Abstract
That the temporal-frequency conception of the modalities plays a key role in the thought of Aristotle has been argued by Jaakko Hintikka, who employs the phrase “statistical interpretation” for what I have called Aristotle’s “temporal-frequency conception” of the modalities.1 One of the principal tasks of this chapter is to build upon the insights of Hintikka and to apply the results to two philosophical problems that face Aristotle, both central to the determinism issue. The first problem is the problem of how there can be contingency in a cosmos which has a necessary “first cause.” The second problem pertains to the application of modal notions to individuals, i.e., to individual things and individual events and states of affairs. It is arguable that, at least in the writings that we possess, Aristotle addresses neither of these problems in a direct and obvious way. However, it is also arguable, I think, that there is material in the corpus relevant to these problems. I shall suggest that this material provides the framework for the subsequent philosophical development of the determinism issue in ancient philosophy.
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References
Hintikka, T&N, p. 103.
Ibid., p. 102.
Ibid.
Cf. An. post. 2.11.94a20ff.
An. pr. 1.15.34a 13–16.
“Propositions,” so conceived, may be thought of as propositional functions with a “free time variable,” the value of which is normally implicitly supplied by the “time of use”: “Socrates is alive (at r).”
Cat. 5.4a23-26.
4a36-b1.
W. V. O. Quine’s concept of an “eternal sentence,” “one that is fixedly true or false,” is intended to fulfill this function: “So the plan I now propose is to take as truth vehicles... eternal-sentence utterance events: utterances of sentences that are eternal sentences for the utterer at the time; or to revert to language language, utterances of sentences that are eternal sentences of the language that the utterer is speaking at the time” (‘Propositional Objects’, in Ontological Relativity and Other Essays (New York and London, 1969 ), p. 143 )
Hintikka, T&N, pp. 151–153.
De partibus animalium 1.1.639b24.
De int. 13.23a21–23.
De gen. et corr. 2.11.338al–4.
Hintikka, T&N, p. 130. More accurately, Hintikka claims in this passage that Aristotle’s distinction between absolute and hypothetical possibility/necessity “serves some of the same purposes” as a distinction between conceivability and actual readability or between logical and physical possibility/necessity. However, Hintikka repeatedly stresses the point — as do Sorabji (NC&B) and Sarah Waterlow (Passage and Possibility: A Study of Aristotle’s Modal Concepts [Oxford, 1982]) — that Aristotle does not have a clear distinction between a logical or conceptual sense of the modalities, on the one hand, and a physical, causal, or natural sense, on the other. 1 entirely agree and return to this point in the first section of Chapter Eight.
Meta. 9.4.
An. post. 1.8.75b24–26.
An. post. 1.4.73b26–27.
An.pr. 1.13.32b8–10.
Alexander Aphrodisiensis, In analyticorum priorum 113, in Commentaria in Aristotelem Graeca, Vol. I, Pars. I (CIAG 1/1), ed. M. Wallies (Berlin, 1883), 162.17–23.
Sorabji, NC&B, p. 21. As Sorabji notes, the type of qualification in question “will differ from one context to another.”
Ibid.
An.pr. 1.10.30b31–40.
Phys. 2.9.200a 17–18.
Cf. Phys. 2.9. This seems to be the import of Aristotle’s claim that “it is clear that in physical things the necessary is that which is spoken of as the ‘matter’ and the motions of this [matter]” (200a30–32).
This issue, which is perhaps most explicitly treated by Aristotle in An. post. 2.12, is discussed at length in Chapter V and in my paper ‘Causes as Necessary Conditions: Aristotle, Alexander of Aphrodisias, and J. L. Mackie’, Canadian Journal of Philosophy, Supplementary Volume X (1984), pp. 157–189
For a concise historical summary of the Hellenistic debates concerning conditionals, see William Kneale and Martha Kneale, The Development of Logic (Oxford, 1962), pp. 128–138
Perhaps “conflation” is a more accurate therm than “equation” here. Related to Aristotle’s lack of a clear distinction between “natural” (“causal,” “physical”) necessity and “conceptual” (“logical”) necessity is his lack of a clear distinction between “natural necessitation” (“causation,” in one sense of the term) and “logical/conceptual necessitation.”
