This paper investigates the correspondence between unactualized certainties, interpreted ontologically, and actualities. It does this first through the lens of a recently proposed enrichment of axiomatic probability which makes it possible to distinguish between actualities and unactualized possibilities, including those which are certain. Two kinds of unactualized certainties are considered: those due to the sample space being a singleton, and those involving a sample space with more than one element. After comparing standard axiomatic probability with the enrichment in regards to how they represent the distinction, attention is then focused on quantum mechanics. There, the correspondence will be examined through the lens of a recently proposed modification of the standard formalism, the Heisenberg Interpretation which, unlike the standard quantum formalism but like the enrichment of probability, also permits distinctions between unactualized possibilities and actualities. Two situations are found to exemplify the correspondence there: one involving partially measured entangled systems and the other involving the Born rule. Finally, it will be shown how the correspondence clarifies the very concept of an unactualized possibility.
This paper investigates the correspondence between unactualized certainties, interpreted ontologically, and actualities. It does this first through the lens of a recently proposed enrichment of axiomatic probability which makes it possible to distinguish between actualities and unactualized possibilities, including those which are certain. Two kinds of unactualized certainties are considered: those due to the sample space being a singleton, and those involving a sample space with more than one element. After comparing standard axiomatic probability with the enrichment in regards to how they represent the distinction, attention is then focused on quantum mechanics. There, the correspondence will be examined through the lens of a recently proposed modification of the standard formalism, the Heisenberg Interpretation which, unlike the standard quantum formalism but like the enrichment of probability, also permits distinctions between unactualized possibilities and actualities. Two situations are found to exemplify the correspondence there: one involving partially measured entangled systems and the other involving the Born rule. Finally, it will be shown how the correspondence clarifies the very concept of an unactualized possibility.
In his book `Physics and Philosophy', Heisenberg suggested that the quantum world is one of ``potentialities or possibilities'' and that the classical realm is one of ``things or facts''. After ascertaining that his categories most naturally have the structure of ontological equivalence classes, we show that they cannot be seriously introduced into the quantum formalism without rendering it incoherent, as under some circumstances the formalism permits an equality between members of distinct equivalence classes. This is labeled the `equality of inequivalents problem'. Three possible reactions are discussed: First, one could deny the problem by challenging some of the assumptions that underlie its formulation; second, one could accept the problem and take it to be grounds for dismissing Heisenberg's or similar distinctions altogether; third, one could accept the problem but take its source to be not Heisenberg's distinction but the quantum formalism. A plausibility argument in support of the third reaction is given by analogy: it is shown that axiomatic probability suffers from a similar problem if one wishes to seriously distinguish between things which are possibilities and things which are not. An enriched axiomatization of probability is proposed which captures the concept of probability as a measure over possibilities and thereby overcomes the equality of inequivalents problem in axiomatic probability.
As we saw in the previous chapter, the Everett interpretation seems to dispense with probabilities in quantum mechanics. Instead of describing a world for which many things are possible, but only some of those possibilities are actualised, it suggests a world in which all possibilities actually happen . Moreover, this is something of which we can be absolutely certain . Obviously, this does not straightforwardly fit our experience. We do not see multiple possibilities becoming actual. Whenever we measure a superposed particle, we observe only one property or another. Moreover, we have a very useful probabilistic rule to help us to predict what we will see. How can the success of this probabilistic rule be explained, if an Everett world does not involve any uncertainty? There are two main moves that are employed in response to this challenge. The first – what I call Stage A – is to show that there is a relevant sort of uncertainty, even in a universe where we are certain that everything will happen. The second move – Stage B – is to try to vindicate the probability of the Born rule in particular. That is, to show that we should not merely be uncertain about the future, but that we have good reason to attach the particular probabilities dictated by the Born rule to the possible outcomes of a quantum experiment. We will consider these two stages in turn.
