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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Notes
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).
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.
Discussing the various concepts of probability and their interpretations is beyond the scope of this paper. For a useful overview, see Mellor (2005).
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).
Note that this is different from saying that curve A is more probable, i.e., that P(Curve A | Data) > P(Curve B | Data).
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”.
See also Sober (2001, p. 14) who calls this variety of simplicity “semantic simplicity”.
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).
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.
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).
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”.
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.
For a useful overview of philosophical accounts of scientific explanation, see Woodward (2011).
An earlier account that identifies scientific explanations with deductive arguments is the Deductive-Nomological account (Hempel 1965).
Thanks to an anonymous reviewer for this point.
Cf. Psillos (2007, pp. 442, 443).
Cf. Kuhn (1977, pp. 320–339).
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.
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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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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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DOI: https://doi.org/10.1007/s10503-015-9367-1