Underdetermination and truth

We say that a statement is underdetermined by available facts when it and an alternative and different statement or theory are equally consistent with that body of facts. It may be that two physical theories have precisely the same empirical consequences -- perhaps wave theory and particle theory represent an example of this possibility. And by stipulation there is no empirical circumstance that could occur that would distinguish between the two theories; no circumstance that would refute T1 and confirm T2. And yet we might also think that the two theories make different assertions about the world. Both statements are underdetermined by empirical facts.

Pierre Duhem further strengthened the case for the underdetermination of scientific theories through his emphasis on the crucial role that auxiliary hypotheses play in the design of experiments in The Aim and Structure of Physical Theory.  Individual theoretical hypotheses -- "light is a wave," "people behave on the basis of their class interests" -- do not have definite empirical implications of their own; rather, it is necessary to bring additional assumptions into play in order to design experiments that might support or refute the theoretical hypothesis.  And here is the crucial point: if an experimental result is inconsistent with the antecedent theory and auxiliary hypotheses, we haven't demonstrated that the hypothesis itself is false, but rather that at least one among the premises is false. And it is possible to save the system by modifying the theory or one or more of the auxiliary assumptions.  As W. V. O. Quine put the point, scientific knowledge takes the form of a "web of belief" (The Web of Belief).  

On the extreme assumption that both statements have precisely the same consequences, we might infer that the two theories must be logically equivalent, since the logical content of a theory is the full range of its deductive consequences and the two theories are stipulated to have the same deductive consequences. So it must be possible to derive each theory from the other. And if T1 and T2 are logically equivalent, then we wouldn't say that they really express different assertions about the world.

A more problematic case is one where two theories have distinct bodies of deductive consequences; but where the subset of deductive consequences that are empirically testable are the same for the two theories. In this situation it is no longer the case that the two theories are logically equivalent but rather "empirically equivalent." And here it would be credible to say that the two make genuinely different assertions about the world -- assertions that cannot be resolved empirically.

A third and still weaker case is one in which T1 and T2 have distinct consequences for both theoretical statements and a specific subset of empirical statements; but they overlap in their consequences for a second body of empirical statements. And consider this possibility: Because a given level of instrumentation and inquiry limit the types of empirical statements that can be evaluated, this body of data does not permit us to differentiate between the theories. So we can distinguish between "currently testable" and "currently not testable". For this third case, we are to imagine that T1 and T2 have distinct implications for theoretical statements and for currently not testable empirical statements; but they have the same consequences for currently testable statements. In this case, T1 and T2 are currently underdetermined -- though advances in instrumentation may result in their being empirically distinguishable in the future.

It is worth noting how heroic is the notion of "determination" of theory by evidence. If we thought that science should issue in theories that are determined by the empirical evidence, we would be committed to the idea that there is one uniquely best theory of everything. This assumption of ultimate theory uniqueness might be thought to follow from scientific and metaphysical realism: the world has a specific and determinate structure and causal properties; this structure gives rise to all observations; well-supported theories are approximately true descriptions of this hidden structure of the world; and therefore there is a uniquely best scientific theory -- the one that refers to this set of entities, processes, and structures. And if an existing theory is false in description of this unobservable reality, then there must be observational circumstances where the false assumptions of the theory give rise to false predictions about observation.  In other words, well-confirmed theories are likely to be approximately true, and the hidden structure of the world can be expected to create observations that refute out false theories.

However, this foundational approach is implausible in virtually every area of science.  Our theories rarely purport to describe the most fundamental level of reality; instead, they are meso-level descriptions of intermediate levels of phenomena. Take the effort to understand planetary motion.  The description of the orbits of the planets as ellipses generated by the gravitational attraction of the planet and the sun turned out to be only approximately true.  Did this refute the pure theory of gravitation? Certainly not; rather, it raised the possibility of other causal processes not yet identified, that interfere with the workings of gravitational attraction.

So how do these general considerations from the philosophy of science affect the situation of knowledge claims in the social sciences?

It would seem that social science claims are even more subject to underdetermination than the claims of mechanics and physics. In addition to the problem of unidentified interfering causes and the need for auxiliary hypotheses, we have the problems of vagueness and specification.  We commonly find that social science theories offer general statements about social causes and conditions that need to be further specified before they can be applied to a given set of circumstances. And there are almost always alternative and equally plausible ways of specifying the concept in a particular setting.

