One of the motivations underlying the psychology of human reasoning has been the assessment of human rationality: that is, comparing human reasoning performance with some standard of rationality provided by a normative theory, be it standard bivalent logic, Bayesian probability theory, expected utility theory, or quantum probability (QP) theory (Chater & Oaksford Reference Chater, Oaksford, Holyoak and Morrison2012). Whether this is a proper function of psychological theories of reasoning has been debated within the pages of Behavioral & Brain Sciences (Elqayam & Evans Reference Elqayam and Evans2011), but QP is a competitor to classical probability (CP) theory precisely at the computational, normative level. Pothos & Busmeyer (P&B) are quite explicit on this point when they observe that under a QP interpretation, the conjunction fallacy is not fallacious. This assertion makes sense only with the understanding that it conforms to the dictates of QP, considered as a normative theory of how people should reason. However, P&B do not provide an account of why, intuitively, QP is rational. Rather, in section 5, “The rational mind,” they concentrate on pointing out existing problems with the claims of CP, to provide an account of rationality.
Although as P&B observe, there are problems for existing normative theories, there are very clear underlying intuitions about why they are rational. For standard bivalent logic, the primary intuition is that contradictions are bad – that is, it is irrational to believe both p and not-p (e.g., chalk is white and chalk is not white). If one follows the laws of logic, one will never fall into contradiction, and, therefore, logic can provide a rational standard. Similarly for probability theory, the primary intuition is that making bets that one is bound to lose is bad. If one follows the laws of probability in the Kolmogorov axioms, one will never make a bet one is bound to lose, and therefore it can provide a rational standard. P&B provide no similar intuitive understanding of how QP is rational, even if this understanding is ultimately deficient in some respects, as they point out for CP. Rather, P&B observe that QP is loosely like bounded rationality, and is consistent with the isotropic and the Quinean nature of human thought.
The lack of an intuitive grasp of rationality in QP relates to the closing sentence of section 5: “For the real, noisy, confusing, ever-changing, chaotic world, QP is the only system that works in physics and, we strongly suspect, in psychology as well.” The world they describe here is actually the microscopic world of quantum events that supplies the underlying domain of QP – that is, the world whose behaviour it is trying to describe. However, the world that provides the appropriate domain for logic and CP is a relatively stable macroscopic world of which we have varying states of knowledge. Insofar as the statements of these theories describe these worlds, they provide a theory of what these statements mean. There are obvious complexities here, but one requirement of a formalism is that, in Susan Haack's (Reference Haack1978) terminology, it should be capable of respecting the appropriate depraved semantics (Haack Reference Haack1978, p. 188) – that is, people's intuitive understanding of a domain.
Logic and CP, to the extent they have a rational foundation, assume a world where events cannot both occur and not occur and where there are objective values. The extent to which one might be inclined to adopt QP is the extent to which one is willing to view the macroscopic world as being much more like the microscopic world than we have so far considered, hence it can provide an appropriate depraved semantics. One might also question whether the actual world of everyday experience is the “noisy, confusing, ever-changing, chaotic” place or whether this is the product of our situatedness within in it. However we view it, one should not underestimate the magnitude of the change in the conception of the macroscopic world underlying human cognition that QP entails.
For example, in quantum logic (Haack Reference Haack1974), which underpins QP in the same way that classical logic underpins CP, the law of the excluded middle, or non-contradiction (not(p and not-p)), does not hold – that is, the intuitive rational basis of classical logic is explicitly denied. Therefore, in the microscopic world, quantum events can occur and not occur. But to embrace QP is – for some events at least, that is, when questions are incompatible – to require people to reject non-contradiction for some macroscopic events, which seems deeply counterintuitive. However, this may not be quite as counterintuitive as it seems.
Although there is no scope to develop the connections here in any detail, there is a semantic account more readily compatible with QP. This account is provided by situation theory (see Barwise & Perry Reference Barwise and Perry1983; for a recent review, see Stojanovic Reference Stojanovic, Newen and Van Riel2012), in which situations – construed as something between the physical and the psychological, simplistically, the bit of world one can see that can include other people who might have a different perspective on the same situation – are the basic building blocks, and objects and regularities only emerge as uniformities against the background of the ever-changing situations in which we find ourselves. Joining such a world view with QP may provide an intuitive, rational handle on QP. For example, perspectival terms, such as “behind” (which are often assimilated to indexicals), reveal apparent breakdowns of non-contradiction. Therefore, for example, “the table is behind the sofa” may be true from my perspective in a situation, but it may be false from yours. “Perspectival relativity” is an important feature of situation semantics.
In summary, whereas one cannot help but be impressed by the empirical grasp of QP, its potential to provide an alternative rational foundation for human reasoning requires further consideration, as for some events, the failure of non-contradiction at the macroscopic level seems deeply counterintuitive. However, there are accounts of the semantics of natural language that appear compatible with QP, and those may provide a much needed intuitive foundation.
