Computational Philosophy of Science

Jan 18, 2023

Paul Thagard's contributions to the computational philosophy of science have been influential in understanding the role of computation in the philosophy of science. This chapter will explore Thagard's biography and his contributions to the computational philosophy of science and will delve into his ideas about how computational modeling can help us understand the complex cognitive processes involved in scientific reasoning. It will also examine Thagard's views on the structure of scientific knowledge and the nature of theories and explanations. Overall, this chapter will provide an extensive exploration of Thagard's work, showing how a computational account can contribute to philosophical understanding and demonstrating the philosophical superiority of computational accounts of theories.

3.1. Short Biography of Paul Thagard

Paul Richard Thagard was born in Yorkton, Saskatchewan, Canada on September 28, 1950. He is a Canadian philosopher who specializes in cognitive science, philosophy of mind, philosophy of science and medicine. He is a graduate of the Universities of Saskatchewan (B.A. in philosophy, 1971), Cambridge (M.A. in philosophy, 1973), Toronto (Ph.D. in philosophy, 1977), and Michigan (M.S. in computer science, 1985). Thagard is a professor emeritus of philosophy at the University of Waterloo. Thagard was married to psychologist Ziva Kunda. Kunda died in 2004. Thagard is an author who has made significant contributions to research in several areas, including analogy and creativity, inference, cognition in the history of science, and the influence of emotion on cognition. Thagard's philosophical approach is characterized by a critical stance towards analytic philosophy, which he sees as overly reliant on intuitions as a source of evidence.

In the philosophy of mind, he is known for his attempts to apply connectionist models of coherence to theories of human thought and action. He is also known for HOTCO ("hot coherence"), which was his attempt to create a computer model of cognition that incorporated emotions at a fundamental level.

In the philosophy of science, Thagard is known for his work on the use of computational models in explaining conceptual revolutions; his most distinctive contribution to the field is the concept of explanatory coherence, which he has applied to historical cases. He is heavily influenced by pragmatists like C. S. Peirce. One of his major works on the philosophy of science is his book Computational Philosophy of Science (1988), which I will be exploring in this chapter, starting with his ideas on computation and the philosophy of science.

3.2. Computation and the Philosophy of Science

As Albert Einstein puts it - “Epistemology without contact with science becomes an empty scheme. Science without epistemology is insofar as it is thinkable at all primitive and muddled”. According to Thagard, “Computational philosophy of science is an attempt to understand the structure and growth of scientific knowledge in terms of the development of computational and psychological structures”. He proffers that the Computational philosophy of science aims to offer new accounts of the nature of theories and explanations and the processes underlying their development. He opines that although allied with investigations in artificial intelligence and cognitive psychology, it differs in having an essential normative component. The philosophy of science and artificial intelligence have much to learn from each other.

3.2.1. Artificial Intelligence, Psychology, and Historical Philosophy of Science

According to Thagard, Artificial intelligence (AI) is the branch of computer science concerned with getting computers to perform intelligent tasks. In its brief three decades of existence, He argues that AI has developed many computational tools for describing the representation and processing of information. He believes that Cognitive psychologists have found these tools valuable for developing theories about human thinking. Similarly, he suggests that the computational philosophy of science can use them for describing the structure and growth of scientific knowledge. He also notes that to a large extent, the concerns of AI, cognitive psychology, and Computational philosophy of science overlap, although philosophy has a greater concern with normative issues than these other two fields. He argues that we must distinguish between descriptive issues, concerning how scientists do think, and normative issues, concerning how scientists ought to think. According to Thagard, “Cognitive psychology is dedicated to the empirical investigation of mental processes and is interested in normative issues only to the extent of characterizing people's departures from assumed norms”. Similarly, he suggests that artificial intelligence understood as cognitive modeling can confine itself to the descriptive rather than the normative. He opined that AI, however, is also sometimes concerned with improving the performance of people and therefore can be interested in what is optimal and normative.

In his view, the Historical philosophy of science has contributed to a much more rich and more subtle account of the nature of science than could be developed within the framework of the logical positivists. He opines that the computational philosophy of science is even more closely tied with psychology, by the link between unrefined AI and current cognitive psychology, which increasingly employs computational models as theoretical tools. He suggests that these three fields can collaborate in developing a computational account of how human scientists think. He argues that many researchers in the philosophy of science and artificial intelligence would prefer to leave psychology out of the picture, and science may indeed someday be performed by computers using processes very different from those in humans. He believes that for now, at least, science is a human enterprise, and understanding of the development of scientific knowledge depends on an account of the thought processes of humans. Hence he notes that the computational philosophy of science overlaps as much with cognitive psychology as it does with unrefined AI. He believes that even its normative prescriptions about how science ought to be done should take human cognitive limitations as starting points. He asserts that the Computational philosophy of science and much of current cognitive psychology employ computational models.

3.2.2. Why Write Programs

Thagard argued that there are at least three major gains that computer programs offer to cognitive psychology and computational philosophy of science:

computer science provides a systematic vocabulary for describing structures and mechanisms.
The implementation of ideas in a running program is a test of internal coherence.
Running the program can provide tests of foreseen and unforeseen consequences of hypotheses.