Take the idea of class conflict as a theory of political behavior.  The theory may assert that "workers act on their material interests." Before we can attempt to evaluate this statement in particular social settings, we have to specify several things: how to characterize "material interests" in the setting and how to represent the cognitive-behavioral models the worker uses as he/she deliberates about action.  Is retaining support from City Hall a material interest? Or are material interests restricted to wages and the workplace? Are workers thought to be rational maximizers of their interests, or do they also embody social commitments that modulate the dictates of maximization? And here is the crucial point: different specifications lead to different predictions about political behavior; so the general theoretical assertion is underdetermined by empirical observation.

This discussion seems to lead us into surprising territory -- not the limited question of underdetermination but the large question of truth and correspondence and the question of the rationality of scientific belief. Do we think that social assertions are true or false in the semantic sense: true by virtue of correspondence to the facts as they really are; or do we think that social assertions are simply ways of speaking about complexes of social phenomena, with no referential force? Is the language of class or ideology or ressentiment just a way of encompassing a range of social behaviors, or are there really classes and ideologies in the social world? And if we affirm the latter possibility, does the evidence of social observation permit us to unambiguously select the true theories?

I suppose one possible approach is to minimize the scope of "truth" when it comes to the social sciences. We might say that there is a limited range of social statements that are unambiguously true or false -- Jones robbed a store, Jones robbed a store because he was economically desperate, people sometimes commit crimes out of economic necessity -- but there is a broader class of statements that have a different status.  These are more akin to interpretive schemes in literary criticism or to a set of metaphors deployed to describe a complex social situation.  The language of class may fall in this category.  And we might say that these statements are not truth claims at all, but rather interpretive schemes that are judged to do a better or worse job of drawing together the complex phenomena to which they are applied.  And in this case, it seems unavoidable that statements like these are radically underdetermined by the empirical facts.

(See Kyle Stanford's essay on underdetermination in the Stanford Encyclopedia of Philosophy.)

Underdetermination and truth

We say that a statement is underdetermined by available facts when it and an alternative and different statement or theory are equally consistent with that body of facts. It may be that two physical theories have precisely the same empirical consequences -- perhaps wave theory and particle theory represent an example of this possibility. And by stipulation there is no empirical circumstance that could occur that would distinguish between the two theories; no circumstance that would refute T1 and confirm T2. And yet we might also think that the two theories make different assertions about the world. Both statements are underdetermined by empirical facts.

Pierre Duhem further strengthened the case for the underdetermination of scientific theories through his emphasis on the crucial role that auxiliary hypotheses play in the design of experiments in The Aim and Structure of Physical Theory.  Individual theoretical hypotheses -- "light is a wave," "people behave on the basis of their class interests" -- do not have definite empirical implications of their own; rather, it is necessary to bring additional assumptions into play in order to design experiments that might support or refute the theoretical hypothesis.  And here is the crucial point: if an experimental result is inconsistent with the antecedent theory and auxiliary hypotheses, we haven't demonstrated that the hypothesis itself is false, but rather that at least one among the premises is false. And it is possible to save the system by modifying the theory or one or more of the auxiliary assumptions.  As W. V. O. Quine put the point, scientific knowledge takes the form of a "web of belief" (The Web of Belief).  

On the extreme assumption that both statements have precisely the same consequences, we might infer that the two theories must be logically equivalent, since the logical content of a theory is the full range of its deductive consequences and the two theories are stipulated to have the same deductive consequences. So it must be possible to derive each theory from the other. And if T1 and T2 are logically equivalent, then we wouldn't say that they really express different assertions about the world.

A more problematic case is one where two theories have distinct bodies of deductive consequences; but where the subset of deductive consequences that are empirically testable are the same for the two theories. In this situation it is no longer the case that the two theories are logically equivalent but rather "empirically equivalent." And here it would be credible to say that the two make genuinely different assertions about the world -- assertions that cannot be resolved empirically.

A third and still weaker case is one in which T1 and T2 have distinct consequences for both theoretical statements and a specific subset of empirical statements; but they overlap in their consequences for a second body of empirical statements. And consider this possibility: Because a given level of instrumentation and inquiry limit the types of empirical statements that can be evaluated, this body of data does not permit us to differentiate between the theories. So we can distinguish between "currently testable" and "currently not testable". For this third case, we are to imagine that T1 and T2 have distinct implications for theoretical statements and for currently not testable empirical statements; but they have the same consequences for currently testable statements. In this case, T1 and T2 are currently underdetermined -- though advances in instrumentation may result in their being empirically distinguishable in the future.

