A Guide to The Logic of Scientific Discovery (The Popular Popper Book 1)

A Guide to The Logic of Scientific Discovery (The Popular Popper)

Reichenbach maintains that philosophy of science includes a description of knowledge as it really is. Discovery, by contrast, is the object of empirical—psychological, sociological—study. According to Reichenbach, the empirical study of discoveries shows that processes of discovery often correspond to the principle of induction, but this is simply a psychological fact Reichenbach This version of the distinction is not necessarily interpreted as a temporal distinction. In other words, it is not usually assumed that a theory is first fully developed and then validated.

Rather, conception and validation are two different epistemic approaches to theory: Within the framework of the context distinction, there are two main ways of conceptualizing the process of conceiving a theory. The second option is to conceptualize the generation of new knowledge as an extended process that includes a creative act as well as some process of articulating and developing the creative idea. Both of these accounts of knowledge generation served as starting points for arguments against the possibility of a philosophy of discovery. In line with the first option, philosophers have argued that neither is it possible to prescribe a logical method that produces new ideas nor is it possible to reconstruct logically the process of discovery.

Only the process of testing is amenable to logical investigation. The initial state, the act of conceiving or inventing a theory, seems to me neither to call for logical analysis not to be susceptible of it. The question how it happens that a new idea occurs to a man—whether it is a musical theme, a dramatic conflict, or a scientific theory—may be of great interest to empirical psychology; but it is irrelevant to the logical analysis of scientific knowledge.

Its questions are of the following kind. Can a statement be justified? And if so, how? Is it logically dependent on certain other statements? Or does it perhaps contradict them? As to the task of the logic of knowledge—in contradistinction to the psychology of knowledge—I shall proceed on the assumption that it consists solely in investigating the methods employed in those systematic tests to which every new idea must be subjected if it is to be seriously entertained. With respect to the second way of conceptualizing knowledge generation, many philosophers argue in a similar fashion that because the process of discovery involves an irrational, intuitive process, which cannot be examined logically, a logic of discovery cannot be construed.

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Other philosophers turn against the philosophy of discovery even though they explicitly acknowledge that discovery is an extended, reasoned process. They present a meta-philosophical objection argument, arguing that a theory of articulating and developing ideas is not a philosophical but a psychological theory. The impact of the context distinction on studies of scientific discovery and on philosophy of science more generally can hardly be overestimated. The view that the process of discovery however construed is outside the scope of philosophy of science proper was widely shared amongst philosophers of science for most of the 20 th century and is still held by many.

The last section shows that there were a few attempts to develop logics of discovery in the s and s. But for several decades, the context distinction dictated what philosophy of science should be about and how it should proceed. The dominant view was that theories of mental operations or heuristics had no place in philosophy of science. Therefore, discovery was not a legitimate topic for philosophy of science. The wide notion of discovery is mostly deployed in sociological accounts of scientific practice.

Until the last third of the 20 th century, there were few attempts to challenge the disciplinary distinction tied to the context distinction. Only in the s did the interest in philosophical approaches to discovery begin to increase. But the context distinction remained a challenge for philosophies of discovery. There are three main lines of response to the disciplinary distinction tied to the context distinction.

Epistemology of science

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Each of these lines of response opens up a philosophical perspective on discovery. Each proceeds on the assumption that philosophy of science may legitimately include some form of analysis of actual reasoning patterns as well as information from empirical sciences such as cognitive science, psychology, and sociology.

All of these responses reject the idea that discovery is nothing but a mystical event. Discovery is conceived as an analyzable reasoning process, not just as a creative leap by which novel ideas spring into being fully formed. All of these responses agree that the procedures and methods for arriving at new hypotheses and ideas are no guarantee that the hypothesis or idea that is thus formed is necessarily the best or the correct one. Nonetheless, it is the task of philosophy of science to provide rules for making this process better.