In his opinion, current cognitive psychology is permeated with computational notions, such as search, spreading activation, buffer, retrieval, and so on. He contends that the birth of cognitive psychology in the 1960s depended on the computer metaphor that provided for the first time a precise means of describing rich internal structures and processes. He maintains that in the 1970s, the interdisciplinary field of Cognitive Science brought together researchers from diverse fields, all concerned with understanding the nature of the mind, having in common primarily the hope that computational models would help. He portrayed that the computational analysis of the mind depends on these correspondences:

Thought	Program
Mental Structures	Data Structures
Processes	Algorithms

He highlights that Behaviorists argued that any speculation about the contents of the mind was metaphysical baggage, but the computer made it possible to be concrete about postulated mental structures and processes, even if the problem of verifying their existence remained difficult. He posits that a program can be understood as a set of data structures along with a set of algorithms that mechanically operate with the data structures. That the structures can be very simple to say, just a list of elements such as (1 2 3). Or that they can become much more complex as in the list processing language LISP, where it is easy to create structures that consist of organized lists embedded within other lists. In Thagard’s view, Algorithms are, in paraphrase “well-defined procedures that can be written to operate on data structures or to create new ones”. That it is a systematic procedure that produces in a finite number of steps the answer to a question or the solution to a problem. Similarly, he posits that the currently most developed and plausible view of the mind postulates internal mental structures or representations accompanied by processes for using those representations. He believes that by writing programs that have data structures corresponding to the postulated representations and algorithms corresponding to the postulated processes, we can develop detailed models of the mind. He contends that for a program to be run on a computer, it has to be explicit, and the exercise of working out the coordinated structure and processes will normally lead to the development of a richer and more complex model than unaided speculation would provide. He proposes that much can be learned about a scientific domain by attempting to analyze it within a complex representational scheme. Because mental processes are postulated to be computational, the computer is potentially an even more powerful tool for psychology than it is for such fields as economics and meteorology which use weak simulations in contrast to psychology's strong simulations. Thagard points out that, in a weak simulation, the computer functions as a calculating device drawing out the consequences of mathematical equations that describe the process simulated. That a computer can valuably simulate a business cycle or a hurricane, but no one contends that it has an economic depression or high winds.

He also notes that, in a strong simulation, however, the simulation itself resembles the process simulated. He portrayed this using an example, that a wind tunnel used to study the aerodynamics of cars is a strong simulation since the flow of air over the car in the tunnel is similar to the flow of air over the car on the highway. In his perspective, a computer model of the car's aerodynamics would only be a weak simulation, whereas for most fields computers will only provide weak simulations, psychology has the possibility of strong simulations if the computational theory of mind is correct. He asserts that merely characterizing data structures and processes in computational terms does not tell us how the mind operates. That even getting the program to run provides a test of sorts. He highlights that some non-computational psychologists tend to assume that anything can be programmed, but this is no more credible than the assumption of some computer scientists that any psychological data can be got by a clever experimenter. He submits that to run, a computer program has to have at least a coherent interrelation of structures and algorithms.

In addition, Thagard argued that the threat of combinatorial explosion puts a severe constraint on the realizability of programs: if the program requires exponentially increasing time to run, it will quickly exhaust the resources of the most powerful computers. He asserts that developing a computer simulation provides a valuable test of the internal coherence of a set of ideas. In his view, a psychological model should be more than internally coherent:

We want it to account for experimental data about how people think. He considers that sometimes if a model is complex, it is not easy to see what its consequences are. Cognitive models, like many models in the social sciences, often postulate many interacting processes. The computer program enables a researcher to see whether the model has all and only the consequences that it was expected to have. Comparison of these consequences against experimental observations provides the means of validating the model in much greater detail than pencil-and-paper calculations might allow.

He contends that the Computational philosophy of science can benefit from the same model-forming and model-testing benefits that AI provides to cognitive psychology.

3.2.3. Psychologism

According to Thagard, the computational philosophy of science is intimately tied to cognitive psychology and artificial intelligence. He believes that if the cognitive sciences suggest a revision of standard views of the structure and growth of knowledge, one would expect those views to have immediate epistemological significance. He maintains that since the split between philosophy and psychology in the second half of the nineteenth century, most philosophers have developed epistemological views in complete independence from the work of empirical psychologists. He asserts that the mingling of philosophical and psychological discussions was branded as "psychologism". He opines that “the most principled reason for philosophers' fear of an association with psychology is that the normative concerns of philosophy will be diluted or abandoned”. He portrayed these arguments against psychologism, akin to ones offered by Frege and Popper - Epistemology, the argument runs, is as unconcerned with psychology as is logic. Psychology describes what inferences people make, but logic is concerned with what inferences people should make, with the normative rather than the descriptive. Similarly, epistemology is the normative theory of objective knowledge, and need not take into account what psychology determines to be the nature of the belief systems in individuals. Propositions, or sentences expressing them, can be conclusions of arguments and can be written down in books for public scrutiny. To examine the structure of individual belief systems would only be to encourage a kind of subjectivism that abandons the traditional noble concerns of epistemology-justification and truth-for-a-vapid relativism. Thagard asserts that Relativism is the philosophical view that truth is relative and may vary from person to person or from time to time, with no objective standards.

3.3. The Structure of Scientific Knowledge

Thagard opines that an understanding of scientific knowledge will require the representation of observations, laws, theories, concepts, and problem solutions. He posits that for a full description of the roles that these play in such activities as problem-solving and discovery, it is necessary to use representations with more structure than a logical model would admit. He believes that the expressive equivalence of two systems does not imply procedural equivalence and procedural questions are crucial for understanding the development and application of scientific knowledge.

