"Explanation" (PDF)

Total Page:16

File Type:pdf, Size:1020Kb

478 Explanation Kaufmann, W. (1968). Existentialism from Dostoevsky be correlated. For example, a falling barometer to Sartre. Cleveland, OH: Meridien Books. may correlate highly with the coming of rain, but Kruks, S. (1990). Situation and human existence: the barometer’s falling has no causal connection to Freedom, subjectivity, and society. London: Unwin the rain. Merely fulfilling the D-N model, thus, Hyman. cannot be sufficient for explanation. Likewise, rea- Merleau-Ponty, M. (1962). Phenomenology of perception sons may count as causes, but reasons do not pro- (C. Smith, Trans.). London: Routledge. vide mechanism and typically rationalize actions Poster, M. (1975). Existential Marxism in postwar rather than explain them in the sense of making the France. Princeton, NJ: Princeton University Press. actions a logical consequence of some antecedently Sartre, J.-P. (1966). Being and nothingness (H. E. Barnes, specified conditions. Trans.). New York: Washington Square Press. A key element involved in criticisms of logical Warnock, M. (1970). Existentialism. Oxford, UK: positivism in the social sciences concerns the place Oxford University Press. of the D-N model and its heirs as defining proper scientific explanation. While some criticisms can be understood as philosophically valid, they can also reflect an animus toward the presumed EXPLANATION absence of any normative concerns underlying this model. There may also be doubts regarding the Three key issues drive discussion of explanation existence in the social sciences of the sorts of laws in the social sciences: First, must explanation be or robust generalizations on which application of of a certain form to be regarded as scientific? the model relies. The question that lingers, how- Second, how does explanation contrast with the ever, is how to evaluate purported explanations, notion of understanding? Third, how can expla- absent some such models. nations be evaluated? The answers interrelate in important ways. Explanation Versus Interpretation The notion of explanation has at its root philo- sophical usage a connection to the provision of In the philosophy of the social sciences, the term causes, and in particular of causal mechanisms. explanation is typically used as a contrast to that This leads by the usual logic of causal or mechanis- of interpretation. The contrast involves many dif- tic explanation to a demand for laws and predic- ferences. The most fundamental concerns whether tions. For, the thought goes, a law is just a or not the goal or purpose of social inquiry should regularity in nature. Hence, any event that can be be to reconstruct actions (i.e., purposive behavior) explained (the explanandum) by adverting to the in terms of an agent’s (individual actor’s) perspec- relevant law that identifies its cause should also be tive. An alternative view maintains that the pur- predictable, given knowledge of the presence of the pose of social inquiry should be to develop antecedent conditions (the explanatia). This is the explanations, that is, accounts that have robust essence of the deductive-nomological (D-N) model predictive value. Explanation, from this point of of explanation. A great virtue of this model (long view, is unconstrained by any need to reflect or associated with logical positivism but surviving its reconstruct the view of agents with respect to the demise) involves the fact that it provides a purely events to be explained. So, for example, economic formal or syntactic criterion by which to adjudge explanations of choice of marital partner or eco- whether an explanation exists. The D-N model logical explanations of cultural traditions employ also provides a straightforward criterion for evalu- underlying regularities to account for observed ating the soundness and not just the formal ade- behaviors but diverge from any account that might quacy of an explanation. be offered of those whose behavior is so However, at this point, matters become conten- explained. tious, for well-known counterexamples to this The aims of interpretation and explanation model exist. The counterexamples demonstrate appear prima facie incompatible. An interpreta- that law-like connections may well have no causal tive account focuses on reasons specific to an connection to the phenomenon to which they may agent, a time, and a situation. The expected result Explanation 479 would be an account that did not generalize but suffices to prove that a statement about some applied only to the people and the time studied. observed regularity expresses a law. These historicist or ethnographic approaches to However, observational data can disprove a the study of human behavior must be distin- supposed law of nature by providing just one guished from case studies because the latter but counterinstance. Thus, some hold that the purpose not the former are taken to provide a basis for of testing should be to seek disconfirming instances generalizations. of laws. Laws that survive repeated attempts to While we owe the term positivism to Auguste disconfirm them may then have claim to some Comte, logical positivism names the philosophical degree of verisimilitude. But whatever one’s view movement (also referred to as the Vienna Circle) of the evaluation of proffered explanations by that emerged in the 1920s and 1930s through the empirical test, the orthodoxy holds that proper writings of associated philosophers, scientists, and explanation requires laws and empirical informa- social scientists. Following the dispersion of these tion that allows for a logical connection between thinkers to England and the United