Presenting the first comprehensive, in-depth study of hyperintensionality, this book equips readers with the basic tools needed to appreciate some of current and future debates in the philosophy of language, semantics, and metaphysics. After introducing and explaining the major approaches to hyperintensionality found in the literature, the book tackles its systematic connections to normativity and offers some contributions to the current debates. The book offers undergraduate and graduate students an essential introduction to the topic, while also helping professionals in related (...) fields get up to speed on open research-level problems. (shrink)

This monograph proposes a new way of implementing interaction in logic. It also provides an elementary introduction to Constructive Type Theory. The authors equally emphasize basic ideas and finer technical details. In addition, many worked out exercises and examples will help readers to better understand the concepts under discussion. One of the chief ideas animating this study is that the dialogical understanding of definitional equality and its execution provide both a simple and a direct way of implementing the CTT approach (...) within a game-theoretical conception of meaning. In addition, the importance of the play level over the strategy level is stressed, binding together the matter of execution with that of equality and the finitary perspective on games constituting meaning. According to this perspective the emergence of concepts are not only games of giving and asking for reasons, they are also games that include moves establishing how it is that the reasons brought forward accomplish their explicative task. Thus, immanent reasoning games are dialogical games of Why and How. (shrink)

We now move to the demonstration of the left-to-right direction of the equivalence result. Let us assume that there is a winning $$\mathbf {P}$$ P -strategy in the dialogical game for $$\varphi $$ φ.

Pure type systems arise as a generalisation of simply typed lambda calculus. The contemporary development of mathematics has renewed the interest in type theories, as they are not just the object of mere historical research, but have an active role in the development of computational science and core mathematics. It is worth exploring some of them in depth, particularly predicative Martin-Löf’s intuitionistic type theory and impredicative Coquand’s calculus of constructions. The logical and philosophical differences and similarities between them will be (...) studied, showing the relationship between these type theories and other fields of logic. (shrink)

According to the sortal conception of the universe of individuals every individual falls under a highest sortal, or category. It is argued here that on this conception the identity relation is defined between individuals a and b if and only if a and b fall under a common category. Identity must therefore be regarded as a relation of the form \, with three arguments x, y, and Z, where Z ranges over categories, and where the range of x and y (...) depends on the value of Z. An identity relation of this kind can be made good sense of in Martin-Löf’s type theory. But identity so construed requires a reformulation of Hume’s Principle that makes this principle unfit for explaining the sortal concept of cardinal number. The Neo-Logicist can therefore not appeal to the sortal conception in tackling the Julius Caesar problem, as proposed by Hale and Wright. (shrink)

In this paper, we provide a detailed critical review of current approaches to ecthesis in Aristotle’s Prior Analytics, with a view to motivate a new approach, which builds upon previous work by Marion & Rückert (2016) on the dictum de omni. This approach sets Aristotle’s work within the context of dialectic and uses Lorenzen’s dialogical logic, hereby reframed with use of Martin-Löf's constructive type theory as ‘immanent reasoning’. We then provide rules of syllogistic for the latter, and provide proofs of (...) e-conversion, Darapti and Bocardo and e-subalternation, while showing how close to Aristotle’s text these proofs remain. (shrink)

Recent literature on dialogical logic discusses the case of tonk and the notion harmony in the context of a rule-based theory of meaning. Now, since the publications of those papers, a dialogical version of constructive type theory has been developed. The aim of the present paper is to show that, from the dialogical point of view, the harmony of the CTT-rules is the consequence of a more fundamental level of meaning characterized by the independence of players. We hope that the (...) following paper will contribute to a better understanding of the dialogical notion of meaning. (shrink)