Abstract
According to factive accounts of the norm of belief and decision-making, you should not believe or base decisions on a falsehood. Even when the evidence misleadingly suggests that a false proposition is true, you should not believe it or base decisions on it. Critics claim that factive accounts are counterintuitive and badly mischaracterize our ordinary practice of evaluating beliefs and decisions. This paper reports four experiments that rigorously test the critic’s accusations and the viability of factive accounts. The results undermine the accusations and provide the best evidence yet of factive norms of belief and decision-making. The results also help discriminate between two leading candidates for a factive norm: truth and knowledge. Knowledge is the superior candidate.
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Acknowledgments
For helpful feedback, I thank Wesley Buckwalter, Clayton Littlejohn, Matt McGrath, David Rose, Angelo Turri, and two anonymous referees for Synthese. This research was supported by the Social Sciences and Humanities Research Council of Canada and an Early Researcher Award from the Ontario Ministry of Economic Development and Innovation.
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Appendices
Appendix 1: stimuli
1.1 Experiment 1 materials
(Watch: True/False) Maria is a watch collector who owns over ten thousand watches. She cannot keep track of all her watches by memory alone, so she maintains a detailed inventory of them. She keeps the inventory up to date. Maria knows that the inventory isn’t perfect, but it is extremely accurate. 
Footnote 1 Today someone asked her, “Maria, I was wondering, do you have a 1990 Rolex Submariner in your collection?” 
Maria consults her inventory. It says that she does have a 1990 Rolex Submariner. [And this is just another case where the inventory is exactly right: she does have one in her collection. / But this is one of those rare cases where the inventory is wrong: she does not have one in her collection.].
(Name: True/False) Mario manages human resources for a company with over ten thousand employees. He cannot keep track of all their names by memory, so he maintains a detailed inventory of them. He keeps the inventory up to date. He knows that the inventory isn’t perfect, but it is extremely accurate. 
Today someone asked him, “Mario, do you have an employee working for you named Rosanna Winchester?” 
Mario consults his inventory. It says that he does have an employee by that name (And this is just another case where the inventory is exactly right: he does have an employee by that name. / But this is one of those rare cases where the inventory is wrong: he does not have an employee by that name.).
1.2 Experiment 2 materials
The stories were exactly the same as in Experiment 1, except for the second paragraph. Below are the new second paragraphs.
(Watch) Today her partner informed her, “Maria, I just talked to the bank. If you have a 1990 Rolex Submariner in your collection, then you need to make an appointment to revise our insurance policy, which will take several hours. But if you don’t have one, then you don’t need to make an appointment.”
(Name) Today his advisor informed him, “Mario, I just got a call from the immigration office. If we have an employee named Rosanna Winchester, then you need to make an appointment to revise the paperwork we filed, which will take several hours. But if we don’t have one, then you don’t need to make an appointment.”
Appendix 2: experiment 4 analyses
A multivariate analysis of variance revealed main and interaction effects of Type and Truth Value on the dependent variables. So I analyzed the data for Believe and Decide conditions separately.
1.1 Believe conditions
In response to the question of what Maria should believe, mean response was significantly higher in True (M \(=\) 2.41, SD \(=\) 0.84) than False (M \(=\) 0.21, SD \(=\) 1.53), independent samples t test, t(115.56) \(=\) 10.87, p \(<\) .001. The magnitude of the mean difference (MD \(=\) 2.91, 95 % CI 1.79–2.60) was extremely large, d \(=\) 2.02. One sample t tests revealed that mean response was significantly above the neutral midpoint (\(=\)0) in True, t(73) \(=\) 24.56, p \(<\) .001, MD \(=\) 2.41, 95 % CI 2.21–2.60, d \(=\) 2.87, whereas it did not differ from the midpoint in False, t(74) \(=\) 1.21, p \(=\) .230, MD \(=\) 0.21, 95 % CI \(-\)0.14 to 0.56. In True, 83 % of participants said that the agent should believe “I definitely do have one” or “I do have one,” compared to only 17 % of participants in False. A \(\chi ^2\) test for independence indicated that the magnitude of the difference in frequencies was extremely large, \(\chi ^2(1, 149) = 80.29\), Cramer’s V \(=\) .734. The mode response in True was “I definitely do have one.” In False it was “I probably do have one.”