3.3.1. Structure and Process

According to Thagard, the case for the epistemological relevance of computation rests on a simple but extremely important point: Structure cannot be separated from process. He believes that one cannot discuss the structure of knowledge without paying attention to the processes that are required to use it. He submits that this point is familiar to most practitioners of artificial intelligence, but is new to philosophers, who have in this century had a relatively simple view of the structure of knowledge. He proffers that since the pioneering work of Frege and Russell, formal logic has been the canonical way of describing the structure of knowledge.

According to Thagard’s perspective in first-order predicate calculus, a simple atomic sentence such as "Leonard is honest" is represented by a predicate and an argument such as H(s). He points out that the AI use of predicate calculus is less cryptic so that the same sentence is represented by honesty (Leonard). He highlights that more complex sentences are built up using connectives like - and, or, and if-then, and by quantifiers such as - some and all. For example, the sentence, "All seminarians are honest." can be represented as (for all x) (if seminarians(x) then honest(x). He contends that Predicate calculus has many strengths as a starting point for representing knowledge, but it does not provide sufficient structure for all processing purposes. He highlights that in twentieth-century philosophy, the most studied technique for using knowledge is a deduction in logical systems, in which rules of inference can be precisely defined. For example, modus ponens which is the rule of logic stating that if a conditional statement (“if p then q”) is accepted, and the antecedent (p) holds, then the consequent (q) may be inferred. Thagard believes that there must be more to a processing system than deduction. He maintains that if a system is large, assembling the relevant information at a particular time can be highly problematic. He argues that in epistemological systems based on logic, a corpus of knowledge is generally taken to consist of all the deductive consequences of a set of statements, even though the set of consequences is infinite. Thagard proposes that for more realistic systems, it becomes crucial to ask the question, what shall we infer? So even in a system designed to do deduction, we need processes that take into account what information is available and what rules of inference are appropriate. He posits that in any system designed for learning as well as performance, for the acquisition of knowledge as well as its use, non-deductive processes are required. He asserts that scientific discovery is multifaceted, requiring diverse processes for generating concepts, forming general laws, and creating hypotheses. That such processes depend on complex representations of concepts and laws.

3.3.2. Scientific Knowledge

Thagard asserts that for one to represent scientific knowledge, one needs to find a formal expression for at least three kinds of information: observations, laws, and theories. He opines that philosophers of science have differed on the relative importance of these aspects in the development of scientific knowledge. He highlights that on one simple account of how science develops, scientists start by making experimental observations, and then use these to generate laws and theories. He also notes that on an equally simple and misleading account, scientists start with laws and theories and make predictions that they then check against observations. He believes that in most scientific practice, there is rather an interplay of hypotheses and observations, with new observations leading to new laws and theories and vice versa. He proffered that “to describe the process of science computationally, one needs to be able to formalize observations, laws, and theories in structures that can be part of computer programs”. In addition, Thagard argues that it is also necessary to use a rich representation of scientific concepts. He posits that formalization is necessary but not sufficient for representation since we could formalize a body of scientific knowledge in predicate calculus or set theory without it being represented in a computationally usable form. He asserts that formalization and representation must go hand in hand, putting the knowledge into a form that can be processed.

3.3.3. Structure and Process in PI

To be more concrete about the importance of rich representations, Thagard proffered an artificial intelligence program called PI, which stands for "processes of induction" and is pronounced, "pie". PI implements in the programming language LISP a general model of problem-solving and inductive inference developed in collaboration with cognitive psychologist Keith Holyoak. His intention in describing PI is not to propose it as a canonical language for doing science; its limitations will be described. Nor is PI claimed to constitute in itself a solution to the host of difficult problems in the philosophy of science concerning explanation, justification, and so on. Rather, Thagard presents it as an illustration of how representation and process interact and of how an integrated general account of scientific discovery and justification can begin to be developed within a computational framework. A comprehensive description of the operation of PI can be found in chapter two of Thagard's work Computational Philosophy of Science (1988), it contains much more detailed information about PI's implementation in LISP and its limitations.

3.3.4. Expressive and Procedural Equivalence

Thagard proffers that the simple distinction between expressive and procedure equivalence has many applications. He opines that given expressive equivalence between two systems and a procedure in one of them, we can always find a corresponding procedure in the other. But he believes that the procedure found may be very inefficient. He portrayed that for Roman numerals, instead of trying to get an algorithm for long division directly, we could simply translate into Arabic numerals, using our familiar algorithm, after which we translate back. Thus he asserts:

However, this process will take much extra time, so it does not challenge the superiority of Arabic numerals. Similarly, the procedures in the same systems can be more efficient for particular kinds of inferences than those found in less specialized logic systems. Any digital computer is computationally equivalent to a Turing machine, which is an extremely simple device consisting of only a tape with squares on it and a head that can write d's and l's in the squares. Anything that can be done computationally on a digital computer can be done on a Turing machine. This fact is not of much interest for understanding intelligence because Turing machines are slow and torturous to program.

He highlights that the design of intelligent systems, whether by natural selection or human engineers, unavoidably takes into account the speed of operations. Hence he maintains that the current wave of research on how parallel architectures for computers can speed up processing is highly relevant for understanding the nature of the mind. He points out that the distinction between expressive and procedural equivalence is also important for theoretical psychology. He noted that debates have raged over whether the mind employs mental images in addition to propositions, and whether it employs large structures called "schemas" in addition to simpler propositions.

