Abstract
The presence of premises expressing comparison is a problem for the Aristotelian theory of the dialectical method, first because there is no general theory of comparison in the Organon and secondly because along with propositions on the opposition and inflexion of the terms, comparative statements seem to fall outside the explicit description which Aristotle gives of possible premises. The purpose of this paper is to offer a synthetic theory of comparisons according to Aristotle’s Topics, in an attempt both to supply the aforementioned absence and to highlight the importance of the second problem. There are three main types of premises on the more, the less and the similar: some comparing the degree of possession of a predicate, others comparing the plausibility of a predication and finally, others expressing an analogy. Once expounded the very marked differences that occur between these three classes of propositions, the paper analyses the various kinds of argumentation based on comparative premises and offers a formalization of its logical laws. The complexity of this theory and the volume of topoi involved in the comparisons show the magnitude of a problem that has not been sufficiently studied.
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Notes
Without taking into account the topoi of the preferable which have special features.
Bodéüs (2002, Int., § IV) has studied in detail the evident connections between the content of the Topics and the treatise the Categories and presented various hypotheses on their historical relationship. Whether this treatise was an introduction to dialectics, as some of the ancient authors thought, or a set of theories taken from the Topics, in our opinion it is very clear that the Categories are as useful for understanding the central Books of the Topics as Book I. It also seems evident that, given the absence of any overlap between the themes dealt with in both of these works, there may have been an attempt to coordinate them. However, neither the Categories nor Book I of the Topics completely covers all the logical doctrines applied in the central Books, and the theory of comparisons, which we will try to explain here, is one of the most outstanding examples.
The term ‘thesis’ has several meanings. It is used here to refer to the proposition supported by the answerer in the debate (Top. VIII, 5, 159a36 f.), not to be confused with the thesis as a contrary judgement to the accepted opinion as seen in Top. I (11, 104b19) nor with the thesis as a type of scientific principle which appears in An. Post. (I, 2, 72a15). There is undoubtedly a connection between these meanings of the word, but this is not analysed here (cf. Slomkowski 1997, 16 f.).
Some have argued that the notion of syllogism that appears in the Topics is a retrospective interpolation without clear justification (cf. Weil 1975, 89–90). Against that it should be pointed out that this inclusion is theoretically justified in An. Post. I, 6, 75a21–27ss., and An. Pr. I, 2, 24a25–28; cf. An. Pr. I, 30, 46a8–10 and An. Post. I, 2, 71b23–24; (cf. Brunschwig 2007, Int. XXXI f.; Barnes 1975b, 90; Crubellier 2009).
Thus, Books II and III are devoted to the refutation of accident, Book IV to that of genus, Book V to that of property and Books VI and VII to the refutation of definition.
In the various forms of dialogue which Aristotle describes, each partner has to recourse to the right opinions (ένδοξα) for the aim of the dialogue, such as the opinion of all, of the wisest, of the common people, of the other partner or of a particular school (Top. I, 10, 104a6–12 and 34 ff.; 11, 104b4–7, 19 ff. and 31 ff; 14, 105a37–105b1; VIII, 5, 159a38–159b2 and 23–27; 9, 160b17–22). The dialectical deduction differs from the demonstrative because its premises are based on the opinions, but both are equally valid syllogisms, for, as Aristotle says: "this will not make difference to the production of the syllogism in either case; for both the demonstrator and the dialectician argue syllogistically after stating that something does or does not belong to something else" (An Pr. I, 2, 24a25. Trans. Pickard-Cambridge (Aristotle 1928); cf. An. Pr. I, 30, 46a3; An. Post. I, 2, 71b23 and 6, 75a20).
There have been many discussions about the validity of laws or rules that appear in the topoi. For some they are only "material" laws whose validity is restricted to certain classes of things (consequentia materialis) cf. Jacobi 1993, XXVIII; Gelber 1987, 13; Bueno 1988, 8). For others, the Topics offer merely reasonable or likely inference rules, without logical validity (Villey 1966, XI). Finally, for many, they are laws that express necessary consequences of universal validity (Wolf 2010, 21; Smith 1997 , Int. XXI, XXXIV; Rubinelli 2009, 23–24). As I see, the laws of the majority of the topoi are formally valid, but they do not use only the functions of first-order logic, but also others, such as to be said as a genre, to be said as an accident, to be contrary, to be a privation of, etc. and also those that will be used in the topoi from the greater and lesser degree. The relationship between the categorical syllogism of the Analytics and the various calculi that could be extracted from the Topics is, in my opinion, analogous to the one which exists between the first order classical calculus and non-classical calculi which are extensions of classical logic (v. gr. deontic logic). It is worth signaling that some kinds of topoi have provided inspiration for logical calculi, as comparative logic (Casari 1987) and others, as the arguments based on the predicables, has been formalized (cf. Gambra 1988, 2001).
