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Most of all, we're afraid of losing control. If you're swimming in shark-inhabited water, you don't want the jaws of a mysterious predator to clamp down on you and determine your fate. Fear is not necessarily something we're born with, but it's something we have developed over time. Infants aren't afraid of snakes and heights, but as adults, our brains become more sensitive to fearful stimuli.

But, oh boy, did our ancestors have a lot to be afraid of! Think back to how ancient people would have survived in their primitive habitats. They would have avoided tall cliffs and wild animals because they knew those threats could potentially kill them, and that's what kept them alive. They learned fear as an adaptation to protect themselves. Biological things like animals are something that we're very prone to fear.

In writing her book, Shark Attacks: Myths, Misunderstandings and Human Fear , Chapman found that the human brain tends to oversimplify numbers. If I tell you there's a one in 3,, chance you could be attacked and killed by a shark , that number is too abstract for your brain to be sensitive to it. If I tell you humans kill about million sharks each year , it could be difficult to process that, as well. The chances of you being eaten alive by a shark are highly unlikely.

You're more likely to die by a dog attack, lightning strike, or car crash. Cancer and heart disease are also way more likely to kill you. The slim chances that a shark attack could happen to us are irrelevant. We hear of the word "shark" and we can't help but immediately fill in the blank after it with "attack. There are a few ways you can make yourself less afraid of sharks. You can give yourself the illusion of control, because when you don't feel in control, things seem scarier. To do this, you can read up on what kinds of sharks live in the water you're about to swim in , or learn about which species of shark have been known to go after humans.

Pro tip: blacktip and spinner sharks sometimes mistake humans for prey.


  • Singularities in Geometry, Topology, Foliations and Dynamics: A Celebration of the 60th Birthday of José Seade, Merida, Mexico, December 2014?
  • This item appears in the following Collection(s)?
  • Scientific Explanation | Erik Weber | Springer.

If you swim in clear water, you can give yourself the illusion of being in control if you did spot a shark. Great whites can reach speeds 10 times faster than typical humans , so logically, if one of these sharks were to come toward you, you wouldn't have time to escape it. But it's more than likely they would spit you back out. To avoid a shark attack, you can also learn how to not be shark bait by avoiding swimming if you're bleeding or lying on a surfboard. As Salmon , p. Similarly, taking birth control pills does not cause Jones' failure to get pregnant and this is why 2.

On this analysis, what 2. As explained above, advocates of the DN model would not regard this diagnosis as very illuminating, unless accompanied by some account of causation that does not simply take this notion as primitive. Salmon in fact provides such an account, which we will consider in Section 4. We should note, however, that an apparent lesson of 2. More generally, if the counterexamples 2.

Explaining an outcome isn't just a matter of showing that it is nomically expectable. There are two possible reactions one might have to this observation. One is that the idea that explanation is a matter of nomic expectability is correct as far as it goes, but that something more is required as well. Something like this idea is endorsed, by the unificationist models of explanation developed by Friedman and Kitcher , which are discussed in Section 5 below.

A second, more radical possible conclusion is that the DN account of the goal or rationale of explanation is mistaken in some much more fundamental way and that the DN model does not even state necessary conditions for successful explanation. As noted above, unless the hidden structure argument is accepted, this conclusion is strongly suggested by examples like 2. It might seem that the contention of the hidden structure strategy that singular causal explanations like 2.

Indeed, any account of explanation that, like Kitcher's unificationist model, insists that laws or generalizations of considerable generality and deductive structure are necessary conditions for successful explanation will need to appeal to something like hidden structure strategy since it is generally accepted that there are many apparent explanations that do not conform to such conditions in their overt structure. Although the hidden structure strategy deserves more attention than it can receive here, several points seem clear.

Are all of these explanations implicit in 2. Railton suggests that an explanatory claim provides information about an underlying ideal text if the former reduces uncertainty about some of the properties of the text, in the sense of ruling in or out various possibilities concerning its structure. As Railton recognizes, this has proposal has many counterintuitive consequences.

This contrasts with the widespread judgment that correlations in themselves are not explanatory. In fact, such a claim is apparently maximally explanatory, since it conveys everything that there is to be said about the ideal explanatory text associated with that event. Examples like these suggest that not every claim that reduces uncertainty about the contents of an ideal explanatory text should be regarded as itself explanatory—such a view allows too much to count as an explanation.

Will the economics explanation really be better according as to whether it conveys as much information as possible about these underlying details? Finally, consider the connection between explanation and understanding. One ordinarily thinks of an explanation as something that provides understanding. Relatedly, part of the task of a theory of explanation is to identify those structural features of explanations or the information they convey in virtue of which they provide understanding. For example, as noted above, the DN model connects understanding with the provision of information about nomic expectability—the idea is that understanding why an outcome occurs is a matter of seeing that it was to be expected on the basis of a law.

It is hard to see how this structure or information can contribute to understanding if it is epistemically hidden in this way. For example, it seems plausible that many if not almost all users of 2. If this is the case, how can the mere obtaining of this DN structure, independently of anyone's awareness of its existence, function so as to provide understanding when 2. Instead, it seems that the features of 2.

Is there any scientific explanation for hypnosis?

A similar point will hold for many other candidate explanations that fail to conform to the DN requirements such as explanations from sciences like economics and psychology that seem to lack laws. What can we conclude from this discussion of the hidden structure strategy? On the other hand, it is possible that there are ways of developing the hidden structure strategy that respond adequately to the difficulties described above.

Suggested Readings. This is reprinted in Hempel, a, along with a number of other papers that touch on various aspects of the problem of scientific explanation. In addition to the references cited in this section, Salmon, , pp. Much of the subsequent literature on explanation has been motivated by attempts to capture the features of causal or explanatory relevance that appear to be left out of examples like 2. Wesley Salmon's statistical relevance or SR model Salmon, is a very influential attempt to capture these features in terms of the notion of statistical relevance or conditional dependence relationships.

The intuition underlying the SR model is that statistically relevant properties or information about statistically relevant relationships are explanatory and statistically irrelevant properties are not. In other words, the notion of a property making a difference for an explanandum is unpacked in terms of statistical relevance relationships. To illustrate this idea, suppose that in the birth control pills example 2.

In other words, if you are a male in this population, taking birth control pills is statistically irrelevant to whether you become pregnant, while if you are a female it is relevant. In this way we can capture the idea that taking birth control pills is explanatorily irrelevant to pregnancy among males but not among females.