Some theorists have argued that since the content of any image or schema can be translated into propositions, there is no need to postulate the additional structures. Thagard on the other hand argues that “images and schemas might have procedures associated with them that would be much more difficult to perform in a purely propositional system; images, for example, can be rotated or otherwise manipulated in systematic ways”. Hence he posits that empirical evidence can be found, using factors such as speed of processing and qualitative differences, to support the existence in human thinking of more complex structures like those found in PI's rules and concepts.

3.4. Theories and Explanations

Thagard asserts that scientific theories are our most important epistemic achievements. He believes that our knowledge of individual pieces of information is little compared to theories such as general relativity and evolution by natural selection that shape our understanding of many different kinds of phenomena. He points out that one might be tempted to think of ordinary knowledge as changing and growing merely by additions and deletions of pieces of information, but theoretical change requires much more complex global alterations. But he inquires about what these entities constitute the most impressive part of our knowledge. He highlights that researchers in the philosophy of science over the past fifty years have employed three different kinds of approaches to the problem of the nature of scientific theories. Following the traditional semiotic classification, Thagard called these “syntactic, semantic, and pragmatic approaches”. He opined that the logical positivists took scientific theories to be syntactic structures-sets of sentences, ideally given an axiomatic formalization in a logistic system. Thagard argues that in the past decade, a semantic (set-theoretic) conception of theories has become increasingly popular; this conception abstracts from particular syntactic formulations of theories and interprets them in terms of sets of models. He also highlights another recent trend, popular among philosophers with a more historical bent, which has been pragmatic in that it considers theories as devices used by scientists in a particular context.

According to him, philosophers who construe theories pragmatically include Kuhn, “who emphasizes the role of paradigms in historical communities”, and Laudan, “who stresses the role of theories in solving empirical and conceptual problems”. The next sections describe some of the strengths and weaknesses of these three approaches. Thagard argued that a fully adequate account of scientific theories must be pragmatic: formalistic concentration on merely syntactic or semantic features of theories unavoidably neglects some of their essential features. However, Thagard believes that the historically oriented pragmatic accounts of Kuhn and others have failed to develop adequate philosophical analyses because they have been unable to add much content to vague ions such as paradigms and problem solutions. He asserts that a more powerful pragmatic account can be developed using computational ideas.

3.4.1. Requirements of an Account of the Nature of Theories

Thagard probes into what we should demand of an account of the nature of scientific theories. He then proposes that an account needs to be adequate at three different but related levels: practical, historical, and philosophical. He argued that we want an account that (1) serves to describe the everyday practice of scientists in using theories, (2) accommodates how theories are developed historically, and (3) gives rise to philosophically satisfactory treatments of such crucial issues in the philosophy of science as the nature of explanation. He proffers that for an account to be practically adequate, it must show how theories can function in the diverse ways scientists use them in explanation, problem-solving, conceptual development, and so on. He opined that use in these intellectual operations entails that a theory must be a psychologically real entity, capable of functioning in the cognitive operations of scientists. He highlights that such functioning is not a purely individual matter, for a theory must be capable of being shared by members of a scientific community and learned by new members. He argued that “if the philosophy of science is to be the philosophy of science rather than abstract epistemology, it must become psychologistic in that its account of the structure of scientific knowledge recapitulates how knowledge is structured in individual minds”. He submits that practical adequacy requires that an account must be broad enough to characterize the uses of both mathematical theories, such as Newton's mechanics, and primarily qualitative ones, such as Darwin's theory of evolution.

He also proffers that for an account to be historically adequate, it must be able to describe how theories develop over time, in a way faithful to the history of science. He maintains that it must be sufficiently flexible to depict how theories are discovered and undergo conceptual change while elucidating the notion of the sameness of theories. He submits that the account must also be capable of describing the dynamic relations among theories, such as the reduction or replacement of one theory by another and explanatory competition between theories in the same domain. He also posits that for an account of the nature of scientific theories to be philosophically adequate, it must contribute to plausible and rigorous solutions to other central problems in the philosophy of science. Most immediately, he posits, an account must suggest an analysis of the nature of scientific explanation. In his view, we need a detailed treatment of scientific problems and their solutions. He believes that we ought to be able to show how a theory can be employed realistically, as purportedly true, but also how it can be construed instrumentally, as a device useful for prediction and other operations. He opines that we ought also to be able to give an account of how a theory is confirmed and justified as more acceptable than competing theories. Finally, Thagard suggests that an account of the nature of theories should suggest an answer to the difficult question of how theoretical terms are meaningful.

3.4.2. Critique of Prevailing Accounts

Thagard, in the bid to argue that a computational account can be more practical, historically, and philosophically adequate than alternatives, reviewed the shortcomings of the Positivist, Kuhnian and Set-Theoretic accounts.