Although the vast majority of the texts of the central Books contain these elements, some of them do not present methods to refute by deductive or syllogistical laws. Among them, in addition to the introductory paragraphs to each book, the following are included: (1) texts that present strategies similar to those that appear in the Book VIII and various recommendations to carry out an advantageous dialogue before an audience (v. gr. Top. II, 5, 111b32–112a15; II, 6, 112b1–20 and VI, 14, 151b18–24); (2) paragraphs that expound logical or metalogical disquisitions of various kinds, without directly presenting procedures of refutation (v. gr. Top. II, 11, 115b12–35; VI, 4, 141b3-b14; VII, 4, 154a12–155a36); (3) texts that provide "material" laws, i.e. valid laws only for a restricted class of objects, among which are the topoi of the preferable (Top. III, 1–3), but not only them; and (4) the texts that employ or treat about the induction, that Aristotle explicitly distinguishes from the deduction or syllogism (Top. I, 12). The text mainly dedicated to induction is Top. II, 2, 109b13–29, in which is not used the term "έπαγωγή" that is however used in other texts where the induction only plays a secondary role (Top. II, 5, 111b38; II, 8, 113b15; II, 8, 113b29; II, 10, 115a5; IV, 2, 122a19; IV, 3, 123b7; cf. Rubinelli 2009, 24).
Trans. Pickard-Cambridge (Aristotle 1928). This example has been chosen because it is short, although the terminology used needs some explanation. This text presents a single topos which generalizes the other presented in Top. IV, 1, 121a10–19, where the following definition is given of the term ‘to partake’ (μετέχειν) used in this text: ‘To partake is defined (ὅρος) as to admit the definition (λόγος) of that which is partaken’. Ὅρος and λόγος can both be translated as ‘definition’, although they differ in scope: the first means the definition in the technical sense of the predicables, while λόγος includes any type of defining expression, whether or not it fulfils the conditions of strict definition by genus and difference. E.g. being and the supreme genera or categories have a λόγος but are not defined by genus and difference (cf. Top. IV, 1, 121a18, 30).
As well as the usual conventional symbols, the following are used here: variables of universal terms: X, Y, Z …; constants of universal terms: A, B, C, …; compound terms [XY]; predication: XY (‘X is predicated of Y’); negative predication: ¬XY; predication determined by predicables XpY (‘X is a property of Y’); ¬XpY (‘X is not a property of Y’); XgY (‘X is a genus of Y’); [ZY]dfX (‘[ZY] is the definition of X’); etc. The symbols used specifically in the comparisons will also be defined later.
This is a simplification of the law which is really more complex and wide-ranging, as it refers both to the λόγους (plural and wider definitions) of genus and also to species and anything which comes under it whether other inferior species or individuals. In fact, this means that the definitions are transmitted from the top down within the Porphyrian Tree.
Trans. Pickard-Cambridge (Aristotle 1928).
This list is not complete, but it includes most of the types of premises which are not predicates determined by the predicables or directly related to them.
In recent authors a more or less complete list is often found of this type of topoi, but without mentioning the difficulty referred to above. Brunschwig (1967, Int, XLI n.) makes a rather obscure distinction between nominal topoi which include those which use the notions of opposition, inflexion and coordination, etc. and the rest called propositional. Slomkowski (1997, 140 f.) makes a detailed study of these topoi, with useful results although his interpretation could be considered flawed in part by his conception of τόπος as πρότασις. Smith (1997, Int., XXXI), on the other hand, points out that the predicables form the highest level of classification of problems and conclusions. But then, referring to the three types of topoi already mentioned above, he says there are ‘other categories of classification of conclusions which are actually more important to the topoi themselves (…) than the predicables’. This is more arguable, as the propositions which express opposition, more and less etc., (except for the topoi of preferable in Book III which is probably an addition to some extent incoherent with the rest of the topoi) are always used as premises and not as conclusion (cf. De Pater 1965, cap. III, § II, B; Rubinelli 2009, 24 ff.).