Cf. “By that which is self-caused, I mean that the essence of which involves existence, or that of which the nature is only conceivable as existent” [emphasis added] (Benedict Spinoza, Ethica, Part I, Definition I, in The Chief Works of Benedict de Spinoza, trans. R. H. M. Elwes, Vol. 2 (New York, 1951), p. 45.
Meta. 2.2.994a8–19.
Detailed elaboration of this claim occurs in Chapters Three and Four. Cf. also Benson Mates, Stoic Logic (Berkeley and Los Angeles, 1961 ), pp. 42–45
Meta. 9.4.1047b 14–21.
Discussed in detail in Section C of this chapter.
1047b27 #x2013;30.
‘Necessity and Unactualized Possibilities in Aristotle’, Philosophical Studies 38 (1980), pp. 287–298; ‘Fatalism and Causal Determinism: An Aristotelian Essay’, The Philosophical Quarterly 31/124 (1981), pp. 231–241
Hintikka, T&N, p. 183.
E.g., see Theodore Guleserian, ‘Factual Necessity and the Libertarian’, Philosophy and Phenomenological Research 32/2 (1971), pp. 188–204
Of course, some compatibilists or reconciliationists will claim that this equivalence does not hold, i.e., that although an action may be “factually necessary” in the sense that I have defined it, it should not be inferred that it is thus “unpreventable.” Various ancient forms of compatibilism, specifically, forms of Stoic compatibilism, are further discussed in Chapter IV.
Meta. 6.3.1027a32–b8.
Alexander, In an. pr. I 15, CIAG 2/1, 184.11–12.
Cf. An. pr. 1.13.32a 18–21.
E.g., Alexander, [De anima libri] mantissa, Supplementum Aristotelicum, Vol. 1, Pars 1 (SA 2/1), ed. Ivo Bruns (Berlin, 1887–1892), 184.14–20. See the discussion in R. W. Sharpies, “Alexander of Aphrodisias, De fato: Some Parallels,” Classical Quarterly 28 (1978), pp. 259–260.
Hintikka, T&N, pp. 210–213; C. J. F. Williams, ‘Aristotle and Corruptibility’, Religious Studies 1 (1966), pp. 203–215; Waterlow, Passage and Possibility, Ch. Six, pp. 49–78.
Hintikka, T&N, p. 110.
An.pr. 1.13.32al8–20.
De caelo 1.12.28lb 18–20. For Aristotle’s argument to go through, “an infinite (apeiron) time” must be taken as implying “all time.” Of course, this entailment does not hold for “modern” (i.e., Cantorian) concepts of infinity.
At De caelo 1.11.280b7ff. Aristotle distinguishes a number of senses of “ageneton” for several of which this implication does not hold. For example, there is a sense of the term that applies to something, “if it now is but formerly was not, without [undergoing any process of] motion or change” (280b7–8).
Rescher and Urquhart discuss the distinction I have in mind here, that is, the distinction between the metaphysical pictures of “branching time,” on the one hand, and of the “same time” as characterized by alternative events/states of affairs, on the other: Nicholas Rescher and Alasdair Urquhart, Temporal Logic (Vienna and New York, 1971 ), pp. 70–74
Cf. Phys. 4.10–13, especially 221alff.
Alexander, Quaestio 1.4, SA 2/2,12.13–18.
‘Fatalism and Causal Determinism’, pp. 232–235.
Phys. 4.11, especially 219bff.
The concept of “genuine” past or present temporal reference is similar to Rescher and Urquhart’s concept of “temporal purity” (Temporal Logic, pp. 138–151). The concept is intended to rule out “implicit” reference to future events/states of affairs through nominally present-or-past events/states of affairs, e.g., the “past” state of affairs of it’s being true yesterday that I will have eggs for breakfast the day after tomorrow.
An.pr. 1.13.32bl 1–12.
Phys. 8.5.256b9–13.
Phys. 8.1.251bl2–13.
De gen. et corr. 2.10.336b27–337al.
De gen. et corr. 2.11.338al8–338b6.
De caelo 2.12.292a20–21.
Phys. 8.4.255a6–7.
256a1–2.
Meta. 9.5.1048al6-21; 9.7.1049a5–18.