3.4.2.1. The Positivist Syntactic Account

Thagard considers first the doctrine of the logical positivists that a theory is an axiomatic set of sentences. Many critics have pointed out that this view has little to do with how most scientific theories are used. In his view, “rigorous axiomatizations are rare in science, and we should be skeptical of maintaining as an ideal what is so rarely realized”. Moreover, he opined that the utility of achieving full axiomatizations is doubtful since axiom systems are awkward tools for performing the tasks of problem-solving and explanation. He submits that formalization of some sort will be necessary for any computational implementation of scientific knowledge, but it will have to be directed toward procedural issues rather than logical rigor. He believes that the emphasis on syntax that is endemic to the view of theories as axiom systems leads to the neglect of semantic considerations crucial to the understanding of conceptual development, and to the neglect of pragmatic considerations that are crucial to justification and explanation. According to Thagard, Axiom systems could be said to be psychologically real if we viewed scientists as solving problems by straightforwardly making deductions from sets of propositions. In sum, for Thagard, the positivist account is not very practically adequate. In his opinion, another major problem with the positivist account concerns the meaning of theoretical terms. He contends that it has been challenged concerning the viability of the notion of partial interpretation, and even more fundamentally concerning the tenability of the distinction between theoretical and observational terms.

3.4.2.2. Kuhn's Paradigms

According to Thagard, T. S. Kuhn's notion of a paradigm has replaced the positivist account of theories in many discussions, particularly in the social sciences. Thagard highlights Kuhn’s notion of paradigm, that “most generally a paradigm is a conceptual scheme representing a group's shared commitments and providing them with a way of looking at phenomena”. Thagard argues that this notion is flexible enough to have much practical and historical applicability, but it is too vague to help with philosophical problems about explanation, justification, and meaning. Thagard submits that despite a professed desire to avoid total subjectivity, Kuhn has not succeeded in describing how paradigms can be rationally evaluated, how different paradigms can relate to the same world, or even what it is for a paradigm to be used in solving a problem. Thagard posits that no accounts have been given of how paradigms can be discovered or modified. He also highlights that Kuhn's ideas about the structure of scientific knowledge are nevertheless rich and suggestive, and can be fleshed out in computational terms.

3.4.2.3. The Set-Theoretic Conception

In Thagard's view, the set-theoretic account connected with its practical inadequacy, faces philosophical limitations. He submits that its abstraction from pragmatic matters of context and epistemic organization creates large impediments to giving satisfactory treatments of explanation and inference. For Thagard, the notion of explanation is not captured adequately by set-theoretic isomorphism.

3.4.3. A Computational Account of the Nature of Theories

3.4.3.1. Rules and Concept

PI represents knowledge using rules organized by concepts. Thagard proffered how such structures can contribute to an account of the nature of scientific knowledge that is both reasonably precise and sufficiently rich to account for the various roles of scientific theories. He submits that focusing on rules alone might suggest that in PI, theories are nothing more than syntactic structures akin to the sets of sentences that, according to the logical positivists, constitute scientific theories. Moreover, Thagard opines that theoretical problem solving and explanation might be thought to have the straightforward deductive character emphasized by the positivists since rule firing is at the root an application of modus ponens, inference from if p then q and p to q. He believes that we might be tempted to say that all that is needed for a computational account of theories is to treat them as rules in a deductive system such as Prolog or a simple production system.

He posits that the conclusion, however, would neglect the importance of concepts in clustering rules together and helping to control the processing of information during problem-solving and learning. He argues that concepts would be unnecessary if we could consider all possible deductions from all existing rules, but we have seen that that is not computationally feasible. He opines that people seem to have, and programs seem to need, the ability to organize knowledge in ways that allow it to be applied in appropriate situations. He maintains that concepts not only organize rules for efficient application; they also organize the storage of problem solutions in ways crucial for analogical problem-solving. Similarly, Thagard highlights that it would be a mistake to argue as follows: "A computer program is, for the computer on which it runs, a purely syntactic entity, so there is no real difference between any computational account and the syntactic accounts of the logical positivists". He posits that the argument has a confusion of levels. He argues that a program is a syntactic entity, but processing can be guided by data structures that are best understood in semantic and pragmatic terms. He proffers that semantics come from the interrelations of rules and concepts, and the world and the pragmatics come from the crucial role that goals and context play in determining the course of processing.

To be more concrete, Thagard described a simple but important theory, the wave theory of sound, whose discovery has been simulated in PI. According to Thagard, this theory goes back to the ancient Greeks, probably originating with the Stoic Chrysippus, although the first systematic discussion he has been able to find is by the Roman architect Vitruvius around the first century A.D. Vitruvius used the wave theory to explain several properties of sound that were important for building amphitheaters: sound spreads out from the source, and if it encounters a barrier it can be reflected, constituting an echo.

These facts to be explained are represented by Thagard in PI by simple rules:

If x is sound, then x propagates.

If x is sound, and x is obstructed, then x reflects.

At first blush, the wave theory of sound might seem to be merely another simple rule, something like

If x is sound, then x consists of waves.

He believes that there are two key respects in which the wave theory of sound differs from the simple rules about sound propagating and reflecting. The first he proffers as the basis for accepting the wave theory of sound is different from the basis for accepting the other rules, which are derived from observations by generalization. In the second part of the wave theory of sound, he proffers the postulation of the novel idea of sound waves, which were not observable, so that the concept of a sound wave could not be derived from observation. He contends that what constitutes the wave theory of sound is thus a complex of rules and concepts. Below is the Structure of the wave theory of sound (FIG 1).

He maintains that “the wave theory of sound, equally important, includes a record of its past successes-here the successful explanation of why sound propagates and why it reflects”. He believes that an explanation or solved problem solution may be complicated, but keeping track of it may be immensely useful in the future for solving similar problems. He submits that a theory, then, is not an explicit data structure like a rule or concept, but a set of associated structures. For the wave theory of sound, these include:

Wave theory of sound:

Concepts: sound, wave.
Theoretical concept: sound-wave.
Rules:

If x is sound, then x is a wave.