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To characterize the SR model more precisely we need the notion of a homogenous partition. Assume for the sake of argument that no other factors are relevant to quick recovery. That is, the probability of quick recovery, given that one has strep, is the same for those who have the resistant strain regardless of whether or not they are treated and also the same for those who have not been treated. By contrast, the probability of recovery is different presumably greater among those with strep who have been treated and do not have the resistant strain. The SR model has a number of distinctive features that have generated substantial discussion.

Instead, an explanation is an assembly of information that is statistically relevant to an explanandum. Salmon argues and takes the birth control example 2. As explained above, in associating successful explanation with the provision of information about statistical relevance relationships, the SR model attempts to accommodate this observation.

A second, closely related point is that the SR model departs from the IS model in abandoning the idea that a statistical explanation of an outcome must provide information from which it follows the outcome occurred with high probability. As the reader may check, the statement of the SR model above imposes no such high probability requirement; instead, even very unlikely outcomes will be explained as long as the criteria for SR explanation are met.

Suppose that, in the above example, the probability of quick recovery from strep, given treatment and the presence of a non-resistant strain, is rather low e.

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For example, if the prior probability of quick recovery among all those with any form of strep is 0. More generally, what matters on the SR model is not whether the value of the probability of the explanandum-outcome is high or low or even high or low in comparison with its prior probability but rather whether the putative explanans cites all and only statistically relevant factors and whether the probabilities it invokes are correct. For example, the same explanans will explain both why a subject with strep and certain other properties e. The intuition that, contrary to the IS model, the value that a candidate explanans assigns to an explanandum-outcome should not matter for the goodness of the explanation it provides can be motivated in the following way.

Suppose that if it is not tossed the coin has probability of 0. According to the IS model, if the coin is tossed and comes up heads, we can explain this outcome by appealing to the fact that the coin was tossed since under this condition the probability of heads is high but if the coin is tossed and comes up tails we cannot explain this outcome, since its probability is low.

The contrary intuition underlying the SR model is that we understand both outcomes equally well. The bias of the coin and the fact that the coin has been tossed are the only factors relevant to either outcome and those factors are common to both outcomes—once we have cited the toss and specified the probability values for heads and tails on tossing , we left nothing out that influences either outcome.

Similarly, Salmon argues, if it is really true that the partition in the example involving quick recovery from strep is objectively homogenous—if there are no other factors that are statistically relevant to quick recovery besides whether the subject has been treated and has a resistant strain—then once we have specified the probability of quick recovery under all combinations of these factors, and the combination of factors possessed by the subject whose recovery or not, as the case may be we want to explain, we have specified all information relevant to recovery and in this sense fully explained the outcome for the subject.

In assessing these claims, it will be useful to take a step back and ask just what it is that these competing models of statistical explanation Hempel's IS model and Salmon's SR model are intended to be reconstructions of. In the literature on this topic two classes of examples or applications figure prominently. First, there are examples drawn from quantum- mechanics QM.

Models of statistical explanation assume that if the particle does penetrate the barrier, QM explains this outcome—the IS and SR models are intended to capture the structure of such explanations. Second, there are examples drawn from biomedical or epidemiological and social scientific applications—recovery from strep or, to cite one of Salmon's extended illustrations Salmon, , the factors relevant to juvenile delinquency in teen-age boys.

This is, to say the least, a heterogeneous class of examples. In the case of QM , the usual understanding is that the various no-hidden variable results establish that any empirically adequate theory of quantum mechanical phenomena must be irreducibly indeterministic. By contrast, it seems quite unlikely that this homogeneity condition will be satisfied in most indeed, in any of the biomedical and sociological illustrations that have figured in the literature on statistical explanation.

In the case of recovery from strep, for example, it is very plausible that there are many other factors besides the two mentioned above that affect the probability of recovery—these additional factors will include the state of the subject's immune system, various features of the subject's general level of health, the precise character of the strain of disease to which the subject is exposed resistant versus non-resistant is almost certainly too coarse-grained a dichotomy and so on.

Similarly for episodes of juvenile delinquency. In these cases, in contrast to the cases from quantum mechanics, we lack a theory or body of results that delimits the factors that are potentially relevant to the probability of the outcome that interests us. Thus, in realistic examples of assemblages of statistically relevant factors from biomedicine and social science, the objective homogeneity condition is unlikely to be satisfied, or in any practical sense, satisfiable.

A related difference concerns the way in which statistical evidence figures in these two sorts of applications. Some quantum mechanical phenomena such as radioactive decay are irreducibly indeterministic. This particularly clear in connection with the social scientific examples such as risk factors for juvenile delinquency that Salmon discusses. Here the relevant methodology involves so-called causal modeling or structural equation techniques. At least on the most straightforward way of applying such procedures, the equations that govern whether a particular individual becomes a juvenile delinquent are if interpreted literally deterministic.

According to such approaches, the phenomena being modeled look as though they are indeterministic because some of the variables which are relevant to their behavior, the influence of which is summarized by a so-called error term, are unknown or unmeasured. Statistical information about the incidence of juvenile delinquency among individuals in various conditions plays the role of evidence that is used to estimate parameters the coefficients in the deterministic equations that are taken to describe the processes governing the onset of delinquency.

A similar point holds for at least many biomedical examples. Several preliminary conclusions are suggested by these observations. First, it is far from obvious that we should try to construct a single, unified model of statistical explanation that applies to both quantum mechanics and macroscopic phenomena like delinquency or recovery from infection.

In other words, if an objective homogeneity condition is imposed on statistical explanation, it is not clear that there will be any examples of successful statistical explanation outside of quantum mechanics. With these observations in mind, let us revisit the question of what is explained by statistical theories, whether quantum mechanical or macroscopic. As we have seen, both Hempel and Salmon, as well as most subsequent contributors to the literature on statistical explanation, have tended to assume that statistical theories that assign a probability to some outcome strictly between 0 and 1 should nonetheless be interpreted as explaining that outcome.

Given this common starting point, Salmon is quite persuasive in arguing that it is arbitrary to hold, as Hempel does, that only individual outcomes with high probability can be explained. But why should we accept the starting point? Why not take Salmon's argument instead to be a reason for rejecting the idea that statistical theories explain individual outcomes, whether of high or low probability? If we take this view, we need not conclude that a theory like QM is unexplanatory. Instead, we may take the explananda of QM to be facts about the probabilities or expectation values of outcomes rather than individual outcomes themselves.

