Cheryl E

Cheryl E. Fitzgerald

The Utility of Accepting Maher's Theory of Verisimilitude: A Look at Betting on Theories

Maher defines verisimilitude as "essentially a measure of the cognitive utility of accepting a hypothesis under different circumstances" (Maher, 226). Simply put this amounts to saying that verisimilitude measures how much one is willing to bet or risk accepting a theory; what is at risk and how will be explicated further ahead. Acceptance of a theory must be understood to mean accepting a theory into one's total corpus of beliefs—holism—not simply accepting the theory by itself (Maher, 142), for the cognitive utility will include how well the theory in question is consistent with one's total corpus. Verisimilitude here is concerned with closeness to the whole truth, not just a theory's closeness to being true; however, this latter notion is a part of how one gets to a measure of verisimilitude. 'How much one is willing to bet’ inevitably means that the notion of verisimilitude put forth here is subjective, and varies from person to person: rather than it being a measure of the actual closeness of a theory to the truth, it is instead a measure of the expected closeness to the truth (Maher, 229). I find this theory preferable to explications of verisimilitude as an objective measure of the actual closeness to the truth.

Maher is motivated by the question, under what conditions do we accept a scientific theory and why? Acceptance of a theory is a choice of action, and Maher's book is an attempt to explain that choice—utilizing Bayesian decision theory—and how to make that choice rationally and scientifically. An essential aspect of his project is that he is trying to adequately represent how some scientists actually do make choices about accepting theories, not how scientists necessarily ought to. This results in a desirable feature, namely, that Maher's theory can coexist with other theories concerning science and acceptance of theories, such as van Fraassen's (Maher, 240-3). Maher disagrees with van Fraassen on a few details, but the point is that their theories can coexist, for there may be some scientists that behave in the way van Fraassen believes they do and there may be some that behave in the way Maher believes they do. But how a person behaves will depend on his or her values; thus, Maher defines what count as scientific values, and these values play a role in cognitive utility and, thus, verisimilitude.

Cognitive utility is the maximal expected utility of cognitive acts (Maher, x), such as accepting a theory, as opposed to physical acts, such as taking an umbrella with me on my errands. Maximal expected utility is a function over probabilities of states and utilities of consequences (Maher, 1). Probabilities of states are determined by the available evidence of the current state and possible states, such as whether or not it will rain while I am out on my errands, and should be understood here specifically as subjective probability (Maher, Ch. 4). Utilities of consequences are determined by one's preferences over the options, the respective consequences of the different acts I may choose (Maher, Ch. 1), such as not getting wet as the result of my decision to take an umbrella on my errands. For acts of acceptance, the consequences will include how a theory coheres with my total corpus. If a theory is contradictory to many of my core beliefs, this will negatively affect the utility of accepting the theory. If a theory is not only consistent with my total corpus but also explains some of my core beliefs, this will positively affect the utility of accepting the theory. Preferences for certain consequences over others is a product of one's values[1], such as my valuing not getting wet while I am on my errands. Thus, values play the starting point of how one makes decisions, and what kinds of values a person has will affect whether or not a person's decisions are rational. Verisimilitude is concerned with values that are both rational and scientific.

There are five values that Maher defines as scientific values. The first is a respect for truth. This means that one must value a true theory at least as much as a false theory: one cannot value false theories over true theories (Maher. 210-12). In cases where the truth is not known, one must use probability as a measure, so that one should value a more probable theory in light of the evidence. The second is a respect for information (Maher, 213). This value stems from the view that science aims to have informative theories, not simply true theories. The result is that a person must be motivated to either accept theories that are revised and expanded in order to account for new observations or discard old theories for new ones that better account for new observations. The third is that one must value a true theory over completely withholding judgment, i.e., agnosticism is not a valuable position when a true theory is available (Maher, 214). The fourth is that one must value the whole truth no matter what the truth turns out to be (Maher, 214). This means that science should be an impartial endeavor. The fifth and last is that one must value the truth over contradiction, and in fact, one cannot even weakly prefer a contradiction to the truth (Maher, 216). These five values do not comprise an exhaustive list of scientific values, but Maher admits that he cannot think of any other plausible possibilities (Maher, 216). Thus, one needs to have at least these five values to be scientific.

