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Why Simpler Arguments are Better

Abstract

In this paper, I argue that, other things being equal, simpler arguments are better. In other words, I argue that, other things being equal, it is rational to prefer simpler arguments over less simple ones. I sketch three arguments in support of this claim: an argument from mathematical proofs, an argument from scientific theories, and an argument from the conjunction rule.

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Fig. 1

Notes

  1. It is also worth noting that, against the attempt by some, like Simon Blackburn, to make philosophy public, i.e., more accessible to a general audience, others have argued that “philosophy is supposed to be difficult” (http://www.theguardian.com/books/booksblog/2011/feb/25/philosophy-technical-everyday-english).

  2. On the use of arguments as tools of rational persuasion, see Hitchcock (2007), Johnson (2000), and Walton (1996). The notion of rational persuasion is supposed to exclude other forms of persuasion, such as threats and other kinds of blackmail. This is also meant to deal with alleged counterexamples where it seems rational to prefer complex arguments. For example, suppose that an eccentric billionaire offers a cash prize for “Most Complex Argument”. In this case, it seems rational to prefer more complex arguments, not for the sake of truth and/or rational persuasion, but rather for the sake of winning a cash prize. Thanks to Andrew Aberdein for this point.

  3. Discussing the various concepts of probability and their interpretations is beyond the scope of this paper. For a useful overview, see Mellor (2005).

  4. Note that this characterization of inductive arguments is broad enough to include non-deductive arguments like abductive arguments (or inferences to the best explanation) and conductive arguments (Govier 2010). For a useful overview, see McKeon (2013).

  5. See, e.g., Sober (1988, 1994). Sober argues that appeals to simplicity are local rather than global, i.e., they depend on local background assumptions and context for their rational justification.

  6. In this paper, I talk about simplicity as a theoretical virtue of arguments in much the same way that simplicity is taken to be a theoretical virtue of mathematical proofs and scientific theories. See, e.g., Baker (2011), Glynn (2010), and Sober (2001). On the virtues of arguers, rather than arguments, see Aberdein (2010).

  7. Note that this is different from saying that curve A is more probable, i.e., that P(Curve A | Data) > P(Curve B | Data).

  8. As an anonymous reviewer helpfully pointed out, the assumption that smoothness is simpler than bumpiness can be operationalized in several ways. For example, the degree of a polynomial can be taken to indicate the number of bumps of the associated graph, in which case, a low degree is preferable to a high degree polynomial. As Armitage et al (2002, p. 378) put it: “Considerations of simplicity suggest that as low an order as possible should be used; for example, we should normally use linear regression unless there is any particular reason to use a higher-degree polynomial”.

  9. See also Sober (2001, p. 14) who calls this variety of simplicity “semantic simplicity”.

  10. In terms of ontological parsimony, a further distinction is often drawn between qualitative parsimony (the number of types of entities postulated) and quantitative parsimony (the number of individual entities postulated). See Baker (2003).

  11. Commenting on Dufour’s Argument and Explanation in Mathematics (2013) at the conference of the Ontario Society for the Study of Argumentation (May 22–25, 2013), Aberdein mentions empirical results suggesting that “mathematicians who completed the study expected explanatory proofs to be precise, useful and not intricate. Or, in other words, simple, fruitful, and exact”. Available at: http://www.academia.edu/3646529/Commentary_on_Michel_Dufour_Argument_and_explanation_in_mathematics.

  12. See also the special issue of Foundations of Science on Mathematical Argumentation (vol. 14, issue 1-2), edited by Aberdein and Dove (2009). For example, according to Coleman (2009, p. 30), “One proof is better than another because it is more elegant, or informative, or shorter, or easier to follow, or less conceptually demanding, or more easily generalisable, or with less fuzzy details, or more direct, or more constructive, or even more novel…” (emphasis added).

  13. As an anonymous reviewer helpfully pointed out, (1.1a) is consistent with there being a particular property F of species X but not Y, which are both species of genus G, that is not the property that makes X and Y different species of G. Perelman and Olbrechts-Tyteca call this kind of argument “argument a pari” (as opposed to argument a contrario). According to Perelman and Olbrechts-Tyteca (1969, p. 241), “These arguments deal with the application or nonapplication to another species of the same genus of what can be asserted about some particular species”.

  14. It is worth noting that, for van Fraassen, these features are merely pragmatic, not epistemic or truth-conducive. I will return to this point in Sect. 5.

  15. See, e.g., Baker (2007), Forster and Sober (1994), and Glynn (2010).

  16. For a useful overview of philosophical accounts of scientific explanation, see Woodward (2011).

  17. An earlier account that identifies scientific explanations with deductive arguments is the Deductive-Nomological account (Hempel 1965).

