There is an interesting fact about science, one that probably Kuhn was first to note: When we perform experiments and enter into a study, the scientist will do his or her best to jam any result into the box, and be completely satisfied with that. End of story. The scientist proved what they thought was or might be the case. This extends well beyond the natural sciences, and is much easier in some of the other empirical sciences, as will be seen in this bog post primarily on economics. I bring all of this up because of a paper I recently came across that deeply bothered me. The title is “Hacking’s historical epistemology: a critique of styles of reasoning” (Studies in History and Philosophy of Science 41 (2010) 158-173) by Martin Kusch. The paper is nothing more than a hatchet job on Hacking —one of a sordid psychology, despite the fact that Kusch explicitly says it is not; very despicable, in my view. I will avoid the primary content, save for mentioning that the real, underlying sentiment of the paper is a displeasure with Hacking for moving from epistemic relativism (see “Language, truth, and reason,” 1982) toward historical epistemology (see “‘Style’ for historians and philosophers,” 1992). My proposal for this blog post is to do four things in the following four paragraphs: 1) set up and explain one of Kusch’s views (in the criticism portion) of his critique of Hacking, 2) discuss a seemingly unrelated piece of work in economics, and point out a very important concomitant result that has, heretofore, been overlooked, and 3) explain why Kusch’s position is flat out wrong, and why Hacking is, at least more correct. Two comments: The first is that I do not completely agree with Hacking, but I think his journey has been more authentic and truth-driven, which was, in my opinion, the reason he has drifted away from relativism; but I will not use this forum as a place for discussing my views in relation to Hacking, and, admittedly, I am not well read enough in Hacking’s vast and august oeuvre to be comfortable in presenting my opinion. The second is that I do not consider Kahneman or Tversky to be at fault for missing, what is in my opinion, a much, much more important result of their work —far and away, more important than the reason for which the Nobel Prize in Economic Sciences was issued for that selfsame work.
To give you a sense of what Hacking is going for in talking about “styles of reason,” here is a list of developments he presents in the former of the two abovementioned works:
- 1640-1693 the emergence of probability
- 1693-1756 the doctrine of chances
- 1756-1821 the theory of error, and moral sciences I
- 1821-1844 the avalanche of printed numbers, and moral sciences II
- 1844-1875 the creation of statistical objects
- 1875-1897 the autonomy of statistical law
- 1897-1933 the era of modeling and fitting (list taken from pg 161 of Kusch, 2010)
It doesn’t take too much to get an intuitive sense about what one is talking about in terms of “style of reasoning.” Were you to go Athens, back in 399 BCE, and ask (supposing he spoke English), “Socrates, does the average Athenian think you are guilty?” his response would be, without a doubt, “what is ‘average’?” More, it is easy to see how scientific worldviews were sculpted by this kind of thinking; just consider the effect population statistics had on evolutionary theory, statistical mechanics on technology, or, more in terms of general outlook, Gustav Klimt’s piece, called “Philosophie.” What is not to be denied is that there are non-systematic elements associated with styles of reasoning that arise and are shaped by those systems, just as general outlooks are psychologically coupled with and constrained by systems of reasoning. What I will show to be completely erroneous is the following portion of Kusch’s relativist disquisition:
The advocates of two different styles of reasoning, R1and R2, can reach conflicting verdicts on one and the same sentence s, even though s expresses a proposition only in R1and not in R2. The advocate of R1 might judge s to be rational, justified or true, while the advocate of R2might conclude that s, precisely because it does not express a proposition in R2 is meaningless. I see no reason why the two advocates of different styles might not value each other as rational beings on grounds unrelated to their current difference, and why they might not each come up to appreciate the internal coherence of each others’ reasoning —and without adopting the other’s style. (Kusch 167)
