unified with those in terms of formal‐logical structures in Formal Semantics. This is done by recasting cognitive/conceptual representations in terms of formal‐logical structures of linguistic meaning and re‐encoding formal‐logical structures of linguistic meaning in terms of cognitive/conceptual representations. Then, these two types of semantic representations, thus shown representationally equivalent, will be related to a series of derivations across levels in neuronal networks and dynamics. The general discussion on unifying cognitive/conceptual representations of linguistic meaning with formal‐logical structures is contextualized within the broader context of theorizing in cognitive science. (shrink)

We consider several puzzles of bounded rationality. These include the Allais- and Ellsberg paradox, the disjunction effect, and related puzzles. We argue that the present account of quantum cognition—taking quantum probabilities rather than classical probabilities—can give a more systematic description of these puzzles than the alternate treatments in the traditional frameworks of bounded rationality. Unfortunately, the quantum probabilistic treatment does not always provide a deeper understanding and a true explanation of these puzzles. One reason is that quantum approaches introduce additional (...) parameters which possibly can be fitted to empirical data but which do not necessarily explain them. Hence, the phenomenological research has to be augmented by responding to deeper foundational issues. In this article, we make the general distinction between foundational and phenomenological research programs, explaining the foundational issue of quantum cognition from the perspective of operational realism. This framework is motivated by assuming partial Boolean algebras. They are combined into a uniform system via a mechanism preventing the simultaneous realization of perspectives. Gleason’s theorem then automatically leads to a distinction between probabilities that are defined by pure states and probabilities arising from the statistical mixture of pure states. This formal distinction relates to the conceptual distinction between risk and ignorance. Another outcome identifies quantum aspects in dynamic macro-systems using the framework of symbolic dynamics. Finally, we discuss several ideas that are useful for justifying complementarity in cognitive systems. (shrink)

Are minds really dynamical or are they really symbolic? Because minds are bundles of computations, and because computation is always a matter of interpretation of one system by another, minds are necessarily symbolic. Because minds, along with everything else in the universe, are physical, and insofar as the laws of physics are dynamical, minds are necessarily dynamical systems. Thus, the short answer to the opening question is “yes.” It makes sense to ask further whether some of the computations that constitute (...) a human mind are constrained by functional, algorithmic, or implementational factors to be essentially of the discrete symbolic variety (even if they supervene on an apparently continuous dynamical substrate). I suggest that here too the answer is “yes” and discuss the need for such discrete, symbolic cognitive computations in communication-related tasks. (shrink)