Abstract
The aim of this paper is to address the question: when does a physical system realize (implement) a certain computation? The most developed account that answers this question is Piccinini’s mechanistic account. Our strategy is to start from Piccinini’s reflections, emphasizing different aspects of the problem of realization and thus proposing a novel account. Our idea is to propose a new definition of realization that makes the original question more tractable and easier to scrutinize. We show that our definition has some advantages when dealing with classical objections to accounts of computation in physical systems.
The paper is structured in four parts: after the introduction, the first part will introduce mapping accounts of implementation discussing some of their problematic aspects; the second part will present and clarify some prerequisite notions for a definition of realization; the third part will introduce our definition – it will turn out that our definition will identify a specific kind of strategy that Piccinini (2015a, b) calls nomological mapping account; the fourth and final part will be dedicated to analysing the advantages of our definition. Concluding remarks follow.
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Notes
- 1.
We intend the term “a physical system” as a sort of rigid designator, that is a physical system is a certain system without considering any of its characteristic. The theory through which we represent and explain the system sheds light on its peculiarities, but this theory is something that comes after a mere designation of the system. Therefore “physical systems” are not necessarily physical in the sense of physics.
- 2.
We rather talk about realization than implementation to make it clearer that the way we are dealing with the problem of computation in physical systems is different from the way computer scientists deal with the same problem. Our goal is to provide a philosophical analysis of the problem and changing the terminology might help in highlighting this gap of approach.
- 3.
From now on we will omit the term “implementation”.
- 4.
The reason for this choice is merely practical. When one evaluates a physical system, it is nearly impossible to be completely rigorous, specifying and keeping track of every possible interaction the system has with its environment and the effects such interactions bring with them. We therefore make use of a good practise from modern natural sciences, bringing the object of our investigation to a partially ideal situation that can find approximate concrete examples in the world. For the purpose of this paper, for example, it is true that, in the real world, physical systems might never be screened from gravitational effects. On the other hand, it is not hard to find situations in which gravity has a physical effect so small that is negligible, e.g. on the computations performed by a personal computer.
- 5.
Note that those characteristics could also be non-observable.
- 6.
We will explain in the following how to make time discrete.
- 7.
It should be remembered that classical mechanics is in principle deterministic, which is fundamental for the construction of the transition function.
- 8.
Even if the difference between “or” and “nor” is not so essential, since the latter is the dual of the former.
- 9.
We are improperly using here the term “state” (to be distinguished from the term “internal state”) because we wish to highlight the connection between the concepts of computational states of a Turing machine and of physical states. Our reasoning can easily be reformulated using the more familiar term “configuration”.
- 10.
Something very similar is maintained in Horsman et al. (2014). The latter’s approach is comparable to ours in the sense that it emphasizes the importance of the relation between computation and physical space. They express something very similar to what we will call condition 2 of our definition. Despite this, our feeling is that their approach, though interesting, is naïve when dealing with epistemological matters.
- 11.
Remember that bis are names that refer to physical states without any intervention of abstraction or modelling. They are somewhat indicators of physical systems as they appear at very specific times.
- 12.
It is not necessary that there are different quadruples for each couple skql.
- 13.
We think that it is advisable to start the reflection on the notion of realizability from Giunti’s (1997; especially par. 16) important study. Our approach is partially similar from a formal point of view, but it is conceptually different, since it involves the laws of physics.
- 14.
We know that measured time is discrete as well, since from a technological point of view there is always a minimal threshold of observability.
- 15.
In general, C will not be surjective, since not all the RTL space is used. Being C injective, the function will be invertible.
- 16.
This condition will be explained later.
- 17.
In this case L is what we have called in the first part a transition function. This transition function is given by our representation of the laws of nature.
- 18.
See Scheutz (1999). Discretization is based on a correspondence with discontinuity points in the state space of the physical system.
- 19.
We do understand that this point is problematic in our approach, especially if we do not specify C explicitly for a given system. We will explore this problem further in future works (Fig. 11.2).
- 20.
Considering this characteristic we could label our view as modal limited pancomputationalism.
- 21.
See also Horsman et al. (2014).
- 22.
This opens the door to the possibility of pancomputationalism. Soon we face this point.
- 23.
Using the words of Chalmers: “The ambitions of artificial intelligence rest on a related claim of computational sufficiency” (Chalmers 1996, p. 309), that is, “the right kind of computational structure suffices for the possession of a mind” (Chalmers 2011, p. 325). So, “computation will provide a powerful formalism for the replication and explanation of mentality” (Chalmers 1996, pp. 309–310). Hilary Putnam’s theorem says that “every ordinary open system is a realization of every abstract finite automaton” (Putnam 1988, p. 121), and its proof requires two physical principles; a principle of continuity, and the principle of Noncyclical behaviour (for more details see Putnam 1988, pp. 120–125). “Together with the thesis of computational sufficiency, this [theorem] would imply that a rock has a mind.” […] “We must either embrace an extreme form of panpsychism or reject the principle on which the hopes of artificial intelligence rest. Putnam himself takes the result to show that computational functionalism cannot provide a foundation for a theory of mind” (Chalmers 1996, pp. 309–310).
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Fano, V., Graziani, P., Tagliaferri, M., Tarozzi, G. (2019). Realizing Computations. In: Falkenburg, B., Schiemann, G. (eds) Mechanistic Explanations in Physics and Beyond. European Studies in Philosophy of Science, vol 11. Springer, Cham. https://doi.org/10.1007/978-3-030-10707-9_11
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