Briefly, we will move into economics. Consider the Nobel Prize winning work of Kahneman and Tversky, and their paper, “Prospect Theory: An Analysis of Decision Under Risk” (Econometrica 47 (1979) 2). A basic arithmetical concept, which was used in Kahneman and Tversky, is called the “Neumann utility function.” One uses it to decide between options that are quantifiable. To calculate the utility of making a particular decision, you multiply possible outcomes by their probability of occurring, and add them up. For any set of outcomes (mathematically expressed as {O1, O2, O3,…On}) and the percentages of each occurring ({P1, P2, P3,…Pn}), the utility (U) of a particular decision is the summation from one to n: U= ∑ (On ∙ Pn). For the non-mathematicians, this is really simple. Here’s how it works: If you have a 10% of winning $20 and a 90% of winning $5, then the utility is: 20 ∙ .1 + 5 ∙ .9 = 6.5; the unit, in this case, is the dollar. (Note that percentages are given in decimals, e.g., 50% as .5, and 100% as 1.0 .) What Kahneman and Tversky found is that many people would make decision that were not optimal, if the one of them was a sure bet. You can see the actual data given in the paper, but the decisions that people were to make was something like this: option 1: 50% chance of winning a coin toss and earning $5,000, with an equal chance of getting $0 or option 2: a guaranteed $2,000. The utility of the first option would be $5,000 ∙ (.5) + $0 ∙ (.5) = $2,500, and the utility of the second option is just $2,000 ∙ (1) = $2,000. The number of people willing to take option 2 was about 80% or a bit more. I have spelled things out for you, and you see the expectation values, that is, the utility for each decision; so you see the irrationality in the behavior, and why this is an important result in the psychological area of economics, called “behavioral economics.” The assumption of humans, as rational economic actors, appears to get defenestrated. However, there is an R1 and an R2 afoot. Can you see them? Okay —so I showed you the mathematics behind behaving rationally, but the participants weren’t so enlightened. In fact, I would speculate that a portion of the, say, 12-17% of people acted rationally weren’t just wild risk-takers, but that they knew a bit of math. One would not get the same distribution if he participants came strictly from math departments. What does that say? It says that a participant with access to Neumann utility functions has access to a rational system, call it —oh, I don’t know— R2. The rational system of the non-mathematically inclined has a reasoning system that says, “get whatever you can, whenever you can get it for sure.” Call this system of reasoning R1. Without a doubt, this satisfies Kusch’s requirement that one system of reasoning be meaningless to the other participant (and math certainly is meaningless to someone without any math education). Now, reread Kusch’s comment, and answer me this: Do you still like his comment?
Kusch’s epistemic relativity takes as a reality a very bizarre notion, namely, that system of reasoning, that is, styles of reasoning, are all equivalent. Bizarre as it may sound at first, I have never ever, ever come across two equally efficacious systems of reasoning. The closest I have come across is a historical one, that of Ptolemy’s system and Copernicus’ systems, as challenged in 1543, though I agree with Kuhn that Ptolemy’s was superior. Even in this, the best I could do to present an example, I fail to cite a couplet of systems that produce the same degree of rationality. That is, I propose, for all structured reasoning system (the more formal portion of styles of reasoning), Rn, it is always the case that a degree of efficacy can be assigned to the systems such that one will be relatively superior to the other, and that under no circumstances, save for mathematical addendum to the rational system, can the degree of efficacy of one system be inverted to prefer the other. Therefore, the efficacies of any two systems are relative in position, but objectively established in their respective rationality, as rational efficacy is not plastic. As an example, the defined R2 will always empirically yield more fruit than R1. Their relation to one another is relative, but R2 is objectively of a higher degree of rationality than R1, and not only is this shown in the mathematics themselves, but also evinced by experience. This is the more important result that has gone unnoticed in the tremendously important work of Kahneman and Tversky. The upshot, with regard to Kusch’s passage, is, no!, two adherents of two different styles of reasoning cannot see the rationality of the other’s and simply agree to disagree. From the standpoint of the portion of the styles that are formalized axiomatic systems, one can only be irrational to accept the objective superiority of another style and yet reject it. The one last thing that needs pointing out is where any two given styles might disagree. Suppose that something that has never been the case is, in fact the case, that two styles possess the same degree of rationality —maybe one models a system using one branch of mathematics, and the second uses another, and, for the sake of argument, assume they are equally potent. The instances in which the styles truly differ, given the fact that the mathematics are really idealized isomorphisms, is in their non-rational elements, and people the people who argue over said element are arguing in the realm of the irrational. Kusch’s line of epistemic relativist thinking has been kicked to the curb, as should his vituperative article.
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