States due to the explanans and the explanandum. Only by vir- the rise of fascism throughout central Europe, tue of the logical connection can one determine logical positivism became the dominant account of whether the observed instances follow from the what defined scientific explanation. Within the statements said to explain them, and only by vir- social sciences, the term positivism enjoys wide use tue of the logical connection can one assess as an epithet attached to all views that insist that whether the generalization appealed to in the the purpose of social science explanation requires explanation has been confirmed or survived dis- being able to apply generalizations to account for confirmation, and so has a real use for purposes of observed cases. Ideally, generalizations used to explanation. All models of scientific explanation, explain would also allow social scientists to make in short, take explanation to consist in a relation predictions. In the terminology of logical positiv- between some theory and instances that the theory ism, a statement of that which is to be explained is is a theory of. termed the explanandum (pl. explananda); explan- Absent any logical connection between explan- ans is the class of statements (pl. explanantia) that ans and explanandum, however, no rational assess- account for the explanandum. ment of an offered explanation appears possible. Because a primary goal of logical positivists This insistence on the syntactic formulation of was to help distinguish scientific from pseudo- explanation, one that provides a logical connec- scientific explanations, two key criteria were tion between explanans and explanandum, remains developed that were thought to capture the rele- an important yet largely unappreciated feature of vant differences. The first offered a syntactic for- positivist accounts of explanations. This syntactic mulation for an explanation. This requirement standard allowed a clear formal criterion by which held that good explanations had a specific form, to identify a candidate explanation. and this form allowed for the logical derivation of A recurrent criticism of positivist models of the explanandum from the explanans. This format explanation concerns the principled absence of any also required the use of an appropriate law-like or need to incorporate the perspective of those whose statistical generalization. actions are to be explained. In addition, the syntac- The second requirement concerns the need for tic structure of positivist explanation is viewed as empirical testability. Logical positivists themselves also precluding any normative evaluations of the differed with regard to the so-called logic of con- actions. Scientific explanations are typically held firmation for explanations. The basic split con- to be purely descriptive. Absent an overt inclusion cerned whether testing of hypotheses should stress of a normative premise, no normative conclusion confirmation or disconfirmation. The essence of can be derived. the controversy involved the fact that no law can For example, in explaining why people might ever be fully confirmed by observed positive cases; be co-opted to be mass murders in the case of the law makes claims about cases seen and unseen, the Holocaust, the use of generalizations that a as well as past, present, and future. Thus, no finite large majority of people simply tend to obey amount of observed evidence, however great, authority might be employed, together with other 480 Explanation information. However, this might lead to complaints experience to apparently agree with what theory that perpetrators are in fact thoughtless, that is, not implies can be accommodated in an ad hoc fashion portrayed as making a choice about how to act. To by the explanatory framework. the extent that perpetrators did not make choices, Moreover, it is important to note that even the then they might appear to be less morally culpable
Recommended publications
  • Values in Science Beyond Underdetermination and Inductive Risk
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by PhilSci Archive Values in Science beyond Underdetermination and Inductive Risk Matthew J. Brown Center for Values in Medicine, Science, and Technology The University of Texas at Dallas [email protected] July 12, 2012 Abstract The thesis that the practice and evaluation of science requires social value- judgment, that good science is not value-free or value-neutral but value-laden, has been gaining acceptance among philosophers of science. The main pro- ponents of the value-ladenness of science rely on either arguments from the underdetermination of theory by evidence or arguments from inductive risk. Both arguments share the premise that we should only consider values once the evidence runs out, or where it leaves uncertainty; they adopt a criterion of lexical priority of evidence over values. The motivation behind lexical pri- ority is to avoid reaching conclusions on the basis of wishful thinking rather than good evidence. The problem of wishful thinking is indeed real|it would be an egregious error to adopt beliefs about the world because they comport with how one would prefer the world to be. I will argue, however, that giving lexical priority to evidential considerations over values is a mistake, and unnec- essary for adequately avoiding the problem of wishful thinking. Values have a deeper role to play in science than proponents of the underdetermination and inductive risk arguments have suggested. 1 Introduction This paper is part of the larger project of trying to understand the structure of values in science, i.e., the role of values in the logic of scientific practice.
