Abstract
This paper argues that the difference between contemporary software intensive scientific practice and more traditional nonsoftware intensive varieties results from the characteristically high conditionality of software. We explain why the path complexity of programs with high conditionality imposes limits on standard error correction techniques and why this matters. While it is possible, in general, to characterize the error distribution in inquiry that does not involve high conditionality, we cannot characterize the error distribution in inquiry that depends on software. Software intensive science presents distinctive error and uncertainty modalities that pose new challenges for the epistemology of science.
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Notes
 1.
See Symons 2008 for a discussion of how computational models have figured in discussions of the metaphysics and epistemology of science.
 2.
Software has begun to perform some of the functions that, in the presoftware era, were considered distinctively human aspects of science. For example, Michael Schmidt and Hod Lipson described how their program Eureqa inferred Newton’s second law and the law of conservation of momentum from descriptions of the behaviour of a doublependulum system (Schmidt and Lipson 2009). More recently, Eugene Loukine and colleagues demonstrated a model that was able to predict unforeseen sideeffects for pharmaceuticals that were already approved for consumption (Eugen 2012). These two papers represent very different examples of software intensive science: one is a system which is capable of generating theoretical insights and lawlike relationships from a data set, while the other makes dramatic progress on a specific practical question of great importance. Examples like these indicate that across a broad swath of scientific endeavor, from highly theoretical to applied science, inquiry itself is no longer purely a matter of individual or collective human effort. Across the sciences, softwareintensive systems are increasingly driving the direction of research and in some cases are already beginning to displace human researchers. Unlike previous improvements in scientific technology, computers not only extend our capacities, but are taking on at least some of the cognitive aspects of theoretical work in the sciences. Fundamental to understanding the character of posthuman science is careful attention to the nature of its distinctive kinds of error and uncertainty.
 3.
Of course, there are trivial counterexamples, such as the case of a program containing the same instruction repeatedly; say for example, the instruction “a = 2” repeated an arbitrary number of times. Such examples are not representative of typical or even useful software and they certainly have no role in scientific inquiry.
 4.
As we use the term here, a method is effective for a class of problems iff (Hunter 1971, pp. 13–15)

it consists of a finite number of exact, finite instructions

when applied to a problem from its class, it always finishes (terminates) after a finite number of steps

when applied to a problem from its class, it always produces a correct answer

 5.
A computer language is Turing complete if it can be simulated on a singletape Turing machine (Boolos et al. 2002). Being Turing complete is a condition of adequacy for being a generalpurpose computer language.
 6.
Here’s why: The equivalent of the “ifthen” schemata is realizable in a Turing machine (e.g., “notx or y” is representable in a Turing machine (Boolos et al. 2002), which is logically equivalent to “if x, then y”). Therefore, any Turing complete language must be able to simulate the “ifthenelse” schemata. How, specifically, one maps the Turingmachine equivalent of the “ifthen” schemata into a particular Turing complete language will in general depend on the particulars of the language of interest. For the purposes of this paper, we do not need to consider the precise details of those mappings: it is enough for our purposes that such mappings exist.
 7.
More precisely, the sample size required to attain a given confidence level is a function of the distribution of interest.
 8.
One can distinguish several kinds of testing in terms of properties of controlflow graphs (Nielson et al. 1999). By “testing every path” in a software system, we mean “executing, and analyzing the results of that execution of, all edges and all combinations of conditionedges in the controlgraph representation of the software system of interest.”
 9.
The pathtest cases for some software could be executed in parallel (Hennessy and Patterson 2007, p. 68); in theory, given a large enough parallel machine, all path tests in such a case could be executed in the same time it takes to execute one test case. But these are special cases. In general, we must consider cases in which we must execute the tests serially.
 10.
High path complexity is not the only aspect of SIS that has not received adequate attention to date by philosophers. As one anonymous referee for this paper points out, the high variability in the methods, algorithms, and language choices evident in SIS also has no counterpart in NSIS, leading to, among other things, fundamental questions of commensurability among different software systems that nominally concern the same subject matter. For example, there are at least 10 widely used numerical methods for solving systems of partial differential equations, and the results they produce are in general not identical (Morton and Mayers 2005). In addition, simply changing the computer language in which an algorithm is realized is not, for some pairs of languages such as Fortran 77 and C, even welldefined because the language standards do not provide an adequate basis for interlanguage translation of certain numerical types (ANSI 1977; ISO/IEC 2005; Feldman et al. 1990). Problems of this kind have led to serious errors whose origin is quite difficult to isolate in practice. (No such problems arise in NSIS.) All these issues clearly bear on the reliability of software and scientific inferences based on the use of software. These topics merit careful treatment in their own right. Here, however, we focus on the distinctively high conditionality of SIS.
 11.
For a derivation, see Hogg et al. 2005 (Sections 2.6 and 9.4).
 12.
An algorithm is an effective method expressed as a finite list of welldefined instructions for calculating a function (Boolos et al. 2002).
 13.
This does not imply, of course, that the software does not have the same error distribution as M: it merely means that we would not have a warrant to make the inference that the software has the error distribution of M, on the basis of the procedure.
 14.
The existence of a requirement for high confidence does not, as such, imply that this requirement is satisfied.
 15.
In some computer languages, this can be done by implicitly accepting the default specification. Socalled “interpreted” languages, which include many of the widely scripting languages in the UNIX family of operating environments, determine “type” only during execution. Type management in these contexts is obviously fragile.
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Acknowledgments
This work benefited from discussions with Sam Arbesman, George Crawford, Paul Humphreys, and Tony Pawlicki. We are grateful to the reviewers of earlier versions of this paper for extensive and insightful criticisms. For any errors that remain, we blame the path complexity of our (biological) software.
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Symons, J., Horner, J. Software Intensive Science. Philos. Technol. 27, 461–477 (2014). https://doi.org/10.1007/s133470140163x
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Keywords
 Models
 Simulations
 Software
 Epistemology
 Complexity
 Posthuman science