Logic of Historical Science

All of these responses can be described as theories of problem solving, whose ultimate goal is to make the generation of new ideas and theories more efficient. But the different approaches to scientific discovery employ different terminologies. Moreover, while each of these responses combines philosophical analyses of scientific discovery with empirical research on actual human cognition, different sets of resources are mobilized, ranging from AI research and cognitive science to historical studies of problem-solving procedures.

Also, the responses parse the process of scientific inquiry differently. Often, scientific inquiry is regarded as having two aspects, viz. At times, however, scientific inquiry is regarded as having three aspects, namely generation, pursuit or articulation, and validation of knowledge.

Philosophers who take this approach argue that the process of discovery follows an identifiable, analyzable pattern section 7. Others argue that discovery is governed by a methodology. The methodology of discovery is a legitimate topic for philosophical analysis section 8. All of these responses assume that there is more to discovery than a eureka moment. Discovery comprises processes of articulating and developing the creative thought.

These are the processes that can be examined with the tools of philosophical analysis. The third response to the challenge of the context distinction also assumes that discovery is or at least involves a creative act.

Falsifiability

But in contrast to the first two responses, it is concerned with the creative act itself. Philosophers who take this approach argue that scientific creativity is amenable to philosophical analysis section 9. The first response to the challenge of the context distinction is to argue that discovery is a topic for philosophy of science because it is a logical process after all.

Advocates of this approach to the logic of discovery usually accept the overall distinction between the two processes of conceiving and testing a hypothesis. They also agree that it is impossible to put together a manual that provides a formal, mechanical procedure through which innovative concepts or hypotheses can be derived: There is no discovery machine. But they reject the view that the process of conceiving a theory is a creative act, a mysterious guess, a hunch, a more or less instantaneous and random process.

Instead, they insist that both conceiving and testing hypotheses are processes of reasoning and systematic inference, that both of these processes can be represented schematically, and that it is possible to distinguish better and worse paths to new knowledge. This line of argument has much in common with the logics of discovery described in section 4 above but it is now explicitly pitched against the disciplinary distinction tied to the context distinction.

There are two main ways of developing this argument. The first is to conceive of discovery in terms of abductive reasoning section 6.

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The second is to conceive of discovery in terms of problem-solving algorithms, whereby heuristic rules aid the processing of available data and enhance the success in finding solutions to problems section 6. One argument, elaborated prominently by Norwood R. Hanson, is that the act of discovery—here, the act of suggesting a new hypothesis—follows a distinctive logical pattern, which is different from both inductive logic and the logic of hypothetico-deductive reasoning.

The argument that it is through an act of abductive inferences that plausible, promising scientific hypotheses are devised goes back to C. This version of the logic of discovery characterizes reasoning processes that take place before a new hypothesis is ultimately justified. The abductive mode of reasoning that leads to plausible hypotheses is conceptualized as an inference beginning with data or, more specifically, with surprising or anomalous phenomena. In this view, discovery is primarily a process of explaining anomalies or surprising, astonishing phenomena.

The outcome of this reasoning process is not one single specific hypothesis but the delineation of a type of hypotheses that is worthy of further attention Hanson According to Hanson, the abductive argument has the following schematic form Hanson More importantly, while there is general agreement that abductive inferences are frequent in both everyday and scientific reasoning, these inferences are no longer considered as logical inferences.

Notably, some philosophers have even questioned the rationality of abductive inferences Koehler ; Brem and Rips Another argument against the above schema is that it is too permissive. There will be several hypotheses that are explanations for phenomena p 1 , p 2 , p 3 …, so the fact that a particular hypothesis explains the phenomena is not a decisive criterion for developing that hypothesis Harman ; see also Blackwell Additional criteria are required to evaluate the hypothesis yielded by abductive inferences. Finally, it is worth noting that the schema of abductive reasoning does not explain the very act of conceiving a hypothesis or hypothesis-type.

The processes by which a new idea is first articulated remain unanalyzed in the above schema. The schema focuses on the reasoning processes by which an exploratory hypothesis is assessed in terms of its merits and promise Laudan ; Schaffner In more recent work on abduction and discovery, two notions of abduction are sometimes distinguished: Selective abduction—the inference to the best explanation—involves selecting a hypothesis from a set of known hypotheses.

