Comparative Models of Inquiry

  • Mario CocciaEmail author
  • Igor Benati
Living reference work entry



Models of inquiry are methods of organized and systematic scientific process used by scholars for controlled investigations and experiments to logically and efficiently solve theoretical and practical problems, and generate whenever possible discoveries and/or science advances. Comparative is a concept that derives from the verb “to compare” (Latin comparare, derivation of par = equal, with prefix com-) and is a systematic comparison, in this case, of the models of inquiry.


Methods of scientific inquiry are important patterns to understand scientific problems and explain causes of natural phenomena and social issues (cf., Coccia and Benati 2018; Coccia 2017a, b). They generally aim to obtain new knowledge in the form of testable explanations, conjectures, and generalizations that scientists can use to explain and predict phenomena in nature and society (Kaplan 2009). The main elements of the methods of inquiry in a hypothetic deductive approach are: (a) observation and measurement of elements concerning a subject investigated; (b) hypothetical explanations of the subject of inquiry; (c) controlled experiments for testing hypotheses; and finally (d) prediction of phenomena (cf., Coccia 2017; Benati and Coccia 2017). In order to clarify the methods of inquiry, it is useful to study their development within the philosophy of science (West Churchman and Ackoff 1950).

Development of the Methods of Scientific Inquiry in the Philosophy of Science

The history of scientific inquiry started with rationalism, which focused on the vital role of reason in science. Within this approach, the Greek mathematicians had the purpose to systematize the general properties of space, i.e., geometry. Reason was a faculty that had fundamental features: it provided information concerning the essence of things, and it showed how to move from it to other characteristics of the world. Reason provides “clear and distinct” ideas and leads to conclusions from such ideas. The history of science seems to show that it is no easy task to identify clear and distinct ideas. Scholars have attempted to use rational methods of inquiry in some scientific fields, but the modern rational method does not always provide scientific truth. Hence, speculation and the clear use of reason are the only viable methods of investigation in certain fields of research, such as religion, morality, and metaphysics (West Churchman and Ackoff 1950).

The priority of reason was questioned by empiricism, which replaced reason with sensation as the source of all knowledge. Starting from simple ideas, and with the aid of the mental operations of compounding, relating, and abstracting, it is possible to show how other facts (ideas) can be derived. Locke tried to show how knowledge of general propositions should be derived through the process of comparing ideas. Berkeley and Hume showed that many ideas, which appeared simple to Locke were actually not so and, consequently, they raised the question of the adequacy of intuition as a criterion of simplicity. Locke’s notion of a mental faculty of abstraction was refuted by Berkeley, who claimed that the mind can only perform generalizations, not abstractions, whereas Hume discarded the faculty of generalization. Berkeley eliminated Locke’s material substance and based all reality in mental substance. Hume also demonstrated the inability to establish any causal connections with certainty. Hence, knowledge is replaced by belief: empirical analysis can only show our impressions (West Churchman and Ackoff 1950).

Subsequently, Kant suggested a synthesis of reason and observation by showing that both sensory observation and general understanding are essential for meaningful experience. It is true that there is something given in sensation (the sensuous intuitions) but, in addition to it, Kant argued that both space and time are a priori forms of experience, which are necessary to identify objects. In this approach, the mind must bring to its experience a principle of regularity: the natural world is well ordered because this is the manner in which the mind makes understandable its sensuous intuitions (West Churchman and Ackoff 1950).

Modern rationalism relies on the speculative method and shares with traditional rationalism the belief that the mind can intuitively grasp truth. Yet, for modern rationalism, truth comes only at the end of the process, and very tentatively. Rational truth, in short, is derived through a process in which generalizations emerge from rich experiences by means of creative acts of the mind. For Hegel, the process was dialectical, proceeding from conflicts and working up by successive syntheses to some higher and richer stage. Bergson saw the process as intuitive, whereas Hall regarded it as imaginative insight. The speculative method is basic to all others and other methods must always make metaphysical or ethical assumptions that can only be justified by rational insight, intuition, faith, and the like (West Churchman and Ackoff 1950).

The positivistic method in science was developed by Hume with an attack on speculative metaphysics. Within this philosophical stream, Comte attempted to demonstrate that metaphysical thinking represented an intermediate historical stage through which man passed on his way to the full maturity of positive or scientific thought. Mach and Pearson conceived of scientific laws as a way of summarizing past experiences and of indicating expectations. These laws were not taken as irrefutable, exact, or as representing necessary connections in nature. They were merely taken as provisional cataloguing instruments (West Churchman and Ackoff 1950).