On this view, the explananda that are explained by QM are a proper subset of those that can be derived from it—at least in this respect, the explanations provided by QM are like DS explanations in structure. Woodward argues that this construal allows us to say all that we might legitimately wish to say about the explanatory virtues of QM.

If this is correct, there is no obvious need for a separate theory of statistical explanation of individual outcomes of the sort that Hempel and Salmon sought to devise But see footnote 7. In the case of juvenile delinquency and causal modeling techniques it is, if anything, even more intuitive that what is being explained is not, e. Again such explananda are deducible from the system of equations used to model juvenile delinquency. Taking this view of what is explained by statistical theories allows us to avoid various unintuitive consequences of Hempel's model e.

At the very least, those who have sought to construct models of statistical explanation of individual outcomes need to provide a more detailed elucidation of why such models are needed and of the features of scientific theorizing they are designed to capture. As we have just seen, the SR model raises a number of interesting questions about the statistical explanation of individual outcomes—questions that are important independently of the details of the SR model itself.

This section will abstract away from such questions and focus instead on the root motivation for the SR model. We may take this to consist of two ideas: i explanations must cite causal relationships and ii causal relationships are captured by statistical relevance relationships.

Even if i is accepted, a fundamental problem with the SR model is that ii is false—as a substantial body of work [ 10 ] has made clear, casual relationships are greatly underdetermined by statistical relevance relationships. These contentions about the connection between causal claims and statistical relevance relations are consequences of a more general principle called the Causal Markov condition which has been extensively discussed in the recent literature on causation.

Two relevant points have emerged from discussion of this condition. The first, which was in effect noted by Salmon himself in work subsequent to his , is that there are circumstances in which the Causal Markov condition fails and hence in which causal claims do not imply the screening off relationships described above. This can happen, for example, if the variables to which the condition is applied are characterized in an insufficiently fine-grained way.

In structures with more variables, this underdetermination of causal relationships by statistical relevance relationships may be far more extreme. Thus a list of statistical relevance relationships, which is what the SR model provides, need not tell us which causal relationships are operative. To the extent that explanation has to do with the identification of the causal relationships on which an explanandum-outcome depends, the SR model fails to fully capture these. Selected Readings. Salmon, a provides a detailed statement and defense of the SR model.

This essay, as well as papers by Jeffrey and Greeno which defend views broadly similar to the SR model, are collected in Salmon, b. Cartwright, contains some influential criticisms of the SR model. Theorems specifying the precise extent of the underdetermination of causal claims by evidence about statistical relevance relationships can be found in Spirtes, Glymour and Scheines, , , chapter 4. In more recent work especially, Salmon, Salmon abandoned the attempt to characterize explanation or causal relationships in purely statistical terms.

Instead, he developed a new account which he called the Causal Mechanical CM model of explanation—an account which is similar in both content and spirit to so-called process theories of causation of the sort defended by philosophers like Philip Dowe The CM model employs several central ideas.

A causal process is a physical process, like the movement of a baseball through space, that is characterized by the ability to transmit a mark in a continuous way. Intuitively, a mark is some local modification to the structure of a process—for example, a scuff on the surface of a baseball or a dent an automobile fender.

A process is capable of transmitting a mark if, once the mark is introduced at one spatio-temporal location, it will persist to other spatio-temporal locations even in the absence of any further interaction. In this sense the baseball will transmit the scuff mark from one location to another. Similarly, a moving automobile is a causal process because a mark in the form of a dent in a fender will be transmitted by this process from one spatio-temporal location to another. Causal processes contrast with pseudo-processes which lack the ability to transmit marks.

An example is the shadow of a moving physical object. The intuitive idea is that, if we try to mark the shadow by modifying its shape at one point for example, by altering a light source or introducing a second occluding object , this modification will not persist unless we continually intervene to maintain it as the shadow occupies successive spatio-temporal positions. In other words, the modification will not be transmitted by the structure of the shadow itself, as it would in the case of a genuine causal process.

We should note for future reference that, as characterized by Salmon, the ability to transmit a mark is clearly a counterfactual notion, in several senses. To begin with, a process may be a causal process even if it does not in fact transmit any mark, as long as it is true that if it were appropriately marked, it would transmit the mark. Moreover, the notion of marking itself involves a counterfactual contrast—a contrast between how a process behaves when marked and how it would behave if left unmarked.

Although Salmon, like Hempel, has always been suspicious of counterfactuals, his view at the time that he first introduced the CM model was that the counterfactuals involved in the characterization of mark transmission were relatively unproblematic, in part because they seemed experimentally testable in a fairly direct way. Nonetheless the reliance of the CM model, as originally formulated, on counterfactuals shows that it does not completely satisfy the Humean strictures described above.

In subsequent work, described in Section 4. The other major element in Salmon's model is the notion of a causal interaction. A casual interaction involves a spatio-temporal intersection between two causal processes which modifies the structure of both—each process comes to have features it would not have had in the absence of the interaction. A collision between two cars that dents both is a paradigmatic causal interaction. Nonetheless, it seems clear enough how the intuitive idea is meant to apply to specific examples.

Suppose that a cue ball, set in motion by the impact of a cue stick, strikes a stationary eight ball with the result that the eight ball is put in motion and the cue ball changes direction. The impact of the stick also transmits some blue chalk to the cue ball which is then transferred to the eight ball on impact. The cue stick, the cue ball, and the eight ball are causal processes, as is shown by the transmission of the chalk mark, and the collision of the cue stick with the cue ball and the collision of the cue and eight balls are causal interactions.

Salmon's idea is that citing such facts about processes and interactions explains the motion of the balls after the collision; by contrast, if one of these balls casts a shadow that moves across the other, this will be causally and explanatorily irrelevant to its subsequent motion since the shadow is a pseudo-process. This explanation proceeds by deriving that motion from information about their masses and velocity before the collision, the assumption that the collision is perfectly elastic, and the law of the conservation of linear momentum.

We usually think of the information conveyed by this derivation as showing that it is the mass and velocity of the balls, rather than, say, their color or the presence of the blue chalk mark, that is explanatorily relevant to their subsequent motion. However, it is hard to see what in the CM model allows us to pick out the linear momentum of the balls, as opposed to these other features, as explanatorily relevant. Part of the difficulty is that to express such relatively fine-grained judgments of explanatory relevance that it is linear momentum rather than chalk marks that matters we need to talk about relationships between properties or magnitudes and it is not clear how to express such judgments in terms of facts about causal processes and interactions.