Abstract This paper develops a metaphysical interpretation of quantum probability under the title Distributed Presence (DP). The central claim is that quantum probabilities should not be understood as measures of ignorance, nor merely as formal devices for predicting measurement outcomes, but as expressions of an objective mode of being: a system’s structured distribution of presence across mutually available channels of realization. On this view, a quantum system prior to measurement is neither fully actual in one determinate outcome nor reducible to a set of hidden definite properties. Rather, it exists in a non-binary mode, articulated by normalized presence fractions associated with the possible outcomes defined by a given interaction context. The Born rule is accordingly not replaced, but reinterpreted: the standard probability assignment is read as the operational expression of an underlying ontological distribution. The paper argues that this framework provides a unified reading of several familiar quantum features. Superposition is understood as a real distribution of presence rather than as epistemic indeterminacy; measurement is interpreted as single-channel actualization rather than as the physical destruction of alternatives; wave-particle duality is recast as the relation between distributed structure and localized realization; and quantum randomness is treated as intrinsic yet structurally constrained. The proposal remains fully compatible with the standard Hilbert-space formalism and introduces no hidden variables, additional collapse dynamics, or many-world branching. Its aim is interpretive rather than revisionary. Beyond its relevance to the foundations of quantum theory, DP is advanced as a contribution to the ontology of probability more broadly. It seeks to show how probability may be objective, physically meaningful, and ontologically basic without collapsing into determinism on the one hand or epistemicism on the other. In that sense, the paper offers a realist, single-world, structurally articulated account of quantum chance.
Classical and quantum physics are standardly contrasted through continuity versus discreteness, determinism versus probability, and definite properties versus measurement-dependent outcomes. This paper argues that beneath these real differences lies a deeper philosophical convergence: both theories rely on mathematical spaces of possibility that must not be confused with reality itself. Classical mechanics describes continuous ranges of possible trajectories, yet actualizes only one constrained path under given causes and conditions. Quantum mechanics describes structured possibilities through states, operators, eigenstates, and eigenvalues, yet these are not realities existing in advance but formal expressions of what may become definite under a physical context of measurement. The paper makes three contributions. First, it develops the concept of constrained actualization as a single modal grammar spanning both theories: reality is neither the free unfolding of all possibilities nor the mere execution of mathematics, but the actualization of what constraints permit. Second, it constructs an eigenvalue bridge from macroscopic to quantum systems: strings, membranes, and engineered structures exhibit constrained eigenmodes, and the decisive difference is that classical eigenmodes reveal the constrained forms of motion, while quantum eigenstates reveal the constrained forms of definite physical answer. Third, it situates the model against Heisenbergian potentia realism, propensity interpretations, dispositionalist metaphysics, and structural realism, showing it to be ontologically more minimal, relational rather than property-based, situational rather than essentialist, and event-preserving, while its compatibility with decoherence and its support from the Kochen–Specker theorem are made explicit. Quantum mechanics, on this account, radicalizes an insight classical mechanics conceals: constraint operates within the very structure of possible outcomes.
There are currently several versions of Everett's relative state interpretation of quantum mechanics, responding to a number of perceived problems for the original proposal. One of those problems is whether Everett's idea is in accord with the standard 'probabilistic' interpretation implicit in the Born rule. I argue in defence of what appears to be Everett's original view on this. The contribution I aim to make is a more complete discussion of the central issues of the identity of objects and observers over time and how the concept of expectation can be applied when all 'possible' outcomes of a measurement process are regarded as actually occurring.
Born's rule is the recipe for calculating probabilities from quantum mechanical amplitudes. There is no generally accepted derivation of Born's rule from first principles. In this paper, it is motivated from assumptions that link the ontological content of a proper physical model to the epistemic conditions of the experimental context. More precisely, it is assumed that all knowable distinctions should correspond to distinctions in a proper model. This principle of "ontological completeness" means, for example, that the probabilistic treatment of the double slit experiment with and without path information should differ. Further, it is assumed that the model should rely only on knowable ontological elements, and that failure to fulfill this principle of "ontological minimalism" gives rise to wrong predictions. Consequently, probabilities should be assigned only to observable experimental outcomes. Also, the method to calculate such probabilities should not rely on the existence of a precise path of the observed object if this path is not knowable. A similar principle was promoted by Born, even though he did not apply it to probability. Another crucial assumption is that the proper rule to calculate probabilities should be generally valid. It should be applicable in all experimental contexts, regardless the setup that determines which attributes of the studied object are observed, together with the probability to observe each of the associated attribute values. There is no need to refer to the Hilbert space structure of quantum mechanics in the present treatment. Rather, some elements of this structure emerge from the analysis.