Or ‘things that are in a like relation’ (Top. V, 7, 137a.20).
Brunschwig (2007, 194) highlights the difference between these first two types of comparisons, something which—as he says himself—most commentators do not do, with Alexander of Aphrodisias as an exception among them. However, Brunschwig does not seem to give this distinction the full breadth which in our opinion it has, as he deals with it only by referring to the case of the property. Slomkowski (1997, 147) points out the difference more clearly and generally.
In fact there is a fourth, but it is not of interest here: the grading of the primary and secondary substances (species and genera in the category of substance) which appear in Cat. 5.
Top. I, 17, 108a6. From this comparison between relations more or less does not seem a possible result, probably because what is the object of comparison does not have degrees, nor a common measure.
Naturally, the degree to which two subjects have the same predicate may be the same, but this possibility is dealt with by Aristotle in a brief, secondary way in the text of VI, 8, 146a19 and does not appear in the classification of the topoi which start from comparisons where the result is likeness (cf. II, 10, 115a15–24).
This characteristic has been considered a property of these categories, but not a property in the strict sense, because not a single one of these categories has it, as is obvious, given that there are at least two of them, nor does all that is in these categories receive it. Cf. Pacius 1966, In Cat., VIII, §29, 49.
Trans. E. M. Edghill (Aristotle 1928) with modifications. Immediately afterwards he points out that in the case of figures (another species of quality) such as the triangle or the square the more or less of the predicate cannot apply: ‘for the things to which the definition (λόγος) applies for triangle or circle are equally triangles or circles’ (11a7).
Trans. Pickard-Cambridge (Aristotle 1928).
This assertion, which I've only considered within the limits of the Topics, has numerous and profound implications which I can only mention briefly. On that one hand, that the genera and the species are said in the same degree of the things that fall essentially under them, it involves reality and objectivity of forms and essences that the understanding can grasp, which are the same for all men: "All men have not the same speech sounds, but the mental experiences, which these directly symbolize, are the same for all, as also are those things of which our experiences are the images" (De Int. 1, 16a6 ff. Trans. E. M. Edghill (Aristotle 1928)). On the other hand, this implies that the diversity of things that fall under a genus or a species have the unity and the identity of what falls under the same universal, which founds the possibility of science: "From experience again—i. e. universal from now stabilized in its entirety within the soul, the one beside the many which is a single identity within them all—originate the skill of the craftsman and the knowledge of the man of science" (An. Post II 19, 100a5. Trans. G. R. G. Mure (Aristotle 1928)). Experimental research of Eleanor Rosch on the cognitive processes of "categorization", or conceptualization (cf. v. gr. Rosch 1975) allowed her to conclude that some members of to category may be "better exemples" of that category than others and that some categories have degrees of membership and no clear boundaries. These experiments served to build the prototype theory which, according to Lakoff, entails a review, from its deepest foundations, both of science and of Western metaphysics, which, in its view, are theories a priori, unrelated to the human mind and body (cf. Lakoff 1987, I, 1–2). No doubt the Aristotelian philosophy has good arguments to reject accusations of Lakoff. Suffice it to recall that Aristotle was perfectly aware of the diversity and gradualness of the significance (theories of homonymy in their various classes, theory of metaphor) as well as the ambiguity, obscurity and vagueness of the concepts, which are always accompanied by images, without being confused with them (De An. III, 9, 432a12). The prototype theory, which in many aspects seems an experimental version of ideas already present in Locke (cf. v. gr. An Essay Concerning Human Understanding, III, III and VI), situate the ‘categorization’ in the semantic and psychological field, regardless of the ontology. By contrast, the uniform possession of the essence defended by Aristotle is a metaphysical thesis, which does not prevent the semantic diversity of words and the psychological gap of images that accompany the concepts. Both theories start from very distant assumptions and are, to some extent, incomparable.
The topos where this law is inserted begins as follows: ‘Moreover, suppose two things to be before you, see if the term to be defined applies more particularly (μᾶλλον λέγεται) to the one to which the content of the definition is less applicable’ (Top. VI, 7, 146a13).