Meta. 9.5.1048a 17–20.
Cf. M. J. White, ‘Aristotle’s Concept of Theoria and the Energeia-Kinesis Distinction’, Journal of the History of Philosophy 18/3 (1980), pp. 253–263.
Cf. Meta. 9.6.1048b23–25.
Cf. De gen. et corr. 2.10.337a2ff.
De gen. et corr. 2.10.336b20–23.
Alexander, Quaestio 3.5, SA 2/2. 89.13–23. Translation in R. W. Sharpies,4 ‘“If What is Earlier, Then of Necessity What Is Later”?: Some Ancient Discussions of Aristotle, De Generatione et Corruptione 2.11’, Bulletin of the Institute of Classical Studies (University of London) (BICS) 26 (1979), p. 31.
Cf. Cicero, De fato 18.
In late scholastic disputes, the question centers on the relation between sufficient and efficacious grace. Does grace sufficient for salvation, which is given to all, become efficacious because of an act of the will of the individual that is not externally determined (Molinism)? Or is there an intrinsic distinction between sufficient and efficacious grace, the latter having the power “infallibly to procure the assent” of the recipient without destroying his power of refusal (the common Thomistic position)?
De mundo 7.401b9–10.
Cf. J. von Arnim, Stoicorum Veterun Fragmenta (SVF), Vol. II (Leipzig, 1903), Nos. 917, 918, 920 (hereafter, in the form 2.917, 2.918, etc.).
Introductory Readings in Metaphysics, ed. Richard Taylor (Englewood Cliffs, 1978), p. 136.
E.g., cf. Susan Haack, Deviant Logic: Some Philosophical Issues (Cambridge, 1974 ), pp. 77 – 82.
G. E. M. Anscombe, ‘Aristotle and the Sea Battle, De Interpretatione, Chapter IX’, in Aristotle: A Collection of Critical Essays, ed. JME. Moravcsik ( Garden City, New York, 1967 ), pp. 15–33.
In An. pr. Aristotle holds that the conclusion of a valid syllogism is conditionally necessary, given the premises (i.e., that it is necessary that if the premises are true, then the conclusion is true as well — L(p ⊃ q)); he does not conclude, however, that all sound syllogisms (valid syllogisms with [assertorically] true premises) have necessarily true or apodictic conclusions (i.e., that if the premises are true, then the conclusion is necessarily true — p ⊃ Lq). Cf, for example, An. pr. 1.10.30b31-40. Haack (Deviant Logic, p. 78) suggests that De int. 9.19a23-36 may be interpreted as drawing what amounts to the distinction between “L(p ⊃ q)” and “p ⊃ Lq.” However, the passage also may be read as distinguishing between an absolute or haplos sense of “necessary” and the temporally relative sense.
I would agree with Anscombe, however, that at 19a29ff. Aristotle does seem to indicate that the necessity of a “disjunction” does not “distribute over the disjuncts.” But I believe that his concern with one or the other of the disjuncts’ becoming necessary derives from sources other than the “purely logical” fallacy of inferring the necessity of the disjuncts from the necessity of a disjunction. If it were the latter fallacy that concerns Aristotle, it seems that he should be concerned with the transferal of the necessity of a disjunction of a pair of contradictory propositions to both disjuncts.
White, ‘Fatalism and Causal Determinism’.
Spinoza, Ethica, Part I, Prop. Ill, in Ethic: From the Latin of Benedict Spinoza, trans. W. Hale White, 4th edition (London, 1923), p. 3.
John Hermann Randall, Jr., The Career of Philosophy, Vol. 1 (New York, 1962 ), p. 607.
Immanuel Kant, Critique of Pure Reason, trans. Norman Kemp Smith (New York, 1965 ), A 91 (B 124), p. 125.
An. post. 1.6.75al0–20.
An.pr. 1.13.32bl8–19.
Phys. 2.5.196b27–28.
196b33–197a20.
Spinoza, Ethica, Part I, Prop. XXVIII, trans. W. H. White, pp. 28-29.
Ibid., Prop. XXIX, p. 29.