One of the motivations underlying the psychology of human reasoning has been the assessment of human rationality: that is, comparing human reasoning performance with some standard of rationality provided by a normative theory, be it standard bivalent logic, Bayesian probability theory, expected utility theory, or quantum probability (QP) theory (Chater & Oaksford Reference Chater, Oaksford, Holyoak and Morrison2012). Whether this is a proper function of psychological theories of reasoning has been debated within the pages of Behavioral & Brain Sciences (Elqayam & Evans Reference Elqayam and Evans2011), but QP is a competitor to classical probability (CP) theory precisely at the computational, normative level. Pothos & Busmeyer (P&B) are quite explicit on this point when they observe that under a QP interpretation, the conjunction fallacy is not fallacious. This assertion makes sense only with the understanding that it conforms to the dictates of QP, considered as a normative theory of how people should reason. However, P&B do not provide an account of why, intuitively, QP is rational. Rather, in section 5, “The rational mind,” they concentrate on pointing out existing problems with the claims of CP, to provide an account of rationality.
Although as P&B observe, there are problems for existing normative theories, there are very clear underlying intuitions about why they are rational. For standard bivalent logic, the primary intuition is that contradictions are bad – that is, it is irrational to believe both p and not-p (e.g., chalk is white and chalk is not white). If one follows the laws of logic, one will never fall into contradiction, and, therefore, logic can provide a rational standard. Similarly for probability theory, the primary intuition is that making bets that one is bound to lose is bad. If one follows the laws of probability in the Kolmogorov axioms, one will never make a bet one is bound to lose, and therefore it can provide a rational standard. P&B provide no similar intuitive understanding of how QP is rational, even if this understanding is ultimately deficient in some respects, as they point out for CP. Rather, P&B observe that QP is loosely like bounded rationality, and is consistent with the isotropic and the Quinean nature of human thought.
The lack of an intuitive grasp of rationality in QP relates to the closing sentence of section 5: “For the real, noisy, confusing, ever-changing, chaotic world, QP is the only system that works in physics and, we strongly suspect, in psychology as well.” The world they describe here is actually the microscopic world of quantum events that supplies the underlying domain of QP – that is, the world whose behaviour it is trying to describe. However, the world that provides the appropriate domain for logic and CP is a relatively stable macroscopic world of which we have varying states of knowledge. Insofar as the statements of these theories describe these worlds, they provide a theory of what these statements mean. There are obvious complexities here, but one requirement of a formalism is that, in Susan Haack's (Reference Haack1978) terminology, it should be capable of respecting the appropriate depraved semantics (Haack Reference Haack1978, p. 188) – that is, people's intuitive understanding of a domain.
Logic and CP, to the extent they have a rational foundation, assume a world where events cannot both occur and not occur and where there are objective values. The extent to which one might be inclined to adopt QP is the extent to which one is willing to view the macroscopic world as being much more like the microscopic world than we have so far considered, hence it can provide an appropriate depraved semantics. One might also question whether the actual world of everyday experience is the “noisy, confusing, ever-changing, chaotic” place or whether this is the product of our situatedness within in it. However we view it, one should not underestimate the magnitude of the change in the conception of the macroscopic world underlying human cognition that QP entails.
For example, in quantum logic (Haack Reference Haack1974), which underpins QP in the same way that classical logic underpins CP, the law of the excluded middle, or non-contradiction (not(p and not-p)), does not hold – that is, the intuitive rational basis of classical logic is explicitly denied. Therefore, in the microscopic world, quantum events can occur and not occur. But to embrace QP is – for some events at least, that is, when questions are incompatible – to require people to reject non-contradiction for some macroscopic events, which seems deeply counterintuitive. However, this may not be quite as counterintuitive as it seems.
Although there is no scope to develop the connections here in any detail, there is a semantic account more readily compatible with QP. This account is provided by situation theory (see Barwise & Perry Reference Barwise and Perry1983; for a recent review, see Stojanovic Reference Stojanovic, Newen and Van Riel2012), in which situations – construed as something between the physical and the psychological, simplistically, the bit of world one can see that can include other people who might have a different perspective on the same situation – are the basic building blocks, and objects and regularities only emerge as uniformities against the background of the ever-changing situations in which we find ourselves. Joining such a world view with QP may provide an intuitive, rational handle on QP. For example, perspectival terms, such as “behind” (which are often assimilated to indexicals), reveal apparent breakdowns of non-contradiction. Therefore, for example, “the table is behind the sofa” may be true from my perspective in a situation, but it may be false from yours. “Perspectival relativity” is an important feature of situation semantics.
In summary, whereas one cannot help but be impressed by the empirical grasp of QP, its potential to provide an alternative rational foundation for human reasoning requires further consideration, as for some events, the failure of non-contradiction at the macroscopic level seems deeply counterintuitive. However, there are accounts of the semantics of natural language that appear compatible with QP, and those may provide a much needed intuitive foundation.