Both the linear momentum and the chalk mark communicated to the cue ball by the cue stick are marks transmitted by the spatio-temporally continuous causal process consisting of the motion of the cue ball. Both marks are then transmitted via an interaction to the eight ball. There appears to be nothing in Salmon's notion of mark transmission or the notion of a causal process that allows one to distinguish between the explanatorily relevant momentum and the explanatorily irrelevant blue chalk mark. Ironically, as Hitchcock goes on to note, a similar observation may be made about the birth control pills example 2.

Spatio-temporally continuous causal processes that transmit marks as well as causal interactions are at work when male Mr. Jones ingests birth control pills—the pills dissolve, components enter his bloodstream, are metabolized or processed in some way, and so on. Similarly, spatio-temporally continuous causal processes albeit different processes are at work when female Ms. Jones takes birth control pills.

However, the pills are irrelevant to Mr. Jones non-pregnancy, and relevant to Ms. Jones' non-pregnancy. Again, it looks as though the relevance or irrelevance of the birth control pills to Mr. Jones' failure to become pregnant cannot be captured just by asking whether the processes leading up to these outcomes are causal processes in Salmon's sense. A similar point holds for the hexed salt example 2. So while mark transmission may well be a criterion that correctly distinguishes between causal processes and pseudo-processes , it does not, as it stands, provide the resources for distinguishing those features or properties of a causal process that are causally or explanatorily relevant to an outcome and those features that are irrelevant.

A second set of worries has to do with the application of the CM model to systems which depart in various respects from simple physical paradigms such as the collision described above. There are a number of examples of such systems. Second, there are a number of examples from the literature on causation that do not involve physically interesting forms of action at a distance but which arguably involve causal interactions without intervening spatio-temporally continuous processes or transfer of energy and momentum from cause to effect.

Many philosophers have been reluctant to accept this assessment. Most explanations in disciplines like biology, psychology and economics fall under this description, as do a number of straightforwardly physical explanations. Salmon appears to regard putative explanations based on at least the first of these generalizations as not explanatory because they do not trace continuous causal processes—he thinks of the individual molecules as causal processes but not the gas as a whole. The usual statistical mechanical treatment, which Salmon presumably would regard as explanatory, does not attempt to do this.

Instead, it makes certain general assumptions about the distribution of molecular velocities and the forces involved in molecular collisions and then uses these, in conjunction with the laws of mechanics, to derive and solve a differential equation the Boltzmann transport equation describing the overall behavior of the gas. This treatment abstracts radically from the details of the causal processes involving particular individual molecules and instead focuses on identifying higher level variables that aggregate over many individual causal processes and that figure in general patterns that govern the behavior of the gas.

This example raises a number of questions. Just what does the CM model require in the case of complex systems in which we cannot trace individual causal processes, at least at a fine-grained level? How exactly does the causal mechanical model avoid the disastrous conclusion that any successful explanation of the behavior of the gas must trace the trajectories of individual molecules? Does the statistical mechanical explanation described above successfully trace causal processes and interactions or specify a causal mechanism in the sense demanded by the CM model, and if so, what exactly does tracing causal processes and interactions involve or amount to in connection with such a system?

As matters now stand both the CM model and the process theories of causation that are its more recent descendants are incomplete. There is another aspect of this example that is worthy of comment. Even if, per impossible , an account that traced individual molecular trajectories were to be produced, there are important respects in which it would not provide the sort of explanation of the macroscopic behavior of the gas that we are likely to be looking for—and not just because such an account would be far too complex to be followed by a human mind. This information is certainly explanatorily relevant to the macroscopic behavior of the gas and we would like our account of explanation to accommodate this fact.

Very roughly, given the laws governing molecular collisions, one can show that almost all i. A similar point holds for explanations of the behavior of other sorts of complex systems, such as those studied in biology and economics. Consider the standard explanation, in terms of an upward shift of the supply curve, with an unchanged demand curve, for the increase in the price of oranges following a freeze. Underlying the behavior of this market are individual spatio-temporally continuous causal processes and interactions in Salmon's sense—there are a myriad of individual transactions in which money in some form is exchanged for physical goods, all of which involve transfers of matter or energy, there is exchange of information about intentions or commitments to buy or sell at various prices, all of which must take place in some physical medium and involve transfers of energy, and so on.

However, it also seems plain that producing a full description of these processes supposing for the sake of argument that it was possible to do this will produce little or no insight into why these systems behave as they do. It is also the case that a great deal of the information contained in such a description will be irrelevant to the behavior we are trying to explain, for the same reason that a detailed description of the individual molecular trajectories will contain information that is irrelevant to the behavior of the gas.

For example, while the detailed description of the individual causal processes involved in the operation of the market for oranges presumably will describe whether individual consumers purchase oranges by cash, check, or credit card, whether information about the freeze is communicated by telephone or email, and so on, all of this is to a first approximation irrelevant to the equilibrium price—given the supply and demand curves, the equilibrium price will be the same as long as there is a market in which consumers are able to purchase oranges by some means, information about the freeze and about prices is available to buyers and sellers in some form, and so on.

In fact, as the above examples illustrate, the requirements that Salmon imposes on causal processes-and in particular the requirement of spatio-temporal continuity—often seem to lead us away from the right level of description. The level at which the spatio-temporal continuity constraint is most obviously respected the level at which, e. In more recent work e. In this new theory which is influenced by the conserved process theory of causation of Dowe Dowe, , Salmon defined a causal process as a process that transmits a non-zero amount of a conserved quantity at each moment in its history.

Conserved quantities are quantities so characterized in physics—linear momentum, angular momentum, charge, and so on. A causal interaction is an intersection of world lines associated with causal processes involving exchange of a conserved quantity. One may doubt that this new theory really avoids reliance on counterfactuals, but an even more fundamental difficulty is that it still does not adequately deal with the problem of causal or explanatory relevance described above.

That is, we still face the problem that the feature that makes a process causal transmission of some conserved quantity or other may tell us little about which features of the process are causally or explanatorily relevant to the outcome we want to explain.

