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Provides a new paradigm capable of integrating and developing research, which, it proposes, gives a better understanding of industrial buyer behaviours. Concludes that the model provided can be used by practitioners as a basis on which to form their marketing message, but not its style of delivery or specific direction.

Whereas Zermelo's foundational program is implicitly reductionist, the precise character of his reductionism is quite unclear. Although Zermelo follows Hubert methodologically, his philosophical viewpoint in 1908 is broadly at odds with that of Hubert. Zermelo's interest in the semantic paradoxes permits an intuitive concept of mathematical definability to play an important role in his formulation of axioms for set theory. By implication, definability figures in Zermelo's philosophical concept of set, which is seen to be nonstructural in character. Zermelo's advocacy of universal definability is intended to blunt tensions between platonists and constructivists. Finally, the method of justification of mathematical axioms is taken to be of an empirical and public character, at least in part, and, as a consequence, threatens Zermelo's foundational program.

In papers published between 1930 and 1935, Zermelo outlines a foundational program, with infinitary logic at its heart, that is intended to (1) secure axiomatic set theory as a foundation for arithmetic and analysis and (2) show that all mathematical propositions are decidable. Zermelo's theory of systems of infinitely long propositions may be termed “Cantorian” in that a logical distinction between open and closed domains plays a signal role. Well-foundedness and strong inaccessibility are used to systematically integrate highly transfinite concepts of demonstrability and existence. Zermelo incompleteness is then the analogue of the Problem of Proper Classes, and the resolution of these two anomalies is similarly analogous.

Abstract.An idea attributable to Russell serves to extend Zermelo's theory of systems of infinitely long propositions to infinitary relations. Specifically, relations over a given domain D of individuals will now be identified with propositions over an auxiliary domain D * subsuming D. Three applications of the resulting theory of infinitary relations are presented. First, it is used to reconstruct Zermelo's original theory of urelements and sets in a manner that achieves most, if not all, of his early aims. Second, the new account of infinitary relations makes possible a concise characterization of parametric definability with respect to a purely relational structure. Finally, based on his foundational philosophy of the primacy of the infinite, Zermelo rejected Gödel's First Incompleteness Theorem; it is shown that the new theory of infinitary relations can be brought to bear, positively, in that connection as well.