Mean evaluation of Maria’s evidence was significantly higher in True (M \(=\) 2.39, SD \(=\) 0.77) than False (M \(=\) 0.68, SD \(=\) 1.47), independent samples t test, 112.27)\(=\) 8.90, p \(<\) .001. The magnitude of the mean difference (M \(=\) 1.71, 95 % CI 1.33–2.10) was extremely large, d \(=\) 1.68. One sample t tests revealed that mean evaluation was significantly above the neutral midpoint in True, t(73) \(=\) 26.61, p \(<\) .001, MD \(=\) 2.39, 95 % CI 2.21–2.57, d \(=\) 3.10, and also in False, t(74) \(=\) 4.0, p \(<\) .001, MD \(=\) .68, 95 % CI 0.34–1.02, d \(=\) 0.46. In True, 99 % of participants agreed that the evidence was good to some degree or other (i.e. “very good,” “good,” or “somewhat good”; in False, 64 % did. A \(\chi ^2\) test for independence indicated that the magnitude of the difference in frequencies was medium, \(\chi ^2(1, 149) = 29.30\), Cramer’s V \(=\) .443. The mode response in True was “very good.” In False it was “good.”
Mean knowledge score was significantly higher in True (M \(=\) 2.31, SD \(=\) 0.68) than False (M \(=\) 0.15, SD \(=\) 1.47), independent samples t test, t(104.76) \(=\) 11.57, p \(<\) .001. The magnitude of the mean difference (M \(=\) 2.164, 95 % CI 1.79–2.54) was extremely large, d \(=\) 2.25. One sample t tests revealed that mean knowledge score was significantly above the neutral midpoint in True, t(73) \(=\) 29.19, p \(<\) .001, MD 2.31, 95 % CI 2.15–2.47, d \(=\) 3.40, whereas it did not differ from the midpoint in False, t(74) \(=\) 0.87, p \(=\) .39, MD \(=\) .15, 95 % CI \(-\)0.19 to 0.48.
1.2 Decide conditions
In response to the question of what Maria should decide to do, mean response was significantly higher in True (M \(=\) 2.33, SD \(=\) 1.20) than False (M \(=\) \(-\)0.76, SD \(=\) 2.16, SEM \(=\) 0.25), independent samples t test, t(115.78) \(=\) 10.85, p \(<\) .001. The magnitude of the mean difference (MD \(=\) 3.09, 95 % CI 2.53–3.65) was extremely large, d \(=\) 2.02. One sample t tests revealed that mean response was significantly above the neutral midpoint in True, t(75) \(=\) 16.86, p \(<\) .001, MD \(=\) 2.33, 95 % CI 2.05–2.60, d \(=\) 1.94, and it was significantly below the midpoint in False, t(74) \(=\) \(-3.05\), p \(=\) .003, MD \(=\) \(-0.76\), 95 % CI \(-1.26\) to \(-0.26\), d \(=\) 0.35. In True, 88 % of participants said that the agent “definitely should” or “should” make the appointment, compared to only 24 % in False. A \(\chi ^2\) test for independence indicated that the magnitude of the difference in frequencies was extremely large, \(\chi ^2(1, 151) = 63.15\), Cramer’s V \(=\) .647. The mode response in True was “definitely should.” In False it was “should not.”
Mean evaluation of Maria’s evidence was significantly higher in True (M \(=\) 2.42, SD \(=\) 0.77, SEM \(=\) 0.09) than False (M \(=\) 0.28, SD \(=\) 1.77, SEM \(=\) 0.20), independent samples t test, t(100.87) \(=\) 9.63, p \(<\) .001. The magnitude of the mean difference (MD \(=\) 2.14, 95 % CI 1.7–2.58) was extremely large, d \(=\) 1.92. One sample t tests revealed that mean evaluation was significantly above the neutral midpoint in True, t(75) \(=\) 27.39, p \(<\) .001, MD \(=\) 2.42, 95 % CI 2.24–2.60, d \(=\) 3.14, but it did not differ from the midpoint in False, t(74) \(=\) 1.37, p \(=\) .174, MD \(=\) 0.28, 95 % CI \(-\)0.13 to 0.69. In True, 99 % of participants agreed that the evidence was good to some degree or other; in False, 56 % did. A \(\chi ^2\) test for independence indicated that the magnitude of the difference in frequencies was large, \(\chi ^2(1, 151) = 39.42\), Cramer’s V \(=\) .511. The mode response in True was “very good.” In False it was “somewhat good.”
Mean knowledge score was significantly higher in True (M \(=\) 2.08, SD \(=\) 1.03, SEM \(=\) 0.12) than False (M \(=\) \(-\)0.75, SD \(=\) 1.64, SEM \(=\) 0.19), independent samples t test, t(124.39) \(=\) 12.68, p \(<\) .001. The magnitude of the mean difference (MD \(=\) 2.83, 95 % CI 2.39–3.68) was extremely large, d \(=\) 2.27. One sample t tests revealed that mean knowledge score was significantly above the neutral midpoint in True, t(75) \(=\) 17.60, p \(<\) .001, MD \(=\) 2.08, 95 % CI 1.84–2.31, d \(=\) 2.02, and it was significantly below the neutral midpoint in False, t(74) \(=\) \(-3.95\), p \(<\) .001, MD \(=\) \(-0.75\), 95 % CI \(-1.12\) to \(-0.37\), d = 0.46.
