Here is a useful and brief description by Luhmann of the core concepts of ‘contingency’ and ‘double contingency’, taken from an essay entitled ‘Generalized Media and the Problem of Contingency’.
If I understand correctly the English term contingency in its present use, it has its core meaning in dependency and draws the attention primarily to the fact that the cause on which something depends performs itself a selection from other possibilities so that the contingent fact comes about in a somewhat chancy, accidental way. If we look into the theological and philosophical tradition of the term, our findings confirm this interpretation. In scholastic philosophy the term contingens belonged to the theory of modal forms. Used to translate the Aristotelian ευδεχοϕυου (=possible) and mixed up with the classical Latin sense of accidens or eveniens, it was narrowed down to signify a special type of possibility i.e. ‘possibility not to be’. This ‘possibility not to be’ was attributed to a world created by the unlimited will of God. Only a contingent world, as the nominalistic scholastics found out, could be conceived as created by God. Contingens was used in a double sense as a general category of modal logic and as a term which includes causal selection as the factor which decides between being and not being. Contingency of the world came to be a corollary of the absoluteness of God. Contingency, therefore, also meant dependency on His creation or the visibility of His free will in His Creation This led the pious to look to God for the elimination of infinite other possibilities and for a guarantee that the selected world was the best of all possible worlds.
This tradition was, of course, known in its results to Descartes and to Hobbes. Finding the transcendent God liberated from any essential commitment to a pre-existing ‘cosmic’ order of nature or ideas they drew on consequences for the individual and for the social order. They secularized the problem of selectivity. Descartes transformed it into a theory of individual and cognitive processes and Hobbes into one of social-political and normative processes. Not yet sociologists, they did not reflect on the interdependence of individual and social processes; nor could they pay sufficient attention to the fact that the problem of contingent selection became urgently relevant in connection with evolutionary changes in the social system of society. Nevertheless, this background of conceptual history helps to see why, and in what sense, contingency is inherent in interaction.
Summarizing what we have discussed so far, contingency means that being depends on selection which, in turn, implies the possibility of not being and the being of other possibilities. A fact is contingent when seen as a selection from other possibilities despite a selection. Implying a potential for negation and the visibility of other possibilities, the concept can be applied only to the meaning of subjective experience and action. This does not limit the range of application and does not, of course, mean that contingency is accessible only by ‘introspection’. Every fact may be seen as contingent: the objective world, the concrete self with its biography, conscious life, decisions and expectations and other persons with their experiences and choices. Contingency is a universal, but it nevertheless presupposes a subjective point of view. It can be applied to all facts but not independently of a subjective potential to negate and conceive other possibilities.
We are now prepared to analyze the special problem of double contingency in interaction. Contingency does not double by erasing the twofold dependence; nor does double contingency signify two contingencies in the sense of a simple addition; nor does it mean interdependence in the sense that ego depends on alter and vice versa, the subjective point of view coming in later and only as an interpretation of this interdependence. The doubling comprehends the whole structure: the generalized potential to conceive of facts as selections implying negations, to negate these negations and to reconstruct other possibilities. Double contingency is ‘double negation virtuelle’ meaning that possibilities of negation can be retained and stabilized as reciprocally not actualized but implied possibilities. The doubling of contingencies is possible because this potential is located in subjects, and subjects can experience other subjects. The doubling does not double the world and does not construct two separate realms of contingency. The potential is universal for each subject and is an aspect of the meaningful constitutions of this encompassing world so that ego has to identify alter as being another subject in his world, and vice versa. Double contingency rests on the fact that contingency is subjective and universal at once.
[…] The point is that we have to conceive of meaningfully organized selectivity as the specific human condition and that we need the outlined conceptual framework to understand evolutionary gains as higher forms of problematization and organization of selective processes. Double contingency is not simply a problematic fact inherent in the nature of interaction. It has the double aspect of high achievement and high risks. It makes the selectivity of other subjects selectively available at increasing risks. The selection chain may be broken and expectations disappointed – a risk which, then, can become a specific (secondary) problem and be solved by specialized mechanisms.
 English speakers may consult Philotheus Boehner, ‘The Tractatus de praesdestinatione et de praescientia Dei et de futuris contingentibus of William Ockham St. Bonaventura N. 4 (1945) pp. 41ff; B. Wright, ‘Necessary and Contingent Being in Science and technology. Thomas’, The New Scholasticism, 25 (1951) pp. 439-466; Edmund F. Byrne, Probability and Opinion (Den Haag: M. Nijhoff, 1968) pp. 188ff.
