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The Method of Levels of Abstraction

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The use of “levels of abstraction” in philosophical analysis (levelism) has recently come under attack. In this paper, I argue that a refined version of epistemological levelism should be retained as a fundamental method, called the method of levels of abstraction. After a brief introduction, in section “Some Definitions and Preliminary Examples” the nature and applicability of the epistemological method of levels of abstraction is clarified. In section “A Classic Application of the Method of Abstraction”, the philosophical fruitfulness of the new method is shown by using Kant’s classic discussion of the “antinomies of pure reason” as an example. In section “The Philosophy of the Method of Abstraction”, the method is further specified and supported by distinguishing it from three other forms of “levelism”: (i) levels of organisation; (ii) levels of explanation and (iii) conceptual schemes. In that context, the problems of relativism and antirealism are also briefly addressed. The conclusion discusses some of the work that lies ahead, two potential limitations of the method and some results that have already been obtained by applying the method to some long-standing philosophical problems.

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  1. See for example Brown (1916). Of course the theory of ontological levels and the “chain of being” goes as far back as Plotin and forms the basis of at least one version of the ontological argument.

  2. The list includes Arbib (1989), Bechtel and Richardson (1993), Egyed and Medvidovic (2000), Gell-Mann (1994), Kelso (1995), Pylyshyn (1984), Salthe (1985).

  3. Poli (2001) provides a reconstruction of ontological levelism; more recently, Craver (2004) has analysed ontological levelism, especially in biology and cognitive science, see also Craver (forthcoming).

  4. The distinction is really a matter of topology rather than cardinality. However, this definition serves our present purposes.

  5. As the reader probably knows, this is done by recording the history of the game: move by move the state of each piece on the board is recorded—in English algebraic notation—by rank and file, the piece being moved and the consequences of the move.

  6. It is interesting to note that the catastrophes of chaos theory are not smooth; although they do appear so when extra observables are added, taking the behaviour into a smooth curve on a higher-dimensional manifold. Typically, chaotic models are weaker than traditional models, their observables merely reflecting average or long-term behaviour. The nature of the models is clarified by making explicit the LoA.

  7. The case of infinite sets has application to analogue systems but is not considered here.

  8. I wish to thank Jesse F. Hughes for having pointed out to me the last requirement, without which only the variables would be related but not the elements of their types.

  9. Direct knowledge is to be understood here as typically knowledge of one’s mental states, which is apparently not mediated; indirect knowledge is usually taken to be knowledge that is obtained inferentially or through some other form of mediated communication with the world.

  10. Newell reached similar conclusions, despite the fact that he treated LoA as LoO, an ontological form of levelism that allowed him to escape relativism and antirealism more easily, see Newell (1982, 1993).

  11. Feynman (1995), the citation is from the Penguin edition, p. 66.


  • Arbib, M. A. (1989). The metaphorical brain 2: Neural networks and beyond. New York, Chichester: Wiley.

    MATH  Google Scholar 

  • Barwise, J., & Etchemendy, J. (1987). The liar: An essay on truth and circularity. New York, Oxford: Oxford University Press.

    MATH  Google Scholar 

  • Bechtel, W., & Richardson, R. C. (1993). Discovering complexity: Decomposition and localization as strategies in scientific research. Princeton: Princeton University Press.

    Google Scholar 

  • Benjamin, P., Erraguntla, M., Delen, D., & Mayer, R. (1998). Simulation modeling and multiple levels of abstraction. In D. J. Medeiros, E. F. Watson, J. S. Carson, & M. S. Manivannan (Eds.), Proceedings of the 1998 Winter Simulation Conference (pp. 391–398). Pistacaway, New Jersey: IEEE Press.

  • Block, N. (1997). Anti-reductionism slaps back. In J. E. Tomberlin (Ed.), Philosophical perspectives 11: Mind, causation, and world (pp. 107–133). Oxford, New York: Blackwell.

    Google Scholar 

  • Brown, H. C. (1916). Structural levels in the scientist’s world. The Journal of Philosohy, Psychology and Scientific Methods, 13(13), 337–345. doi:10.2307/2012309.

    Article  Google Scholar 

  • Craver, C. F. (2004). A field guide to levels, Proceedings and Addresses of the American Philosophical Association, 77(3).

  • Craver, C. F. (forthcoming), Explaining the brain: A mechanist’s approach.