Values lead one to be disposed[2] to act a certain way, namely, to act in such a way that maximally satisfies one's values. This is another way of stating that we have preferences for our actions--those actions that satisfy our values. Preferences for certain actions are preferences for the consequences of those actions, which are, in this case, the satisfaction of our values. The consequence of my taking my umbrella with me on my errands is that I do not get wet, and my not getting wet satisfies my value of not getting wet, because frankly, I don't enjoy going to the store while wearing wet clothes. Analogously, the consequences of accepting Einstein's theories of relativity over Newtonian physics satisfies my values of accepting theories that accord better with the observations (a scientific value). A preference for the consequences of some act is the utility of that act.

But if one wants to be scientific, or at least rational, the utility of an act cannot be the only factor in deciding whether or not to perform the act, for no matter what I prefer, the actual state of affairs has no obligation to accord with what I want. If the actual state of affairs played no part, then I would prefer not to carry an umbrella for the simple fact that it can pose an inconvenience to me: it's another thing I have to carry and not accidentally leave somewhere, and at times it can be cumbersome. But the actual state of affairs does play a part, and from here there is a high probability that it will rain. The high probability of rain changes my initial preference of not carrying an umbrella, for the probability of rain forces me to consider another one of my values, namely, not getting wet. My preferences are forced to interact with a real world: my dispositions affect me to act a certain way, but there is an external environment that affects me as well.

Thus, probability must also play a role in one's decisions to act, and the case is no different when that action is a cognitive act such as acceptance. But some philosophers have claimed that a theory based on values and subjective probabilities is too subjective, and that a disagreement between two scientists with differing values and probabilities cannot be resolved (Maher, 216-17). However, this view does not take into consideration the principle of conditionalization[3] (Maher, 85): new evidence and observations would shift the subjective probabilities of the theory, either up or down, enough so that one of the scientists, if he has the minimum of scientific values, namely, those listed above, would have to change his subjective probability for the theory (Maher, 217). Disagreement can always be resolved as long as all parties have the minimum set of scientific values and enough observation and evidence can be gathered.

Of the scientific values listed, four of them are concerned with valuing truth and one of them is concerned with valuing information. Maher states, and many other philosophers have stated, that science aims at accepting theories that are both true and informative, and this follows from that list of scientific values.

Acceptance involves a trade-off of two competing considerations: the concern to be right (which would lead one to accept hypotheses of high probability), and the desire for informative hypotheses (which tends to favor hypotheses with low probability). Thus, a theory of acceptance needs to take into account the scientist's goals or values, and specifically the relative weights put on the goals of truth and informativeness (Maher, 140).

Since truth and informativeness are both considerations for accepting a theory, both are factors in verisimilitude. This makes verisimilitude the measure of the subjective "trade-off” between the two competing goals, again, how much one is willing to bet or risk for accepting a theory.

But while truth and informativeness are both valuable, they do not have the same measure of value to each person: some scientists will value truth and high probability more than informativeness and vice versa. Thus, the measure of verisimilitude for a theory will inevitably vary from person to person depending on how much one is willing to risk for information. The larger the informational content of a theory the harsher the consequences will be if the theory is wrong, for example, a much larger setback to progress than if the content were less. To repeat, verisimilitude is a measure of the "trade-off” between the two competing goals, meaning that there are three factors in the formula: informational content, the truth the theory, a.k.a., the distance from the truth, and the weight, or risk or "trade-off”, one is willing to put on the informational content.

The informational content of the theory is a measure of how much the theory answers one's cognitive questions and values, and is, thus, subjective (Maher, 231). In the case of scientific values, how much a theory answers to those values is inevitably to some degree indeterminate. Because our scientific values are concerned with truth and informativeness they require us to choose theories with high measures of verisimilitude. But the informativeness of a theory partially depends on its verisimilitude, for how informative a theory is depends on how close to the truth it is. A theory that is very far from the whole truth is not as informative as a theory that is closer to the whole truth. For example, Newtonian mechanics is not as informative as Einstein's theories of relativity because the latter is closer to the whole truth. This is not to say that a theory like Newtonian mechanics is not informative, for even a small measure of informativeness is still more informative than no information at all. But it does mean that our scientific values and cognitive questions are better answered by a theory with a higher measure of verisimilitude. So the informational content of a theory must be to some degree indeterminate, and this is in agreement with our intuitions, which do point out theories closer to the truth as more informative to us.