Cf. An. post. 1.19ff. and the discussion in Jonathan Lear, Aristotle and Logical Theory (Cambridge, 1980 ), Ch. Two, ‘Completeness and Compactness’, pp. 15–33.
Phys. 2.5.197a5–6. The other necessary condition of a chance or spontaneous occurrence is that it “mimic” a telic occurrence: in the case of chance, this telic occurrence will involve choice, but in the case of the broader spontaneous occurrence, conscious choice need not be involved. “So that it is clear that among those things that, generally speaking, come-to-be for the sake of something, when their cause is external and they do not come-to-be for the sake of what results, then we say that they come-to-be spontaneously. [And we say that those things come-to-be] by chance that come-to-be spontaneously, having been chosen by those [agents] having the capacity of choice” (197bl8–22).
Meta. 6.2.1027a8–ll.
Meta. 9.5.1047b35–1048al0.
It is not, I think, clear whether Aristotle’s considered opinion is that (i) a rational potentiality is a single potentiality for two opposing or contradictory effects or (ii) a rational potentiality has a single effect but implies the existence, in its possessor, of another distinct potentiality for the opposing effect. It is obvious that in the preceding argument view (i) much better serves Aristotle’s purpose.
These “attendant circumstances” are perhaps most often conceived of negatively: i.e. a given potentiality will “naturally” be actualized in the absence of “preventing” (koluonta) factors. For further discussion of the “asymmetrical” treatment of causal factors, see Ch. Seven, Section B.
See the beginning of the passage: 1047b35–1048a2.
This Aristotelian phrase becomes a technical phrase connoting the responsibility of the agent for actions in the Hellenistic determinism — responsibility debates. The interpretation of Boethius as limiting “indeterminacy” or contingency to causal chains begun by the “new starts” of human decisions has been suasively defended by Norman Kretzmann, “Nos lpsi Principia Sumus: Boethius and the Basis of Contingency” (unpublished manuscript).
1027a 13-15.
1050b21–22.
De int. 13.22b36–23a4.
I have in mind, of course, Plato’s account of the receptacle, and his closely related conception of (a kind of) necessity and “errant cause,” in the Timaeus. Cf. Cornford: “I have maintained that Plato recognizes in the working of the universe, a factor which confronts the divine Reason and is neither ordained nor completely controlled by it. This means that irrational and merely necessary motions and changes, with casual and undesigned results, actually occur in Nature at all times, as well as those which are subservient to rational ends. It is only ‘for the most part’ that Reason can persuade Necessity. Were it otherwise, Plato’s Demiurge would be represented as an omnipotent creator who had designed the whole contents of the universe, not as a craftsman who ‘takes over’ materials in disorderly motion and does the best he can with them” (F. M. Cornford, Plato’s Cosmology: The ‘Timaeus’ of Plato (London, 1937 ), p. 209 ). A very Neoplatonic-sounding identification of “not-being” (to me on) as the ground of chance and spontaneity in “external causes” and of “what is up to us” (to eph’ hemin) in the case of human beings is found in Alexander’s Mantissa (SA 2/1), 171.1–172.15. Sharpies has discussed the question of whether this passage (and the position it sets forth) can be attributed to Alexander: R. W. Sharpies, “Responsibility, Chance and Not-Being (Alexander of Aphrodisias mantissa 169–172),” BICS, No. 22 (1975), pp. 37–63.
However, in De gen. et corr. 2.9, Aristotle contrasts Plato’s account, in the Phaedo, of coming-to-be solely in terms of “participation in the Forms” with an account of kinesis solely in terms of matter. Although he thinks the latter account less far from the truth than the former, he seems to criticize it for making matter “too active”: “for to undergo (to paschein) and to be moved is characteristic of matter, to move and to act of some other power” (335b30–31).
Boethius, Commentaria in librum Aristotelis ‘Peri hermeneias’, (editio secuna) ed. C. Meiser (Leipzig, 1877), Vol. 2, 208.
Boethius makes it clear (ibid., 208) that this “mutability” of truth-value is “not a consequence of our ignorance or knowledge.”
Ammonius, In Aristotelis de interpretatione commentarius, ed. A. Busse, CIAG 4/5, 128-131.
Hintikka, T&N, p. 169.
Cf. the discussion of Hintikka, ibid., pp. 170–171.
