Several formal accounts of carrying information have been proposed by philosophers. On Fred Dretske’s (1981) extremely influential account, R carries the information that S if and only if R provides a guarantee that S is true. More formally, R carries the information that S if and only if P(S | R) = 1 and P(S) < 1. For example, the thermometer reading 72° carries the information that the temperature is 72° because the probability that the temperature is 72° given that the thermometer reads 72° is 1.
Another popular account cashes out carrying information in terms of counterfactuals rather than in terms of objective probabilities. According to Cohen and Meskin (2004), R carries the information that S if and only if R would not have occurred if S were not true. For example, the thermometer reading 72° carries the information that the temperature is 72° because the thermometer would not read 72° if the temperature were not 72°.
These two accounts of information carrying can also be applied to videos. Consider, for example, a video that convincingly depicts a particular well-known politician taking a bribe. On Dretske’s account, the video carries the information that the politician took a bribe if and only if the existence of the video guarantees that the politician actually took a bribe. On Cohen and Meskin’s account, the video carries the information that the politician took a bribe if and only if the video would not exist if the politician had not actually taken a bribe.
Unfortunately, Dretske’s account and Cohen and Meskin’s account rule out the possibility of information carrying coming in degrees. On their accounts, something only carries the information that S if it provides a guarantee that S is true. In other words, something only carries the information that S if it is not possible for this thing to occur when S is false. Thus, on their accounts, carrying information is an all-or-nothing affair.
Admittedly, Dretske and Cohen and Meskin can say that a member of one class of things (such as videos) is less likely to carry information about some state of affairs S than a member of another class of things (such as handmade drawings).Footnote 10 But the only way that one particular thing can carry less information about S than any other thing is for it to carry no information about S at all. And if we are trying to decide whether the politician took a bribe, what matters is how much information the particular video that we are watching carries about that state of affairs.
Fortunately, more recent accounts of carrying information weaken Dretske’s stringent requirement of providing an absolute guarantee (see Stegmann 2015, 870). The specific account of carrying information that I endorse comes from Skyrms (2010). It was developed in an attempt to understand how animal signals carry information to other animals. For example, the elaborate tails of peacocks carry information about their quality as potential mates, the alarm calls of prairie dogs carry the information that predators are in the vicinity, and the red, yellow, and black stripes of coral snakes carry the information that they are venomous.
On Skyrms’s account, a signal R carries information about a state of affairs S whenever it distinguishes between the state of affairs where S is true and the state where S is false. That is, R carries the information that S when the likelihood of R being sent when S is true is greater than the likelihood of R being sent when S is false. More formally, R carries the information that S if and only if P(R | S) > P(R | not-S).Footnote 11 For instance, the prairie dog’s alarm call carries the information that there is a predator in the vicinity because it is more likely to occur when there is a predator in the vicinity than when there is not.
Unlike Dretske and Cohen and Meskin, Skyrms thinks that a signal R can carry the information that S even if R sometimes occurs when S is false. In other words, Skyrms allows for the possibility of false positives. For instance, a prairie dog might mistake a seagull for a hawk and, thus, give the alarm call when there is no predator in the vicinity. In addition, one species might mimic a signal that is commonly sent by another species. For instance, after the venomous coral snake evolved its distinctive appearance to warn potential predators to stay away, the non-venomous scarlet king snake subsequently evolved to resemble the coral snake in order to free ride on this warning system (see Forbes 2009, 241). Thus, seeing a snake with red, yellow, and black stripes does not guarantee that one is dealing with a venomous snake.
As a result, on Skyrms’s account, information carrying comes in degrees. Basically, the more likely it is for a signal R to be sent in the state where S is true than it is for R to be sent in the state where S is false, the more information that R carries about S. In other words, the higher the probability of a true positive relative to the probability of a false positive, the more information that a signal carries. Conversely, the higher the probability of a false positive relative to the probability of a true positive is, the less information that a signal carries. We can formalize this idea using likelihood ratios. A signal R carries more information than a signal Q about a state of affairs S if and only if P(R | S) / P(R | not-S) > P(Q | S) / P(Q | not-S).Footnote 12 For example, if it is less likely to be deployed by “low-quality” individuals, the peacock’s tail carries more information about his reproductive fitness than the sage grouse’s strutting behavior carries about his.