    [Show full text]
  • Is Structural Underdetermination Possible?
    In: Synthese , special issue “Theoretical Frameworks and Empirical Underdetermination”. Submitted November 2008, revised March 4, 2009. Is Structural Underdetermination Possible? Holger Lyre 1 Abstract Structural realism is sometimes said to undermine the theory underdetermination (TUD) argument against realism, since, in usual TUD scenarios, the supposed underdetermination concerns the object-like theoretical content but not the structural content. The paper explores the possibility of structural TUD by considering some special cases from modern physics, but also questions the validity of the TUD argument itself. The upshot is that cases of structural TUD cannot be excluded, but that TUD is perhaps not such a terribly serious anti-realistic argument. 1. The Thesis of Theory Underdetermination and its Neighbours For some the thesis of theory underdetermination (TUD) belongs to the common wisdom of philosophy of science: TUD: For any theory T and any body of observation O there exists another theory T*, such that T and T* are empirically equivalent, but ontologically different. The central intuition behind TUD is that since theory exceeds observation it is more than plausible to assume that there always exit many, if not infinitely many, rivals to any given theory that satisfy the corresponding body of empirical evidence. The TUD thesis can in particular be found in Quine (1975): „If all observable events can be accounted for in one comprehensive scientific theory – one system of the world... – then we may expect that they can all be accounted for equally in another, conflicting system of the world. We may expect this because of how scientists work. For they do not resist with mere inductive generalizations of their observations: mere extrapolations to observable events from similar observed events.
    [Show full text]
  • FAKHRI-THESIS.Pdf (304.2Kb)
    An Underdetermination Argument against Underdetermination by Omar Fakhri, B.A. A Thesis In PHILOSOPHY Submitted to the Graduate Faculty of Texas Tech University in Partial Fulfillment of the Requirements for the Degree of MASTER OF ARTS Approved Dustin Tucker Chair of Committee Jonathan Dorsey Peggy Gordon Miller Dean of the Graduate School May, 2012 Copyright 2012, Omar Fakhri Texas Tech University, Omar Fakhri, May 2012 ACKNOWELDGEMENTS I would like to thank Professor Dustin Tucker and Professor Jonathan Dorsey. Without their constant help and comments, this thesis would have not been manageable. I owe a great deal to Professor Tucker for helpful tips on writing style. He spent hours working on clarifying the text, without which my thesis would be substantially less clear. I would also like to thank Dr. Mark Webb, the Chair of the philosophy department, and Dr. Daniel Nathan, for allowing me to stay for an extra year and work on this thesis. Of course, any error in this thesis is my fault and my fault alone. ii Texas Tech University, Omar Fakhri, May 2012 TABLE OF CONTENTS ACKNOWELDGEMENTS ............................................................................................................. ii ABSTRACT .................................................................................................................................... iv I. INTRODUCTION ........................................................................................................................ 1 II. TWO EXAMPLES OF UNDERDETERMINATION ARGUMENTS .....................................
    [Show full text]
  • Defending Underdetermination Or Why the Historical Perspective Makes a Difference
    Defending Underdetermination or Why the Historical Perspective Makes a Difference Wolfgang Pietsch, Chair for Philosophy of Science, Technische Universität München, Germany ([email protected]) Abstract: The old antagonism between the Quinean and the Duhemian view on underdetermination is reexamined. In this respect, two theses will be defended. First, it is argued that the main differences between Quine‘s and Duhem‘s versions of underdetermination derive from a different attitude towards the history of science. While Quine considered underdetermination from an ahistorical, a logical point of view, Duhem approached it as a distinguished historian of physics. On this basis, a logical and a historical version of the underdetermination thesis can be distinguished. The second thesis of the article is that the main objections against underdetermination are fatal only to the logical rendering. Taken together, the two theses constitute a defence of underdetermination. 1. Introduction It is revealing to compare W.V.O. Quine‘s ―Two dogmas of empiricism‖, the locus classicus for his underdetermination thesis, with the relevant passages about underdetermination in Pierre Duhem‘s ―The Aim and Structure of Physical Theory‖. While Duhem‘s book is filled with examples from the history of physics, in Quine‘s text historical references are almost completely lacking. While Duhem, the acclaimed historian of physics, was practising philosophy of science from a genuinely historical perspective, Quine approached underdetermination from an ahistorical, a logical point of view. In Section Two, it will be argued that the respective attitudes towards the history of science lie at the origin of the most important differences between these two main versions of the underdetermination thesis.