It is worth noting how heroic is the notion of "determination" of theory by evidence. If we thought that science should issue in theories that are determined by the empirical evidence, we would be committed to the idea that there is one uniquely best theory of everything. This assumption of ultimate theory uniqueness might be thought to follow from scientific and metaphysical realism: the world has a specific and determinate structure and causal properties; this structure gives rise to all observations; well-supported theories are approximately true descriptions of this hidden structure of the world; and therefore there is a uniquely best scientific theory -- the one that refers to this set of entities, processes, and structures. And if an existing theory is false in description of this unobservable reality, then there must be observational circumstances where the false assumptions of the theory give rise to false predictions about observation.  In other words, well-confirmed theories are likely to be approximately true, and the hidden structure of the world can be expected to create observations that refute out false theories.

However, this foundational approach is implausible in virtually every area of science.  Our theories rarely purport to describe the most fundamental level of reality; instead, they are meso-level descriptions of intermediate levels of phenomena. Take the effort to understand planetary motion.  The description of the orbits of the planets as ellipses generated by the gravitational attraction of the planet and the sun turned out to be only approximately true.  Did this refute the pure theory of gravitation? Certainly not; rather, it raised the possibility of other causal processes not yet identified, that interfere with the workings of gravitational attraction.

So how do these general considerations from the philosophy of science affect the situation of knowledge claims in the social sciences?

It would seem that social science claims are even more subject to underdetermination than the claims of mechanics and physics. In addition to the problem of unidentified interfering causes and the need for auxiliary hypotheses, we have the problems of vagueness and specification.  We commonly find that social science theories offer general statements about social causes and conditions that need to be further specified before they can be applied to a given set of circumstances. And there are almost always alternative and equally plausible ways of specifying the concept in a particular setting.

Take the idea of class conflict as a theory of political behavior.  The theory may assert that "workers act on their material interests." Before we can attempt to evaluate this statement in particular social settings, we have to specify several things: how to characterize "material interests" in the setting and how to represent the cognitive-behavioral models the worker uses as he/she deliberates about action.  Is retaining support from City Hall a material interest? Or are material interests restricted to wages and the workplace? Are workers thought to be rational maximizers of their interests, or do they also embody social commitments that modulate the dictates of maximization? And here is the crucial point: different specifications lead to different predictions about political behavior; so the general theoretical assertion is underdetermined by empirical observation.

This discussion seems to lead us into surprising territory -- not the limited question of underdetermination but the large question of truth and correspondence and the question of the rationality of scientific belief. Do we think that social assertions are true or false in the semantic sense: true by virtue of correspondence to the facts as they really are; or do we think that social assertions are simply ways of speaking about complexes of social phenomena, with no referential force? Is the language of class or ideology or ressentiment just a way of encompassing a range of social behaviors, or are there really classes and ideologies in the social world? And if we affirm the latter possibility, does the evidence of social observation permit us to unambiguously select the true theories?

I suppose one possible approach is to minimize the scope of "truth" when it comes to the social sciences. We might say that there is a limited range of social statements that are unambiguously true or false -- Jones robbed a store, Jones robbed a store because he was economically desperate, people sometimes commit crimes out of economic necessity -- but there is a broader class of statements that have a different status.  These are more akin to interpretive schemes in literary criticism or to a set of metaphors deployed to describe a complex social situation.  The language of class may fall in this category.  And we might say that these statements are not truth claims at all, but rather interpretive schemes that are judged to do a better or worse job of drawing together the complex phenomena to which they are applied.  And in this case, it seems unavoidable that statements like these are radically underdetermined by the empirical facts.

(See Kyle Stanford's essay on underdetermination in the Stanford Encyclopedia of Philosophy.)

Underdetermination and truth

We say that a statement is underdetermined by available facts when it and an alternative and different statement or theory are equally consistent with that body of facts. It may be that two physical theories have precisely the same empirical consequences -- perhaps wave theory and particle theory represent an example of this possibility. And by stipulation there is no empirical circumstance that could occur that would distinguish between the two theories; no circumstance that would refute T1 and confirm T2. And yet we might also think that the two theories make different assertions about the world. Both statements are underdetermined by empirical facts.

