Academic journal article Canadian Journal of Experimental Psychology

A Bayesian Approach to the Argument from Ignorance

Academic journal article Canadian Journal of Experimental Psychology

A Bayesian Approach to the Argument from Ignorance

Article excerpt


In this paper, we re-examine a classic informal reasoning fallacy, the so-called argumentam ad ignorantiam. We argue that the structure of some versions of this argument parallels examples of inductive reasoning that are widely viewed as unproblematic. Viewed probabilistically, these versions of the argument from ignorance constitute a legitimate form of reasoning; the textbook examples are inductive arguments that are not unsound but simply weak, due to the nature of the premises and conclusions involved. In an experiment, we demonstrated some of the variables affecting the strength of the argument, and conclude with some general considerations towards an empirical theory of argument strength.

Argumentation, in one form or other, pervades most aspects of our everyday lives. People argue about whether someone should be convicted of a crime, whether taking drugs is right or wrong, whether you should allow a 15-year-old to stay out to midnight, and so on. Most of these arguments are informal (i.e., they cannot simply be encoded in standard logic). This is for several reasons. First, these arguments are often dialogical, that is, they are conducted between two or more participants, possessing differing goals and background knowledge (Perelman & Olbrechts-Tyteca, 1969; Walton, 1989). Second, the relationships that are important are defined at a higher level than the microstructures of reasoning investigated in formal logic (Freeman, 1991). Third, by the standards of formal logic these arguments are often invalid or fallacious.

Although informal argumentation has been studied intensively in social (for a review see, Voss & Van Dyke, 2001), developmental (for a review see, Felton & Kuhn, 2001), and other areas of psychology (e.g., Rips, 1998, 2002), to our knowledge, with a few exceptions (Neuman & Weizman, 2003; Rips, 2002), the informal fallacies that philosophers, logicians, and rhetoricians have identified over the last two millennia have not been investigated experimentally. Moreover, we know of no attempts to extend psychological theories of reasoning to try and account for these patterns of informal argument. We argue that a probabilistic approach to human reasoning (Chater & Oaksford, 2001; Oaksford & Chater, 1998, 2001) may be extended to many of these informal arguments. The goal of this paper is to provide a Bayesian analysis of at least some versions of the argument from ignorance (Walton, 1992). This is "the mistake that is committed whenever it is argued that a proposition is true simply on the basis that it has not been proved false, or that it is false because it has not been proved true." For example:

(1) Ghosts exist because no one has proved that they do not.

This argument seems unacceptable. However, we argue that this is not because the argument structure it embodies is fallacious as has traditionally been assumed from a logician's perspective. Rather, the argument is structurally perfectly acceptable, but weak due to its specific contents. We present a Bayesian analysis and report an experiment showing that the acceptability of the argument from ignorance is affected by the factors that a Bayesian analysis would predict.

Generally, logic and the acceptability of informal arguments dissociate. There are arguments that are logically invalid but that are regarded as informally acceptable, and there are arguments that are logically valid but that are regarded as informally unacceptable. For example, an argument of the form, the key was turned because the car started and if you turn the key the car starts, is an instance of the logical fallacy of affirming the consequent. However, it also an instance of inference to the best explanation (Harman, 1965), that is, the best explanation of why the car started is that the key was turned. Furthermore, the inference from the key was turned to the key was turned can be described as the claim that if the key was turned, then the key was turned. …

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