This research is the result of a fruitful connection and provides a sign- cant link between two topics of a logical and philosophical enquiry. It tries to provide a solution to the problem of analyticity: with this expression I understand, on the one hand, the essential nature of analytic truths and, on the other, the related explanation of the analytic nature of logical inference. The connection between these two sides of what will be referred to as the Analyticity Principle, can be brie?y explained as follows: by analytic truth one understands in general a sentence whose content is logically true; by logically true one understands moreover truth independent from matters of fact or empirical data, a truth which is therefore established by logical criteria only. On this basis, it follows that a logical inference represents a purely analytic process, in opposition to its property of being able to produce knowledge, a situation which is exempli?ed by the con?icting - tions of validity and utility. The question-begging topic of this research is therefore that of analyticity, the inspiring problem for which a solution is formulated in the present book. If analyticity represents the starting point of this research, the other part of its content is the result of a far more complex question; to represent the notion of Information in the context of logical calculi.
This book develops a philosophical and logical interpretation of the concept of information within the formal structure of Constructive Type Theory (CTT), in a manner concurrent with a diverse range of contemporary perspectives on the philosophy of information. On the basis of this conceptual framework, the problem of analyticity for logical derivations is faced and a solution is proposed.
The text begins with a presentation of the formal structure of CTT, paying particular attention to some topics that have been neglected by current researchers in Type Theory. The treatment is especially formulated for logicians with a philosophical background, but without neglecting a complete formulation of all the technicalities and formal properties. The problem of analyticity is then introduced via an historically and theoretically oriented formulation, beginning with Kant and Bolzano and following its development up to the introduction of the notion of information, extending some lines of research introduced in the contemporary debate by Hintikka. The semantical approach to information is reconsidered in the light of a constructive approach to epistemology, leading to a theoretical analysis of knowledge systems. This allows for the presentation of a formal structure, based on certain typical operations in the formalization of CTT and the use of formal properties of Kripke models, in which the notions of information and knowledge are defined as epistemically different. These definitions involve an extension of constructive epistemology, bringing new material to the extremely open range of problems determined by the notion of verification and the related theory of meaning.
Information and Knowledge presents a new interesting perspective on the constructive interpretation of knowledge processes, suggesting the reliability of such an approach for the logical modeling of epistemic problems and proposing a unifying frame from one of the more important contemporary philosophical perspectives.