    [Show full text]
  • Evidence for the Deterministic Or the Indeterministic Description? a Critique of the Literature About Classical Dynamical Systems
    Charlotte Werndl Evidence for the deterministic or the indeterministic description? A critique of the literature about classical dynamical systems Article (Accepted version) (Refereed) Original citation: Werndl, Charlotte (2012) Evidence for the deterministic or the indeterministic description? A critique of the literature about classical dynamical systems. Journal for General Philosophy of Science, 43 (2). pp. 295-312. ISSN 0925-4560 DOI: 10.1007/s10838-012-9199-8 © 2012 Springer Science+Business Media Dordrecht This version available at: http://eprints.lse.ac.uk/47859/ Available in LSE Research Online: April 2014 LSE has developed LSE Research Online so that users may access research output of the School. Copyright © and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Users may download and/or print one copy of any article(s) in LSE Research Online to facilitate their private study or for non-commercial research. You may not engage in further distribution of the material or use it for any profit-making activities or any commercial gain. You may freely distribute the URL (http://eprints.lse.ac.uk) of the LSE Research Online website. This document is the author’s final accepted version of the journal article. There may be differences between this version and the published version. You are advised to consult the publisher’s version if you wish to cite from it. Evidence for the Deterministic or the Indeterministic Description? { A Critique of the Literature about Classical Dynamical Systems Charlotte Werndl, Lecturer, [email protected] Department of Philosophy, Logic and Scientific Method London School of Economics Forthcoming in: Journal for General Philosophy of Science Abstract It can be shown that certain kinds of classical deterministic descrip- tions and indeterministic descriptions are observationally equivalent.
    [Show full text]
  • Carrierunderdetermination As an Epistemological Test Tube PU Final
    CORE Metadata, citation and similar papers at core.ac.uk Provided by Philsci-Archive Martin Carrier Department of Philosophy, Bielefeld University P.O.B. 100 131, 33501 Bielefeld [email protected] Underdetermination as an Epistemological Test Tube: Expounding Hidden Values of the Scientific Community Abstract: Duhem-Quine underdetermination plays a constructive role in epistemology by pinpointing the impact of non-empirical virtues or cognitive values on theory choice. Un- derdetermination thus contributes to illuminating the nature of scientific rationality. Scientists prefer and accept one account among empirical equivalent alternatives. The non-empirical virtues operating in science are laid open in such theory choice decisions. The latter act as an epistemological test tube in making explicit commitments to how sci- entific knowledge should be like. 1. Introduction The underdetermination thesis states that any given set of data can always be represented by different, conceptually incompatible accounts. I will elaborate this claim later but it is clear already from this brief description that the thesis proceeds on the as- sumption that the evidence is given. The issue is to assess the impact of the evidence on the credibility of theoretical principles. The reputation of the underdetermination thesis has undergone various changes in the past decades. It was considered highly plausible in the days of Logical Empiricism (with its strict distinction between facts of experience and pragmatic criteria) and during the period of the theory-change debate (with its emphasis on historical contingency). Since then, its reputation has dropped off (see Laudan & Lep- lin 1991). The high point in its esteem during the 1970s marked the inception of social 2 constructivism with its attempt to fill the room left open to human choice by underdeter- mination with social factors.
    [Show full text]
  • Contextualism and the Problem of the External World I
    1 Contextualism and the Problem of the External World I believe that I have hands. But does my evidence support this belief? Skeptics think not. More generally, they think that our evidence can’t support our beliefs about the external world.1 This skeptical claim can be spelled out in different ways.2 But in this paper I shall not examine the differences among different versions of the claim. For I am interested in targeting the very idea that there is any such epistemic gap between my evidence and my beliefs about the external world. I shall argue that, in so far as this gap obtains, it is a gap of our own making: it is by entering into certain contexts of epistemic appraisal that we create the gap between the appraisee’s evidence and her beliefs about the external world. Such “contextualism” in epistemology may by now be all too familiar. But current versions of epistemological contextualism all suffer from a common problem: they all claim that the skeptic raises the standards for knowledge.3 I shall argue that the skeptic operates not by raising the standards for knowledge, but rather by disqualifying certain mental states from counting as evidence. Thereby the skeptic makes it impossible for us to attain even what, by ordinary standards, counts as knowledge of the external world. The skeptic is not making the uninteresting claim that we do not meet unusually stringent standards of knowledge. Rather, she is claiming that we do not meet ordinary 2 standards for knowledge.4 But she can make this claim truthfully only because she restricts what counts as our evidence.