‘Take, for instance, the definition of ‘fire’ as ‘the body that consists of the most rarefied particles’. For ‘flame’ is more ‘fire’ than ‘light’, but ‘flame’ is less ‘the body that consists of the most rarefied particles’ than is ‘light’: whereas both ought to belong in a greater degree to the same thing, if they had been the same’ (Top.VI, 7, 146a16).
Top. II, 10, 114b38 and VI, 7, 146a7 and according to a possible interpretation, also in Top. V, 8, 137b14.
‘The same quality, moreover, is said to subsist in a thing in varying degrees at different times. A body, being white, is said to be whiter at one time than it was before’ (Cat. 5, 4a1).
Which in the case of increase, is only one, but at different times.
Note that in some of the texts in the Topics, Aristotle seems to admit that any predicate can be determined by more or less, although the texts which place most emphasis on this have probably been manipulated.
This occurs in the topoi in Books IV–VI which start from the more or less explicit comparison of the degree of the predicate (cf. Top. IV, 6, 127b18; IV, 6, 127b37–128a4; VI, 7, 145b34; VI, 7, 146a3 y VI, 8, 146a13).
Aristotle describes a plurality of dialogue forms which have different aims (Top. I, 2; Soph. El. 2). In them each interlocutor has to make use of the opinions relevant to this aim, such as the opinions of all, of the wisest, of the common people, of the other interlocutor or of a particular school (Top. I, 10, 104a6–12 and 34; 11, 104b47, 19 y 31; 14, 105a37–105b1; VIII, 5, 159a38–159b2, 23–27; 9, 160b17–22; cf. Krabbe (2000), 207 f.; Gourinat (2002); Gambra (2002a, 107 f.).
Εἰκὸς is only used a couple of times in the central Books of the Topics. Both are in the same text and seem to be used as a variant on ‘likely’, or seemingly (δοκοῦν), which is used in the same paragraph a few lines later (Top. II, 10, 115a6f.). Generally speaking these two words do not have the same meaning. The difference between them, in my opinion, is that ‘probable’ refers to a high frequency of the predication (An. Pr. II, 27, 70a5) and δοκοῦν to its degree of likelihood. Howewer, in the Topics they are used interchangeably. These notions have given rise to numerous discussions by Aristotelian scholars, which cannot be detailed here (Barnes 1975a; Mignucci 1981; Racionero 1990, 33 n. and 51 n.; Slomkowski 1997, 147).
In contrast, there is nothing absurd in saying that it is necessary that something occurs frequently (cf. An. Post. I, 6, 75a21f.).
The comparison in this case refers to the simple predication.
Aristotle does not develop all these possibilities for each of the modes of predication or predicables, but they form a set explained in a fairly systematic way throughout the work.
Evidently, at the same time this expresses that the predication of X over Z is less likely than that of X over Y.
As will be recalled, some of these statements express either that a predicate is said to belong more to one subject than to another or that it increases, or only that it is said to be more or less, without adding other details, or finally that it can be said to belong more or less.
Treatises of Rhetoric and Dialectic, from Cicero to the modern theory of argumentation and of legal reasoning, include a series of loci or arguments called with different names (a maiore, a minore, a simili, a pari, a fortiori), which are inspired more or less remotely in the arguments based on the comparison of predication. However, the authors understand such arguments in very different ways. Some medieval treaties of logic are faithful to Aristotle (Peter of Spain 1972, 73–74). On the contrary, the jurists seem to be inspired by Cicero, who understood these loci in a rather vague way (Rubinelli 2009, 73–75), and they describe them in a way that is very different from that offered by Aristotle. For example, Klug thinks that the argument a maiore is nothing but an application of the law of subalternance (Klug 1966, 132 ff.).
Trans. Pickard-Cambridge (Aristotle 1928).
For this reason what the formulae above present are not laws, nor do they express valid metalinguistic formulae. The asterisks substitute the functors which mean predication modes (or predicables) but it is not enough to replace both asterisks by the same functor to obtain a logical law with any certainty, as the validity of the formula will depend on the functor in question. Even so, these schema are useful, because the formulae which are valid have this structure.