Pierre Duhem further strengthened the case for the underdetermination of scientific theories through his emphasis on the crucial role that auxiliary hypotheses play in the design of experiments in The Aim and Structure of Physical Theory.  Individual theoretical hypotheses -- "light is a wave," "people behave on the basis of their class interests" -- do not have definite empirical implications of their own; rather, it is necessary to bring additional assumptions into play in order to design experiments that might support or refute the theoretical hypothesis.  And here is the crucial point: if an experimental result is inconsistent with the antecedent theory and auxiliary hypotheses, we haven't demonstrated that the hypothesis itself is false, but rather that at least one among the premises is false. And it is possible to save the system by modifying the theory or one or more of the auxiliary assumptions.  As W. V. O. Quine put the point, scientific knowledge takes the form of a "web of belief" (The Web of Belief).  

On the extreme assumption that both statements have precisely the same consequences, we might infer that the two theories must be logically equivalent, since the logical content of a theory is the full range of its deductive consequences and the two theories are stipulated to have the same deductive consequences. So it must be possible to derive each theory from the other. And if T1 and T2 are logically equivalent, then we wouldn't say that they really express different assertions about the world.

A more problematic case is one where two theories have distinct bodies of deductive consequences; but where the subset of deductive consequences that are empirically testable are the same for the two theories. In this situation it is no longer the case that the two theories are logically equivalent but rather "empirically equivalent." And here it would be credible to say that the two make genuinely different assertions about the world -- assertions that cannot be resolved empirically.

A third and still weaker case is one in which T1 and T2 have distinct consequences for both theoretical statements and a specific subset of empirical statements; but they overlap in their consequences for a second body of empirical statements. And consider this possibility: Because a given level of instrumentation and inquiry limit the types of empirical statements that can be evaluated, this body of data does not permit us to differentiate between the theories. So we can distinguish between "currently testable" and "currently not testable". For this third case, we are to imagine that T1 and T2 have distinct implications for theoretical statements and for currently not testable empirical statements; but they have the same consequences for currently testable statements. In this case, T1 and T2 are currently underdetermined -- though advances in instrumentation may result in their being empirically distinguishable in the future.

It is worth noting how heroic is the notion of "determination" of theory by evidence. If we thought that science should issue in theories that are determined by the empirical evidence, we would be committed to the idea that there is one uniquely best theory of everything. This assumption of ultimate theory uniqueness might be thought to follow from scientific and metaphysical realism: the world has a specific and determinate structure and causal properties; this structure gives rise to all observations; well-supported theories are approximately true descriptions of this hidden structure of the world; and therefore there is a uniquely best scientific theory -- the one that refers to this set of entities, processes, and structures. And if an existing theory is false in description of this unobservable reality, then there must be observational circumstances where the false assumptions of the theory give rise to false predictions about observation.  In other words, well-confirmed theories are likely to be approximately true, and the hidden structure of the world can be expected to create observations that refute out false theories.

However, this foundational approach is implausible in virtually every area of science.  Our theories rarely purport to describe the most fundamental level of reality; instead, they are meso-level descriptions of intermediate levels of phenomena. Take the effort to understand planetary motion.  The description of the orbits of the planets as ellipses generated by the gravitational attraction of the planet and the sun turned out to be only approximately true.  Did this refute the pure theory of gravitation? Certainly not; rather, it raised the possibility of other causal processes not yet identified, that interfere with the workings of gravitational attraction.

So how do these general considerations from the philosophy of science affect the situation of knowledge claims in the social sciences?

It would seem that social science claims are even more subject to underdetermination than the claims of mechanics and physics. In addition to the problem of unidentified interfering causes and the need for auxiliary hypotheses, we have the problems of vagueness and specification.  We commonly find that social science theories offer general statements about social causes and conditions that need to be further specified before they can be applied to a given set of circumstances. And there are almost always alternative and equally plausible ways of specifying the concept in a particular setting.

Take the idea of class conflict as a theory of political behavior.  The theory may assert that "workers act on their material interests." Before we can attempt to evaluate this statement in particular social settings, we have to specify several things: how to characterize "material interests" in the setting and how to represent the cognitive-behavioral models the worker uses as he/she deliberates about action.  Is retaining support from City Hall a material interest? Or are material interests restricted to wages and the workplace? Are workers thought to be rational maximizers of their interests, or do they also embody social commitments that modulate the dictates of maximization? And here is the crucial point: different specifications lead to different predictions about political behavior; so the general theoretical assertion is underdetermined by empirical observation.

