Abstract
Computational models fail to shed light on general metaphysical questions concerning the nature of emergence. At the same time, they may provide plausible explanations of particular cases of emergence. This paper outlines the kinds of modest explanations to which computational models are suited.
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The term ‘technological enhancement’ in this context is due to Humphreys (2004). There, Humphreys provides a detailed consideration of some of the epistemological implications of increasing reliance on computational modeling for science. Not all such enhancements simply leverage the computational power of machines. Some, for instance the automatic telescopes discussed by Humpreys (ibid 6) serve to overcome non-epistemic limitations such as fatigue or slow reaction times.
An emphasis on the role of models in scientific explanation has been one of the central characteristics of the semantic tradition in the philosophy of science (Suppes 1962; Van Fraassen 1980). According to the semantic view of scientific theories (esp. Suppe 1977; Van Fraassen 1980) scientific inquiry and explanation is largely a matter of the construction of models. The semantic view of theories emphasizes the abstract structure of theory rather than on the particular syntactic presentation of the theory (Van Fraassen 1972). While models are central to the semantic view of theories, when we consider specifically computational models, we encounter a layer of philosophical challenges of which philosophers in the semantic tradition in the philosophy of science were mostly unaware. In computational modeling, the question of application and implementation are unavoidable. While it is useful to consider theories as abstract structures, in the context of computational modeling as Humphreys points out: “(s)yntax matters… The importance of syntax to applications, and especially to computational tractability, is something that the semantic account of theories, for all its virtues, is essentially incapable of capturing.” (2002, p. S3)
Peter Cariani (1991) also emphasized the role of observers in a similar, though less formal manner, when describing what he calls ‘computational emergence’.
For the sake of simplicity, I will focus on the individuals-based models. However, it should be noted that many of the most interesting computational models are hybrid, rather than pure CA. So, for example Christina Warrender’s models of the peripheral immune system (2004) employ both an agent based and a particle-systems model. Cells involved in the earliest stages of infection are small in number and are not appropriately modeled by continuous representations. However, the number of molecules involved in an infection far outstrips the number of cells and so she models the molecular environment of cells as well as many of the components of each cell state as continuous variables.(2004, 17). While much of my argument will involve a comparison of CA and differential equation models, the argument for modesty can also be extended to the hybrid cases.
Cellular automata became especially well-known in the early 1970’s with the appearance of two articles by Martin Gardner in Scientific American devoted to the Game of Life.
For von Neumann’s thoughts on recursivity and self-replication see Burks A. W. (Ed.) (1970).
Following Holland’s explanation of the role of transition function (only slightly modified) we begin with some set of states S {s1, s2, s3, …} which is taken to be finite for the sake of computational tractability. A transition function takes as its argument some state of the system in combination with some input at a time and gives as a value a state of the system. For any input of type j there will be an associated set of possible input values Ij. Thus, Ij = {ij1, ij 2, ij 3, …}, where ij2 names state number 2 of the input j. Given k types of input for the system there will be k sets of possible input values {I1, I2, I3, …Ik}. The set of all combinations for the system is given as the product of the sets I1 × I2 × I3 … × Ik. Now, the transition function can be defined as f: (I1 × I2 × I3 … × Ik) × S → S and the temporal dynamic of the system can be defined as S(t+1) = f(I1(t), I2(t), I3(t), …Ik(t), S(t)). The iteration of f generates the state trajectory of the system.
I am very grateful to Paul Humphreys for his suggestions here.
For some discussion of the technical aspects involved in verification, validation and certification of computational models see Balci 2003.
If a functional property E is instantiated on a given occasion in virtue of one of its realizers, Q, being instantiated, then the causal powers of this instance of E are identical with the causal powers of this instance of Q.
Symons 2001 proposes a response to this argument against emergent properties.
Rueger points out that there is an objective reason, namely “The peculiar ‘singular limit’ relation between the micro and macro descriptions of the hole-and-peg system” that “the macro description seems to tell us ‘something different’ than the micro description, and why the former is not reducible to the latter in a way that would support a reductive explanation. In such singular limit cases, regular perturbation theoretic approaches to solving the problem break down, and the solutions provided by singular perturbation schemes automatically introduce different levels or scales into the problem, making it clear, for instance, how the macroscopic explanation considered by Putnam manages to bring out “certain relevant structural features of the situation” which are invisible in the micro description. Explanations based on such singular limit relations thus defy the very aim of reductive explanations, viz., to give an account at a single ‘basic’ level (2001, p. 504).
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Acknowledgments
I am very grateful for the assistance that I have had in writing this paper. Paul Humphreys, Clifford Hill and most especially Philippe Huneman have provided challenging and insightful critical comments on earlier versions of this paper. Participants in colloquia and talks at University College Dublin, the IHPST in Paris and the London School of Economics have raised many excellent points which were of great help in writing the paper.
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Symons, J. Computational Models of Emergent Properties. Minds & Machines 18, 475–491 (2008). https://doi.org/10.1007/s11023-008-9120-8
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DOI: https://doi.org/10.1007/s11023-008-9120-8