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For example, a moving billiard ball will transmit many conserved quantities linear momentum, angular momentum, charge etc. What is it that entitles us to single out the linear momentum of the balls, rather than these other conserved quantities as the property that is causally relevant to their subsequent motion? In cases in which there appear to be no conservation laws governing the explanatorily relevant property i. While one may say that both birth control pills and hexed salt are causal processes because both consist, at some underlying level, of processes that unambiguously involve the transmission of conserved quantities like mass and charge, this observation does not by itself tell us what, if anything, about these underlying processes is relevant to pregnancy or dissolution in water.

In a still more recent paper Salmon, , Salmon conceded this point. He agreed that the notion of a causal process cannot by itself capture the notion of causal and explanatory relevance. He suggested, however, that this notion can be adequately captured by appealing to the notion of a causal process and information about statistical relevance relationships that is, information about conditional and unconditional in dependence relationships , with the latter capturing the element of causal or explanatory dependence that was missing from his previous account:.

This suggestion is not developed in any detail in Salmon's paper, and it is not easy to see how it can be made to work. Railton suggests that an explanatory claim provides information about an underlying ideal text if the former reduces uncertainty about some of the properties of the text, in the sense of ruling in or out various possibilities concerning its structure. As Railton recognizes, this has proposal has many counterintuitive consequences. This contrasts with the widespread judgment that correlations in themselves are not explanatory.

In fact, such a claim is apparently maximally explanatory, since it conveys everything that there is to be said about the ideal explanatory text associated with that event. Examples like these suggest that not every claim that reduces uncertainty about the contents of an ideal explanatory text should be regarded as itself explanatory—such a view allows too much to count as an explanation. Will the economics explanation really be better according as to whether it conveys as much information as possible about these underlying details?

Finally, consider the connection between explanation and understanding. One ordinarily thinks of an explanation as something that provides understanding. Relatedly, part of the task of a theory of explanation is to identify those structural features of explanations or the information they convey in virtue of which they provide understanding. For example, as noted above, the DN model connects understanding with the provision of information about nomic expectability—the idea is that understanding why an outcome occurs is a matter of seeing that it was to be expected on the basis of a law.

It is hard to see how this structure or information can contribute to understanding if it is epistemically hidden in this way. For example, it seems plausible that many if not almost all users of 2. If this is the case, how can the mere obtaining of this DN structure, independently of anyone's awareness of its existence, function so as to provide understanding when 2. Instead, it seems that the features of 2. A similar point will hold for many other candidate explanations that fail to conform to the DN requirements such as explanations from sciences like economics and psychology that seem to lack laws.

What can we conclude from this discussion of the hidden structure strategy? On the other hand, it is possible that there are ways of developing the hidden structure strategy that respond adequately to the difficulties described above. Suggested Readings. This is reprinted in Hempel, a, along with a number of other papers that touch on various aspects of the problem of scientific explanation.

In addition to the references cited in this section, Salmon, , pp. Much of the subsequent literature on explanation has been motivated by attempts to capture the features of causal or explanatory relevance that appear to be left out of examples like 2. Wesley Salmon's statistical relevance or SR model Salmon, is a very influential attempt to capture these features in terms of the notion of statistical relevance or conditional dependence relationships. The intuition underlying the SR model is that statistically relevant properties or information about statistically relevant relationships are explanatory and statistically irrelevant properties are not.

In other words, the notion of a property making a difference for an explanandum is unpacked in terms of statistical relevance relationships. To illustrate this idea, suppose that in the birth control pills example 2. In other words, if you are a male in this population, taking birth control pills is statistically irrelevant to whether you become pregnant, while if you are a female it is relevant.

In this way we can capture the idea that taking birth control pills is explanatorily irrelevant to pregnancy among males but not among females. To characterize the SR model more precisely we need the notion of a homogenous partition. Assume for the sake of argument that no other factors are relevant to quick recovery.

That is, the probability of quick recovery, given that one has strep, is the same for those who have the resistant strain regardless of whether or not they are treated and also the same for those who have not been treated. By contrast, the probability of recovery is different presumably greater among those with strep who have been treated and do not have the resistant strain. The SR model has a number of distinctive features that have generated substantial discussion. Instead, an explanation is an assembly of information that is statistically relevant to an explanandum. Salmon argues and takes the birth control example 2.

As explained above, in associating successful explanation with the provision of information about statistical relevance relationships, the SR model attempts to accommodate this observation. A second, closely related point is that the SR model departs from the IS model in abandoning the idea that a statistical explanation of an outcome must provide information from which it follows the outcome occurred with high probability.

As the reader may check, the statement of the SR model above imposes no such high probability requirement; instead, even very unlikely outcomes will be explained as long as the criteria for SR explanation are met. Suppose that, in the above example, the probability of quick recovery from strep, given treatment and the presence of a non-resistant strain, is rather low e.

For example, if the prior probability of quick recovery among all those with any form of strep is 0. More generally, what matters on the SR model is not whether the value of the probability of the explanandum-outcome is high or low or even high or low in comparison with its prior probability but rather whether the putative explanans cites all and only statistically relevant factors and whether the probabilities it invokes are correct. For example, the same explanans will explain both why a subject with strep and certain other properties e.

The intuition that, contrary to the IS model, the value that a candidate explanans assigns to an explanandum-outcome should not matter for the goodness of the explanation it provides can be motivated in the following way. Suppose that if it is not tossed the coin has probability of 0. According to the IS model, if the coin is tossed and comes up heads, we can explain this outcome by appealing to the fact that the coin was tossed since under this condition the probability of heads is high but if the coin is tossed and comes up tails we cannot explain this outcome, since its probability is low.

The contrary intuition underlying the SR model is that we understand both outcomes equally well. The bias of the coin and the fact that the coin has been tossed are the only factors relevant to either outcome and those factors are common to both outcomes—once we have cited the toss and specified the probability values for heads and tails on tossing , we left nothing out that influences either outcome.

Similarly, Salmon argues, if it is really true that the partition in the example involving quick recovery from strep is objectively homogenous—if there are no other factors that are statistically relevant to quick recovery besides whether the subject has been treated and has a resistant strain—then once we have specified the probability of quick recovery under all combinations of these factors, and the combination of factors possessed by the subject whose recovery or not, as the case may be we want to explain, we have specified all information relevant to recovery and in this sense fully explained the outcome for the subject.

