 The second case study related to science has to do not with collaborations among scientists, but in lay reactions to scientific research. How should ordinary people think about science reporting or about the actual articles that are published by scientists? Should their motto also take no one's word for it? Should they be citizen scientists and build their own Large Hadron Collider? Or do they just sometimes have to take things on faith, or at least on trust? How can they respond in an epistemically virtuous way to the reports of scientists? This is a really important topic that relates not only to conspiracy theories about, for instance, the safety and effectiveness of vaccines, but various other kinds of lay reactions to scientific research, including denial of the evidence for anthropocentric climate change, denial of evidence for neo-darwinism, acceptance of homeopathy, denial of the connection of citizens, gun ownership with deadly violence, and so on. We need to have some way for scientists to communicate effectively with lay people without just turning scientists into priests whose word has to be taken as gospel. One problem, then, is that, on the one hand, lay people do need to be skeptical about scientific research, but on the other hand, they need to be not so skeptical that they can just believe whatever they want, no matter what the evidence suggests. A recent paper by Dan Cahan and colleagues on the topic of motivated numeracy shows what we have in mind here. Cahan defines numeracy as the ability to understand graphs and figures and the results of scientific research. He has the worry that people only apply their numeracy when the results support what they already believe. And that would suggest that people are suffering from what's known as confirmation bias in the psychological literature, that they trust the evidence when it tells them what they want to hear, and that they distrust it or that they refuse to process it effectively when it tells them something they didn't want to hear. Cahan presented participants the results of a hypothetical drug study, a study on the effectiveness of a new skin cream for healing rashes. You can see one example of what he showed participants here on the slide. This is a contingency table, which means that the numbers represent the number of people in each cell. So for instance, 223 people did use the new skin cream and got better, whereas 75 people used the skin cream and got worse, 107 people did not use the skin cream and got better, whereas 21 did not use the skin cream and got worse. What Cahan asked people to do was to study this table and decide whether the results indicate that the skin cream makes people get better or makes people get worse. Is it effective or not? It's actually kind of a tricky question. What you need to do is calculate the probability of getting better or worse in each row. So that means you look first only at patients who did use the skin cream. There are 298 of them, 223 of them got better, 75% in other words. Then we look at the second row and we see that there are 128 people and 107 of them got better, meaning 84%. So which row would you prefer to be in? Well, you should prefer to be in the second row unless you like having rashes because you have a better chance of having a rash get better if you don't use the skin cream than if you do. Most people who don't look at this carefully though have a lot of difficulty in picking out the correct answer and that means they really need to exercise their numeracy in order to get the correct answer on this question. Now whether a hypothetical cream is effective at relieving rashes doesn't have to do with people's prior beliefs or at least not much. So Kahan then showed people the same contingency table and instead of rashes getting better and worse based on application of a skin cream, the question had to do with gun control. This is a very controversial issue in the United States where people on the political right, conservatives and republicans, tend to think that gun control leads to more violence whereas people on the political left and democrats tend to think that gun control leads to a decrease in crime. What you can see here are the four conditions that participants could have seen when they took Kahan's study. The one at the top right, condition B, is the one that we just discussed and the other three are very minor modifications. So at the top left, condition A, all we do is switch whether the rash gets worse or better. We switch the columns but the numbers remain the same and then in conditions C and D instead of the rash and cream, we're looking at crime and gun control. So this means that if you're just reading the numbers and not paying attention to the political issue, you should be able to get the answer right just as easily in condition B, as in conditions A, C and D. But if what's happening is that people are only exercising their numeracy when it will give them the conclusion that they already agree with, we should see a difference between these conditions. And in fact, this is what Kahan found. So start with the top right graph. These are people who are high in numeracy as measured by an independent test and they're the ones who took the version of the study that had to do with the skin treatment. As you can see, liberals represented by the blue lines and conservatives represented by the red lines are pretty much indistinguishable. The x-axis here represents how frequently they got the right answer and the y-axis represents how many of them got the answer correct at that level. And as you can see, where the conservatives might be just slightly less effective at getting the right answer, it's more or less indistinguishable. The low numeracy condition at top left shows that, yes, as we would expect, people who are lower in numeracy get the answer correct less often. And once again, conservatives and liberals are pretty much indistinguishable here. However, if we go to the bottom left where we're talking about the gun ban, we find that low numeracy conservatives have a huge divergence from the previous conditions. So if the evidence suggested that crime increased, then they got it right most of the time. But if the evidence suggested that crime decreased, they got it wrong almost the entire time, about 15% of them got it right. By contrast, low numeracy liberals basically couldn't tell what the right answer was, and they were more or less guessing. They got the correct answer about 40% of the time. Then we can look at the most depressing graph here, the one for high numeracy individuals who are reasoning about the gun ban. And we can see that high numeracy conservatives get the correct answer almost every single time when crime increases. But they look like low numeracy people when crime decreases. You can see there that the peak is around 15%. By contrast, high numeracy liberals get the correct answer when crime decreases, almost every time, about 80%. But they get the answer wrong when crime increases. What this suggests is that people only exercise their numeracy, their intellectual abilities and epistemic virtues when it suits them, when the results of doing so will support what they already think. And this suggests that trust and distrust in science by lay people is going to be a very large problem unless the lay population can be led to exercise their own capacities more effectively. So to summarize these two case studies, scientists need various source, receiver, conduit and echo virtues. And lay people need various receiver and echo virtues as well. Moreover, scientists need lay people to have various receiver and echo virtues. So that means that there's a second order requirement for scientists. Similarly, lay people need scientists to be trustworthy. Otherwise, they really should be skeptical of everything that scientists had to say. And that means that there's a kind of interdependency among scientists and lay people and that no one particular group can be held responsible for failures of scientific communication.