Medical diagnosis exemplifies this kind of abduction. Creative abduction, by contrast, involves generating a new, plausible hypothesis. This happens, for instance, in medical research, when the notion of a new disease is articulated. However, it is still an open question whether this distinction can be drawn, or whether there is a more gradual transition from selecting an explanatory hypothesis from a familiar domain selective abduction to selecting a hypothesis that is slightly modified from the familiar set and to identifying a more drastically modified or altered assumption.

The advantage of the neural account of human reasoning is that it covers features such as the surprise that accompanies the generation of new insights or the visual and auditory representations that contribute to it. The concern with the logic of discovery has also motivated research on artificial intelligence at the intersection of philosophy of science and cognitive science.

In this approach, scientific discovery is treated as a form of problem-solving activity Simon ; see also Newell and Simon , whereby the systematic aspects of problem solving are studied within an information-processing framework. The aim is to clarify with the help of computational tools the nature of the methods used to discover scientific hypotheses.

These hypotheses are regarded as solutions to problems. Philosophers working in this tradition build computer programs employing methods of heuristic selective search e. The problem space comprises all possible configurations in that domain e. There are two special states, namely the goal state, i. There are operators, which determine the moves that generate new states from the current state.

There are path constraints, which limit the permitted moves. Problem solving is the process of searching for a solution of the problem of how to generate the goal state from an initial state. In principle, all states can be generated by applying the operators to the initial state, then to the resulting state, until the goal state is reached Langley et al. A problem solution is a sequence of operations leading from the initial to the goal state.

The basic idea behind computational heuristics is that rules can be identified that serve as guidelines for finding a solution to a given problem quickly and efficiently by avoiding undesired states of the problem space. These rules are best described as rules of thumb. The aim of constructing a logic of discovery thus becomes the aim of constructing a heuristics for the efficient search for solutions to problems.

A solution is not guaranteed, but heuristic searches are advantageous because they are more efficient than exhaustive random trial and error searches. Insofar as it is possible to evaluate whether one set of heuristics is better—more efficacious—than another, the logic of discovery turns into a normative theory of discovery. Arguably, because it is possible to reconstruct important scientific discovery processes with sets of computational heuristics, the scientific discovery process can be considered as a special case of the general mechanism of information processing.

The computer programs that embody the principles of heuristic searches in scientific inquiry simulate the paths that scientists followed when they searched for new theoretical hypotheses. The program would note, for instance, that the values of a dependent term are constant or that a set of values for a term x and a set of values for a term y are linearly related. AI-based theories of scientific discoveries have helped identify and clarify a number of problem-solving strategies. An example of such a strategy is heuristic means-ends analysis, which involves identifying specific differences between the present and the goal situation and searches for operators processes that will change the situation that are associated with the differences that were detected.

Another important heuristic is to divide the problem into sub-problems and to begin solving the one with the smallest number of unknowns to be determined Simon AI-based approaches have also highlighted the extent to which the generation of new knowledge draws on existing knowledge that constrains the development of new hypotheses. As accounts of scientific discoveries, computational heuristics have some limitations. Most importantly, because computer programs require the data from actual experiments the simulations cover only certain aspects of scientific discoveries.

They do not design new experiments, instruments, or methods. Moreover, compared to the problem spaces given in computational heuristics, the complex problem spaces for scientific problems are often ill defined, and the relevant search space and goal state must be delineated before heuristic assumptions could be formulated Bechtel and Richardson Earlier critics of AI-based theories of scientific discoveries argued that a computer cannot devise new concepts but is confined to the concepts included in the given computer language Hempel Subsequent work has shown that computational methods can be used to generate new results leading to refereed scientific publications in astronomy, cancer research, ecology, and other fields Langley The most recent computational research on scientific discovery is no longer driven by philosophical interests in scientific discovery, however.