The method of logical positivism was a new empiricism that, unlike its historical predecessor, used logical rather than psychological analysis as an approach for the study of science. It took the understanding of language in terms of its form (syntax), content (semantics), and uses (pragmatics) to be basic to an understanding of methodological problems. It attempted to show how language construction can take place from a basic set of elements and rules. Language can be considered quite apart from any factual meaning. Meanings are fundamentally assigned by means of linguistic rules referring ultimately to protocol statements, which are more or less directly verified in experience. Explanation and prediction can then be given precise definitions as aspects of the scientific method (West Churchman and Ackoff 1950).

The pragmatic method operated a further synthesis and conceived science not in terms of what it actually does, but in terms of its aims. In Dewey’s approach, the emphasis was on the resolution of an indeterminate situation, leading to a determinate one. In order to consider the meaning of science in a more precise sense, pragmatism introduced the distinction between goals (which are presumably attainable objectives) and ideals (which are unattainable but approachable within limits). Lastly, the attitude of pragmatism toward metaphysics and positivism was that they represent useful but partial methods, none of which are final in themselves (West Churchman and Ackoff 1950).

General Models of Inquiry

In light of the above, the models of scientific inquiry can be divided into classical and pragmatic approaches:
  • The classical model of scientific inquiry in science is based on deduction and induction. The origin of this scientific method dates back to Aristotle (384 BCE–322 BCE), who was one of the first to describe the deductive process, while Bacon (1561–1626) was the first scientist to develop inductive reasoning, which Galileo (1564–1642) later completed by adding his own mathematical formalization. The etymology of these concepts comes from the Latin verb ducere, to lead. The prefixes in- and de- indicate “in” and “from,” respectively. In particular, to induce may mean “to lead to, to infer” and induction is “to lead to conclusions.” To deduce may mean “to lead from, to draw from” and deduction is “to draw conclusions from.” These approaches have the purpose of solving problems in science.

In particular, the deductive model of inquiry is “inference by reasoning from generals to particulars” or “the process of deducing from something known or assumed” (Rothchild 2006). The deductive approach is the process of reasoning from one or more statements (premises) to reach a logically certain conclusion. It starts from theory and general ideas in order to predict new laws and, therefore, explain/discover new phenomena and/or problems. If the premises are true and the rules of deductive logic are followed, then the conclusion reached is necessarily true. Deductive reasoning (top-down logic) contrasts with inductive reasoning (bottom-up logic, cf., Rothchild 2006).

The inductive model of inquiry relies on collecting data and then deriving theoretical implications from them. Specifically, the inductive method starts from the observation of phenomena and traces back the laws that regulate them by means of hypotheses, analogies, and experiments (cf., Coccia 2017). Induction is riskier than deduction because it can lead to conclusions that may be uncertain. Overall, then, while the conclusion of a deductive argument is certain, the truth of the conclusion of an inductive argument may be probable (Rothchild 2006).

The hypothetico-deductive model of inquiry uses hypotheses to make predictions, rather than deriving laws from observations (Hempel 1965). Scholars, using the hypothetico-deductive method of inquiry, state hypotheses and then do experiments to test them. The hypothetico-deductive method of scientific inquiry can be applied according to either Popper’s approach (1959) or Hempel’s perspective (1965). Popper’s approach is based on falsifying theories, whereas Hempel aims to confirm them, as illustrated in Fig. 1 (cf., Thagard 1988, p. 192ff).
Fig. 1

Hypothetico-deductive method. (Adapted from Thagard (1988, p. 192))

Hanson (1958) criticized this model of inquiry because theory and observation were much more intertwined. Scientific realism argued that science is not restricted to observable facts but knowledge can be also achieved of what is not observable.
  • The pragmatic model by Peirce (1992) is characterized by a “struggle” to replace doubt with “settled belief.” This method of science is an experimental method, and the application of the pragmatist maxim reveals how hypotheses can be subject to experimental test (the concept of maxim is to: “consider what effects, which might conceivably have practical bearings, we conceive the object of our conception to have. Then, our conception of those effects is the whole of our conception of the object”, Peirce 1992, vol. 1, p. 132). Dewey’s conception of inquiry, found in his Logic: the Theory of Inquiry, is to understand a problem by describing its elements and identifying their relations. Identifying a problem that we need to solve is a sign that we are already making scientific progress; inquiry here is: “the controlled or directed transformation of an indeterminate situation into one that is so determinate in its constituent distinctions and relations as to convert the elements of the original situation into a unified whole” (Dewey 1938, pp. 104–105). Smith (1978, p. 98, original emphasis) argued that: “Peirce aimed at ‘fixing’ belief, whereas Dewey aimed at ‘fixing’ the situation.”