Technical problems encountered in identifying necessity with the “upper limit” of degrees of probability (i.e., the “most probable”) and impossibility with the lower limit are discussed in Ch. Eight, Section A.
Alexander, for example, holds (and attributes to Aristotle the view) that individuals are not capable of temporal recurrence: Quaestio 3.5, SA 2/2, 88.13-16.
An. post. 2.12.95a24–36.
For further discussion of Aristotle on conditional necessity involving relations between non-contemporaneous events/states of affairs see Ch. Five and my paper “Causes as Necessary Conditions.”
Those are cases where the “consequent” is eternally recurrent, a fact that also entails that the relation is also one of a fronte conditional necessity (perhaps through some “intermediate” states of affairs). See the discussion in Ch. Five and in White, ‘Causes as Necessary Conditions’.
Dorothea Frede, Aristoteles und die “Seeschlacht”: Das Problem der Comingentia Futura in De Interpretatione 9 (Goettingen, 1970), pp. 24–27.
De div. per somn. 2.463b28–33.
337b3–8.
In particular, the three-valued prepositional logic of J. Lukasiewicz. See Lukasiewicz, “On 3-valued Logic”, and ‘Many-Valued Systems of Propositional Logic’, translated and reprinted in Polish Logic (Oxford, 1967).
Boethius, In librum Arist. PH, (editio prima), ed. Meiser, 123.
The formal logical difficulty in preserving the “law of excluded middle” (the dis junction of any proposition and its denial is always [logically] true) while denying ‘bivalence’ (i.e. allowing for propositions that are neither true nor false) has, I think, rendered this interpretation of the position of Aristotle (and of a number of his commentators) unpopular among contemporary scholars. However, several scholars (e.g., Haack, Deviant Logic. pp.85–87) have recognized that the consistency of this interpretation can be rigorously demonstrated using B. van Fraassen’s “supervaluational” semantics for (classical) propositional logic. Such a formal modeling of the interpretation has been carried out in some detail in my paper ‘Necessity and Unactualized Possibilities in Aristotle’. See also, for formal details concerning supervaluational semantics, van Fraassen, ‘Presuppositions, Supervaluations, and Free Logic’, in The Logical Way of Doing Things, ed. K. Lambert (New Haven, 1969), pp. 67–91.
Hintikka, T&N, p. 173.
For a discussion of the relation among the notion of a relatively closed system, the temporal asymmetry of inferences (temporally prior to posterior and the converse), and the anisotropy of time, see A. Gruenbaum, Philosophical Problems of Space and Time (New York, 1963 ), pp. 281–329.
Philoponus, In Aristotelis de generations et corruptione, ed. H. Vitelli, CIAG 14/2, 308.
Alexander, Quaestio 3.5., SA 2/2, 88.25ff. The passage is discussed in Sharpies, ‘“If What is Earlier,...’”.
This I take to be a corollary of those elements of Aristotle’s conception of time to which the terms “nunc fluens” or “dynamic present/past” might be applied. For details, see my discussion in ‘Fatalism and Causal Determinism: An Aristotelian Essay.’ Lloyd suasively argues that the Stoics worked out the technical details of such a view: “The upshot of this would be that verbs in a genuine past or future tense did not refer, in the technical sense, to things or events in the past or future. Therefore, unlike verbs in the present tense, they did not imply the existence of any particular in the sense of identifiable time” (A. C. Lloyd, “Activity and Description in Aristotle and the Stoa,” Dawes Hicks Lecture on Philosophy, British Academy (London, 1971), p. 13).
Hintikka, T&N, p. 175.
According to some versions of the frequency conception of probability, the idea of the probability of occurrence of an individual event, relative to some set of background conditions, is “literally meaningless.”
J. Hintikka, with U. Remes and S. Knuuttila, Aristotle on Modality and Determinism, Acta Philosophica Fennica 29/1 (Amsterdam, 1977 ).
See Daniel W. Graham, ‘States and Performances: Aristotle’s Test’, Philosophical Quarterly (St Andrews) 30 (April, 1980), pp. 117–130; White, ‘Aristotle’s Concept of Theoria and the Energeia-Kinesis Distinction’.