This discussion seems to lead us into surprising territory -- not the limited question of underdetermination but the large question of truth and correspondence and the question of the rationality of scientific belief. Do we think that social assertions are true or false in the semantic sense: true by virtue of correspondence to the facts as they really are; or do we think that social assertions are simply ways of speaking about complexes of social phenomena, with no referential force? Is the language of class or ideology or ressentiment just a way of encompassing a range of social behaviors, or are there really classes and ideologies in the social world? And if we affirm the latter possibility, does the evidence of social observation permit us to unambiguously select the true theories?

I suppose one possible approach is to minimize the scope of "truth" when it comes to the social sciences. We might say that there is a limited range of social statements that are unambiguously true or false -- Jones robbed a store, Jones robbed a store because he was economically desperate, people sometimes commit crimes out of economic necessity -- but there is a broader class of statements that have a different status.  These are more akin to interpretive schemes in literary criticism or to a set of metaphors deployed to describe a complex social situation.  The language of class may fall in this category.  And we might say that these statements are not truth claims at all, but rather interpretive schemes that are judged to do a better or worse job of drawing together the complex phenomena to which they are applied.  And in this case, it seems unavoidable that statements like these are radically underdetermined by the empirical facts.

(See Kyle Stanford's essay on underdetermination in the Stanford Encyclopedia of Philosophy.)

The inexact science of economics

Image: social accounting matrix, Bolivia, 1997

Economics is an "inexact" science; or so Daniel Hausman argues in The Inexact and Separate Science of Economics (Google Books link).  As it implies, this description conveys that economic laws have only a loose fit with observed economic behavior.  Here are the loosely related interpretations that Hausman offers for this idea, drawing on the thinking of John Stuart Mill:

1. Inexact laws are approximate.  They are true within some margin of error.
2. Inexact laws are probabilistic or statistical.  Instead of stating how human beings always behave, economic laws state how they usually behave.
3. Inexact laws make counterfactual assertions about how things would be in the absence of interferences.
4. Inexact laws are qualified with vague ceteris paribus clauses. (128)

Economics has also been treated by economists as a separate science: a science capable of explaining virtually all the phenomena in a reasonably well-defined domain of social phenomena.  Here is Hausman's interpretation of a separate science:

1. Economics is defined in terms of the causal factors with which it is concerned, not in terms of a domain.
2. Economics has a distinct domain, in which its causal factors predominate.
3. The "laws" of the predominating causal factors are already reasonably well-known.
4. Thus, economic theory, which employs these laws, provides a unified, complete, but inexact account of its domain. (90-91)

These characteristics of economic theories and models have implications for several important areas: truth, prediction, explanation, and confirmation.  Is economics a scientific theory of existing observable economic phenomena?  Or is it an abstract, hypothetical model with only tangential implications for the observable social world?  Is economics an empirical science or a mathematical system?

Let's look at these questions in turn.  First, can we give a good interpretation of what it would mean to believe that an inexact theory or law is "true"?  Here is a possible answer: we may believe that there are real but unobservable causal processes that "drive" social phenomena.  To say that a social or economic theory is true is to say that it correctly identifies a real causal process -- whether or not that process operates with sufficient separation to give rise to strict empirical consequences.  Galilean laws of mechanics are true for falling objects, even if feathers follow unpredictable trajectories through turbulent gases.

Second, how can we reconcile the desire to use economic theories to make predictions about future states with the acknowledged inexactness of those theories and laws? If a theory includes hypotheses about underlying causal mechanisms that are true in the sense just mentioned, then a certain kind of prediction is justified as well: "in the absence of confounding causal factors, the presence of X will give rise to Y." But of course this is a useless predictive statement in the current situation, since the whole point is that economic processes rarely or never operate in isolation. So we are more or less compelled to conclude that theories based on inexact laws are not a useable ground for empirical prediction.

Third, in what sense do the deductive consequences of an inexact theory "explain" a given outcome -- either one that is consistent with those consequences or one that is inconsistent with the consequences? Here inexact laws are on stronger ground: after the fact, it is often possible to demonstrate that the mechanisms that led to an outcome are those specified by the theory. Explanation and prediction are not equIvalent. Natural selection explains the features of Darwin's finches -- but it doesn't permit prediction of future evolutionary change.

