Abstract
In this paper we consider a claim that in the natural world there is no fact of the matter about the spatio-temporal separation of events. In order to make sense of such a notion and construct useful models of the world, it is proposed to use elements of a non-classical logic. Specifically, we focus here on causality, as a concept tightly related with the assumption of there being distinct, separate events, proposing a model according to which it can be considered to be spatio-temporally graded. It is outlined how this can be described using the formalism of fuzzy sets theory, with the degree of causality varying between 1, that is no separation between causes and effects, and 0, that is perfect separation between causes and their effects as in classical ’billiard balls’ models of physical systems, namely such based on the notion of ideal mathematical point. Our model posits that subjective moments of time are like fuzzy sets, with their extension determined by local degrees of causality, resulting from information integration processes extended gradually in space and time. This, we argue, is how a notion of causality could be, to a certain degree, spared and reconciled with a variant of Bergsonian duration theory as formulated in the theory of continuous change. Relation of the proposed viewpoint to other theories, as well as possible solutions it suggests to various problems, in particular the measurement problem, are also discussed.
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Notes
Note that ‘cause’, and so ‘causation’/‘causality’ as well, are said to be “truly obscure [concepts]” (see [1]). Here, by ‘cause’ (‘effect’) we will mean simply an event, that may potentially be a cause (effect) of another events. And by ‘event’ (from the lack of clear definition of which this “obscurity” in part stems), we will mean, when talking about phenomenal consciousness—a particular content of an experience, and when talking more generally about the world—a state of (a part of) the world at a time t [1].
Note on terminology: we will be using here the somewhat informal term ‘blob’, which, however, we see as a relatively accurate illustration of the idea (possibly reflecting our limited cognitive abilities, allowing us to think productively only in terms of space and time).
Not to be confused with a notion of graded causation as considered, for example, in [11], which posits that a causal relation between distinct events, say, C and E, can be taken to be graded, that is, that one could say that a causal link between C and E might have certain ‘weight’. Also in contrast, it takes a common-sensical, composite notion of events (for instance: “a lightning strike [event C] caused the forest fire [event E]”).
Different positions along the CC axis (or, dimension) represent blobs of different ‘size’, that is, CCs of different ‘rate’, slower or more ‘rapid’, respectively [6].
To be precise, instead of ‘subjective moment of time’ we should rather say of ‘subjective event’, as this is what is modeled (imperfectly) with the notion of a ‘blob’ extended in both time and space (with no clear-cut distinction into separate temporal or spatial continua). This would more accurately reflect the idea of CC being a general concept from which specific notions of time and space may potentially be derived, as discussed further on in the paper, and as such it would potentially cause less confusion. However, we nevertheless settled on using the term ‘subjective moment’, interchangeably with ‘event’, here and throughout the rest of the paper, and the main reason behind this decision is to be able to directly refer and compare our proposed viewpoint in this regard to others from the literature, pertaining in particular to phenomenology of time, where this temporal aspect is of primary interest. We hope that this note, as well as a specific Discussion on the notions of time and space and their possible relation with CC later on, will suffice to make reader aware of this salient point and recognize the particular contexts in which these terms are being used.
The convention of using symbol “1” to denote no causality might seem unintuitive, however, given the relation between causality (or lack thereof) and extension of events, as discussed in the text, denoting with 1 a lack of separation between events and ‘full’ membership to a set (that is, ‘belonging’ of certain ‘underlying’ events being integrated to the set representing a given subjective moment) feels arguably more natural than the alternative, that would be using 1 to denote a ‘perfect’ separation between events and no membership.
Nonetheless, we reserve the right to abstain from taking a definite position as to whether the effect of ‘blur’, graded nature, or ‘vagueness’, of separation between ‘events’, as discussed here, are of merely epistemological nature, or rather there is indeed no fact of the matter about their respective separatedness’es. We have been arguing here that not accepting the latter alternative would require considering the existence of a reality radically different from anything we have ever directly experienced. The main concern of the present paper, however, is simply to point at certain questionable assumptions and thus a potential inadequacy of existing conceptual frameworks, attributed specifically to the notion of ideal mathematical point on which they are based, and outline an alternative perspective, but not taking instead another definite metaphysical stance (a move that we think might be possible). Conceivably, one could also ask, accepting our CC viewpoint, is there still some another, underlying reality consisting of ideal mathematical point-like objects over which the ‘integration’ would ultimately occur? we consider this kind of question to be a truly meta-physical one, which, as such, goes beyond the intended scope and ambitions of this paper.
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Jura, B. Spatio-temporally Graded Causality: A Model. Found Phys 54, 22 (2024). https://doi.org/10.1007/s10701-024-00761-x
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DOI: https://doi.org/10.1007/s10701-024-00761-x