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Although the organizational practice of using “contingent or non-traditional workers” has been escalating since the mid-1980s, only recently has research begun to focus on the consequences of this practice. In unionized workplaces, labor leaders have begun to organize these workers. Although it is believed that contingent workers are responding positively to union organizing drives, little is known about the attitudes and behaviors of contingent workers as union members. Using the Union Commitment scale developed by Gordon, Philpot, Burt, Thompson and Spiller (1980), the research project reported here compares the Union Commitment of traditional faculty and three categories of adjunct faculty. The results reveal that there are no significant differences across these employee groups for the factors of Union Loyalty, Responsibility to the Union, Willingness to Work for the Union and Alienation from the Union. The implications of these findings for research and practice are discussed.

Mathematics is associated with abstraction, generality, and simplicity, whereas reality is associated with specificity and complexity. Because of this, it might be argued that the humanities disciplines are better than mathematics at providing accounts of the history of societies and the lives of individuals. The aim here is to counter this argument by presenting a mathematical account of a specific complex social reality. This is in accordance with recent appeals to peace scientists to engage with scholars in history and other humanities disciplines. Here, Shakespeare's A Midsummer Night's Dream is studied. The advantage of studying this piece is that the set of events is sufficiently complex to present a challenge to the modeler and yet sufficiently circumscribed to allow a reasonable coverage of the entire reality within the space of a paper.

The play is analyzed in terms of mathematical social science concepts. The analysis considers how people and groups participate in within-group and between-group activities over space and time. The value and power relationships in the activities are analyzed and the following concepts are deployed: roles, rules, hierarchy, anarchy, social divisions, and inequality. Some of the activities involve movement through space-time, and the set of movements can give rise to encounters. These may or may not be planned, and so alternative histories are in play. The analysis then switches to a more detailed level, and dialogic expressions of power relationships are noted. Finally, the logical structure of beliefs and dialogue is analyzed using “dynamic social propositional calculus.”

I am interested in a set X of entities and refer to this as a multiple-entity system unless the set contains just a single entity. Each entity can be characterised either by a single attribute or by many attributes. In general, then we have a system of n entities with m attributes, giving nm attributes in all. A model of a system usually focuses on the variables associated with the attributes. So a model for a unitary entity with nm attributes, a model for a system of nm entities each with just one attribute and a model for a system of n entities with m attributes may be all formally identical with one another.

The Wikipedia (2008) entry for mathematical sociology cites four books with ‘mathematical sociology’ in the title: Coleman (1964), Fararo (1973), Leik and Meeker (1975) and Bonacich (2008). Fararo (1973, pp. 764–766) provides a guide to the literature in mathematical sociology covering journals, bibliographies, reviews and expository essays, readers, texts, original monographs and research papers. Many of the references are either broader than mathematical sociology, for example, concerning the behavioural sciences in general, or narrower, dealing with a particular topic within sociology, or concerning a related field such as social psychology. Three classical original monographs are identified: Dodd (1942), Zipf (1949) and Rashevsky (1951). Included in a second generation of monographs is Coleman's (1964) ‘An Introduction to Mathematical Sociology’. Could it be that this is the first use of the phrase ‘mathematical sociology’?

Consider now the set of all possible events that can occur in a given context. There is a distinction between an elementary event and a compound event. The set of elementary events is exhaustive, exclusive and elementary: the elementary events cover all the possible events; no two of them can occur at the same time; and all other events are constituted by compounds of these. Denoting the set of all elementary events by E, the set of all (possibly compound) events is the power set of E, S ^E. The set of events, S ^E, consists of pairs of events: for each event e there is its complementary event not-e; and for the event not-e there is its complementary event not-(not-e)=e. In any given world only one event of any complementary pair can occur.

Set theory provides a foundational approach to mathematics, and mathematics provides an abstract way of looking at social reality. The first section presents some of the elementary concepts of set theory. The second section presents a variety of examples of social reality and shows how the abstract features of reality can be modelled by set theory. The third section shows how set theory can provide a way of looking at the accounts of social reality presented in humanities disciplines such as history and literature. The fourth section briefly indicates how set theory and the concept of a structure provide a foundational approach to mathematics. The fifth section looks at the debates surrounding realism and, albeit warily, espouses mathematical social science realism.

In his discussion of early lexical development in children Barrett (1995) notes that utterances can be of the following types: an expression of an internal state, a response to a specific context, a social-pragmatic utterance and a referential utterance. A referential utterance can be thought of in the following way: the thing referred to, a mental representation, a word representation and a word sound. An utterance may refer to an object, an action, an attribute or an event. Some utterances are used as the names of classes of objects while other utterances are used as the proper names of individual objects. Looking at this in abstract we might say that, in the early years of childhood, language is used to refer to elements, sets, functions and relations – in other words to the mathematical structures which were discussed in Chapter 2. Of course although early language is used to refer to mathematical objects, the character of the language itself takes the form of ordinary language.