  18. On IBE, see Lipton (2004). Cf. Bird (2007) who argues that there is a form of IBE, namely, inference to the only explanation, in which the truth of the premises guarantees the truth of the conclusion.

  19. Thanks to an anonymous reviewer for this point.

  20. Cf. Psillos (2007, pp. 442, 443).

  21. Cf. Kuhn (1977, pp. 320–339).

  22. Another important question raised by an anonymous reviewer is the following: Is there a simpler argument than the ones sketched in this paper for the claim that simpler arguments are better? If we allow for zero-premise arguments, then perhaps the simplest argument for the claim that simpler arguments are better is this: simpler arguments are better. It must be noted, however, that zero-premise arguments are said to be valid “when and only when the conclusion is a tautology” (Corcoran 2001, p. 67). The claim that simpler arguments are better may be evident but it doesn’t seem to be a tautology.

References

  • Aberdein, A., and I.J. Dove. (eds). 2009. Mathematical argumentation. Foundations of Science 14(1–2): 1–152.

  • Aberdein, A. 2010. Virtue in argument. Argumentation 24: 165–179.

    Article  Google Scholar 

  • Aberdein, A. 2013. Commentary on Michel Dufour’s Argument and Explanation in Mathematics. Ontario Society for the Study of Argumentation. http://www.academia.edu/3646529/Commentary_on_Michel_Dufour_Argument_and_explanation_in_mathematics. Accessed 22–25 May 2013.

  • Aigner, M., and G.M. Ziegler. 2004. Proofs from The Book, 3rd ed. Berlin: Springer.

    Book  Google Scholar 

  • Armitage, P., G. Berry, and J.N.S. Matthews. 2002. Statistical methods in medical Research, 4th ed. Malden: Blackwell Science.

    Book  Google Scholar 

  • Baker, A. 2003. Quantitative parsimony and explanatory power. British Journal for the Philosophy of Science 54: 245–259.

    Article  Google Scholar 

  • Baker, A. 2007. Occam’s razor in science: A case study from biogeography. Biology and Philosophy 22: 193–215.

    Article  Google Scholar 

  • Baker, A. (2011). Simplicity. In The Stanford encyclopedia of philosophy (Summer 2011 Edition), ed. Zalta, E.N. http://plato.stanford.edu/entries/simplicity/.

  • Bird, A. 2007. Inference to the only explanation. Philosophy and Phenomenological Research 74: 424–432.

    Article  Google Scholar 

  • Coleman, E. 2009. The surveyability of long proofs. Foundations of Science 14: 27–43.

    Article  Google Scholar 

  • Copi, I., and C. Cohen. 2005. Introduction to logic, 12th ed. Upper Saddle River: Prentice Hall.

    Google Scholar 

  • Corcoran, J. 2001. Second-order logic. In Logic, meaning, and computation, ed. C.A. Anderson, and M. Zelëny, 61–75. Berlin: Springer.

    Chapter  Google Scholar 

  • Craig, E. 2002. Philosophy: A very short introduction. New York: Oxford University Press.

    Book  Google Scholar 

  • Danto, A.C. 2005. Nietzsche as philosopher. New York: Columbia University Press.

    Google Scholar 

  • Fisher, R.A. 1925. Statistical methods for research workers. Edinburgh: Oliver & Boyd.

    Google Scholar 

  • Forster, M., and E. Sober. 1994. How to tell when simpler, more unified, or less ad hoc theories will provide more accurate predictions. British Journal for the Philosophy of Science 45: 1–36.

    Article  Google Scholar 

  • Gauch, H. 2003. Scientific method in practice. Cambridge: Cambridge University Press.

    Google Scholar 

  • Glynn, I. 2010. Elegance in science: The beauty of simplicity. New York: Oxford University Press.

    Google Scholar 

  • Godfrey-Smith, P. 2003. Theory and reality: An introduction to the philosophy of science. Chicago: University of Chicago Press.

    Book  Google Scholar 

  • Govier, T. 2010. A practical study of argument, 7th ed. Belmont: Wadsworth.

    Google Scholar 

  • Hempel, C. 1965. Aspects of scientific explanation and other essays in the philosophy of science. New York: Free Press.

    Google Scholar 

  • Hitchcock, D. 2007. Informal logic and the concept of argument. In Philosophy of logic, ed. D. Jacquette, 101–129. Amsterdam: Elsevier.

    Chapter  Google Scholar 

  • Johnson, R. 2000. Manifest rationality. Mahwah: Lawrence Erlbaum Associates.

    Google Scholar 

  • Kelly, T. 2011. Following the argument where it leads. Philosophical Studies 154: 105–124.