If x is sound, then x is a sound-wave.

Problem solution:

Explanation of why sound propagates.
Explanation of why sound reflects.

According to Thagard, the diagram above (FIG 1), depicts the complex of interlinked structures that make up the wave theory of sound, after the attempt to explain why sound reflects and propagates, has led to the formation of the rule that sounds are waves. He submits that the new concept sound-wave, formed by conceptual combination, is a subordinate of the concepts of sound and wave. Also, the new solution to the problem of explaining why sound reflects and propagates is stored with attachments to the concepts of sound, propagates, and reflects.

3.4.3.2. The Importance of Schemas

According to Thagard, PI forms problem-solving schemas and this greatly improves problem-solving performance. He posits that this facilitation is especially clear for theories, which invariably provide rich explanatory schemas. He asserts that the primary function of a theory is to explain different laws, which in turn generalize many observations. He highlights that a theory will typically involve a narrow set of principles that are applied in similar ways to explain each law and by extension the particular events that fall under the laws. He submits that the convergence schema and problem schema formation involve a kind of abstraction. He believes that such abstractions are important in scientific explanations, where idealizations are often used. He highlights that scientists talk blithely of inclined planes without friction, falling objects without air resistance, and ideal gases.

On the view of scientific theories as axiom systems, he posits that it can be hard to understand such utterances. For him, idealization makes sense if one sees a theory as part of a processing system that uses default rules and abstract problem-solving schemas to generate explanations. He submits that “the view just described also has the virtue of being compatible with the empirical results of Chi, Feltovich, and Glaser”. He highlights that experts differed significantly from novices in how they categorized physics problems and theorized that experts' abilities were a result of their possession of superior problem schemas. He believes that novices tend to categorize problems by surface features, such as "blocks on inclined planes"; experts tend to classify according to the major physics principle governing the solution to each problem. Thagard posits that during problem-solving experiments, experts take longer to classify problems than novices, but their classifications are much more effective in leading to solutions. He points out that knowledge of physics here obviously goes well beyond knowledge of a set of sentences encompassing the principles of physics since novices are familiar with those principles too. He believes that what novices lack is the procedural knowledge about how and when to apply those principles, knowledge that is most appropriately coded in problem schemas.

3.4.4. Practical Adequacy of the Computational Account

In the last section, theories were analyzed as complexes of rules, concepts, and problem solutions. Thagard posits that the practical adequacy of such an account is best shown by its ability to explain experimental results of problem-solving better than alternative models. He contends that it is also interesting to see how the model serves to give an account of more anecdotal phenomena.

He started by returning to Kuhn's, according to Thagard, notoriously vague notion of a paradigm. According to Thagard, “Kuhn often used the term paradigm to refer to a theory or world-view, as in the Newtonian paradigm”. For him, this usage has become widespread, but it is different from the pre-Kuhn understanding of a paradigm as a standard pattern or example, for instance, of a verb declension. Thagard still points out that in the postscript to the second edition of The Structure of Scientific Revolutions, Kuhn regrets using the term "paradigm" both for a scientist's general world-view and for the concrete examples of problem solutions that, Kuhn had argued, were largely responsible for the construction of the worldview. He highlights that “Kuhn offers the term exemplar for the concrete problem solutions that he came to see as the more fundamental sense of paradigm”.

According to Thagard, Kuhn rejects the common view that students learn a scientific field by learning a theory plus rules for applying it to problems. Thagard proffers that they learn a theory by doing the problems, solving subsequent problems by modeling them on previous solutions-examples. He highlights that learning a theoretical formula such as F = RNA is of minor importance compared to learning the complex manipulations needed to solve various problems about free fall, the pendulum, and so on. He points out that students who claim to know the formulas but are unable to do the problems are missing the point: knowing the theory is being able to do the problems. He went on to submit that by working away at standard problems, students eventually assimilate what Kuhn calls a "time-tested and group-licensed way of thinking".

Thagard proposes that a computational model such as PI can capture both the exemplar and the world-view aspects of scientific practice. He proffers that PI's mechanisms for solving and storing problems make possible just the kind of analogical problem-solving that Kuhn points to. According to Thagard, “exemplars are successful problem solutions that are stored with relevant concepts”. He posits that if much use of such exemplars has taken place, they can be abstracted and stored as problem schemas like the abstraction from the ray and fortress problems. He maintains that a full-blown conceptual network with many stored problem solutions would constitute a paradigm in Kuhn's larger sense, providing a kind of world-view, a systematic way of approaching problems in the world. He believes that the existence of such a network need not remain a vague hypothesis, since they can be simulated in computational models with a sufficiently rich set of data structures, including concepts and problem solutions. That it then becomes possible to address more precisely such philosophical issues as the alleged incommensurability of rival theories and the methodological conservatism of proponents of a theory. This completes Thagard’s case for the practical adequacy of the computational approach to scientific theories. His attempt to show that a computational account of theories is more philosophically adequate than alternatives now begins with a discussion of scientific explanation.