And finally, what is involved in trying to use empirical data to confirm or disconfirm an inexact theory?  Given that we have stipulated that the theory has false consequences, we can't use standard confirmation theory.  So what kind of empirical argument would help provide empirical evaluation of an inexact theory?  One possibility is that we might require that the predictions of the theory should fall within a certain range of the observable measurements -- which is implied by the idea of "approximately true" consequences.  But actually, it is possible that we might hold that a given theory is inexact, true, and wildly divergent from observed experience.  (This would be true of the application of classical mechanics to the problem of describing the behavior of light, irregular objects shot out of guns under water.)  Hausman confronts this type of issue when he asks why we should believe that the premises of general equilibrium theory are true. But here too there are alternatives, including piecemeal confirmation of individual causal hypotheses. Hausman refers to this possibility as a version of Mill's deductive method.

I take up some of these questions in my article, "Economic Models in Development Economics" link, included in On the Reliability of Economic Models: Essays in the Philosophy of Economics.  This article discusses some related questions about the reliability and applicability of computable general equilibrium models in application to the observed behavior of real economies.  Here are some concluding thoughts from that article concerning the empirical and logical features that are relevant to the assessment of CGE models:

"The general problem of the antecedent credibility of an economic model can be broken down into more specific questions concerning the validity, comprehensiveness, robustness, reliability, and autonomy of the model. I will define these concepts in the following terms.

• Validity is a measure of the degree to which the assumptions employed in the construction of the model are thought to correspond to the real processes underlying the phenomena represented by the model.
• Comprehensiveness is the degree to which the model is thought to succeed in capturing the major causal factors that influence the features of the behavior of the system in which we are interested.
• Robustness is a measure of the degree to which the results of the model persist under small perturbations in the settings of parameters, formulation of equations, etc.
• Autonomy refers to the stability of the model's results in face of variation of contextual factors.
• Reliability is a measure of the degree of confidence we can have in the data employed in setting the values of the parameters.

These are epistemic features of models that can be investigated more or less independently and prior to examination of the empirical success or failure of the predictions of the model."

(Hausman's book is virtually definitive in its formulation of the tasks and scope of the philosophy of economics.  When conjoined with the book he wrote with Michael McPherson, Economic Analysis, Moral Philosophy and Public Policy, the philosophy of economics itself becomes a "separate science": virtually all the important questions are raised throughout a bounded domain, and a reasonable set of theories are offered to answer those questions.)

The inexact science of economics

Image: social accounting matrix, Bolivia, 1997

Economics is an "inexact" science; or so Daniel Hausman argues in The Inexact and Separate Science of Economics (Google Books link).  As it implies, this description conveys that economic laws have only a loose fit with observed economic behavior.  Here are the loosely related interpretations that Hausman offers for this idea, drawing on the thinking of John Stuart Mill:

1. Inexact laws are approximate.  They are true within some margin of error.
2. Inexact laws are probabilistic or statistical.  Instead of stating how human beings always behave, economic laws state how they usually behave.
3. Inexact laws make counterfactual assertions about how things would be in the absence of interferences.
4. Inexact laws are qualified with vague ceteris paribus clauses. (128)

Economics has also been treated by economists as a separate science: a science capable of explaining virtually all the phenomena in a reasonably well-defined domain of social phenomena.  Here is Hausman's interpretation of a separate science:

1. Economics is defined in terms of the causal factors with which it is concerned, not in terms of a domain.
2. Economics has a distinct domain, in which its causal factors predominate.
3. The "laws" of the predominating causal factors are already reasonably well-known.
4. Thus, economic theory, which employs these laws, provides a unified, complete, but inexact account of its domain. (90-91)

These characteristics of economic theories and models have implications for several important areas: truth, prediction, explanation, and confirmation.  Is economics a scientific theory of existing observable economic phenomena?  Or is it an abstract, hypothetical model with only tangential implications for the observable social world?  Is economics an empirical science or a mathematical system?

Let's look at these questions in turn.  First, can we give a good interpretation of what it would mean to believe that an inexact theory or law is "true"?  Here is a possible answer: we may believe that there are real but unobservable causal processes that "drive" social phenomena.  To say that a social or economic theory is true is to say that it correctly identifies a real causal process -- whether or not that process operates with sufficient separation to give rise to strict empirical consequences.  Galilean laws of mechanics are true for falling objects, even if feathers follow unpredictable trajectories through turbulent gases.