The measure of distance from the truth is a measure of how close a theory is to being true, which means that the distance will vary according to the different states (Maher, 237). Truth itself is an objective notion, and all true theories will have a distance of zero. But a measure of the distance from the truth must also take into account our interests in the true and false consequences of a theory. The distance is measured by the utility of accepting the theory when it is true minus the utility of accepting it when it is false, divided by a scaling factor. Because utility is a measure of one's preferences for the consequences, the resulting measure of distance satisfies our need to include our interests in the true and false consequences of the theory; thus, distance from truth is another subjective notion. (See also Maher, 169-71).

Once we have a measure of informational content and distance-our two aims for scientific theories, Le., informativeness and truth-we must decide how much we are willing to risk for the information. The distance is multiplied by a risk factor, 1/k, for some k that measures the relative weight we put on the informational content (Maher, 144). Verisimilitude is the resulting measure of the trade-off between informativeness and distance from truth, and is thus measured by multiplying the distance by the risk factor and subtracting from the informational content (Maher, 240). And this fulfills the initial quoted definition of verisimilitude as "a measure of the cognitive utility of accepting a hypothesis under different circumstances."

I find Maher's explication of verisimilitude to be preferable to a contrasting explication such as Graham Oddie's in his Likeness to the Truth (1986). Oddie claims that we have intuitions about verisimilitude and we ought to trust those intuitions. "An intuitive grasp of the concept comes before any theory. Not only will intuitive examples be used in judging the adequacy of each theory, but the very act of judging presupposes an acquaintance with the notion of a good 'fit' of theory to the known facts" (Oddie, 8). In his explication of verisimilitude he uses hypothetical examples of different theories about some true state. At first glance we have clear intuitions about which of the theories is closest to the true state. He defines what it means for a theory to have the best fit to the true state, and shows, using the examples, how each hypothetical theory is measured against the true state to find which one is the best fit. (See Oddie, Ch. 4). I will not go into detail about his theory, for it is not necessary.

While I find Oddie's theory to present a very adequate method of measuring theories against the true state to find which theory is most like the truth, i.e., the best fit, I find his theory less preferable to Maher's. For Oddie, verisimilitude represents how close a theory actually is to truth. In each of his examples, theories are measured against the true state: in order to measure the truthlikeness, one needs to know the true state. It is unclear to me how this could prove useful in understanding science. We do not know the true state of the world to measure our theories against, and even if we did, measuring our false theories against it would seem nothing more than an afterthought, to perhaps see how close we were.

But science is about developing theories that we believe are closer to the truth than older theories. And it is clear to me that Maher's theory does the job and best coheres with how scientists actually go about their business. Nothing in Maher's theory prompts us to need to know anything about the true state, other than the available observations and experiments[4], in order to determine the verisimilitude of a theory. Again, an important part of Maher's project is that it coincide with how scientists actually do make decisions about theories and their acceptance of certain theories over others. It is a vital aspect of his theory that scientists prefer true theories over false theories that are empirically adequate, which is van Fraassen's view. This does make his theory susceptible to confirmation or disconfirmation by empirical evidence, such as a survey of scientists and their preferences. "I suspect that if such a survey were conducted, we would find that scientists typically have a higher cognitive utility for accepting a theory when it is true than when it is false but empirically adequate" (Maher, 242). I believe Maher is right about this: I have read the works of some scientists, and Maher has captured a true representation of how typical scientists do their work.

A common objection to Maher's theory is that it represents scientists as behaving too subjectively when making decisions about acceptance of theories. This is similar to Thomas Kuhn's theory in The Structure of Scientific Revolutions, and the theories of other anthropologists, sociologists, and historians of science. However, conclusions about the apparent subjectivity in the work of scientists appears to stem from misunderstandings about why scientists make the decisions they do. Steven Weinberg addresses this very issue in his book Dreams of a Final Theory (1992), pp. 166-90. He affirms the claim that scientists do behave subjectively, but that this subjectivity is absolutely necessary in order for scientists to understand the observations and experiments that they make, as well as necessary for science to make progress.

