ABSTRACT
This chapter provides the principles of Cartesian analysis, along with the conviction that all genuine knowledge is necessary, grounded in a universal and an analytic concept of truth and meaning. It distinguishes the "causal" independence in Crawford's summary from account, since the independence investigating is logical, or logico-mathematical. The chapter analyzes the structure of negative prehension requires care. It argues that the analysis of possibility is intensional because possibilities are relations, and not set-theoretic points patiently awaiting our notice in some set-theoretic caricature of a "possible world". The chapter insists that the connections are the formal basis for characterizing logic—in line with Peirce, Dewey, and Hintikka—as the theory of inquiry and explains the abstract with the concrete. Perception is more abstract than prehension, but far less abstract than concrescence and transition. The chapter finally illustrates the subtle relationship by considering the "Impossible Snowflake". Algebraic approaches examine collections of functionally equivalent structures, instead of listing proof transformations in a sequence.
