Studying Controversies: Unification, Contradiction, Integration

  • Stefan Petkov


My aim here is to show that approximate truth as a paraconsistent notion (neutral to the realism/anti-realism debate) can be successfully incorporated into the analysis of scientific unification, thus advancing towards a more realistic representation of theory development that takes into account the controversies that often loom alongside the progress of research programmes. I support my analysis with a case study of the recent debate in ecology centred around the existence of the paradox of enrichment and the controversy between ecological models of predation that employ prey-dependent and ratio-dependent functional responses. These models were initially proposed as equally good representations of the basic aspects of predator–prey dynamics. However, both models generated inconsistent observational consequences and, therefore, introduced a contradiction within predator–prey theory. I argue that by accepting these models as approximately true representations of predator–prey dynamics we can convey how the available observational data have been successfully systematized in a consistent way under them. This first step in resolving the controversy relied on building a series of contrastive arguments based on both models’ derivations about population dynamics and the available empirical data. The heightening of this contrast between the models, in turn, was also essential in defining a limiting function which can be used to integrate both models and reach a new unified expression of predator–prey dynamics.


Unification Contradictions Approximate truth Predator–prey models 


  1. Abrams, P. A. (1994). The fallacies of ratio-dependent predation. Ecology, 75, 1842–1850.CrossRefGoogle Scholar
  2. Abrams, P. A. (2014). Why ratio dependence is (still) a bad model of predation. Biological Reviews, 90, 794–814.CrossRefGoogle Scholar
  3. Abrams, P. A. (2015). Why ratio dependence is (still) a bad model of predation. Biological Reviews Cambridge Philosophy of Society, 90, 794–814.CrossRefGoogle Scholar
  4. Abrams, P. A., & Ginzburg, L. (2000). The nature of predation: Prey-dependent, ratio-dependent or neither? Trends in Ecology and Evolution, 15, 337–341.CrossRefGoogle Scholar
  5. Arditi, R., & Akcakaya, H. R. (1990). Underestimation of mutual interference of predators. Oecologia, 83, 358–361.CrossRefGoogle Scholar
  6. Arditi, R., & Ginzburg, L. (1989). Coupling in predator–prey dynamics: Ratio-dependence. Journal of Theoretical Biology, 139(3), 311–326.CrossRefGoogle Scholar
  7. Arditi, R., & Ginzburg, L. (2012). How species interact: Altering the standard view on trophic ecology. New York: Oxford University Press.CrossRefGoogle Scholar
  8. Bangu, S. (2016). Scientific explanation and understanding: Unificationism reconsidered. European Journal for Philosophy of Science. Scholar
  9. Barraquand, F. (2014). Functional responses and predator–prey models: A critique of ratio dependence. Theoretical Ecology, 7, 3–20.CrossRefGoogle Scholar
  10. Bartelborth, T. (2002). Explanatory unification. Synthese, 130, 91–107.CrossRefGoogle Scholar
  11. Beddington, J. (1975). Mutual interference between parasites or predators and its effect on searching efficiency. Journal of Animal Ecology, 44, 331–340.CrossRefGoogle Scholar
  12. Benham, R., Mortensen, C., & Priest, G. (2014). Chunk and permeate III: The Dirac delta function. Synthese, 191, 3057–3062.CrossRefGoogle Scholar
  13. Brauer, F., & Castillo-Chavez, C. (2012). Mathematical models in population biology and epidemiology (Vol. 2). New York: Springer.CrossRefGoogle Scholar
  14. Brown, B. (2002). Approximate truth: A paraconsistent account. In J. Meheus (Ed.), Inconsistency in science (pp. 81–103). Dordrecht: Kluwer Academic Publishers.CrossRefGoogle Scholar
  15. Brown, B. (2013). Consequence as preservation: Some refinements. In F. Berto, E. Mares, K. Tanaka, & F. Paoli (Eds.), Paraconsistency: Logic and applications (pp. 123–139). Springer.Google Scholar
  16. Brown, B. (2015). Peter Vickers: Understanding inconsistent science (book review). Journal for General Philosophy of Science, 46(2), 413–418.CrossRefGoogle Scholar
  17. Brown, B., & Priest, G. (2004). Chunk and permeate: A paraconsistent inference strategy-part 1—The infinitesimal calculus. The Journal of Philosophical Logic, 33, 379–388.CrossRefGoogle Scholar
  18. Brown, B., & Priest, G. (2008). Chunk and permeate II: Weak aggregation, permeation and old quantum theory. Melbourne: Fourth World Congress on Paraconsistency.Google Scholar
  19. Chowell, G., & Viboud, C. (2016). Is it growing exponentially fast? Impact of assuming exponential growth for characterizing and forecasting epidemics with initial near-exponential growth dynamics. Infectious Disease Modelling, 1(1), 71–78.CrossRefGoogle Scholar
  20. Cottingham, K. L., Rusak, J. A., & Leavitt, P. R. (2000). Increased ecosystem variability and reduced predictability following fertilisation: Evidence from palaeolimnology. Ecology Letters, 3, 340–348.CrossRefGoogle Scholar
  21. Davey, K. (2014). Can good science be logically inconsistent? Synthese, 191, 3009–3026.CrossRefGoogle Scholar
