Abstract
In philosophical logic and metaphysics there is a long-standing debate around the most appropriate structures to represent indeterministic scenarios concerning the future. We reconstruct here such a debate in a computational setting, focusing on the fundamental difference between moment-based and history-based structures. Our presentation is centered around two versions of an indeterministic scenario in which a programmer wants a machine to perform a given task at some point after a specified time. One of the two versions includes an assumption about the future behaviour of the machine that cannot be encoded in any programming instruction; such version has models over history-based structures but no model over a moment-based structure. Therefore, our work adds a new stance to the debate: moment-based structures can be said to rule out certain indeterministic scenarios that are computationally unfeasible.
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Notes
However, it is worth noting that our belief that we can influence the future does not necessarily rely on an intuition of indeterminism; indeed, there is a recent debate in experimental philosophy concerning whether folk intuition can be regarded as compatibilist; to deepen this topic, see Lim and Chen (2017).
Some philosophers tend to reduce the open future debate to the question of human abilities. They take the claim that ‘the future is open’ to express the idea that ‘humans can affect what will happen’ (though, as we pointed out at the beginning, the latter is just one of the possible ways of expressing the former). Such a characterization of the open future debate is problematic. First it seems that if the future is open, then it was also open prior to the existence of any human agent. For example, it might be argued that, one hundred million years ago, it was open whether dinosaurs would disappear and humanity would emerge. Secondly, there is at least one sense in which the future may be said to be open that does not involve any agent: time could come to an end, with no ontological commitment to future things standing in the way (Correia and Rosenkranz 2018, p. 99). The question of the open future seems thus to exceed what humans may claim to have power on, and should therefore not be reduced to the question of our abilities.
See, for instance, the discussion in Lüthy and Palmerino (2016).
Notice that there are many problematic aspects of tree-like structures that will not be discussed in this paper. For example, tree-like structures might appear like a metaphysics in which it is perfectly settled how the future will be, but we just do not know where we will be in the future (cf. Rosenkranz 2013 and Cameron 2015). Moreover, tree-like structures seem to have difficulties in accounting for radical openness (i.e. the possibility that the world will not continue beyond a certain time) (cf. Cameron 2015), and for time-travel (cf. Miller 2005 and Norton 2018).
As observed by Belnap et al. (2001, p. 201), this is a matter of possibility, not of probability. Indeed, according to standard probability theory, the probability of an infinite sequence of tails in the machine scenario is zero.
In the case of P1, it is useful to observe that any moment \((n,i+1)\), with \(i=n\), is possible in the immediate future of a moment of kind \((\infty ,i)\) and p is true at \((n,i+1)\).
As already pointed out, this debate relies on a notion of possibility that is broader than the one arising from standard probability theory. Indeed, branching-time structures include, in general, infinite sequences of outcomes whose standard probability is zero.
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Acknowledgements
Vincent Grandjean was supported by two grants: (i) Swiss National Science Foundation Consolidator Grant The Metaphysics of Time and its Occupants (BSCGI0_157792); (ii) Bourse de la Société Académique de Genève (2020/52). Furthermore, he would like to thank the members of eidos, the Genevan centre for metaphysics. Matteo Pascucci was supported by a grant of the Action Austria-Slovakia for postdoctoral research (2019). Furthermore, he would like to thank the audience of various seminars held on related topics at Salzburg University, SAS and CEU.
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Grandjean, V., Pascucci, M. The Machine Scenario: A Computational Perspective on Alternative Representations of Indeterminism. Minds & Machines 31, 59–74 (2021). https://doi.org/10.1007/s11023-020-09530-x
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DOI: https://doi.org/10.1007/s11023-020-09530-x