Weinberg cites J. J. Thomson's discovery of the electron in his famous 1897 experiment with a cathode ray tube. At about the same time Thomson performed his experiment, Walter Kaufmann in Berlin performed the exact same experiment, and it was even better than Thomson's (Weinberg, 178). However, Kaufmann did not report that he discovered a new particle, while Thomson did. The difference is that Thomson had a subjective belief about what he observed, while Kaufmann resisted any kind of subjective conclusions-he only stuck to reporting the mere observations. The point is that typically scientists do have subjective beliefs about their observations, and without them, scientists could not make the discoveries they have made or develop the theories they have. Thomson held a belief that he discovered a new particle, but he did not know this from his experiment. It took several further experiments to prove that he was right (Weinberg, 179). Thomson made a bet, a risk, that he discovered a new particle.

He then cites the theory of quarks put forth by Murray Gell-Mann and George Zweig in the early 1960s (Weinberg, 182). At that time, particle physics was overloaded by a "zoo of particles" that resulted in tremendous complexity in the theories governing particles. Gell-Mann and Zweig, motivated by their own subjective views about the structure of the world as composed of smaller and simpler parts, "proposed that almost all of these particles are composed of a few simple (and even more elementary) particles that Gell-Mann named quarks" (Weinberg, 182). But several attempts by physicists during the 1960s and 1970s to discover these quarks in experiments failed. It was not until the theory of quantum chromodynamics, which explains why quarks cannot be freed from each other so as to be observed in isolation, was shown to be correct in 1973 that the theory of quarks was accepted (Weinberg, 182-3). And the point here is that Gell-Mann and Zweig had a hunch based on their own subjective beliefs about the structure of the world that led them to propose a theory that could not at that time be empirically confirmed, but was shown later to be a correct theory.

Lastly, Weinberg cites Andrew Pickering from his book Constructing Quarks where he makes the claim "that the content of the scientific theories that become accepted is what it is because of the social and historical setting in which the theories are negotiated" (Weinberg, 186). Weinberg recounts Pickering's description of why a change of emphasis in high-energy experimental physics took place in the late 1960s and early 1970s. The change of emphasis was from "concentrating on the most conspicuous phenomena in collisions of high-energy particles (Le., the fragmentation of the particles into great numbers of other particles)" to a focus on "rare events, such as those in which some high-energy particle emerges from the collision at a large angle to the incoming beam direction" (Weinberg, 187). But the change did not occur because of shifts in the subjective negotiations between scientists at that time in history, which sounds like something similar to changes in fashion. Weinberg states that the change occurred because while "these may be the most conspicuous collisions, they are too complicated to allow us to calculate w hat should happen according to our current theory of quarks and gluons and so they are useless for testing that theory" (Weinberg, 187). The rare events, on the other hand, are not so complicated and are calculable by our current theories. It appears, then, that Pickering misunderstood why the change in emphasis occurred, despite the fact that, as Weinberg himself states, Pickering is quite knowledgeable about the theoretical background surrounding the issue.

Thus, subjectivity in science as Weinberg describes it agrees with Maher's theories of acceptance and verisimilitude as representations of how scientists do make decisions about theory acceptance. Consider this quote from Weinberg:

A party of mountain climbers may argue over the best path to the peak...but in the end either they find a good path to the peak or they do not, and when they get there they know it. (No one would give a book about mountain climbing the title Constructing Everest.) I cannot prove that science is like this, but everything in my experience as a scientist convinces me that it is. The "negotiations" over changes in scientific theory go on and on, with scientists changing their minds again and again in response to calculations and experiments, until finally one view or another bears an unmistakable mark of objective success.[5] It certainly feels to me that we are discovering something real in physics, something that is what it is without any regard to the social or historical conditions that allowed us to discover it.

I find this passage to represent perfect agreement with Maher's claim that scientists typically have a higher cognitive utility for accepting true theories than false theories that are empirically adequate. It is apparent that Maher's explication of verisimilitude coheres perfectly with the way some scientists do make decisions about accepting theories that they are willing to believe are closer to the truth than previous theories. To contrast again with Oddie's theory, Maher's theory proves to be more useful in our understanding of the process of accepting or rejecting scientific theories. This gives Maher's theory a higher cognitive utility for us, so that we ought, if we are to be consistent with rational and scientific values, prefer and choose to accept Maher's theory over one such as Oddie's, i.e., a theory that defines verisimilitude subjectively utilizing cognitive utility, and may vary from person to person, as opposed to objectively as a measure of the actual closeness of a theory to the truth that is the same measure for everyone.