Second, how can we reconcile the desire to use economic theories to make predictions about future states with the acknowledged inexactness of those theories and laws? If a theory includes hypotheses about underlying causal mechanisms that are true in the sense just mentioned, then a certain kind of prediction is justified as well: "in the absence of confounding causal factors, the presence of X will give rise to Y." But of course this is a useless predictive statement in the current situation, since the whole point is that economic processes rarely or never operate in isolation. So we are more or less compelled to conclude that theories based on inexact laws are not a useable ground for empirical prediction.

Third, in what sense do the deductive consequences of an inexact theory "explain" a given outcome -- either one that is consistent with those consequences or one that is inconsistent with the consequences? Here inexact laws are on stronger ground: after the fact, it is often possible to demonstrate that the mechanisms that led to an outcome are those specified by the theory. Explanation and prediction are not equIvalent. Natural selection explains the features of Darwin's finches -- but it doesn't permit prediction of future evolutionary change.

And finally, what is involved in trying to use empirical data to confirm or disconfirm an inexact theory?  Given that we have stipulated that the theory has false consequences, we can't use standard confirmation theory.  So what kind of empirical argument would help provide empirical evaluation of an inexact theory?  One possibility is that we might require that the predictions of the theory should fall within a certain range of the observable measurements -- which is implied by the idea of "approximately true" consequences.  But actually, it is possible that we might hold that a given theory is inexact, true, and wildly divergent from observed experience.  (This would be true of the application of classical mechanics to the problem of describing the behavior of light, irregular objects shot out of guns under water.)  Hausman confronts this type of issue when he asks why we should believe that the premises of general equilibrium theory are true. But here too there are alternatives, including piecemeal confirmation of individual causal hypotheses. Hausman refers to this possibility as a version of Mill's deductive method.

I take up some of these questions in my article, "Economic Models in Development Economics" link, included in On the Reliability of Economic Models: Essays in the Philosophy of Economics.  This article discusses some related questions about the reliability and applicability of computable general equilibrium models in application to the observed behavior of real economies.  Here are some concluding thoughts from that article concerning the empirical and logical features that are relevant to the assessment of CGE models:

"The general problem of the antecedent credibility of an economic model can be broken down into more specific questions concerning the validity, comprehensiveness, robustness, reliability, and autonomy of the model. I will define these concepts in the following terms.

• Validity is a measure of the degree to which the assumptions employed in the construction of the model are thought to correspond to the real processes underlying the phenomena represented by the model.
• Comprehensiveness is the degree to which the model is thought to succeed in capturing the major causal factors that influence the features of the behavior of the system in which we are interested.
• Robustness is a measure of the degree to which the results of the model persist under small perturbations in the settings of parameters, formulation of equations, etc.
• Autonomy refers to the stability of the model's results in face of variation of contextual factors.
• Reliability is a measure of the degree of confidence we can have in the data employed in setting the values of the parameters.

These are epistemic features of models that can be investigated more or less independently and prior to examination of the empirical success or failure of the predictions of the model."

(Hausman's book is virtually definitive in its formulation of the tasks and scope of the philosophy of economics.  When conjoined with the book he wrote with Michael McPherson, Economic Analysis, Moral Philosophy and Public Policy, the philosophy of economics itself becomes a "separate science": virtually all the important questions are raised throughout a bounded domain, and a reasonable set of theories are offered to answer those questions.)

The inexact science of economics

Image: social accounting matrix, Bolivia, 1997

Economics is an "inexact" science; or so Daniel Hausman argues in The Inexact and Separate Science of Economics (Google Books link).  As it implies, this description conveys that economic laws have only a loose fit with observed economic behavior.  Here are the loosely related interpretations that Hausman offers for this idea, drawing on the thinking of John Stuart Mill:

1. Inexact laws are approximate.  They are true within some margin of error.
2. Inexact laws are probabilistic or statistical.  Instead of stating how human beings always behave, economic laws state how they usually behave.
3. Inexact laws make counterfactual assertions about how things would be in the absence of interferences.
4. Inexact laws are qualified with vague ceteris paribus clauses. (128)

Economics has also been treated by economists as a separate science: a science capable of explaining virtually all the phenomena in a reasonably well-defined domain of social phenomena.  Here is Hausman's interpretation of a separate science:

1. Economics is defined in terms of the causal factors with which it is concerned, not in terms of a domain.
2. Economics has a distinct domain, in which its causal factors predominate.
3. The "laws" of the predominating causal factors are already reasonably well-known.
4. Thus, economic theory, which employs these laws, provides a unified, complete, but inexact account of its domain. (90-91)

These characteristics of economic theories and models have implications for several important areas: truth, prediction, explanation, and confirmation.  Is economics a scientific theory of existing observable economic phenomena?  Or is it an abstract, hypothetical model with only tangential implications for the observable social world?  Is economics an empirical science or a mathematical system?

