Mercier and Sperber's (M&S's) hypothesis–“the function of reasoning is argumentative. It is to devise and evaluate arguments intended to persuade” (see their abstract)–is a timely and important thesis that sits well with related arguments in the literature. For example, Hahn & Oaksford (Reference Hahn and Oaksford2007) argued:
Typically, reasoning takes place in the service of argumentation, that is, in the attempt to persuade yourself or others of a particular position. Argumentation is the overarching human activity that studies of deductive reasoning, inductive reasoning, judgment, and decision making are really required to explain. (p. 705)
M&S argue that demonstrations “that people are skilled at assessing arguments seems to stand in sharp contrast with findings from the psychology of reasoning” (sect. 2.1, para. 3). They discuss participants' failures to employ logical rules but not the frequent endorsement of logical fallacies, although they suggest that, “unlike logical fallacies, fallacies of argumentation come in degrees” (sect. 2.1, para. 4). Many argumentation theorists argue that all argumentation, not just the fallacies, is a matter of degree. For example, Perelman and Olbrechts-Tyteca (Reference Perelman and Olbrechts-Tyteca1969) argued, “The aim of argumentation is not to deduce consequences from given premises; it is rather to elicit or increase the adherence of the members of an audience to theses that are presented for their consent” (p. 9). Here we argue that logical fallacies and logical rules subserve argumentation but only to the extent that they to “come in degrees.” A corollary to this argument is that judgmental fallacies such as base-rate neglect may also arise in the same context.
I focus on the deductive fallacy of denying the antecedent (DA) in conditional reasoning, for example:
If a bird is a swan, then it is white
That bird was not a swan
Therefore That bird was not white
This instance of DA is clearly a logical fallacy as there are white birds that are not swans. However, suppose someone (Con) is deploying DA against someone (Pro) who has argued that a particular bird was white via the logical rule of modus ponens (MP), if a bird is a swan, then it is white, that bird was a swan, therefore, it was white. To refute Pro's argument the respondent must deny one of the premises. Con chooses to “deny the antecedent”–that is, to deny that the bird was a swan, from which it “follows” that the bird was not white (Godden & Walton Reference Godden and Walton2004). From an argumentative perspective this seems like a perfectly sound strategy.
However, the falsity of the consequent–the bird was not white–could not follow logically from this use of DA. Rather it undermines another property of Pro's intended conclusion–that is, “that it should be believed” (Godden & Walton Reference Godden and Walton2004, p. 232). A Bayesian probabilistic approach to argument strength for the conditional cashes out this intuition (Hahn & Oaksford Reference Hahn and Oaksford2007; Oaksford & Hahn Reference Oaksford, Hahn, Feeney and Heit2007). Hahn and Oaksford (Reference Hahn and Oaksford2007) proposed that people's degree of belief in the conclusion given the premises provides one measure of argument strength. They equate this measure with the conditional probability of the conclusion given the premises: for MP this is Pr(bird is white|bird is a swan) (see Oaksford & Chater Reference Oaksford and Chater2007; Oaksford et al. Reference Oaksford, Chater and Larkin2000). Another measure, which they refer to as “argument force,” is the change in degree of belief brought about by the argument. They equate this measure with the likelihood ratio, which maps the prior odds into the posterior odds: for MP this ratio is Pr(bird is white|bird is a swan)/Pr(bird is white|bird is not a swan).
It is quite easy to show that contexts can arise where both Pro's and Con's arguments seem warranted. Suppose that the swans are in a bird sanctuary containing equal numbers of white and black swans: Pr(bird is white|bird is a swan)=0.5, and that most of the birds in the sanctuary are neither white nor swans: for example, Pr(bird is white)=Pr(bird is a swan)=0.1. On this distribution, the likelihood ratio for the MP argument is 9; the bird is 9 times more likely to be white given it is a swan than if it were not a swan. In contrast, the likelihood ratio for DA, Pr(bird is not white|bird is not a swan)/Pr(bird is not white|bird is a swan), is much lower; the bird is only about 2 times more likely not to be white given it is not a swan than if it were a swan. So, in terms of the force of the respective arguments, MP seems stronger than DA, which seems to warrant Pro's opening argument.
Con's DA counter-argument can be characterised as noting that priors matter and that it is highly unlikely that the bird was a swan. That is, his counter-argument suggests that Pro has neglected the base rates, a common bias in judgement research (Bar-Hillel Reference Bar-Hillel1980; Kahneman & Tversky Reference Kahneman and Tversky1973). When priors are taken in to account, Pro's MP argument is weak; that is, the posterior probability is only 0.5. In contrast, the posterior probability of the DA argument, Pr(bird is not white|bird is not a swan), is 0.94. So, in this context, in terms of the strength of the respective arguments DA seems stronger than MP, which seems to warrant Con's counter-argument: The conclusion of the DA argument should be believed more than the conclusion of the MP argument. The next exchange between Pro and Con would probably focus on Pro's grounds for apparently neglecting the base rate and believing that for this particular bird, Pr(bird is a swan) > 0.1.
This analysis supports M&S's contention that reasoning is for argument but only when we give a probabilistic analysis of how logical rule and fallacies affect people's degrees of belief in their conclusions. In conclusion, we would argue that putting reasoning and judgment in their proper argumentative place compels us to a probabilistic understanding of deductive reasoning.