Top. VII, 3, 154a8. Therefore, the formula [XV]dfY::[XV]dfZ → ([XV]dfY ↔ [XV]dfZ) and the formula [XV]dfY > [XV]dfZ → ([XV]dfZ → [XV]dfY) are not laws. This is also valid for the property (cf. Top. V, 7, 137a7–20; 138a13–20; Brunschwig 2007).
Trans. Pickard-Cambridge (Aristotle 1928).
De Pater and other authors have confused this analogy which Aristotle mentions with the analogy the scholastics called proper proportionality. This is in our opinion an unjustified and premature projection because, in the first treatises of the Organon, there are no convincing reasons to believe that Aristotle had already conceived the semantic notion of non-casual homonymy, which he would speak of later, or that he had a clear notion of the analogous concept. There are many more reasons to think that at that time Aristotle conceived the unity of the like as the unity between paronyms. It was only later that Aristotle developed the theory of voluntary homonymy based on analogy, which is what the scholastics called analogy of proportionality (cf. De Pater 1965, 194f.; Gambra 2002b, 22f.).
Cf. the dialectical instrument which consists in ‘the investigation of likeness’ in Top. I, 13 and 17.
It is common today to distinguish between literal analogy (which compare members of the same class) and figurative analogy (which draw comparisons between members of different classes or experiences) (Wilcox and Ewbank 1979, 1). The analogy for Aristotle is a similarity of relations between things that serves as basis both in the semantic theories of the homonymy (cf. Gambra 2002b, 24 ff.) and metaphor (cf. Gambra 1990) as well as to the kind of argument that I am referring here. When it comes to these issues, Aristotle also employs the distinction between the similarity of distant things (πόρρωθεν) and of things that belong to the same genus (συγγενής), or other similar distinctions. He does so especially when analyzing the homonymy (Fis. VIII, 4, 249a23) and the metaphor by analogy (Poet. 21, 1457b9; Ret.III, 2, 1405a35; 11, 1412a12), but also when dealing with the dialectical reasoning based on the similarity of relations (Top., I, 18, 108b23; cf. Perelman and Olbrechts-Tyteca 1970, 499–549).
However it is not appropriate here, as in the comparison of predications, to differentiate the case in which the repeated term is the subject or the predicate, since the comparison is not made between predications, but between relations of any type.
This expression is equivalent to saying that the predicate belongs essentially to the subject.
References
Aristotle. 1928. The works of Aristotle. In ed. William David Ross. Oxford: Clarendon Press.
Barnes, Jonathan. 1975a. Aristotle’s theory of demonstration. In Articles on Aristotle, ed. Jonathan Barnes, Malcolm Schofield, and Richard Sorabji, 65–87. London: Duckworth.
Barnes, Jonathan. 1975b. Aristotle’s posterior analytics. (trans with notes: Barnes, J.). Oxford: Clarendon Press.
Bodéüs, Richard. 2002. Aristote. Catégories. Texte établi et traduit par Bodéüs. Paris: Les Belles Lettres.
Brunschwig, Jacques. 1967. Aristote. Topiques. Tome I. Livres I-IV. Texte établi et traduit par J. Brunschwig. Paris: Les Belles Lettres.
Brunschwig, Jacques. 2007. Aristote. Topiques. Tome II. Livres V-VIII. Texte établi et traduit par J. Brunschwig. Paris: Les Belles Lettres.
Bueno, Anibal A. 1988. Aristotle, the fallacy of accident and the nature of predication. Journal of the History of Philosophy 26: 5–24.
Casari, Ettore. 1987. Comparative logics. Synthese 73: 421–449.
Crubellier, Michel. 2009. Y a-t-il un ‘syllogisme topique’ chez Aristote? In Les lieux de l’argumentation. Histoire du syllogisme topique d’Aristote à Leibniz, eds. Joël Biärd, Fosca Mariani Zini, 11–32. Belgium: Brepols.
De Pater, W.A. 1965. Les Topiques d’Aristote et la dialectique platoniciènne. Méthodologie de la définition. Fribourg Suisse: Editions St. Paul.
Gambra, José Miguel. 1988. La lógica aristotélica de los predicables. Anuario Filosófico XXI/2:89–118.
Gambra, José Miguel. 1990. La Metáfora en Aristóteles. Anuario Filosófico XXXIII/2:51–68.
