# Studying Controversies: Unification, Contradiction, Integration

- 1 Downloads

## Abstract

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.

## Keywords

Unification Contradictions Approximate truth Predator–prey models## References

- Abrams, P. A. (1994). The fallacies of ratio-dependent predation.
*Ecology,**75,*1842–1850.CrossRefGoogle Scholar - Abrams, P. A. (2014). Why ratio dependence is (still) a bad model of predation.
*Biological Reviews*,*90*, 794–814.CrossRefGoogle Scholar - 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 - 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 - Arditi, R., & Akcakaya, H. R. (1990). Underestimation of mutual interference of predators.
*Oecologia,**83,*358–361.CrossRefGoogle Scholar - Arditi, R., & Ginzburg, L. (1989). Coupling in predator–prey dynamics: Ratio-dependence.
*Journal of Theoretical Biology,**139*(3), 311–326.CrossRefGoogle Scholar - Arditi, R., & Ginzburg, L. (2012).
*How species interact: Altering the standard view on trophic ecology*. New York: Oxford University Press.CrossRefGoogle Scholar - Bangu, S. (2016). Scientific explanation and understanding: Unificationism reconsidered.
*European Journal for Philosophy of Science*. https://doi.org/10.1007/s13194-016-0148-y.CrossRefGoogle Scholar - Barraquand, F. (2014). Functional responses and predator–prey models: A critique of ratio dependence.
*Theoretical Ecology,**7,*3–20.CrossRefGoogle Scholar - Beddington, J. (1975). Mutual interference between parasites or predators and its effect on searching efficiency.
*Journal of Animal Ecology,**44,*331–340.CrossRefGoogle Scholar - Benham, R., Mortensen, C., & Priest, G. (2014). Chunk and permeate III: The Dirac delta function.
*Synthese,**191,*3057–3062.CrossRefGoogle Scholar - Brauer, F., & Castillo-Chavez, C. (2012).
*Mathematical models in population biology and epidemiology*(Vol. 2). New York: Springer.CrossRefGoogle Scholar - Brown, B. (2002). Approximate truth: A paraconsistent account. In J. Meheus (Ed.),
*Inconsistency in science*(pp. 81–103). Dordrecht: Kluwer Academic Publishers.CrossRefGoogle Scholar - 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 - Brown, B. (2015). Peter Vickers: Understanding inconsistent science (book review).
*Journal for General Philosophy of Science*,*46*(2), 413–418.CrossRefGoogle Scholar - 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 - Brown, B., & Priest, G. (2008).
*Chunk and permeate II: Weak aggregation, permeation and old quantum theory*. Melbourne: Fourth World Congress on Paraconsistency.Google Scholar - 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 - 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 - Davey, K. (2014). Can good science be logically inconsistent?
*Synthese,**191,*3009–3026.CrossRefGoogle Scholar - DeAngelis, D. L., Goldstein, R. A., & O’Neill, R. V. (1975). A model for trophic interaction.
*Ecology,**56,*881–892.CrossRefGoogle Scholar - Friedman, M. (1974). Explanation and scientific understanding.
*Journal of Philosophy,**71,*5–19.CrossRefGoogle Scholar - Ginzburg, L., & Colyvan, M. (2004).
*Ecological orbits: How planets move and populations grow*. New York: Oxford University Press.Google Scholar - 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 - 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 - 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. https://doi.org/10.4039/Ent91293-5.CrossRefGoogle Scholar - 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 - Jensen, C. (2008). Predation and its consequences: Insights into the modeling of interference. Stony Brook Theses & Dissertations [SBU], Stony Brook University. https://dspace.sunyconnect.suny.edu/handle/1951/44258. Accessed 09 May 2017.
- Jost, C. (1998).
*Comparing predator–prey models qualitatively and quantitatively with ecological time-series data*. Paris: Institut national agronomique Paris-Grignon.Google Scholar - 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 - Laudan, L. (1981). A confutation of convergent realism.
*Philosophy of Science,**48,*19–48.CrossRefGoogle Scholar - Morrison, M. (2000).
*Unifying scientific theories*. Cambridge: Cambridge University Press.CrossRefGoogle Scholar - Petkov, S. (2015). Explanatory unification and conceptualization.
*Synthese,**192,*3695–3717.CrossRefGoogle Scholar - Priest, G. (2002). Inconsistency and the empirical sciences. In J. Meheus (Ed.),
*Inconsistency in science*(pp. 119–128). Dordrecht: Kluwer Academic Publishers.CrossRefGoogle Scholar - Priest, G. (2006).
*In contradiction*. Oxford: Clarendon Press.CrossRefGoogle Scholar - 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 - Psillos, S. (2017). World-involving scientific understanding.
*Balkan Journal of Philosophy,**9*(1), 5–18.CrossRefGoogle Scholar - Psillos, S. (2018). Realism and theory change in science. In Zalta, E. N. (Ed.),
*The Stanford Encyclopedia of Philosophy*, Summer 2018 Edition. https://plato.stanford.edu/archives/sum2018/entries/realism-theory-change/. Accessed 26 August 2018. - Rosenzweig, M. L. (1971). Paradox of enrichment: Destabilization of exploitation ecosystems in ecological time.
*Science,**171,*385–387.CrossRefGoogle Scholar - Schotch, P. K., & Jennings, R. E. (1980). Inference and necessity.
*Journal of Philosophical Logic,**9,*327–340.CrossRefGoogle Scholar - Shovonlal, R., & Chattopadhyay, J. (2007). The stability of ecosystems: A brief overview of the paradox of enrichment.
*Journal of Biosciences,**32*(2), 421–428. https://doi.org/10.1007/s12038-007-0040-1.CrossRefGoogle Scholar - 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 - 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 - 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 - Vickers, P. (2013).
*Understanding inconsistent science*. Oxford: Oxford University Press.CrossRefGoogle Scholar - Vickers, P. (2014). Theory flexibility and inconsistency in science.
*Synthese,**191,*2891–2906.CrossRefGoogle Scholar - Volterra, V. (1926a). Fluctuations in the abundance of a species considered mathematically.
*Nature,**118,*558–560.CrossRefGoogle Scholar - Volterra, V. (1926b). Variazioni e fluttuazioni del numerod’individui in specie animaliconviventi, Memorie della R.
*Accademia Nazional edei Lincei,**2,*5–112.Google Scholar - Weber, E., & Van Dyck, M. (2002). Unification and explanation: A comment on Halonen and Hintikka, and Schurz.
*Synthese,**131,*145–154.CrossRefGoogle Scholar