    Article  Google Scholar 

  • Kitcher, P. 1989. Explanatory unification and the causal structure of the world. In Scientific explanation, ed. P. Kitcher, and W. Salmon, 410–505. Minneapolis: University of Minnesota Press.

    Google Scholar 

  • Kitcher, P. 1993. The advancement of science: Science without legend, objectivity without illusions. New York: Oxford University Press.

    Google Scholar 

  • Kuhn, T.S. 1977. The essential tension: Selected studies in scientific tradition and change. Chicago: The University of Chicago Press.

    Google Scholar 

  • LeBon, T. 1999. Philosophy and the perils of popularisation. Practical Philosophy 2: 15–17.

    Google Scholar 

  • Lipton, P. 2004. Inference to the best explanation, 2nd ed. London: Routledge.

    Google Scholar 

  • Longino, H.E. 1995. Gender, politics, and the theoretical virtues. Synthese 104: 383–397.

    Article  Google Scholar 

  • McKeon, M. 2013. Argument. In Internet encyclopedia of philosophy, eds. Fieser, J., and Dowden, B. http://www.iep.utm.edu/argument/.

  • Mellor, D.H. 2005. Probability: A philosophical introduction. New York: Routledge.

    Google Scholar 

  • Norman, D.A. 2011. Living with complexity. Cambridge: The MIT Press.

    Google Scholar 

  • Perelman, C., and Olbrechts-Tyteca, L. 1969. The new rhetoric: A treatise on argumentation (trans: Wilkinson, J., and Weaver, P.). Notre Dame: University of Notre Dame Press.

  • Protevi, J. 2001. Political physics. New York: The Athlone Press.

    Google Scholar 

  • Psillos, S. 2007. The fine structure of inference to the best explanation. Philosophy and Phenomenological Research 74: 441–448.

    Article  Google Scholar 

  • Quine, W.V.O. 1981. Theories and things. Cambridge: Harvard University Press.

    Google Scholar 

  • Russell, B. 1918. Mysticism and logic. London: Longmans, Green, and Co.

    Google Scholar 

  • Sinnott-Armstrong, W., and R. Fogelin. 2010. Understanding arguments: An Introduction to informal logic, 8th ed. Belmont: Wadsworth.

    Google Scholar 

  • Sober, E. 1988. Reconstructing the past: Parsimony, evolution and inference. Cambridge: MIT Press.

    Google Scholar 

  • Sober, E. 1994. Let’s razor Ockham’s razor. In From a biological point of view, ed. E. Sober, 136–157. Cambridge: Cambridge University Press.

    Chapter  Google Scholar 

  • Sober, E. 1998. Simplicity (in scientific theories). In Routledge encyclopedia of philosophy, vol. 8, ed. E. Craig, 780–783. London: Routledge.

    Google Scholar 

  • Sober, E. 2001. What is the problem of simplicity? In Simplicity, inference, and modeling: Keeping it sophisticatedly simple, ed. A. Zellner, H. Keuzenkamp, and M. McAleer, 13–31. Cambridge: Cambridge University Press.

    Google Scholar 

  • Tversky, A., and D. Kahneman. 1983. Extensional versus intuitive reasoning: The conjunction fallacy in probability judgment. Psychological Review 90: 293–315.

    Article  Google Scholar 

  • van Fraassen, B.C. 1980. The scientific image. New York: Oxford University Press.

    Book  Google Scholar 

  • van Fraassen, B.C. 1985. Empiricism in the philosophy of science. In Images of science: Essays on realism and empiricism, ed. P.M. Churchland, and C.A. Hooker, 245–308. Chicago: University of Chicago Press.

    Google Scholar 

  • Walton, D. 1996. Argument structure: A pragmatic theory. Toronto: University of Toronto Press.

    Google Scholar 

  • Wood, A.W. 2004. Karl Marx, 2nd ed. New York: Routledge.

    Google Scholar 

  • Woodward, J. 2011. Scientific explanation. In The Stanford encyclopedia of philosophy (Winter 2011 Edition), ed. Zalta, E.N. http://plato.stanford.edu/entries/scientific-explanation/.

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Acknowledgments

I am grateful to Andrew Aberdein and three anonymous reviewers of Argumentation for helpful comments on earlier drafts.

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Correspondence to Moti Mizrahi.

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Mizrahi, M. Why Simpler Arguments are Better. Argumentation 30, 247–261 (2016). https://doi.org/10.1007/s10503-015-9367-1

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Keywords

  • Argument
  • Deduction
  • Elegance
  • Explanation
  • Induction
  • Parsimony
  • Proof
  • Simplicity
  • Theory