In assessing these claims, it will be useful to take a step back and ask just what it is that these competing models of statistical explanation Hempel's IS model and Salmon's SR model are intended to be reconstructions of. In the literature on this topic two classes of examples or applications figure prominently. First, there are examples drawn from quantum- mechanics QM. Models of statistical explanation assume that if the particle does penetrate the barrier, QM explains this outcome—the IS and SR models are intended to capture the structure of such explanations. Second, there are examples drawn from biomedical or epidemiological and social scientific applications—recovery from strep or, to cite one of Salmon's extended illustrations Salmon, , the factors relevant to juvenile delinquency in teen-age boys.

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This is, to say the least, a heterogeneous class of examples. In the case of QM , the usual understanding is that the various no-hidden variable results establish that any empirically adequate theory of quantum mechanical phenomena must be irreducibly indeterministic. By contrast, it seems quite unlikely that this homogeneity condition will be satisfied in most indeed, in any of the biomedical and sociological illustrations that have figured in the literature on statistical explanation.

In the case of recovery from strep, for example, it is very plausible that there are many other factors besides the two mentioned above that affect the probability of recovery—these additional factors will include the state of the subject's immune system, various features of the subject's general level of health, the precise character of the strain of disease to which the subject is exposed resistant versus non-resistant is almost certainly too coarse-grained a dichotomy and so on.

Similarly for episodes of juvenile delinquency. In these cases, in contrast to the cases from quantum mechanics, we lack a theory or body of results that delimits the factors that are potentially relevant to the probability of the outcome that interests us. Thus, in realistic examples of assemblages of statistically relevant factors from biomedicine and social science, the objective homogeneity condition is unlikely to be satisfied, or in any practical sense, satisfiable.

A related difference concerns the way in which statistical evidence figures in these two sorts of applications. Some quantum mechanical phenomena such as radioactive decay are irreducibly indeterministic. This particularly clear in connection with the social scientific examples such as risk factors for juvenile delinquency that Salmon discusses. Here the relevant methodology involves so-called causal modeling or structural equation techniques. At least on the most straightforward way of applying such procedures, the equations that govern whether a particular individual becomes a juvenile delinquent are if interpreted literally deterministic.

According to such approaches, the phenomena being modeled look as though they are indeterministic because some of the variables which are relevant to their behavior, the influence of which is summarized by a so-called error term, are unknown or unmeasured. Statistical information about the incidence of juvenile delinquency among individuals in various conditions plays the role of evidence that is used to estimate parameters the coefficients in the deterministic equations that are taken to describe the processes governing the onset of delinquency.

A similar point holds for at least many biomedical examples. Several preliminary conclusions are suggested by these observations. First, it is far from obvious that we should try to construct a single, unified model of statistical explanation that applies to both quantum mechanics and macroscopic phenomena like delinquency or recovery from infection.

In other words, if an objective homogeneity condition is imposed on statistical explanation, it is not clear that there will be any examples of successful statistical explanation outside of quantum mechanics. With these observations in mind, let us revisit the question of what is explained by statistical theories, whether quantum mechanical or macroscopic.

As we have seen, both Hempel and Salmon, as well as most subsequent contributors to the literature on statistical explanation, have tended to assume that statistical theories that assign a probability to some outcome strictly between 0 and 1 should nonetheless be interpreted as explaining that outcome. Given this common starting point, Salmon is quite persuasive in arguing that it is arbitrary to hold, as Hempel does, that only individual outcomes with high probability can be explained. But why should we accept the starting point? Why not take Salmon's argument instead to be a reason for rejecting the idea that statistical theories explain individual outcomes, whether of high or low probability?

If we take this view, we need not conclude that a theory like QM is unexplanatory. Instead, we may take the explananda of QM to be facts about the probabilities or expectation values of outcomes rather than individual outcomes themselves. On this view, the explananda that are explained by QM are a proper subset of those that can be derived from it—at least in this respect, the explanations provided by QM are like DS explanations in structure.

Woodward argues that this construal allows us to say all that we might legitimately wish to say about the explanatory virtues of QM. If this is correct, there is no obvious need for a separate theory of statistical explanation of individual outcomes of the sort that Hempel and Salmon sought to devise But see footnote 7.

In the case of juvenile delinquency and causal modeling techniques it is, if anything, even more intuitive that what is being explained is not, e. Again such explananda are deducible from the system of equations used to model juvenile delinquency. Taking this view of what is explained by statistical theories allows us to avoid various unintuitive consequences of Hempel's model e. At the very least, those who have sought to construct models of statistical explanation of individual outcomes need to provide a more detailed elucidation of why such models are needed and of the features of scientific theorizing they are designed to capture.

As we have just seen, the SR model raises a number of interesting questions about the statistical explanation of individual outcomes—questions that are important independently of the details of the SR model itself. This section will abstract away from such questions and focus instead on the root motivation for the SR model. We may take this to consist of two ideas: i explanations must cite causal relationships and ii causal relationships are captured by statistical relevance relationships. Even if i is accepted, a fundamental problem with the SR model is that ii is false—as a substantial body of work [ 10 ] has made clear, casual relationships are greatly underdetermined by statistical relevance relationships.

These contentions about the connection between causal claims and statistical relevance relations are consequences of a more general principle called the Causal Markov condition which has been extensively discussed in the recent literature on causation. Two relevant points have emerged from discussion of this condition. The first, which was in effect noted by Salmon himself in work subsequent to his , is that there are circumstances in which the Causal Markov condition fails and hence in which causal claims do not imply the screening off relationships described above.

This can happen, for example, if the variables to which the condition is applied are characterized in an insufficiently fine-grained way. In structures with more variables, this underdetermination of causal relationships by statistical relevance relationships may be far more extreme. Thus a list of statistical relevance relationships, which is what the SR model provides, need not tell us which causal relationships are operative. To the extent that explanation has to do with the identification of the causal relationships on which an explanandum-outcome depends, the SR model fails to fully capture these.

Selected Readings. Salmon, a provides a detailed statement and defense of the SR model. This essay, as well as papers by Jeffrey and Greeno which defend views broadly similar to the SR model, are collected in Salmon, b. Cartwright, contains some influential criticisms of the SR model.