Gambra, José Miguel. 2001. La première logique formelle d’Aristote. In Logique et Métaphysique dans l’Organon d’Aristote, ed. Michel Bastit, and Jacques Follon, 35–62. Louvain la Neuve: Peeters.
Gambra, José Miguel. 2002a. Dialéctica, Ciencia y Metafísica en Aristóteles. Anuario Filosófico XXXV/1:81–125.
Gambra, José Miguel. 2002b. La Analogía en General. Síntesis Tomista de Santiago Ramírez. Pamplona: Eunsa.
Gelber, Hester Goodenough. 1987. The fallacy of accident and the Dictum de Omni: late medieval controversy over a reciprocal pair. Vivarium XXV/2:110–145.
Gourinat, Jean B. 2002. Diálogo y Dialéctica en los Tópicos y en la Refutaciones Sofísticas de Aristóteles. Anuario Filosófico XXXV/2:463–495.
Jacobi, Klaus. 1993. General introduction. In Argumentationstheory, ed. K. Jacobi, XXIII–XXXI. Leiden: Brill.
Kienpointner, Manfred. 1997. On the art of finding arguments: what ancient and modern masters of invention have to tell us about the ‘Ars Inveniendi’. Argumentation 11: 225–236.
Klug, Ulrich. 1966. Juristische Logik. Berlín: Springer.
Krabbe, Erik C.W. 2000. Meeting the house of Callias. Rhetoric and dialectic. Argumentation 14: 205–217.
Lakoff, George. 1987. Woman, fire, and dangerous things. What categories reveal about the mind. Chicago: University of Chicago Press.
Mignucci, Mario. 1981. Ὡς ἐπί τὸ πολύ et nécessaire dans la conception aristotélicienne de la science. In Aristotle on science. The posterior analytics, ed. Enrico Berti, 173–203. Padova: Editrice Antenore.
Pacius, Julius. 1966. In Porphyrii Isagogen et Aristotelis Organon Commenatrius Analyticus. Hildesheim: Georg Olms.
Perelman, Ch., L. Olbrechts-Tyteca. 1970. Traité de l’argumentation. La nouvelle Rhétorique. Bruxelles: Editions de l’Université de Bruxelles.
Peter of Spain. 1972. Tractatus, called afterwards Summule Logicales, ed. Lambert Marie de Rijk. Assen: VanGorcum.
Racionero, Quintín. 1990. Aristóteles. Retórica. Introducción, traducción y notas de Q. Racionero. Madrid: Gredos.
Reinhardt, Tobias. 2000. Das Buch E der Aristotelischen Topik. Untersuchungen zur Echtheitsfrage. Göttingen: Vandenhoeck und Ruprecht.
Rosch, Eleanor. 1975. Cognitive reference points. Cognitive Psychology 7: 532–547.
Rubinelli, Sara. 2002. Problemas de τόποι en Aristóteles. Notas sobre una Hipótesis Diacrónica. In Anuario Filosófico XXXV/2:367–407.
Rubinelli, Sara. 2009. Ars Topica. Springer.
Slomkowski, Paul. 1997. Aristotle’s Topics. Leiden, New York, Köln: Brill.
Smith, Robin. 1997. Aristotle. Topics. Books I and VIII with excerpts from related texts (trans with a commentary: Smith, R.). Oxford: Clarendon Press.
Villey, Michel. 1966. Liminaire: données historiques. Archives de philosophie du droit 11:VII–XVI.
Weil, E. 1975. The place of logic in Aristotle’s thought. In Articles on Aristotle, ed. Jonathan Barnes, Malcolm Schofield, and Richard Sorabji, 88–113. London: Duckworth.
Wilcox, James R., and Henry L. Ewbank. 1979. Analogy for Rhetors. Philosophy and Rethoric 12(1): 1–20.
Wolf, Simon. 2010. A system of argumentation forms in Aristotle. Argumentation 24(1): 19–40.
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Gambra Gutiérrez, J.M. The Topoi from the Greater, the Lesser and the Same Degree: An Essay on the σύγκρισις in Aristotle’s Topics . Argumentation 26, 413–437 (2012). https://doi.org/10.1007/s10503-012-9263-x
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DOI: https://doi.org/10.1007/s10503-012-9263-x