3.4.5. Explanation

Thagard contends that the explanation of observed phenomena is one of the most important scientific activities. Much contemporary work in the philosophy of science has been concerned with providing necessary and sufficient conditions for a scientific explanation. Thagard points out that “the main focus of this discussion has been Hempel's powerful deductive nomological model of explanation”. Thagard did not attempt to summarize all the criticisms of the model, but instead, he developed an alternative conception of explanation consonant with the computational approach to theories outlined above. For him, since most concepts in natural language are not susceptible to the definition in terms of necessary and sufficient conditions, it would be folly to attempt to provide such conditions for an explanation. He asserts that indeed, the view of concept formation associated with the processing views that he has been discussing suggests that conceptual analysis must take the form of characterizing what holds typically of a notion rather than universally. According to Thagard, the term “explanation" is highly ambiguous. He highlights that Hempel and many others use it to refer to a syntactic structure consisting of deductively related sentences including explanans and explanandum. He submits that in informal discourse, we often mean by "explanation" a theory that figures in an explanation in the Hempelian sense: Newtonian theory is an explanation of the tides. Thagard explored a third sense of the term, in which explanation is not an explanatory structure, nor something that explains, but a process of providing understanding. He contends that explanation is then something that people do, not an eternal property of sets of sentences. Thagard pointed out that this sense of "explanation" is to be distinguished from a sense becoming common in AI concerning “explanation-based learning", in which an explanation is a description of how a program achieved some result.

3.4.5.1. Understanding

Thagard probes that, while explanation is a process of providing or achieving understanding, what then is understanding? Thagard posits that generally “to understand a phenomenon is to fit it into a previously organized pattern or context”. But this characterization is uninformative without specification of the nature of the patterns and contexts. He believes that much of the plausibility of the deductive-nomological model of Hempel derives from the precise way a logistic system, in which a theory is a set of sentences and an explanation is a deduction from these axioms, provides a structured and well-understood context.

We shall see how Thagard proves that a computational account can provide richer sorts of structure and context. On Schank and Abelson's computational view, according to Thagard, “to understand an event is to retrieve from memory a knowledge structure that the event instantiates”. Again for him, to understand a sentence like "Leonard went to the junior seminary at the age of 12 and got his degree at the age of 24," a subject must activate a structure (frame, script, schema) that describes typical seminary training stages. He believes that the slots in the seminary frame will be matched with the information provided in the sentence, and then the additional information contained in the frame can be used to answer questions about Leonard's case described in the sentence. He opines that an adequate program would be able to answer "Why did Leonard get his degree at the age of 24?" by applying the knowledge incorporated in the summoned frame, that in Nigeria seminaries one typically spends six years in the junior seminary, one for junior apostolic work, another one year in spiritual year and then four years studying philosophy. He highlights that deriving an answer to the question is relatively easy computationally once the appropriate frame has been found. He opines that the key step in achieving understanding is the procedural one of retrieving a frame that matches the central aspects of the event to be explained.

For Thagard, the explanation is not by reference to implied laws or unspecified statistical generalizations, but by application of a structure that describes typical occurrences. He maintains that understanding is achieved primarily through a process of locating and matching, rather than deduction. According to Thagard, this account would be fine if we had precompiled frames for all events to be explained. He also pointed out that still it cannot account for our ability to give explanations for unique or unusual events. According to his view, suppose we want to explain why Leonard also studies Software Engineering in the seminary within those twelve years. The seminary frame and the Software Engineering Study frame will not be much help. Thagard highlighted that for increased flexibility,, Schank proposed that knowledge must be organized into smaller structures that Schank calls "memory organization packets". Thagard contends that PI gains flexibility by attaching to concepts various rules, which can, once activated, work independently to generate an explanation. Thus, according to him, “PI's explanations involve both matching to a situation, as relevant concepts are activated and deduction, as rules are fired”. Thagard proffers that this process can be described as the application of a constructed "mental model" to a situation.

3.4.5.2. Explanation and Problem Solving

According to Thagard, in PI, the explanation is a kind of problem-solving and a description of how the program works should help in showing the relations between these two important scientific activities. He opines that a problem is specified by giving its starting conditions and its goals to be accomplished. For him, a problem solution is a set of steps, simulated or carried out that leads from the starting conditions to the goal. Thagard explains that in PI, the simplest kind of explanation problem is one in which the goals are not states to be reached, but states known to be true. Nevertheless, he pointed out that the process of rule-firing to generate the goals is the same, with one important difference: whereas in problem-solving PI does projected actions, in explanation PI forms hypotheses that can lead to an explanation. To portray this concretely according to Thagard's view, imagine that your problem is to help your new lecturer out on how to get to the Bigard Admin Block. You can project various actions that will take him from the classroom to Bigard Admin Block.

Structurally, we have

PROBLEM:
START: N is the Admin Block.
GOAL: N is in Bigard.

In a more realistic problem, Thagard believes that the set of starting conditions would be significantly larger, and the goals would include additional constraints on what would constitute a problem solution. He proffers that the analogous explanation would have a similar structure, with an "explanandum"-what is to be explained instead of the goal:

EXPLANATION-PROBLEM:
START: N is the Admin Block.
EXPLANANDUM: N is in Bigard.

He points out that here you would try to use what you know about N, about the Admin Block, and about Bigard to generate an answer to why N is in Bigard. He posits that the same general mechanisms of spreading activation and rule-firing that enable PI to figure out how to get N to Bigard will also generate an explanation of why N is there, except that, instead of producing projected actions, the program generates possible hypotheses (such as that N is at a conference) that might explain.