Peirce called his pragmatism the logic of abduction, based on the simple visualization of phenomena. In fact, many visual stimuli are impoverished or ambiguous and people are adept at imposing order on them, creating hypotheses to explain what has been observed. Hence, abductive reasoning (also called abduction) is a form of logical inference, which starts with an observation then seeks to find the simplest and most likely explanation. In abductive reasoning, unlike deductive reasoning, the premises do not guarantee the conclusion (Thagard 1988).
  • Finally, analogy has a vital role in models of inquiry, because the solution of problems in one scientific field – source domain – can be used for solving and explaining theoretical and empirical problems in other scientific fields – target domains, such as similar target therapy for different cancers in medicine (cf., Oppenheimer 1955).

Specific Methods of Inquiry in Social Sciences

Although it is difficult to provide a comprehensive review of all specific methods of inquiry adopted in science, some of the most common approaches are described below.

Experimental Method

This research method aims to explain human behavior by means of controlled laboratory experiments (e.g., Milgram’s experiment on obedience). In particular, a sample of individuals is analyzed on specific activities and, so as to provide reliable results, the participants are motivated with cash in order to mimic the real world.

Counterfactual Methods

The counterfactual method of causation can be explained in terms of counterfactual conditionals, in the form: “If A had not occurred, C would not have occurred.” Most counterfactual analyses focus on singular causation: “event C caused event E.” The best known counterfactual analysis of causation is by Lewis (1973). However, heated discussions have raised doubts about the adequacy of any simple analysis of singular causation in terms of counterfactuals (Collins et al. 2004).

Multiple Working Hypotheses

The method of multiple working hypotheses (MWH) involves the development, prior to research, of several hypotheses that might explain the phenomenon under study, which is likely to result from several causes, not just one (Chamberlin 1897). All possible hypotheses are considered and compared to clarify the scientific problem under study, including the possibility that none of them are correct and that some new explanations may emerge (Johnson 1990; Railsback 2004).

Game Theory

A “game” is any activity with the structure of a contest, in which what one player decides to do, simultaneously or not simultaneously, depends on what that player expects the other players to do. The crucial element is the payoff – player’s preferences over outcomes – associated with each possible combination of moves by the two sides (Watson 2002, p. 39). In this model, it is supposed that a rational choice is made among alternative strategies of action. This logical approach has been applied to economic bargaining, political negotiation, the conduct of war, social behavior of cooperation (envelope game), etc.

Multi-agent Programmable Modeling Environment

This approach can make use of different software platforms, such as NetLogo, an agent-based programming language and integrated modeling environment. The environment created by the software enables the exploration of complex phenomena by testing hypotheses in a virtual lab. These platforms are based on extensive libraries including models in a variety of scientific fields, such as economics, biology, physics, chemistry, psychology, etc.


The methods of inquiry in social and natural sciences include many phases to develop the process of scientific research: study concept, study design, working hypotheses formation, data acquisition, experiments, data analysis and interpretation, statistical analyses, and critical revision of results for important intellectual content. Reproducibility of results by other scholars is vital to reanalyze scientific data to validate or reject findings and/or theories. In general, science advances are essentially due to individual scientists (principal investigators) who form hypotheses, and perform controlled experiments to solve/explain problems, leading teams. However, modern science is more and more often performed by communities of scholars through international collaboration (Coccia and Wang 2016). In fact, the phases of the process of scientific inquiry are assigned to different scholars and/or teams across the world (e.g., in medicine, astronomy, etc.). This dynamics of science generates the convergence between applied and basic sciences, as explained by Coccia and Wang (2016), and likely the application of similar methods of inquiry in different research fields to solve/explain problems. Overall, then, scientific discoveries and science advances in current interdisciplinary research fields are increasingly multifaceted, requiring diverse models of inquiry to generate concepts, create new hypotheses, and perform controlled experiments involving various teams worldwide. Induction, deduction, and the other methods of inquiry described above may differ from one another but they are never contradictory. Rather, they are complementary tools that facilitate problem solving and accelerate knowledge creation within and across research fields.



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Authors and Affiliations

  1. 1.CNR – National Research Council of ItalyTorinoItaly
  2. 2.Arizona State UniversityTempeUSA