\(\lambda \) -Philosophy: The General Program

This chapter and the rest of the book discuss a long argument intended to show the relevance and contributions of \(\lambda \) -philosophy. The main goal of \(\lambda \) -philosophy is to explore topics discussed by analytic philosophy but using the \(\lambda \) -calculus as the underlying logical system. A main contribution of \(\lambda \) -philosophy is the construction of a new intuitive and graphical, cognitive science-based logical notation for the untyped \(\lambda \) -calculus called the container notation. Another contribution is an elucidation of the kind of logico-philosophical analysis practiced in the field. So, the transformative analysis of a given input expression E consists in the explicit \(\lambda \) -definition or \(\lambda \) -encoding of E in the \(\lambda \) -calculus. Moreover, the \(\lambda \) -calculus has a very remarkable feature: it admits a great variety of interpretations for its \(\lambda \) -terms. The semantic prism of the \(\lambda \) -calculus is an analogy formulated to emphasize its semantic richness and the considerable amount of creativity that transformative philosophical analysis brings. Once a certain expression \(\alpha \) has been analyzed, \(\alpha \) can be interpreted at least as a function, a logical expression, a computer (functional) program, a data structure, and an algorithm. Finally, a motivation for the container notation and a relationship with Viète’s work in algebra are also discussed.