It should be noted that talk about how much information a signal carries can be translated into talk about the reliability of the evidence that the signal provides. Namely, R carries information about S if and only if R is evidence that S is the case. Also, R carries more information about S than Q if and only if R is more reliable evidence that S is the case than Q is. But for purposes of this paper, and following Cohen and Meskin (2004), I use the language of information theory to cash out the intuitive idea that photographs and videos carry information.
The fact that information carrying comes in degrees means that different signals can carry different amounts of information. The probability of a false positive for one signal can be higher or lower than the probability of a false positive for another signal. For example, prairies dogs actually have distinct alarm calls for different predators (see Slobodchikoff et al. 2009, 67). And the alarm call for a coyote in the vicinity carries more information than the alarm call for a hawk in the vicinity if the prairie dog is less likely to mistake something innocuous for a coyote than she is to mistake something innocuous for a hawk. Basically, how much information is carried by a signal can vary with the specific content of the signal.
The fact that information carrying comes in degrees also means that the amount of information carried by a particular signal can change over time. As the environmental situation changes, the probability of a false positive may increase or decrease. So, for example, if the number of king snake mimics increases in a particular region, the coral snake’s appearance will not carry as much information about its being a venomous snake as it once did. And it is important to note that these probabilities should not simply be interpreted as observed frequencies. For example, if there is an influx of king snake mimics into a particular region, the probability of a false positive will increase even if none of the new mimics have yet been observed.Footnote 13
Another extremely important aspect of Skyrms’s account is that he is not measuring the amount of information carried by a signal from God’s eye view. Instead, Skyrms is concerned with how much information is carried to the animal receiving the signal. Consider, for example, the signals of the coral snake and the king snake.
As with most animal mimics, the king snake’s appearance is not a perfect copy of the coral snake’s appearance. As is pointed out in the handy rhyme (“Red next to yellow, kill a fellow. Red next to black, venom lack”), the stripes are in a different order in the two species. So, from God’s eye view, the coral snake’s appearance does guarantee that you are dealing with a venomous snake.
However, potential predators, such as hawks and coyotes, are not able to distinguish between the red, yellow, and black stripes of the coral snake and the red, yellow, and black stripes of the king snake.Footnote 14 Thus, from their perspective, the coral snake’s appearance does not guarantee that they are dealing with a venomous coral snake. As far as potential predators can tell, there is a possibility that they are dealing with a non-venomous king snake. Their inability to distinguish the coral snake’s appearance from the king snake’s appearance is part of what determines the probability of a false positive.Footnote 15 As a result, the coral snake’s appearance carries much less information about what kind of snake it is to potential predators than it does to a human who is familiar with the aforementioned rhyme.
Even though how much information the coral snake’s appearance carries is relative to the observer, it is still an objective matter. The coral snake’s appearance carries a certain amount of information to anyone in a given epistemic position regardless of whether anyone in that position actually observes the snake or forms a belief about what kind of snake it is. Consider an analogy. In a deterministic world, a fair coin is definitely going to come up heads or it is definitely going to come up tails. So, from God’s eye view, the probability of heads is either 1 or 0. However, from the limited epistemic position of humans, the probability is 1/2. And this is an objective matter (see Beebee and Papineau 1997). The probability is 1/2 regardless of whether anyone observes the coin or forms a belief about the chances that it will land heads.
Finally, it is important to keep in mind that Skyrms’s account of carrying information is a mathematical model of a real-world phenomenon. And as Edwin Mansfield (1994, 13) points out with respect to microeconomic theory, “to be useful, a model must in general simplify and abstract from the real situation.” Skyrms’s model is intended to capture the important structural features of the phenomenon of signals (and, as I describe in the following section, it can do the same for the phenomenon of videos). The goal is not to calculate precisely how much information is carried by particular signals, such as the prairie dog’s alarm call or the peacock’s tail.