    [Show full text]
  • Course Descriptions
    Course Descriptions Spring 2020 Updated: 11/4/19 2:01 PM Undergraduate Courses CAS PH 100 A1 Introduction to Philosophy Professor Derek Anderson Tuesday, Thursday 9:30AM-10:45AM Introduces the nature of philosophical activity through careful study of major philosophical topics. Topics may include the nature of reality, knowledge, God's existence, and the significance of human life. Carries humanities divisional credit in CAS. In the 2018- 19 Academic Year this course fulfills a single unit in each of the following BU Hub areas: Critical Thinking and Philosophical Inquiry and Life's Meaning. Effective Fall 2019, this course fulfills a single unit in each of the following BU Hub areas: Philosophical Inquiry and Life's Meanings, Ethical Reasoning, Critical Thinking. CAS PH 100 B6 Introduction to Philosophy Professor Derek Anderson Tuesday, Thursday 12:30PM-1:45PM Introduces the nature of philosophical activity through careful study of major philosophical topics. Topics may include the nature of reality, knowledge, God's existence, and the significance of human life. Carries humanities divisional credit in CAS. In the 2018- 19 Academic Year this course fulfills a single unit in each of the following BU Hub areas: Critical Thinking and Philosophical Inquiry and Life's Meaning. Effective Fall 2019, this course fulfills a single unit in each of the following BU Hub areas: Philosophical Inquiry and Life's Meanings, Ethical Reasoning, Critical Thinking. CAS PH 110 A1 Great Philosophers Professor Benjamin Crowe Monday, Wednesday, Friday 1:25PM-2:15PM An introduction to philosophy through a reading of great figures in western thought. The list may include Plato, Aristotle, Descartes, Roussesau, Nietzsche, Russell.
    [Show full text]
  • Chapter 10 Underdetermination, Induction, Falsifiability
    Chapter 10 Underdetermination, Induction, Falsifiability 10.1 Homework Readings – DW 5-7 + Duhem, Russel and Popper Study Questions – Give a short answer to the following questions: 1. What are the three main claims constituting the Duhem-Quine thesis? Ex- plain how these claims can be interpreted either in a rather weak and uncon- troversial way, or in a stronger and more controversial way. 2. What is the axiomatic method? Explain why it is hard to see such a method work in natural sciences. Is there another domain in which it works well? 3. What is the hypothetico-deductive model? How does it fit your views on science? 4. Explain what the problem of induction is (as formulated by Hume). Explain why appealing to the fact that induction has always worked in the past is a circular argument. 5. Explain Hempel’s raven paradox. What is the proper conclusion that we should take from it. 6. Explain Goodman’s new riddle of induction. 7. Explain what it is to treat a scientific theory as unfalsifiable. Explain why falsifiability is better understood as an attitude than as a property of a theory. 8. Dewitt states p. 64: ”[...] the issues discussed above are clearly philosophical issues, rather than issues that affect working scientists”. Do you agree? Why? Why not? 87 10.2 A rough history of philosophy of science up to early 20th century Aristotle and the Axiomatic approach – Deductive reasoning for “certain” knowledge Agree on the most general principles and definitions: axioms Once we have agreed on the principles (the axioms), everything should logi- cally deduced, such that the conclusions, if the principles are true, are neces- sarily true.