  • Davidson, D. (1974). On the very idea of a conceptual scheme. Proceedings and Addresses of the American Philosophical Association, 47. (Reprinted in Inquiries into Truth and Representation, pp. 183–198, 1984, Oxford: Clarendon Press. All page numbers to the quotations in the text refer to the reprinted version).

  • de Roever, W.-P., & Engelhardt, K. (1998). Data refinement: Model-oriented proof methods and their comparison. Cambridge: Cambridge University Press.

    MATH  Google Scholar 

  • Dennett, D. C. (1971). Intentional systems. The Journal of Philosophy, 68, 87–106. doi:10.2307/2025382.

    Article  Google Scholar 

  • Dennett, D. C. (1987). The intentional stance. Cambridge, MA, London: MIT Press.

    Google Scholar 

  • Egyed, A., & Medvidovic, N. (2000). A formal approach to heterogeneous software modeling. In T. Mailbaum (Ed.), Proceedings of the Third International Conference on the Fundamental Approaches to Software Engineering (Fase 2000, Berlin, Germany, March–April)—Lecture Notes in Computer Science, No. 1783. Berlin/Heidelberg: Springer-Verlag.

  • Feynman, R. P. (1995). Six easy pieces. Boston, MA: Addison-Wesley.

    Google Scholar 

  • Floridi, L. (2003). On the intrinsic value of information objects and the infosphere. Ethics and Information Technology, 4(4), 287–304. doi:10.1023/A:1021342422699.

    Article  Google Scholar 

  • Floridi, L. (2004a). Information. In L. Floridi (Ed.), The blackwell guide to the philosophy of computing and information (pp. 40–61). Oxford, New York: Blackwell.

    Chapter  Google Scholar 

  • Floridi, L. (2004b). The informational approach to structural realism. final draft available as IEG—Research Report 22.11.04,

  • Floridi, L. (2004c). On the logical unsolvability of the gettier problem. Synthese, 142(1), 61–79. doi:10.1023/B:SYNT.0000047709.27594.c4.

    Article  MATH  MathSciNet  Google Scholar 

  • Floridi, L. (2005a). Consciousness, agents and the knowledge game. Minds and Machines, 15(3–4), 415–444. doi:10.1007/s11023-005-9005-z.

    Article  Google Scholar 

  • Floridi, L. (2005b). Presence: From epistemic failure to successful observability. Presence: Teleoperators and Virtual Environments, 14(6), 656–667. doi:10.1162/105474605775196553.

    Article  Google Scholar 

  • Floridi, L. (forthcoming-a). Information ethics: Its nature and scope. In J. van den Hoven & J. Weckert (Eds.), Moral philosophy and information technology. Cambridge: Cambridge University Press.

  • Floridi, L. (forthcoming-b). Levels of abstraction: From computer science to philosophy, Journal of Applied Logic.

  • Floridi, L., & Sanders, J. W. (2004a). The method of abstraction. In M. Negrotti (Ed.), Yearbook of the artificial—nature, culture and technology, models in contemporary sciences (pp. 177–220). Bern: Peter Lang.

    Google Scholar 

  • Floridi, L., & Sanders, J. W. (2004b). On the morality of artificial agents. Minds and Machines, 14(3), 349–379. doi:10.1023/B:MIND.0000035461.63578.9d.

    Article  Google Scholar 

  • Foster, C. L. (1992). Algorithms, abstraction and implementation: Levels of detail in cognitive science. London: Academic Press.

    Google Scholar 

  • Gell-Mann, M. (1994). The quark and the jaguar: Adventures in the simple and the complex. London: Little Brown.

    MATH  Google Scholar 

  • Hales, S. D., & Welshon, R. (2000). Nietzsche’s perspectivism. Urbana: University of Illinois Press.

    Google Scholar 

  • Hayes, I., & Flinn, B. (1993). Specification case studies (2nd ed.). New York, London: Prentice Hall.

    MATH  Google Scholar 

  • Heil, J. (2003). Levels of reality. Ratio, 16(3), 205–221. doi:10.1111/1467-9329.00218.

    Article  Google Scholar 

  • Hoare, C. A. R., & He, J. (1998). Unifying theories of programming. London: Prentice Hall.

    Google Scholar 

  • Hughes, P., & Brecht, G. (1976). Vicious circles and infinity: A panoply of paradoxes. London: Cape. Originally published: Garden City, N.Y.: Doubleday, 1975.