 The negation refers, as Leibniz did make clear, not to the possibility itself – this would mean impossibility – but to the being whose possibility is stated. Contingens is a positive statement about the possibility of negative being.
 See Gerard Smith, ‘Avicenna and the Possiblies’, The New Scholasticism, 17 (1943) pp. 340-357; Celestino Solaguren, ‘Contingencia y creación en la filosofía de Duns Escoto’, Verdad y Vida, 24 (1966) pp. 55-100.
Particularly clear on the double sense of the term is the statement of an anonymous author of the fifteenth century, reprinted by Léon Baudry (ed.) La querelle des futures contingents (Louvain 1465-1475) (Paris: J Vrin, 1950) pp. 126-133 (127): ‘contingens igitur in prima sui divisione est duplex. Unum quod ex significato idem est quod possible; et is accipitur contingents absolute, non considerando contingens per habitudinem et respectum ad causam suam. Aliud est contingens quod est distinguitur a possibili quia includit habitudinem et respectum ad causam que in producendo (procedendo?) potest inhibiri.’
 Here we should note at least the astonishing fact that the conceptual preparation for modern society preceded its institutionalization: High, contingent, selectivity was a problem of thinking, before any real needs came up to organize mechanisms for contingent selection on a large scale. Parsons could see here a corroboration of his hypothesis, that large-scale evolutionary change is controlled on the highest cybernetic level, i.e. by the cultural subsystem of the action system. Cf. Societies: Evolutionary and Comparative Perspectives (Englewood Cliffs: Prentice Hall, 1966) pp. 113ff.
 The scientific and empirical status of these ‘other possibilities’ is, bluntly stated, unknown. Its clarification will be one of the most important theoretical and methodological tasks of social sciences in the future. Max Black in his important essay on ‘possibility’ leads us into doubts about the ‘ghostly view’ of other possibilities as pure illusions, shatters en passant the traditional construction of possibilities in terms of a theory of modalities – and leaves the scared reader on the edge of this precipice with the advise ‘to undertake a detailed survey of how we do in fact use the words possible, possibility, and their cognates.’ See Models and Metaphors: Studies in Language and Philosophy (Itaca, N.Y.: Cornell University Press, 1962) pp. 140-152.
 The contingency of ‘the’ world implies, however, a metaworld as the horizon of all possibilities from which the actual world is selected by creation or by evolution.
 The Cartesian tradition of subjective metaphysics would deny this statement and exempt consciousness from contingency. But the immediacy of experience of one’s own consciousness is no sufficient reason to exclude its contingency.
 See, however, James Olds, The Growth and Structure of Motives: Psychological Studies in the Theory of Action (Glencoe, Ill.: The Free Press, 1956) pp. 198ff.: ‘Within a presented object system, contingency is single in the sense that if I perform a particular set of behaviours I will achieve a particular outcome for my labours. Within a non-presented object system, there is double contingency: If I perform the behaviours that will take me to that object successfully, then, if I perform a certain set of behaviours (manipulating the object) I will achieve a particular outcome for my labours.’ Social contingency (double contingency in the sense of Parsons), then, is only a special case of this two-step dependence. But this argument confounds contingency and dependence. Consequently, social contingency, i.e. the interaction of subjects knowing each other as subjects, is constructed as a special case of a much too simple case.
 Parsons in some formulations comes close to this view. See Talcott Parsons, Robert F. Bales and Edward A. Shils, Working Papers in the Theory of Action (Glencoe, Ill.: The Free Press, 1953) p. 35.
 We owe this splendid formulation to Paul Valéry Animalités, Oeuvres, (Paris: ed La Pléiade, 1957) p. 402.
 James Old op. cit. touches upon this point at p. 205 describing the gain in terms of economy of time and movement. See also Donald M. MacKay ‘Communication and Meaning – a Functional Approach’, F.S.C. Northrop and Helen H. Livingston (eds) Cross-Cultural Understanding: Epistemology in Anthropology (New York: Harper & Row, 1964) pp. 162-79 (163).
Luhmann, N. ‘Generalized Media and the Problem of Contingency’, in Loubser J. et al (eds) Explorations in General Theory in Social Science: Essays in Honour of Talcott Parsons (vol. II) (New York: The Free Press, 1976) 507-532, pp. 508-509.