Theorems specifying the precise extent of the underdetermination of causal claims by evidence about statistical relevance relationships can be found in Spirtes, Glymour and Scheines, , , chapter 4. In more recent work especially, Salmon, Salmon abandoned the attempt to characterize explanation or causal relationships in purely statistical terms. Instead, he developed a new account which he called the Causal Mechanical CM model of explanation—an account which is similar in both content and spirit to so-called process theories of causation of the sort defended by philosophers like Philip Dowe The CM model employs several central ideas.

A causal process is a physical process, like the movement of a baseball through space, that is characterized by the ability to transmit a mark in a continuous way. Intuitively, a mark is some local modification to the structure of a process—for example, a scuff on the surface of a baseball or a dent an automobile fender.

A process is capable of transmitting a mark if, once the mark is introduced at one spatio-temporal location, it will persist to other spatio-temporal locations even in the absence of any further interaction. In this sense the baseball will transmit the scuff mark from one location to another. Similarly, a moving automobile is a causal process because a mark in the form of a dent in a fender will be transmitted by this process from one spatio-temporal location to another.

Causal processes contrast with pseudo-processes which lack the ability to transmit marks. An example is the shadow of a moving physical object. The intuitive idea is that, if we try to mark the shadow by modifying its shape at one point for example, by altering a light source or introducing a second occluding object , this modification will not persist unless we continually intervene to maintain it as the shadow occupies successive spatio-temporal positions. In other words, the modification will not be transmitted by the structure of the shadow itself, as it would in the case of a genuine causal process.

We should note for future reference that, as characterized by Salmon, the ability to transmit a mark is clearly a counterfactual notion, in several senses. To begin with, a process may be a causal process even if it does not in fact transmit any mark, as long as it is true that if it were appropriately marked, it would transmit the mark.

Moreover, the notion of marking itself involves a counterfactual contrast—a contrast between how a process behaves when marked and how it would behave if left unmarked. Although Salmon, like Hempel, has always been suspicious of counterfactuals, his view at the time that he first introduced the CM model was that the counterfactuals involved in the characterization of mark transmission were relatively unproblematic, in part because they seemed experimentally testable in a fairly direct way.

Nonetheless the reliance of the CM model, as originally formulated, on counterfactuals shows that it does not completely satisfy the Humean strictures described above. In subsequent work, described in Section 4. The other major element in Salmon's model is the notion of a causal interaction. A casual interaction involves a spatio-temporal intersection between two causal processes which modifies the structure of both—each process comes to have features it would not have had in the absence of the interaction.

A collision between two cars that dents both is a paradigmatic causal interaction. Nonetheless, it seems clear enough how the intuitive idea is meant to apply to specific examples. Suppose that a cue ball, set in motion by the impact of a cue stick, strikes a stationary eight ball with the result that the eight ball is put in motion and the cue ball changes direction. The impact of the stick also transmits some blue chalk to the cue ball which is then transferred to the eight ball on impact. The cue stick, the cue ball, and the eight ball are causal processes, as is shown by the transmission of the chalk mark, and the collision of the cue stick with the cue ball and the collision of the cue and eight balls are causal interactions.

Salmon's idea is that citing such facts about processes and interactions explains the motion of the balls after the collision; by contrast, if one of these balls casts a shadow that moves across the other, this will be causally and explanatorily irrelevant to its subsequent motion since the shadow is a pseudo-process.

This explanation proceeds by deriving that motion from information about their masses and velocity before the collision, the assumption that the collision is perfectly elastic, and the law of the conservation of linear momentum. We usually think of the information conveyed by this derivation as showing that it is the mass and velocity of the balls, rather than, say, their color or the presence of the blue chalk mark, that is explanatorily relevant to their subsequent motion.

However, it is hard to see what in the CM model allows us to pick out the linear momentum of the balls, as opposed to these other features, as explanatorily relevant. Part of the difficulty is that to express such relatively fine-grained judgments of explanatory relevance that it is linear momentum rather than chalk marks that matters we need to talk about relationships between properties or magnitudes and it is not clear how to express such judgments in terms of facts about causal processes and interactions.

Both the linear momentum and the chalk mark communicated to the cue ball by the cue stick are marks transmitted by the spatio-temporally continuous causal process consisting of the motion of the cue ball. Both marks are then transmitted via an interaction to the eight ball. There appears to be nothing in Salmon's notion of mark transmission or the notion of a causal process that allows one to distinguish between the explanatorily relevant momentum and the explanatorily irrelevant blue chalk mark.

Ironically, as Hitchcock goes on to note, a similar observation may be made about the birth control pills example 2. Spatio-temporally continuous causal processes that transmit marks as well as causal interactions are at work when male Mr. Jones ingests birth control pills—the pills dissolve, components enter his bloodstream, are metabolized or processed in some way, and so on. Similarly, spatio-temporally continuous causal processes albeit different processes are at work when female Ms.

Jones takes birth control pills. However, the pills are irrelevant to Mr. Jones non-pregnancy, and relevant to Ms. Jones' non-pregnancy. Again, it looks as though the relevance or irrelevance of the birth control pills to Mr. Jones' failure to become pregnant cannot be captured just by asking whether the processes leading up to these outcomes are causal processes in Salmon's sense.

A similar point holds for the hexed salt example 2. So while mark transmission may well be a criterion that correctly distinguishes between causal processes and pseudo-processes , it does not, as it stands, provide the resources for distinguishing those features or properties of a causal process that are causally or explanatorily relevant to an outcome and those features that are irrelevant. A second set of worries has to do with the application of the CM model to systems which depart in various respects from simple physical paradigms such as the collision described above.

There are a number of examples of such systems. Second, there are a number of examples from the literature on causation that do not involve physically interesting forms of action at a distance but which arguably involve causal interactions without intervening spatio-temporally continuous processes or transfer of energy and momentum from cause to effect. Many philosophers have been reluctant to accept this assessment.

Most explanations in disciplines like biology, psychology and economics fall under this description, as do a number of straightforwardly physical explanations. Salmon appears to regard putative explanations based on at least the first of these generalizations as not explanatory because they do not trace continuous causal processes—he thinks of the individual molecules as causal processes but not the gas as a whole. The usual statistical mechanical treatment, which Salmon presumably would regard as explanatory, does not attempt to do this.

Instead, it makes certain general assumptions about the distribution of molecular velocities and the forces involved in molecular collisions and then uses these, in conjunction with the laws of mechanics, to derive and solve a differential equation the Boltzmann transport equation describing the overall behavior of the gas.