He believes that the structural similarity between explanation and problem-solving is clear at the level of explanation of particular facts, such as N's location. He also opines that scientific explanation concerns not only particular facts but also general laws. According to Thagard, The sort of explanation and problem-solving he discusses is a significant part of everyday scientific practice, but from a global, epistemic point of view, another level of explanation is more important. He suggests that this is the explanation of general patterns of events, rather than the occurrence of particular events. For him, such an explanation has usually been understood as the deduction of empirical generalizations from axiomatized theories. He highlights that Kepler's laws of the motions of planets are said to be derivable from Newtonian mechanics; optical refraction is explained by deriving Snell's law from either the wave or particle theories and so on. Thagard used an example that is simple enough for PI to deal with. He asserts that the wave theory of sound has to explain the general law that sound propagates, whose simplest expression is a rule with the condition (sound (x) true) and the action (propagates (x) true). He submits that to explain such a rule is simple, PI creates a problem using an arbitrary object x:

EXPLANATION-PROBLEM:
START: x is sound.
EXPLANANDUM: x propagates.

Thagard perceives that explanation even of laws can be undertaken in PI by the various mechanisms of problem-solving. He points out that it is easy within the computational framework to block trivial explanations, such as that x propagates just because it is sound, or propagates because it propagates.

According to Thagard, there is more to the explanation than the discussion of problem-solving so far would suggest. He argues that to adapt an example from “Bromberger”, we could assign a student a problem of calculating the height of a flagpole given the length of its shadow, trigonometric formulas, and the law of the rectilinear propagation of "light. He opines that the student's calculation that the flagpole was n feet high would solve the problem, but it would not explain why the flagpole is n feet high. He points out that the calculation does not provide us with an understanding of why the flagpole has the height it does.

For him, such understanding requires more contextual features, and it is easy to see how a system such as PI could provide these. Thus he highlights:

We have much background information about flagpoles, in particular about the causes of their construction. The flagpole concept would contain a rule that flagpoles are manufactured objects. Activating the concept of manufactured objects would make available the rule that designers and factories produce such objects. We would be led by PI's sub-goaling process to look for designers and factories that produced the flagpole, and even farther back for an explanation of why the designers planned as they did. The rules about trigonometry and the behavior of light would not normally get activated at all.

He feels that setting up the problem with them as part of the starting conditions is a bad joke. In Thagard view, it is unlikely that it would produce such a derivation, that PI does not currently have the resources to reject a derivation of the height of the flagpole using its shadow as a non-explanation. He points out that its problem-solving apparatus would, if it had the relevant knowledge and if the appropriate explanation based on human design were not found, arrive at and accept the shadow account. He explains that the problem is that PI currently lacks a sufficient understanding of causality. He pointed out that as Brody argues, “it is plausible to suppose that what distinguishes real explanations from the flagpole examples and other counterexamples to the deductive-nomological model is the reference to a causal or essential feature”.

Similarly, he also points out that Hausman has argued that “causal asymmetries are the key to seeing why the flagpole's height cannot be explained using the length of its shadow: our background knowledge tells us that the heights of flagpoles determine the lengths of shadows, not vice versa”. He highlights that PI needs to be able to acquire the kind of knowledge that it currently lacks, involving high-level knowledge of what kinds of things cause what. According to Thagard an acquisition of such "causal schemas” will require an ability to distinguish between accidental generalizations based on mere co-occurrence of things and genuine causal connections. He believes that “such performance will require a much deeper understanding of causality than PI or any other AI program currently has, taking into account such factors as a temporal priority and patterns of the interconnectedness of kinds of events”. He submits that the advantage of a computational approach over a much more austere syntactic one is that it should be possible to enrich PI to be able to acquire and use such knowledge.

Thagard asserts that critics have used the flagpole example to argue that the deductive nomological model of explanation is too loose, but they have also accused the model of being too strict in always requiring laws. He explains that PI can get by with much looser kinds of explanations since the rules it uses in its explanations need not be general laws: they need only express default expectations about what will happen.

Thagard noted that the accounts he sketched do not even come close to providing sufficient conditions for a good scientific explanation. He highlights that Theology, astrology, and related disciplines can be said to provide explanations in the loose sense of using rules and concepts to generate conclusions. He contends that people have conceptual systems for all sorts of mythologies and ideologies, and we want to distinguish the explanations provided by these from the explanations rightly valued in science. However, he feels, this task concerns epistemological matters that go beyond the issue of the structure of theories and explanations. Thagard does not think that we can in general distinguish on structural grounds between the systems and explanations of science and those of pseudoscience and non-science. He opines that demarcation is a complicated matter of the historical context of a discipline, including the presence of competing theories and the record of the discipline over time. He proffers that theology and astrology differ from scientific systems concerning validation, not structure.

Moreover, he believes that a full account of the explanation would include a description of the epistemic conditions that a system of concepts and rules has to meet before we honor it as being fully explanatory. He submits that candidates for such conditions include truth, confirmation, and the best available theory. Thagard has been using the honorific sense of “explanation"· in which we say that only a good (true, acceptable, confirmed) theory explains. His previous discussion was intended to capture the more general sense of “explanation" in which we can talk of a false theory explaining. This concludes Thagard’s attempt to show how a computational account can contribute to philosophical understanding and also to demonstrate the philosophical superiority of computational accounts of theories.