Let's look at these questions in turn.  First, can we give a good interpretation of what it would mean to believe that an inexact theory or law is "true"?  Here is a possible answer: we may believe that there are real but unobservable causal processes that "drive" social phenomena.  To say that a social or economic theory is true is to say that it correctly identifies a real causal process -- whether or not that process operates with sufficient separation to give rise to strict empirical consequences.  Galilean laws of mechanics are true for falling objects, even if feathers follow unpredictable trajectories through turbulent gases.

Second, how can we reconcile the desire to use economic theories to make predictions about future states with the acknowledged inexactness of those theories and laws? If a theory includes hypotheses about underlying causal mechanisms that are true in the sense just mentioned, then a certain kind of prediction is justified as well: "in the absence of confounding causal factors, the presence of X will give rise to Y." But of course this is a useless predictive statement in the current situation, since the whole point is that economic processes rarely or never operate in isolation. So we are more or less compelled to conclude that theories based on inexact laws are not a useable ground for empirical prediction.

Third, in what sense do the deductive consequences of an inexact theory "explain" a given outcome -- either one that is consistent with those consequences or one that is inconsistent with the consequences? Here inexact laws are on stronger ground: after the fact, it is often possible to demonstrate that the mechanisms that led to an outcome are those specified by the theory. Explanation and prediction are not equIvalent. Natural selection explains the features of Darwin's finches -- but it doesn't permit prediction of future evolutionary change.

And finally, what is involved in trying to use empirical data to confirm or disconfirm an inexact theory?  Given that we have stipulated that the theory has false consequences, we can't use standard confirmation theory.  So what kind of empirical argument would help provide empirical evaluation of an inexact theory?  One possibility is that we might require that the predictions of the theory should fall within a certain range of the observable measurements -- which is implied by the idea of "approximately true" consequences.  But actually, it is possible that we might hold that a given theory is inexact, true, and wildly divergent from observed experience.  (This would be true of the application of classical mechanics to the problem of describing the behavior of light, irregular objects shot out of guns under water.)  Hausman confronts this type of issue when he asks why we should believe that the premises of general equilibrium theory are true. But here too there are alternatives, including piecemeal confirmation of individual causal hypotheses. Hausman refers to this possibility as a version of Mill's deductive method.

I take up some of these questions in my article, "Economic Models in Development Economics" link, included in On the Reliability of Economic Models: Essays in the Philosophy of Economics.  This article discusses some related questions about the reliability and applicability of computable general equilibrium models in application to the observed behavior of real economies.  Here are some concluding thoughts from that article concerning the empirical and logical features that are relevant to the assessment of CGE models:

"The general problem of the antecedent credibility of an economic model can be broken down into more specific questions concerning the validity, comprehensiveness, robustness, reliability, and autonomy of the model. I will define these concepts in the following terms.

• Validity is a measure of the degree to which the assumptions employed in the construction of the model are thought to correspond to the real processes underlying the phenomena represented by the model.
• Comprehensiveness is the degree to which the model is thought to succeed in capturing the major causal factors that influence the features of the behavior of the system in which we are interested.
• Robustness is a measure of the degree to which the results of the model persist under small perturbations in the settings of parameters, formulation of equations, etc.
• Autonomy refers to the stability of the model's results in face of variation of contextual factors.
• Reliability is a measure of the degree of confidence we can have in the data employed in setting the values of the parameters.

These are epistemic features of models that can be investigated more or less independently and prior to examination of the empirical success or failure of the predictions of the model."

(Hausman's book is virtually definitive in its formulation of the tasks and scope of the philosophy of economics.  When conjoined with the book he wrote with Michael McPherson, Economic Analysis, Moral Philosophy and Public Policy, the philosophy of economics itself becomes a "separate science": virtually all the important questions are raised throughout a bounded domain, and a reasonable set of theories are offered to answer those questions.)