This treatment abstracts radically from the details of the causal processes involving particular individual molecules and instead focuses on identifying higher level variables that aggregate over many individual causal processes and that figure in general patterns that govern the behavior of the gas. This example raises a number of questions. Just what does the CM model require in the case of complex systems in which we cannot trace individual causal processes, at least at a fine-grained level?

How exactly does the causal mechanical model avoid the disastrous conclusion that any successful explanation of the behavior of the gas must trace the trajectories of individual molecules? Does the statistical mechanical explanation described above successfully trace causal processes and interactions or specify a causal mechanism in the sense demanded by the CM model, and if so, what exactly does tracing causal processes and interactions involve or amount to in connection with such a system?

As matters now stand both the CM model and the process theories of causation that are its more recent descendants are incomplete. There is another aspect of this example that is worthy of comment. Even if, per impossible , an account that traced individual molecular trajectories were to be produced, there are important respects in which it would not provide the sort of explanation of the macroscopic behavior of the gas that we are likely to be looking for—and not just because such an account would be far too complex to be followed by a human mind.

This information is certainly explanatorily relevant to the macroscopic behavior of the gas and we would like our account of explanation to accommodate this fact. Very roughly, given the laws governing molecular collisions, one can show that almost all i. A similar point holds for explanations of the behavior of other sorts of complex systems, such as those studied in biology and economics. Consider the standard explanation, in terms of an upward shift of the supply curve, with an unchanged demand curve, for the increase in the price of oranges following a freeze.

Underlying the behavior of this market are individual spatio-temporally continuous causal processes and interactions in Salmon's sense—there are a myriad of individual transactions in which money in some form is exchanged for physical goods, all of which involve transfers of matter or energy, there is exchange of information about intentions or commitments to buy or sell at various prices, all of which must take place in some physical medium and involve transfers of energy, and so on. However, it also seems plain that producing a full description of these processes supposing for the sake of argument that it was possible to do this will produce little or no insight into why these systems behave as they do.

It is also the case that a great deal of the information contained in such a description will be irrelevant to the behavior we are trying to explain, for the same reason that a detailed description of the individual molecular trajectories will contain information that is irrelevant to the behavior of the gas. For example, while the detailed description of the individual causal processes involved in the operation of the market for oranges presumably will describe whether individual consumers purchase oranges by cash, check, or credit card, whether information about the freeze is communicated by telephone or email, and so on, all of this is to a first approximation irrelevant to the equilibrium price—given the supply and demand curves, the equilibrium price will be the same as long as there is a market in which consumers are able to purchase oranges by some means, information about the freeze and about prices is available to buyers and sellers in some form, and so on.

In fact, as the above examples illustrate, the requirements that Salmon imposes on causal processes-and in particular the requirement of spatio-temporal continuity—often seem to lead us away from the right level of description. The level at which the spatio-temporal continuity constraint is most obviously respected the level at which, e.

In more recent work e. In this new theory which is influenced by the conserved process theory of causation of Dowe Dowe, , Salmon defined a causal process as a process that transmits a non-zero amount of a conserved quantity at each moment in its history. Conserved quantities are quantities so characterized in physics—linear momentum, angular momentum, charge, and so on. A causal interaction is an intersection of world lines associated with causal processes involving exchange of a conserved quantity.

One may doubt that this new theory really avoids reliance on counterfactuals, but an even more fundamental difficulty is that it still does not adequately deal with the problem of causal or explanatory relevance described above. That is, we still face the problem that the feature that makes a process causal transmission of some conserved quantity or other may tell us little about which features of the process are causally or explanatorily relevant to the outcome we want to explain. For example, a moving billiard ball will transmit many conserved quantities linear momentum, angular momentum, charge etc.

What is it that entitles us to single out the linear momentum of the balls, rather than these other conserved quantities as the property that is causally relevant to their subsequent motion? In cases in which there appear to be no conservation laws governing the explanatorily relevant property i. While one may say that both birth control pills and hexed salt are causal processes because both consist, at some underlying level, of processes that unambiguously involve the transmission of conserved quantities like mass and charge, this observation does not by itself tell us what, if anything, about these underlying processes is relevant to pregnancy or dissolution in water.

In a still more recent paper Salmon, , Salmon conceded this point.

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He agreed that the notion of a causal process cannot by itself capture the notion of causal and explanatory relevance. He suggested, however, that this notion can be adequately captured by appealing to the notion of a causal process and information about statistical relevance relationships that is, information about conditional and unconditional in dependence relationships , with the latter capturing the element of causal or explanatory dependence that was missing from his previous account:.

This suggestion is not developed in any detail in Salmon's paper, and it is not easy to see how it can be made to work. We noted above that statistical relevance relationships often greatly underdetermine the causal relationships among a set of variables. What reason is there to suppose that appealing to the notion of a causal process, in Salmon's sense, will always or even usually remove this indeterminacy?

We also noted that the notion of a causal process cannot capture fine grained notions of relevance between properties, that there can be causal relevance between properties instances of which at least at the level of description at which they are characterized are not linked by spatio-temporally continuous or transference of conserved quantities, and that properties can be so linked without being causally relevant recall the chalk mark that is transmitted from one billiard ball to another. As long as it is possible and why should it not be?

Selected Readings: Salmon, provides a detailed statement of the Causal Mechanical model, as originally formulated. Salmon, and provide a restatement of the model and respond to criticisms. For discussion and criticism of the CM model, see Kitcher, , especially pp. The basic idea of the unificationist account is that scientific explanation is a matter of providing a unified account of a range of different phenomena.

This idea is unquestionably intuitively appealing. Successful unification may exhibit connections or relationships between phenomena previously thought to be unrelated and this seems to be something that we expect good explanations to do. Moreover, theory unification has clearly played an important role in science. Paradigmatic examples include Newton's unification of terrestrial and celestial theories of motion and Maxwell's unification of electricity and magnetism. The key question, however, is whether our intuitive notion or notions of unification can be made more precise in a way that allows us to recover the features that we think that good explanations should possess.

Michael Friedman is an important early attempt to do this. Friedman's formulation of the unificationist idea was subsequently shown to suffer from various technical problems Kitcher, and subsequent development of the unificationist treatment of explanation has been most associated closely with Philip Kitcher especially Kitcher, Let us begin by introducing some of Kitcher's technical vocabulary.

A schematic sentence is a sentence in which some of the nonlogical vocabulary has been replaced by dummy letters.