According to Humean theories of objective chance, the chances reduce to patterns in the history of occurrent events, such as frequencies. According to non-Humean accounts, the chances are metaphysically fundamental, existing independently of the "Humean Mosaic" of actually-occurring events. It is therefore possible, by the lights of non-Humeanism, for the chances and the frequencies to diverge wildly. Humeans often allege that this undermines the ability of non-Humean accounts of chance to rationalize adherence to David Lewis' Principal Principle (PP), which states (...) that an agent's degrees of belief should match what they take to be the objective chances. In this paper, I propose two approaches to justifying (PP) for non-Humean chance, hence defusing the Humean objection. The first approach justifies (PP) via the role it plays in informing outright beliefs about long-run frequencies. The second approach justifies (PP) by showing that adherence to (PP), even for non-Humean chance, maximizes expected epistemic utility according to the actual objective chance function. I then address an objection to this approach, concerning the alleged circularity of the derivations. (shrink)

It is generally assumed that compatibility with special relativity is guaranteed by the invariance of the fundamental equations of quantum physics under Lorentz transformations and the impossibility of transferring energy or information faster than the speed of light. Despite this, various contradictions persist, which make us suspect the solidity of that compatibility. This paper focuses on collapse theories—although they are not the only way of interpreting quantum theory—in order to examine what seems to be insurmountable difficulties we encounter when trying (...) to construct a space–time picture of such typically quantum processes as state vector reduction or the non-separability of entangled systems. The inescapable nature of such difficulties suggests the need to go further in the search for new formulations that surpass our current conceptions of matter and space–time. (shrink)

We propose an interpretation of physics named potentiality realism. This view, which can be applied to classical as well as to quantum physics, regards potentialities (i.e. intrinsic, objective propensities for individual events to obtain) as elements of reality, thereby complementing the actual properties taken by physical variables. This allows one to naturally reconcile realism and fundamental indeterminism in any theoretical framework. We discuss our specific interpretation of propensities, that require them to depart from being probabilities at the formal level, though (...) allowing for statistics and the law of large numbers. This view helps reconcile classical and quantum physics by showing that most of the conceptual problems that are customarily taken to be unique issues of the latter -- such as the measurement problem -- are actually in common to all indeterministic physical theories. (shrink)

In order to solve a system of nonlinear rate equations one can try to use some soliton methods. The procedure involves three steps: find a ‘Lax representation’ where all the kinetic variables are combined into a single matrix \, all the kinetic constants are encoded in a matrix H; find a Darboux–Bäcklund dressing transformation for the Lax representation \]\), where f models a time-dependent environment; find a class of seed solutions \ that lead, via a nontrivial chain of dressings \ (...) to new solutions, difficult to find by other methods. The latter step is not a trivial one since a non-soliton method has to be employed to find an appropriate initial \. Procedures that lead to a correct \ have been discussed in the literature only for a limited class of H and f. Here, we develop a formalism that works for practically any H, and any explicitly time-dependent f. As a result, we are able to find exact solutions to a system of equations describing an arbitrary number of species interacting through catalytic feedbacks, with general time dependent parameters characterizing the nonlinearity. Explicit examples involve up to 42 interacting species. (shrink)

The paper introduces mathematical encoding for subjective experience and meaning in natural cognition. The code is based on a quantum-theoretic qubit structure supplementing classical bit with circular dimension, functioning as a process-causal template for representation of contexts relative to the basis decision. The qubit state space is demarcated in categories of emotional experience of animals and humans. Features of the resulting spherical map align with major theoreties in cognitive and emotion science, modeling of natural language, and semiotics, suggesting several generalizations (...) and improvements. The developed model bridges psychological, quantum-theoretic, and semiotic perspectives, allowing for an integrative account of subjectivity, agency, and meaning in living Nature.Graphical abstract. (shrink)

We present a derivation of the third postulate of relational quantum mechanics from the properties of conditional probabilities. The first two RQM postulates are based on the information that can be extracted from interaction of different systems, and the third postulate defines the properties of the probability function. Here we demonstrate that from a rigorous definition of the conditional probability for the possible outcomes of different measurements, the third postulate is unnecessary and the Born’s rule naturally emerges from the first (...) two postulates by applying the Gleason’s theorem. We demonstrate in addition that the probability function is uniquely defined for classical and quantum phenomena. The presence or not of interference terms is demonstrated to be related to the precise formulation of the conditional probability where distributive property on its arguments cannot be taken for granted. In the particular case of Young’s slits experiment, the two possible argument formulations correspond to the possibility or not to determine the particle passage through a particular path. (shrink)