Meta. 9.6.1048b 18–36.
Phys. 3.1.201a9-ll.
Aristotle on Modality and Determinism, p. 72.
Ibid., pp. 73–74.
Cf., for example, ibid., pp. 18–21; “As our quotations show and as was already mentioned, the absence of external hindrances has to be built (according to Aristotle) into the full definition of the potentiality in question” (p. 37); “When a change is not yet taking place, there is no evidence of a full-fledged dynamis being present at all. At most a lower-order dynamis can therefore be operative in such circumstances” (p. 62).
Aristotle on Modality and Determinism, p. 75.
Meta. 6.2.1026b22-24.
Meta. 6.3.1027a29–32.
Hintikka, Aristotle on Modality and Determinism, p. 102.
Ibid., pp. 103–104.
W. D. Ross, Aristotle’s Metaphysics: A Revised Text with Introduction and Commentary, Vol. I (Oxford, 1924 ), p. 362.
VM See, for example, Pierre Chantrain, Histoire du parfait grec (Paris, 1927); John Lyons, Structural Semantics: An Analysis of Part of the Vocabulary of Plato (Oxford, 1972 ), pp. 111–118.
Aristotle, Physics 2.5.196b21ff.
Cf., for example, An. post. 1.13-14; l.,18,1.31,2.3–4.
Sorabji, NC&B, Ch. Two, ‘Is Cause Related to Necessitation or to Explanation?’.
Most contemporary scholars contrast the interpretation of Ammonius and Boethius with the (temporary) truth-gap interpretation, usually reserving the rubric “traditional interpretation” for the latter. Thus, Sorabji, NC&B, pp. 91–103. There may have been other “traditional” interpretations, differing from that of Ammonius and Boethius in denying for future contingents either excluded middle or, less plausibly, noncontradiction. Cicero seems to allude to an Epicurean conception of future contingents of this sort at De fato 16.37: “nisi forte volumus Epicureorum opinionem sequi, qui tales enuntiones nec veras nec falsas esse dicunt, aut, cum id pudet, illud tamen dicunt, quod est impudentius, veras esse ex contrariis disiunctiones, sed quae in his enuntiata sint, eorum neutrum esse verum.” There obviously are two views being reported here. The second I would take to be identical — or at least very similar — to Ammonius’ and Boethius’ interpretation of Aristotle. The first view — Cicero implies (by contrasting it with the second) but does not actually state — restricts excluded middle for future contingents. This may be the sort of view of future contingents enshrined in an interpretation of Aristotle ascribed by Boethius to “the Stoics” (among others) but explicitly rejected by him: “Putaverunt autem quidam, quorum stoici quoque sunt, Aristotlem dicere, in futuro contingentes nec veras, nec falsas” (Boethius, In librum Arist. PH [editio secunda], ed. Meiser, 208). Aristotle himself (at De int. 9.18b 16–25) maintains that “it is not possible to say that neither [of a contradictory pair of future contingents] is true, for example (oion) that it neither will-be nor will-not-be.” He proceeds to argue that such a view would take away contingency (hopoter’ etuchen), leading to such conclusions as that “it would be necessary that a sea battle neither come-to-be tomorrow nor that it not-come-to-be tomorrow.” It also seems to be the case that noncontradiction would be violated by such a view if “not not-come-to-be” is equivalent to “come-to-be.”Boethius states that the view Aristotle here consideres and rejects, viz., the view that neither of the contradictory future contingents is true, is equivalent to the view that both are false; Boethius also implies that some have mistakenly read Aristotle as asserting this view and contrasts it with his own interpretation: “Neque enim idem est dicere neutra vera est quod dicere neutra vera est definite. Futurum enim esse eras navale bellum, et non futurum, non dicitur, quoniam utraeque omnino falsae sint, sed quoniam neutra vera sit definite, aut quaelibet ipsarum definite sit falsa, sed haec quidem vera, ilia vero falsa, non tamen una ipsarum definite, sed quaelibet illarum contingenter” (editio secunda, ed. Meiser, 215).
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White, M.J. (1985). The Legacy of Aristotle. In: White, M.J. (eds) Agency and Integrality. Philosophical Studies Series in Philosophy, vol 32. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-5339-0_2
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