Three Paradigms of Computer Science

Abstract

We examine the philosophical disputes among computer scientists concerning methodological, ontological, and epistemological questions: Is computer science a branch of mathematics, an engineering discipline, or a natural science? Should knowledge about the behaviour of programs proceed deductively or empirically? Are computer programs on a par with mathematical objects, with mere data, or with mental processes? We conclude that distinct positions taken in regard to these questions emanate from distinct sets of received beliefs or paradigms within the discipline:

  • The rationalist paradigm, which was common among theoretical computer scientists, defines computer science as a branch of mathematics, treats programs on a par with mathematical objects, and seeks certain, a priori knowledge about their ‘correctness’ by means of deductive reasoning.

  • The technocratic paradigm, promulgated mainly by software engineers and has come to dominate much of the discipline, defines computer science as an engineering discipline, treats programs as mere data, and seeks probable, a posteriori knowledge about their reliability empirically using testing suites.

  • The scientific paradigm, prevalent in the branches of artificial intelligence, defines computer science as a natural (empirical) science, takes programs to be entities on a par with mental processes, and seeks a priori and a posteriori knowledge about them by combining formal deduction and scientific experimentation.

We demonstrate evidence corroborating the tenets of the scientific paradigm, in particular the claim that program-processes are on a par with mental processes. We conclude with a discussion in the influence that the technocratic paradigm has been having over computer science.

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Notes

  1. 1.

    To which Wegner also refers as ‘cultures’ or ‘disciplines’ interchangeably.

  2. 2.

    The “Denning report” (Denning et al. 1989) authored by the task force which was commissioned to investigate “the core of computer science” also lists three “paradigms” of the discipline: theory/mathematics, abstraction/science, and design/engineering. According to this report, these paradigms are “cultural styles by which we approach our work”. They conclude however that “in computing the three processes are so intricately intertwined that it is irrational to say that any one is fundamental”.

  3. 3.

    For example, the statement ‘programs are abstract’ shall be taken to assert that ‘program-scripts and program-processes are abstract’.

  4. 4.

    Also known as machine code or object code.

  5. 5.

    The program adds 3 to the product of two numbers, encoded in the 8086 microprocessor assembly language (Adapted from Georick et al. 1997).

  6. 6.

    For example, consider the difficulty of spotting and correcting errors in the program in Table 1.

  7. 7.

    The program adds 3 to the product of two numbers, encoded here in the syntax of Scheme (Abelson and Sussman 1996), a dialect of Lisp

  8. 8.

    A statement most widely attributed to Dijkstra.

  9. 9.

    We follow Colburn (2000) in taking a priori knowledge about a program to be knowledge that is prior to experience with it, namely knowledge emanating from analyzing the program-script, and a posteriori knowledge to be knowledge following from experience with observed phenomena, namely knowledge concerning a given set of specific program-processes generated from a given script.

  10. 10.

    Delivered, according to Mahoney (2002), in 1985 during his Inaugural Lecture as Professor of Computation at Oxford.

  11. 11.

    Which were later accompanied by algorithms and abstract state machines.

  12. 12.

    Dijkstra (1988) offered an explanationto how this ‘fact’ escaped mathematicians and programmers alike: “Programs were so much longer formulae than [mathematics] was used to that [many] did not even recognize them as such.

  13. 13.

    Bill Rapaport (2007) notes that such a position has interesting consequences on the question whether programs can be copyrighted or patented.

  14. 14.

    \({\mathbf{tech\cdot noc\cdot ra\cdot cy}}\,\, n.\) A government or social system controlled by technicians, especially scientists and technical experts. (The American Heritage® Dictionary of the English Language: Fourth Ed., 2000.)

  15. 15.

    These events have led to the seminal NATO conference held in the fall of 1968 (Naur and Randell 1969) concerning the trouble that the software industry had been experiencing in producing reliable computing systems. In the introduction to the conference’s report, Robert McClure (2001) argues that although the term ‘software engineering’ was not in general use at that time, its adoption for the titles of these conferences was deliberately provocative and played a major role in gaining general acceptance for the term.

  16. 16.

    At most, lip-service is paid to the role of verification in ‘safety-critical software systems’.

  17. 17.

    For example, the Debian GNU/Linux 3.1 version of the Linux operating system (Debian 2007) is the product of contributions made by thousands of individuals that are entirely unrelated except in their attempt to improve it.

  18. 18.

    One petabyte (1PB) is 1,024 terabytes or 250 bytes.

  19. 19.

    We ignore, for the moment, difficulties arising from concurrency and the possibility of suspending the execution of program-processes.

  20. 20.

    That is, the computational process by the central processing unit depends on the consumption of energy; if suspended, program-processes cease to exist.

  21. 21.

    Turing forecast named the year 2000 as a target. During that year, Jim Moor conducted an experiment which refuted Turing’s prediction, but he hastens to add: “Of course, eventually, 50 years from now or 500 years from now, an unrestricted Turing test might be passed routinely by some computers. If so, our jobs as philosophers would just be beginning”. (Moor 2000)

  22. 22.

    Hoare (2006) has recently conceded that “Because of its effective combination of pure knowledge and applied invention, Computer Science can reasonably be classified as a branch of Engineering Science.”

  23. 23.

    To which Bertrand Meyer (1997) satirical critique offers valuable insights.

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Acknowledgements

Special thanks go to Ray Turner for reviewing draft arguments and for his guidance and continuous support, without which this paper would not have been possible; to Jack Copeland for his guidance on matters of traditional philosophy; and to Bill Rapaport for his detailed comments. We also thank Tim Colburn (2000) and Bill Rapaport (2005) without whose extensive contributions the nascent discipline of philosophy of computer science would not exist; Barry Smith for his guidance; Susan Stuart for developing the contentions made of this paper; Naomi Draaijer for her support; Yehuda Elkana, Saul Eden-Draaijer, and Mary J. Anna for their inspiration. This research was supported in part by grants from UK’s Engineering and Physical Sciences Research Council and the Royal Academy of Engineering.

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Correspondence to Amnon H. Eden.

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Eden, A.H. Three Paradigms of Computer Science. Minds & Machines 17, 135–167 (2007). https://doi.org/10.1007/s11023-007-9060-8

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Keywords

  • Philosophy of computer science
  • Ontology and epistemology of computer programs
  • Scientific paradigms