Instead, the main motivation is to contribute computational tools to aid scientists in their research Addis et al. Many philosophers maintain that discovery is a legitimate topic for philosophy of science while abandoning the notion that there is a logic of discovery. Kuhn identifies a general pattern of discovery as part of his account of scientific change. A discovery is not a simple act, but an extended, complex process, which culminates in paradigm changes.

Paradigms are the symbolic generalizations, metaphysical commitments, values, and exemplars that are shared by a community of scientists and that guide the research of that community. Paradigm-based, normal science does not aim at novelty but instead at the development, extension, and articulation of accepted paradigms. A discovery begins with an anomaly, that is, with the recognition that the expectations induced by an established paradigm are being violated.

The process of discovery involves several aspects: It is the mark of success of normal science that it does not make transformative discoveries, and yet such discoveries come about as a consequence of normal, paradigm-guided science. The more detailed and the better developed a paradigm, the more precise are its predictions. The more precisely the researchers know what to expect, the better they are able to recognize anomalous results and violations of expectations:. Anomaly appears only against the background provided by the paradigm.

Drawing on several historical examples, Kuhn argues that it is usually impossible to identify the very moment when something was discovered or even the individual who made the discovery. Kuhn illustrates these points with the discovery of oxygen see Kuhn []: Oxygen had not been discovered before and had been discovered by Even before , Lavoisier had noticed that something was wrong with phlogiston theory, but he was unable to move forward.

Two other investigators, C. Scheele and Joseph Priestley, independently identified a gas obtained from heating solid substances. In , Lavoisier presented the oxygen theory of combustion, which gave rise to fundamental reconceptualization of chemistry. But according to this theory as Lavoisier first presented it, oxygen was not a chemical element.

In pre-paradigmatic periods or in times of paradigm crisis, theory-induced discoveries may happen. In these periods, scientists speculate and develop tentative theories, which may lead to novel expectations and experiments and observations to test whether these expectations can be confirmed.

Even though no precise predictions can be made, phenomena that are thus uncovered are often not quite what had been expected. In these situations, the simultaneous exploration of the new phenomena and articulation of the tentative hypotheses together bring about discovery. In cases like the discovery of oxygen, by contrast, which took place while a paradigm was already in place, the unexpected becomes apparent only slowly, with difficulty, and against some resistance.

Only gradually do the anomalies become visible as such. Eventually, a new paradigm becomes established and the anomalous phenomena become the expected phenomena. These studies examine the neural processes that are involved in the recognition of anomalies and compare them with the brain activity involved in the processing of information that is consistent with preferred theories. The studies suggest that the two types of data are processed differently Dunbar et al.

In these approaches, the distinction between the contexts of discovery and the context of justification is challenged because the methodology of discovery is understood to play a justificatory role. Advocates of a methodology of discovery usually rely on a distinction between different justification procedures, justification involved in the process of generating new knowledge and justification involved in testing it.

The justification involved in discovery, by contrast, is conceived as generative as opposed to consequential justification section 8.

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Again, some terminological ambiguity exists because according to some philosophers, there are three contexts, not two: Only the initial conception of a new idea the creative act is the context of discovery proper, and between it and justification there exists a separate context of pursuit Laudan But many advocates of methodologies of discovery regard the context of pursuit as an integral part of the process of justification. They retain the notion of two contexts and re-draw the boundaries between the contexts of discovery and justification as they were drawn in the early 20 th century.

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Yale University Press, 42— Epistemological theories Revolvy Brain revolvybrain. Some standpoint theorists suggest exploiting this similarity for creativity research. An innovator in mathematics, statistics, philosophy, research methodology, and various sciences, Peirce considered himself, first and foremost, a logician. Logic from the Ancient Greek: History The scientific method was argued for by Enlightenment philosopher Francis Bacon, ro The program would note, for instance, that the values of a dependent term are constant or that a set of values for a term x and a set of values for a term y are linearly related.

The methodology of discovery has sometimes been characterized as a form of justification that is complementary to the methodology of testing Nickles , , According to the methodology of testing, empirical support for a theory results from successfully testing the predictive consequences derived from that theory and appropriate auxiliary assumptions. Generative justification complements consequential justification. Advocates of generative justification hold that there exists an important form of justification in science that involves reasoning to a claim from data or previously established results more generally.