Mercier and Sperber's (M&S's) hypothesis–“the function of reasoning is argumentative. It is to devise and evaluate arguments intended to persuade” (see their abstract)–is a timely and important thesis that sits well with related arguments in the literature. For example, Hahn & Oaksford (Reference Hahn and Oaksford2007) argued:
Typically, reasoning takes place in the service of argumentation, that is, in the attempt to persuade yourself or others of a particular position. Argumentation is the overarching human activity that studies of deductive reasoning, inductive reasoning, judgment, and decision making are really required to explain. (p. 705)
M&S argue that demonstrations “that people are skilled at assessing arguments seems to stand in sharp contrast with findings from the psychology of reasoning” (sect. 2.1, para. 3). They discuss participants' failures to employ logical rules but not the frequent endorsement of logical fallacies, although they suggest that, “unlike logical fallacies, fallacies of argumentation come in degrees” (sect. 2.1, para. 4). Many argumentation theorists argue that all argumentation, not just the fallacies, is a matter of degree. For example, Perelman and Olbrechts-Tyteca (Reference Perelman and Olbrechts-Tyteca1969) argued, “The aim of argumentation is not to deduce consequences from given premises; it is rather to elicit or increase the adherence of the members of an audience to theses that are presented for their consent” (p. 9). Here we argue that logical fallacies and logical rules subserve argumentation but only to the extent that they to “come in degrees.” A corollary to this argument is that judgmental fallacies such as base-rate neglect may also arise in the same context.
I focus on the deductive fallacy of denying the antecedent (DA) in conditional reasoning, for example:
This instance of DA is clearly a logical fallacy as there are white birds that are not swans. However, suppose someone (Con) is deploying DA against someone (Pro) who has argued that a particular bird was white via the logical rule of modus ponens (MP), if a bird is a swan, then it is white, that bird was a swan, therefore, it was white. To refute Pro's argument the respondent must deny one of the premises. Con chooses to “deny the antecedent”–that is, to deny that the bird was a swan, from which it “follows” that the bird was not white (Godden & Walton Reference Godden and Walton2004). From an argumentative perspective this seems like a perfectly sound strategy.
However, the falsity of the consequent–the bird was not white–could not follow logically from this use of DA. Rather it undermines another property of Pro's intended conclusion–that is, “that it should be believed” (Godden & Walton Reference Godden and Walton2004, p. 232). A Bayesian probabilistic approach to argument strength for the conditional cashes out this intuition (Hahn & Oaksford Reference Hahn and Oaksford2007; Oaksford & Hahn Reference Oaksford, Hahn, Feeney and Heit2007). Hahn and Oaksford (Reference Hahn and Oaksford2007) proposed that people's degree of belief in the conclusion given the premises provides one measure of argument strength. They equate this measure with the conditional probability of the conclusion given the premises: for MP this is Pr(bird is white|bird is a swan) (see Oaksford & Chater Reference Oaksford and Chater2007; Oaksford et al. Reference Oaksford, Chater and Larkin2000). Another measure, which they refer to as “argument force,” is the change in degree of belief brought about by the argument. They equate this measure with the likelihood ratio, which maps the prior odds into the posterior odds: for MP this ratio is Pr(bird is white|bird is a swan)/Pr(bird is white|bird is not a swan).
It is quite easy to show that contexts can arise where both Pro's and Con's arguments seem warranted. Suppose that the swans are in a bird sanctuary containing equal numbers of white and black swans: Pr(bird is white|bird is a swan)=0.5, and that most of the birds in the sanctuary are neither white nor swans: for example, Pr(bird is white)=Pr(bird is a swan)=0.1. On this distribution, the likelihood ratio for the MP argument is 9; the bird is 9 times more likely to be white given it is a swan than if it were not a swan. In contrast, the likelihood ratio for DA, Pr(bird is not white|bird is not a swan)/Pr(bird is not white|bird is a swan), is much lower; the bird is only about 2 times more likely not to be white given it is not a swan than if it were a swan. So, in terms of the force of the respective arguments, MP seems stronger than DA, which seems to warrant Pro's opening argument.
Con's DA counter-argument can be characterised as noting that priors matter and that it is highly unlikely that the bird was a swan. That is, his counter-argument suggests that Pro has neglected the base rates, a common bias in judgement research (Bar-Hillel Reference Bar-Hillel1980; Kahneman & Tversky Reference Kahneman and Tversky1973). When priors are taken in to account, Pro's MP argument is weak; that is, the posterior probability is only 0.5. In contrast, the posterior probability of the DA argument, Pr(bird is not white|bird is not a swan), is 0.94. So, in this context, in terms of the strength of the respective arguments DA seems stronger than MP, which seems to warrant Con's counter-argument: The conclusion of the DA argument should be believed more than the conclusion of the MP argument. The next exchange between Pro and Con would probably focus on Pro's grounds for apparently neglecting the base rate and believing that for this particular bird, Pr(bird is a swan) > 0.1.
This analysis supports M&S's contention that reasoning is for argument but only when we give a probabilistic analysis of how logical rule and fallacies affect people's degrees of belief in their conclusions. In conclusion, we would argue that putting reasoning and judgment in their proper argumentative place compels us to a probabilistic understanding of deductive reasoning.