  22. DeAngelis, D. L., Goldstein, R. A., & O’Neill, R. V. (1975). A model for trophic interaction. Ecology, 56, 881–892.CrossRefGoogle Scholar
  23. Friedman, M. (1974). Explanation and scientific understanding. Journal of Philosophy, 71, 5–19.CrossRefGoogle Scholar
  24. Ginzburg, L., & Colyvan, M. (2004). Ecological orbits: How planets move and populations grow. New York: Oxford University Press.Google Scholar
  25. Ginzburg, L., & Jensen, C. (2008). From controversy to consensus: The indirect interference functional response. Verhandlungen der InternationalenVereinigung für Theoretische und Angewandte Limnologie, 30, 297–301.Google Scholar
  26. Hassell, M. P., & Varley, G. C. (1969). New inductive population model for insect parasites and its bearing on biological control. Nature, 223, 1133–1137.CrossRefGoogle Scholar
  27. Holling, C. S. (1959). The components of predation as revealed by a study of small-mammal predation of the European pine sawfly. The Canadian Entomologist, 91(5), 293–320. Scholar
  28. Holt, R. D. (2011). Natural enemy-victim interactions: Do we have a unified theory yet? In S. M. Scheiner & M. R. Willig (Eds.), The theory of ecology (pp. 125–161). Chicago: University of Chicago Press.Google Scholar
  29. Jensen, C. (2008). Predation and its consequences: Insights into the modeling of interference. Stony Brook Theses & Dissertations [SBU], Stony Brook University. Accessed 09 May 2017.
  30. Jost, C. (1998). Comparing predator–prey models qualitatively and quantitatively with ecological time-series data. Paris: Institut national agronomique Paris-Grignon.Google Scholar
  31. Kitcher, P. (1989). Explanatory unification and the causal structure of the world. In P. Kitcher & W. Salmon (Eds.), Scientific explanation (pp. 410–505). Minneapolis: University of Minnesota Press.Google Scholar
  32. Laudan, L. (1981). A confutation of convergent realism. Philosophy of Science, 48, 19–48.CrossRefGoogle Scholar
  33. Morrison, M. (2000). Unifying scientific theories. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  34. Petkov, S. (2015). Explanatory unification and conceptualization. Synthese, 192, 3695–3717.CrossRefGoogle Scholar
  35. Priest, G. (2002). Inconsistency and the empirical sciences. In J. Meheus (Ed.), Inconsistency in science (pp. 119–128). Dordrecht: Kluwer Academic Publishers.CrossRefGoogle Scholar
  36. Priest, G. (2006). In contradiction. Oxford: Clarendon Press.CrossRefGoogle Scholar
  37. Prokopenko, M. C., Turgeon, K., & Fryxell, J. M. (2017). Evaluation of alternative prey-, predator-, and ratio-dependent functional response models in a zooplankton microcosm. Canadian Journal of Zoology, 95, 177–182.CrossRefGoogle Scholar
  38. Psillos, S. (2017). World-involving scientific understanding. Balkan Journal of Philosophy, 9(1), 5–18.CrossRefGoogle Scholar
  39. Psillos, S. (2018). Realism and theory change in science. In Zalta, E. N. (Ed.), The Stanford Encyclopedia of Philosophy, Summer 2018 Edition. Accessed 26 August 2018.
  40. Rosenzweig, M. L. (1971). Paradox of enrichment: Destabilization of exploitation ecosystems in ecological time. Science, 171, 385–387.CrossRefGoogle Scholar
  41. Schotch, P. K., & Jennings, R. E. (1980). Inference and necessity. Journal of Philosophical Logic, 9, 327–340.CrossRefGoogle Scholar
  42. Schurz, G. (1999). Explanation as unification. Synthese, 120, 94–114.CrossRefGoogle Scholar
  43. Shovonlal, R., & Chattopadhyay, J. (2007). The stability of ecosystems: A brief overview of the paradox of enrichment. Journal of Biosciences, 32(2), 421–428. Scholar
  44. Slavov, N., et al. (2014). Constant growth rate can be supported by decreasing energy flux and increasing aerobic glycolysis. Cell Reports, 7(3), 705–714.CrossRefGoogle Scholar
  45. Tyson, R., Haines, S., & Hodges, K. (2010). Modelling the Canada lynx and snowshoe hare population cycle: The role of specialist predators. Theoretical Ecology, 3(2), 97–111.CrossRefGoogle Scholar
  46. Tyutyunov, Y., Titova, L., & Arditi, R. (2008). Predator interference emerging from trophotaxis in predator–prey systems: An individual-based approach. Ecological Complexity, 5, 48–58.CrossRefGoogle Scholar
  47. Vickers, P. (2013). Understanding inconsistent science. Oxford: Oxford University Press.CrossRefGoogle Scholar
  48. Vickers, P. (2014). Theory flexibility and inconsistency in science. Synthese, 191, 2891–2906.CrossRefGoogle Scholar
  49. Volterra, V. (1926a). Fluctuations in the abundance of a species considered mathematically. Nature, 118, 558–560.CrossRefGoogle Scholar
  50. Volterra, V. (1926b). Variazioni e fluttuazioni del numerod’individui in specie animaliconviventi, Memorie della R. Accademia Nazional edei Lincei, 2, 5–112.Google Scholar
  51. Weber, E., & Van Dyck, M. (2002). Unification and explanation: A comment on Halonen and Hintikka, and Schurz. Synthese, 131, 145–154.CrossRefGoogle Scholar

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© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.School of PhilosophyBeijing Normal UniversityBeijingChina

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