This note is a comment on the paper “Knowledge before belief” by Phillips et al., which argues that it is better not to regard knowledge in the cognitive sciences as a special kind of belief, but as a prior category that requires different treatment. Its aim is to endorse this conclusion, not only for the cognitive sciences, but also for economics and other disciplines that rely on rational choice theory, where the need to prioritize knowledge over belief is equally pressing. However, the approach I advocate requires departing even more than Phillips et al. from the traditional philosophical characterization of knowledge as “justified true belief” (Binmore, Reference Binmore2011a).
The orthodoxy in rational choice theory is Bayesianism, as formulated for applications in small worlds by Leonard Savage (Reference Savage1954) in his Foundations of Statistics. It is argued that if Alice's decisions are sufficiently consistent with each other, then she will behave as though maximizing the expected value of a utility function calculated using subjectively determined probabilities. In Savage's treatment, it is taken for granted that Alice knows the set of all possible events in advance of any analysis. In particular, when conditioning on some new information, probabilities are updated using Bayes' rule on the assumption that Alice now knows that the set of possible events is reduced to only those events consistent with her information.
What do the standard Bayesian assumptions about such information sets imply about what Alice knows? The answer is that knowledge must satisfy all the axioms that philosophers attribute to necessity (Binmore, Reference Binmore2009, Reference Binmore2011b). But a proposition is said to be necessary if and only if it is true in all possible worlds, and hence is literally impossible to refute. The foundations of Bayesianism, therefore, implicitly take for granted that knowledge is prior to belief, but users of rational choice theory nevertheless typically take for granted that knowledge should be modeled as certitude, interpreted as meaning “belief with probability one.”
There is, for example, an unsettled dispute in game theory about the extent to which games more general than Chess can be solved, in principle, by working backward from all possible final positions. Is Robert Aumann (Reference Aumann1995) right to claim that common knowledge of rationality implies backward induction in all finite games of perfect information? I think the answer is no if knowledge is interpreted as certitude, but trivially yes if knowledge is interpreted as proposed in what follows (Binmore, Reference Binmore2011b).
An official orthodoxy in economics is the theory of revealed (or attributed) preference (Samuelson, Reference Samuelson1947). Suppose we are told that Alice has made certain choices. If she always chooses consistently, it is then possible to predict some of the choices she will make in the future. The Bayesian approach to belief is a late fruit of this approach. My suggestion is that it is sometimes useful to study knowledge from the same perspective, so that Alice is said to be behaving as though she knows some proposition if she always chooses as though it were true. Religious faith is a good example. I call this behavioral characterization knowledge-as-commitment to distinguish it from the orthodox notion of knowledge-as-belief.
An objection to knowledge-as-commitment is that one not only has to give up the idea that knowledge is a kind of belief, but also that Alice can only be said to know propositions that she can justify as being true. Knowledge-as-commitment captures this requirement only to the extent that attributing such knowledge to Alice requires that she never modify a proposition that she is said to know. After all, if Alice were to change her mind in ordinary life, we would say that she was mistaken to claim that she knew the proposition in the first place.
It is a hard bullet to bite that knowledge-as-commitment can survive even outright contradiction, but Donald Trump has taught us how evidence that contradicts propositions to whose truth we are committed can be dismissed by calling it “fake news.” However, it is not only antivaxxers and homeopaths that can be effectively modeled using the idea of knowledge-as-commitment. As Kuhn (Reference Kuhn1947) argues, normal science also explains away data that apparently refutes standard models by treating it as fake or irrelevant news. Dark matter illustrates this point in two ways. At first, physicists ignored the discovery that galaxies would not hold together if only the mass in visible stars were present. When this was no longer possible, they invented dark matter rather than meddle with the orthodox theory of gravitation.
However, my favorite example occurred when Socrates sought to explain why the Delphic Oracle had named him as the wisest man in Greece. He reasoned that it must be because he was unique in knowing that he knew nothing – by which apparently contradictory remark, I think he meant that he was committed to the view that all his beliefs were open to doubt, including those of which he was most certain. That is to say, Socrates had knowledge-as-commitment that knowledge-as-belief is always open to revision.