    [Show full text]
  • Inference to the Best Explanation (Article)
    W.H. Newton-Smith (ed) A Companion to the Philosophy of Science (Blackwell, 2000) 184-193. Inference to the Best Explanation PETER LIPTON Science depends on judgments of the bearing of evidence on theory. Scientists must judge whether an observation or the result of an experiment supports, disconfirms, or is simply irrelevant to a given hypothesis. Similarly, scientists may judge that, given all the available evidence, a hypothesis ought to be accepted as correct or nearly so, rejected as false, or neither. Occasionally, these evidential judgements can be make on deductive grounds. If an experimental result strictly contradicts an hypothesis, then the truth of the evidence deductively entails the falsity of the hypothesis. In the great majority of cases, however, the connection between evidence and hypothesis is non-demonstrative or inductive. In particular, this is so whenever a general hypothesis is inferred to be correct on the basis of the available data, since the truth of the data will not deductively entail the truth of the hypothesis. It always remains possible that the hypothesis is false even though the data are correct. One of the central aims of the philosophy of science is to give a principled account of these judgements and inferences connecting evidence to theory. In the deductive case, this project is well-advanced, thanks to a productive stream of research into the structure of deductive argument that stretches back to antiquity. The same cannot be said for inductive inferences. Although some of the central problems were presented incisively by David HUME in the eighteenth century, our current understanding of inductive reasoning remains remarkably poor, in spite of the intense efforts of numerous epistemologists and philosophers of science.
    [Show full text]
  • Underdetermination and the Claims of Science
    University at Albany, State University of New York Scholars Archive Philosophy Faculty Scholarship Philosophy 3-2003 Underdetermination and the Claims of Science P.D. Magnus University at Albany, State University of New York, [email protected] Follow this and additional works at: https://scholarsarchive.library.albany.edu/cas_philosophy_scholar Part of the Philosophy Commons Recommended Citation Magnus, P.D. (2003) Underdetermination and the Claims of Science. PhD Thesis in Philosophy. University of California, San Diego This Dissertation is brought to you for free and open access by the Philosophy at Scholars Archive. It has been accepted for inclusion in Philosophy Faculty Scholarship by an authorized administrator of Scholars Archive. For more information, please contact [email protected]. UNIVERSITY OF CALIFORNIA, SAN DIEGO Underdetermination and the Claims of Science A dissertation submitted in partial satisfaction of the requirements for the degree Doctor of Philosophy in Philosophy by P.D. Magnus Committee in charge: Professor Paul M. Churchland Professor Donald Rutherford Professor Nancy Cartwright Professor Naomi Oreskes Professor Martin Sereno 2003 I completed my dissertation after digital technology had overtaken word pro- cessing, but before it overtook the submission and archiving of dissertations. I prepared it in LATEX, processed it as a PDF, printed it on cotton paper, and submitted it in duplicate to the Office of Graduate Studies and Research. OGSR sent both copies to the library, and one copy was forwarded to University Mi- crofilms, Inc. UMI photographed the pages so as to make a copy on microfilm, scanned the microfilm, and made the scans available as a PDF. It is a grainy, uneven scan.
    [Show full text]
  • On Choosing Between Deterministic and Indeterministic Models: Underdetermination and Indirect Evidence
    On Choosing Between Deterministic and Indeterministic Models: Underdetermination and Indirect Evidence Forthcoming in Synthese Charlotte Werndl, Lecturer, [email protected] Department of Philosophy, Logic and Scientific Method London School of Economics Abstract There are results which show that measure-theoretic deterministic models and stochastic models are observationally equivalent. Thus there is a choice between a deterministic and an indeterministic model and the question arises: Which model is preferable relative to evidence? If the ev- idence equally supports both models, there is underdetermination. This paper first distinguishes between different kinds of choice and clarifies the possible resulting types of underdetermination. Then a new answer is presented: the focus is on the choice between a Newtonian determinis- tic model supported by indirect evidence from other Newtonian models which invoke similar additional assumptions about the physical systems and a stochastic model that is not supported by indirect evidence. It is argued that the deterministic model is preferable. The argument against underdetermination is then generalised to a broader class of cases. Fi- nally, the paper criticises the extant philosophical answers in relation to the preferable model. Winnie's (1998) argument for the deterministic model is shown to deliver the correct conclusion relative to observations which are possible in principle and where there are no limits, in princi- ple, on observational accuracy (the type of choice Winnie was concerned with). However, in practice the argument fails. A further point made is that Hoefer's (2008) argument for the deterministic model is untenable. 1 Contents 1 Introduction 3 2 Deterministic and Indeterministic Models 4 2.1 Deterministic Models .
    [Show full text]