Economics, Logic & Science January 9, 2011Posted by larry in economics, Logic, Science.
I would like to reflect on Bill Mitchell’s observation on Sunday, 9 January in his blog, that “Macroeconomics is hard to learn because it involves these abstract variables that are never observed”, such as the interest rate and the aggregate price level.
This is undoubtedly true. However, it seems to me that there are at least three other factors involved. I also want to propose a more useful set of models as a salutary basis for a scientific grounding for economic theory.
First: the abstractions economists use are not often tied closely enough to concrete examples. Take the difference between nominal GDP and real GDP. While I understand that Bill is being concise and assuming a certain level of understanding when he refers to these, many people don’t understand the difference without practical illustrations. [See * fn below]
Second: one economist can take a given set of data and conclude A, while another, taking the same data, may conclude not-A and never mention why it would be wrong to conclude A on the basis of the data at hand. Consider what is going on re the current crisis. This latter propensity does tend to make economics look more like an ideological enterprise than a rationalist, scientific one (a la Lakatos). I am not suggesting Bill does the latter, only that it is often done. For someone not trained in a social science, both of these factors combined can make economic discourse look like exercises in nonsense. (Part of the reason for this lies in the values that are smuggled in, explicitly or implicitly, in assessments of the economic state of a society at a given point in time. These values form part of a complete economic explanation, but I must leave this aside for the moment.)
Third: A further contributing factor in certain circumstances is where economists give the impression that economics is like physics. This looks premature at best. Given that a standard formalization of physics, by no means complete, is in terms of an extensional predicate calculus of fourth order and that certain economic explanations need to refer to psychological states of actors, economic formalization would need to be intensional in character, i.e., non-extensional (non-truth functional). There are a number of intensional logics, but none developed with economics in mind. This renders physics a misleading guide for economics.
Finally – and more positively – I want to propose that theoretical ecology might be a more relevant mathematical scenario for economists to refer to as a guide. Ecological models tend to be quite specific to certain species and environments or to specific activities found in certain predator-prey relations (such as the Lotka-Volterra equations that some economists refer to). This would suggest specific models for specific situations over general models. Ecological models don’t include the psychological states of the animals, or not directly. They deal with the animals’ behavior, not their mental states, whatever these may be.
Ecologists know that in dealing with human behavior, they need to take mental states into account in some way. This can’t be done with the current mathematical tools that are available. Thus, they are unable to completely mathematize these accounts. Since most of their work does not need to take account of human mental states, most of their modeling can safely ignore this. But they can’t say that it is thereby irrelevant altogether in a complete account that included human activity. Which is what might be concluded were physics considered to be the field to be “mimicked”. Hence, if economists were to view their theoretical activity as analogous to that of ecologists, it might be easier to view whatever degree of mathematization that is carried out as an incomplete approximation and, thus, where and what further developments are needed.
My point, which is not a deep one, is that it isn’t only the abstractness of the discussion that makes economic discourse hard for the uninitiated to follow, it is also the lack of clear, concrete applications employed as explanatory aids in an appropriate logical context.
*I want to take this a bit further, simplifying if I may, using the predicate calculus as an example and, in particular, the definition of “if, then” or “if …, then ___”. In the propositional calculus, as I expect you know, the variables range over sentences. Hence, where A and B are arbitrary sentences, “if A then B” is also a sentence. Now, these are not just any old sentences, but declarative sentences, such as “John is a large man”, or “the man in the car is carrying a gun”. It also helps if one explains the ‘use-mention’ distinction.
In the predicate calculus, we have individual variables and predicate variables, covering nouns, pronouns, and adjectives (adverbs are explicitly avoided). We then have the universal and existential quantifiers, for which I shall use A and E. I’m sure you are familiar with all this. (But a superb discussion of logical grammar can be found in Belnap, “Grammatical Propadeutic”, in Anderson and Belnap, Entailment (vol. 1).)
At this point, the general reader benefits greatly from a concrete example. If a character in a B-western is wearing a black shirt and a black hat, then this character in such a film is a villain. If this character in such a film is a villain, then this character will either end up dead or in jail at the end of the film. Simplifying, we can restate the situation this way. Every character in a B-western wearing a black shirt and a black hat is a villain. Every villain in a B-western ends up dead or in jail at the end of the film.
This can be formalized as: Ax(if Wx then, Bx); Ax(if Bx, then Jx). We can conclude from this, via certain rules of inference and other assumptions, that Ax( Wx, then Jx), that is, every character in a B-western wearing a black shirt and a black hat will end up dead or in jail at the end of the film. While this is logically trivial, it may not be trivial in a setting where someone is trying to figure out how to do this sort of thing. It is not logically trivial, however, to formalize the following: it is an ill wind that blows nobody any good.
ADDENDUM: To see a rather concise, albeit incomplete, discussion of the complexity of the scientific enterprise, one can do no better than to have a look at Patrick Suppes’ Models of Data from 1962.