You have
Access
This note is a comment on the paper “Knowledge before belief” by Phillips et al., which argues that it is better not to regard knowledge in the cognitive sciences as a special kind of belief, but as a prior category that requires different treatment. Its aim is to endorse this conclusion, not only for the cognitive sciences, but also for economics and other disciplines that rely on rational choice theory, where the need to prioritize knowledge over belief is equally pressing. However, the approach I advocate requires departing even more than Phillips et al. from the traditional philosophical characterization of knowledge as “justified true belief” (Binmore, Reference Binmore2011a).
The orthodoxy in rational choice theory is Bayesianism, as formulated for applications in small worlds by Leonard Savage (Reference Savage1954) in his Foundations of Statistics. It is argued that if Alice's decisions are sufficiently consistent with each other, then she will behave as though maximizing the expected value of a utility function calculated using subjectively determined probabilities. In Savage's treatment, it is taken for granted that Alice knows the set of all possible events in advance of any analysis. In particular, when conditioning on some new information, probabilities are updated using Bayes' rule on the assumption that Alice now knows that the set of possible events is reduced to only those events consistent with her information.
What do the standard Bayesian assumptions about such information sets imply about what Alice knows? The answer is that knowledge must satisfy all the axioms that philosophers attribute to necessity (Binmore, Reference Binmore2009, Reference Binmore2011b). But a proposition is said to be necessary if and only if it is true in all possible worlds, and hence is literally impossible to refute. The foundations of Bayesianism, therefore, implicitly take for granted that knowledge is prior to belief, but users of rational choice theory nevertheless typically take for granted that knowledge should be modeled as certitude, interpreted as meaning “belief with probability one.”
There is, for example, an unsettled dispute in game theory about the extent to which games more general than Chess can be solved, in principle, by working backward from all possible final positions. Is Robert Aumann (Reference Aumann1995) right to claim that common knowledge of rationality implies backward induction in all finite games of perfect information? I think the answer is no if knowledge is interpreted as certitude, but trivially yes if knowledge is interpreted as proposed in what follows (Binmore, Reference Binmore2011b).
An official orthodoxy in economics is the theory of revealed (or attributed) preference (Samuelson, Reference Samuelson1947). Suppose we are told that Alice has made certain choices. If she always chooses consistently, it is then possible to predict some of the choices she will make in the future. The Bayesian approach to belief is a late fruit of this approach. My suggestion is that it is sometimes useful to study knowledge from the same perspective, so that Alice is said to be behaving as though she knows some proposition if she always chooses as though it were true. Religious faith is a good example. I call this behavioral characterization knowledge-as-commitment to distinguish it from the orthodox notion of knowledge-as-belief.
An objection to knowledge-as-commitment is that one not only has to give up the idea that knowledge is a kind of belief, but also that Alice can only be said to know propositions that she can justify as being true. Knowledge-as-commitment captures this requirement only to the extent that attributing such knowledge to Alice requires that she never modify a proposition that she is said to know. After all, if Alice were to change her mind in ordinary life, we would say that she was mistaken to claim that she knew the proposition in the first place.
It is a hard bullet to bite that knowledge-as-commitment can survive even outright contradiction, but Donald Trump has taught us how evidence that contradicts propositions to whose truth we are committed can be dismissed by calling it “fake news.” However, it is not only antivaxxers and homeopaths that can be effectively modeled using the idea of knowledge-as-commitment. As Kuhn (Reference Kuhn1947) argues, normal science also explains away data that apparently refutes standard models by treating it as fake or irrelevant news. Dark matter illustrates this point in two ways. At first, physicists ignored the discovery that galaxies would not hold together if only the mass in visible stars were present. When this was no longer possible, they invented dark matter rather than meddle with the orthodox theory of gravitation.
However, my favorite example occurred when Socrates sought to explain why the Delphic Oracle had named him as the wisest man in Greece. He reasoned that it must be because he was unique in knowing that he knew nothing – by which apparently contradictory remark, I think he meant that he was committed to the view that all his beliefs were open to doubt, including those of which he was most certain. That is to say, Socrates had knowledge-as-commitment that knowledge-as-belief is always open to revision.
Conflict of interest
None.