According to these rules, general propositions are established by deducing them from the phenomena. The notion of generative justification seeks to preserve the intuition behind classic conceptions of justification by deduction. Generative justification amounts to the rational reconstruction of the discovery path in order to establish its discoverability had the researchers known what is known now, regardless of how it was first thought of Nickles , The reconstruction demonstrates in hindsight that the claim could have been discovered in this manner had the necessary information and techniques been available.

Generative justification is a weaker version of the traditional ideal of justification by deduction from the phenomena. Justification by deduction from the phenomena is complete if a theory or claim is completely determined from what we already know. The demonstration of discoverability results from the successful derivation of a claim or theory from the most basic and most solidly established empirical information. Discoverability as described in the previous paragraphs is a mode of justification. Like the testing of novel predictions derived from a hypothesis, generative justification begins when the phase of finding and articulating a hypothesis worthy of assessing is drawing to a close.

Other approaches to the methodology of discovery are directly concerned with the procedures involved in devising new hypotheses. The argument in favor of this kind of methodology is that the procedures of devising new hypotheses already include elements of appraisal. Weak evaluations are relevant during the process of devising a new hypothesis. They provide reasons for accepting a hypothesis as promising and worthy of further attention. Strong evaluations, by contrast, provide reasons for accepting a hypothesis as approximately true or confirmed.

Strong evaluation procedures are rigorous and systematically organized according to the principles of hypothesis derivation or H-D testing. A methodology of preliminary appraisal, by contrast, articulates criteria for the evaluation of a hypothesis prior to rigorous derivation or testing. It aids the decision about whether to take that hypothesis seriously enough to develop it further and test it. For advocates of this version of the methodology of discovery, it is the task of philosophy of science to characterize sets of constraints and methodological rules guiding the complex process of prior-to-test evaluation of hypotheses.

In contrast to the computational approaches discussed above, strategies of preliminary appraisal are not regarded as subject-neutral but as specific to particular fields of study. Because the analysis of criteria for the appraisal of hypotheses has mostly been made with regard to the study of biological mechanism, the criteria and constraints that have been proposed are those that play a role in the discovery of biological mechanisms.

Biological mechanisms are entities and activities that are organized in such a way that they produce regular changes from initial to terminal conditions Machamer et al. Philosophers of biology have developed a fine-grained framework to account for the generation and preliminary evaluation of these mechanisms Darden ; Craver ; Bechtel and Richardson ; Craver and Darden Some philosophers have even suggested that the phase of preliminary appraisal be further divided into two phases, the phase of appraising and the phase of revising.

According to Lindley Darden, the phases of generation, appraisal and revision of descriptions of mechanisms can be characterized as reasoning processes governed by reasoning strategies. Different reasoning strategies govern the different phases Darden , ; Craver ; Darden The discovery of the mechanism of protein synthesis involved the instantiation of an abstract schema for chemical reactions: The actual mechanism of protein synthesis was found through specification and modification of this schema.

It is important to appreciate the status of these reasoning strategies. They are not necessarily strategies that were actually used. Neither of these strategies is deemed necessary for discovery, and they are not prescriptions for biological research. The methodology of the discovery of mechanisms is an extrapolation from past episodes of research on mechanisms and the result of a synthesis of rational reconstructions of several of these historical episodes. The methodology of discovery is only weakly normative in the sense that the strategies for the discovery of mechanisms that have been identified so far may prove useful in future biological research.

Moreover, the sets of reasoning strategies that have been proposed are highly specific. It is still an open question whether the analysis of strategies for the discovery of biological mechanisms can illuminate the efficiency of scientific problem solving more generally Weber The approaches to scientific discovery presented in the previous sections focus on the adoption, articulation, and preliminary evaluation of ideas or hypotheses prior to rigorous testing.