  • Kant, I. (1998). Critique of pure reason repr. w. corr. (trans: Guyer, P., & Wood, A. W., Eds.). Cambridge: Cambridge University Press.

  • Kelso, J. A. S. (1995). Dynamic patterns: The self-organization of brain and behavior. Cambridge, MA, London: MIT Press.

    Google Scholar 

  • Marr, D. (1982). Vision: A computational investigation into the human representation and processing of visual information. San Francisco: W.H. Freeman.

    Google Scholar 

  • McClamrock, R. (1991). Marr’s three levels: A re-evaluation. Minds and Machines, 1, 185–196. doi:10.1007/BF00361036.

    Article  Google Scholar 

  • Mesarovic, M. D., Macko, D., & Takahara, Y. (1970). Theory of hierarchical, multilevel, systems. New York: Academic Press.

    MATH  Google Scholar 

  • Nagel, T. (1974). What is it like to be a bat? The Philosophical Review, 83(4), 435–450. doi:10.2307/2183914.

    Article  Google Scholar 

  • Newell, A. (1982). The knowledge level. Artificial Intelligence, 18, 87–127. doi:10.1016/0004-3702(82)90012-1.

    Article  Google Scholar 

  • Newell, A. (1990). Unified theories of cognition. Cambridge, MA, London: Harvard University Press.

    Google Scholar 

  • Newell, A. (1993). Reflections on the knowledge level. Artificial Intelligence, 59, 31–38. doi:10.1016/0004-3702(93)90166-9.

    Article  MathSciNet  Google Scholar 

  • Oppenheim, P., & Putnam, H. (1958). The unity of science as a working hypothesis. In H. Feigl, M. Scriven & G. Maxwell (Eds.), Minnesota studies in the philosophy of science. Concepts, theories, and the mind-body problem (Vol. 2, pp. 3–36). Minneapolis: University of Minnesota Press.

    Google Scholar 

  • Poli, R. (2001). The basic problem of the theory of levels of reality. Axiomathes, 12, 261–283. doi:10.1023/A:1015845217681.

    Article  Google Scholar 

  • Pylyshyn, Z. W. (1984). Computation and cognition: Toward a foundation for cognitive science. Cambridge, MA: MIT Press.

    Google Scholar 

  • Robinson, J. (1989). Vintage timecharts: The pedigree and performance of fine wines to the year 2000. London: Mitchell Beazley.

    Google Scholar 

  • Russell, B. (1902). Letter to Frege. In J. van Heijenoort (Ed.), From frege to gödel: A source book in mathematical logic, 1879–1931 (pp. 124–125). Harvard University Press: Cambridge, MA, 1967.

  • Salthe, S. N. (1985). Evolving hierarchical systems: Their structure and representation. New York: Columbia University Press.

    Google Scholar 

  • Schaffer, J. (2003). Is there a fundamental level? Nous, 37(3), 498–517. doi:10.1111/1468-0068.00448.

    Article  Google Scholar 

  • Simon, H. A. (1969). The sciences of the artificial, 1st ed. Cambridge, MA, London: MIT Press. (The text was based on the Karl Taylor Compton lectures, 1968).

  • Simon, H. A. (1996). The sciences of the artificial (3rd ed.). Cambridge, MA, London: MIT Press.

    Google Scholar 

  • Spivey, J. M. (1992). The Z notation: A reference manual (2nd ed.). New York, London: Prentice-Hall.

    Google Scholar 

  • Tarski, A. (1944). The semantic conception of truth and the foundations of semantics. Philosophy and phenomenological research, 4, (pp. 341–376). (Reprinted in Semantics and the Philosophy of Language, by L. Linsky, Ed., 1952, Urbana: University of Illinois Press).

  • Wimsatt, W. C. (1976). Reductionism, levels of organization and the mind-body problem. In G. Globus, G. Maxwell, & I. Savodnik (Eds.), Consciousness and the brain (pp. 199–267). New York: Plenum.

    Google Scholar 

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I wish to thank Jeff Sanders, who should really be considered a co-author of this paper, with the exception of any of its potential mistakes; Gian Maria Greco, Jesse F. Hughes, Gianluca Paronitti and Matteo Turilli for their discussions of several previous drafts; Paul Oldfield for his editorial suggestions; Carl Craver for having made his forthcoming research available to me; and finally the anonymous referees of the journal for their constructive feedback.

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Floridi, L. The Method of Levels of Abstraction. Minds & Machines 18, 303–329 (2008).

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