They do not illuminate how a novel hypothesis or idea is first thought up. Even among philosophers of discovery, the predominant view has long been that there is an initial step of discovery that is best described as a eureka moment, a mysterious intuitive leap of the human mind that cannot be analyzed further but see Stokes The concept of discovery as hypothesis-formation as it is encapsulated in the traditional distinction between context of discovery and context of justification does not explicate how new ideas are formed.

According to accounts of discovery informed by evolutionary biology, the generation of new ideas is akin to random, blind variations of thought processes, which have to be inspected by the critical mind and assessed as neutral, productive, or useless Campbell ; see also Hull While the evolutionary approach to discovery offers a more substantial account of scientific discovery, the key processes by which random ideas are generated are still left unanalyzed. Today, many philosophers hold the view that creativity is not mysterious and can be submitted to analysis.

Psychologist Margaret Boden has offered helpful analyses of the concept of creativity. According to Boden, a new development is creative if it is novel, surprising, and important. She distinguishes between psychological creativity P-creativity and historical creativity H-creativity. P-creativity is a development that is new, surprising and important to the particular person who comes up with it.

H-creativity, by contrast, is radically novel, surprising, and important—it is generated for the first time Boden The majority of recent philosophical studies of scientific discovery today focus on the act of generation of new knowledge. The second part of Realism demonstrates a significant development of his ideas about probability from The Logic of Scientific Discovery. The thrust is the same, to attack the subjectivist interpretation of the probability calculus and the belief that probability measures a subjective degree of ignorance.

In The Logic he pursued his objective interpretation of the probability calculus using the frequency interpretation but in Realism he rejected the frequency interpretation and instead proposed his own propensity interpretation. This evolved from a theory of probability to become a whole cosmology — a world of propensities!

The first addressed the way that non-justificationism the conjectural theme supports rationality refutes subjectivist and sceptical claims about the logical limits of criticism hence the limits to rationality. The Open Universe makes a distinction between two kinds of arguments for determinism, the scientific and the metaphysical. The systematic nature of his thinking comes through in the connection that can be traced between subjective interpretations of probability and the way that metaphysical determinism persists in quantum physics even while the physicist may resist the scientific form of determinism.

The chapter on metaphysical issues describes the theory of propensities as a gain for science. An Afterword and two especially interesting and important addenda are attached. This looked like an epic achievement in reducing chemistry to physics because the theory led to the discovery of new elements, and more than that, it led to the prediction of some of their optical properties and some properties of their chemical compounds.

We felt, rightly, this was it: Bohr had hit rock bottom. But soon the dream of reduction was dashed due to work by Soddy , Thomson , Aston Thus the rock bottom suddenly gave way: But his edifice still stood. It seems that some systems can export entropy into their environment and increase rather than decrease their internal order.

It may thus open the way to understanding the reason why the creativeness of life does not contradict the laws of physics. The theme of the third volume of the Postscript is the way that the Copenhagen interpretation of quantum physics has been influenced by unstated and uncriticised metaphysical assumptions, especially determinism, subjectivism and instrumentalism. Of course the Copenhagen people are scientific indeterminists but Popper argues that there is a metaphysical form of determinism that they have not eliminated from their thinking.

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There are four chapters after a Preface and an Introduction. In the Introduction he argues for an interpretation of quantum physics without the observer and he sharply formulated thirteen thesis to challenge the Copenhagen interpretation of the observer as an integral part of the system. He still maintained that the problem of interpreting quantum theory is bound up with the interpretation of probability theory, and he argued that the theory of propensities that he described in the first and second volumes of the Postscript should be applied to the interpretation of quantum theory, thus resolving the difficulties that arise in the Copenhagen interpretation.

The discussion includes the nature of quantum jumps and the existence or non-existence of particles. Chapter III attempts a resolution of the paradoxes of quantum theory, using the propensity interpretation of probability, applied to 1 the indeterminacy relations, 2 the expirement of Einstein, Podolsky and Rosen, and 3 the two-slit experiment. The long fourth chapter is the Metaphysical Epilogue. This covers a lot of ground, starting with a brief statement of the theory of metaphysical research programs below.