We apply some tools developed in categorical logic to give an abstract description of constructions used to formalize constructive mathematics in foundations based on intensional type theory. The key concept we employ is that of a Lawvere hyperdoctrine for which we describe a notion of quotient completion. That notion includes the exact completion on a category with weak finite limits as an instance as well as examples from type theory that fall apart from this.

We analyse the category-theoretical structures involved with the notion of continuity within the framework of formal topology. We compare the category of basic pairs to other categories of “spaces” by means of canonically determined functors and show how the definition of continuity is determined in a certain, canonical sense. Finally, we prove a standard adjunction between the algebraic approach to spaces and the category of topological spaces.

The standard presentation of topological spaces relies heavily on (naïve) set theory: a topology consists of a set of subsets of a set (of points). And many of the high-level tools of set theory are required to achieve just the basic results about topological spaces. Concentrating on the mathematical structures, category theory offers the possibility to look synthetically at the structure of continuous transformations between topological spaces addressing specifically how the fundamental notions of point and open come about. As a (...) byproduct of this, one may look at the different approaches to topology from an external perspective and compare them in a unified way. Technically, the category of sober topological spaces can be seen as consisting of (co)algebraic structures in the exact completion of the elementary category of sets and relations. Moreover, the same abstract construction of taking the exact completion, when applied to the category of topological spaces and continuous functions produces an extension of it which is cartesian closed. In other words, there is one general mathematical construction that, when applied to a very elementary category, generates the category of topological spaces and continuous functions, and when applied to that category produces a very suitable category where to deal with all sorts functions spaces. Yet, via such free constructions it is possible to give a new meaning to Marshall Stone’s dictum: “always topologize” as the category of sets and relations is the most natural way to give structure to logic and the category of topological spaces and continuous functions is obtained from it by a good mix of free – i.e. syntactic – constructions. (shrink)

Plotkin suggested using a polymorphic dual intuitionistic/linear type theory as a metalanguage for parametric polymorphism and recursion. In recent work the first two authors and R.L. Petersen have defined a notion of parametric LAPL-structure, which are models of image, in which one can reason using parametricity and, for example, solve a large class of domain equations, as suggested by Plotkin.In this paper, we show how an interpretation of a strict version of Bierman, Pitts and Russo’s language image into synthetic domain (...) theory presented by Simpson and Rosolini gives rise to a parametric LAPL-structure. This adds to the evidence that the notion of LAPL-structure is a general notion, suitable for treating many different parametric models, and it provides formal proofs of consequences of parametricity expected to hold for the interpretation. Finally, we show how these results, in combination with Rosolini and Simpson’s computational adequacy result, can be used to prove consequences of parametricity for image. In particular, we show that one can solve domain equations in image up to ground contextual equivalence. (shrink)

Current health care standards, in many countries, Australia included, are regrettably poor. Surprisingly, practitioners and treating teams alike in mental health and disability sectors, in particular, make far too many basic care-related mistakes, in addition to the already abundant diagnostic mistakes that cause and amplify great harm. In part, too many practitioners also fail to distinguish adverse effects for what they are and all too often treat adverse effects, instead, as comorbidities. Diagnostic failures are dangerous, the result of which generates (...) and perpetuates harms that are extremely costly in terms of patient welfare, in addition to the financial burden placed on everyone. In this essay, I contend that the authority bestowed upon psychiatry is misplaced. Subsequently, this misplaced authority affects the governing and investigatory institutions reliant and informed by psychiatry. The examination process undertaken in this investigation traces the metaphysics of psychiatric disorders relative to the Diagnostic-Statistical-Manual (DSM) in all its iterations and to the epistemological construction process that serves to underpin the fundamentals of psychiatric practice. There exists a crisis of confidence in psychiatric practice and I urge drastic reform be undertaken to arrest the damage. (shrink)

Antonio Signorini’s contribution to the constitutive theory of non-linear elasticity is reconstructed and analyzed. Some uninformed opinions suggesting he had a minor role, lacking of significant results, are discussed and refuted. It is shown that Signorini should be rightly credited for being among the first scholars aware of the central problem of non-linear elasticity: the determination of the general form of the elastic potential.

This book is a systematic analysis of John R. Searle’s philosophy of mind. Searle’s view of mind, as a set of subjective _and_ biologically embodied processes, can account for our being part of nature _qua_ mindful beings. This model finds support in neuroscience and offers reliable solutions to the problems of consciousness, mental causation, and the self.

What is the relevance of organizing knowledge in distinct conceptual fields when everything has become cultural with no distinct areas anymore? Is, for example, Western traditional aesthetics as an autonomous cognitive discipline always relevant in the age of multiculturalism? This essay argues, albeit controversially, that the perspective of socalled cultural studies has opened new doors by adopting a more radically pluralistic and inclusive approach – one whereby aesthetic categories are thought in terms of cultural practices. Despite the many defects of (...) such culture-related studies – such as their eclecticism, lack of scientific rigor, or methodological unreliability – the challenges of today’s multicultural society demand that we pay more attention at all levels to the roles played by difference and dialogue with otherness. This includes overcoming any form of ethnocentricity in our cognitive cultural disciplines; incorporating new topical horizons, whether economic, political or social; and rethinking the very nature of value, meaning and way of life. (shrink)

La morte dell'uomo come metafora dello sradicamento ontologico -- Partecipazione e sradicamento : la morte come rottura della comunione intersoggettiva -- L'amore come apertura alla dimensione partecipativa : in cammino verso la salvezza.

Parte prima. Profili speculativi -- Parte seconda. Profili sociali, politici, giuridici -- Parte terza. Profili antropologici.

The _Maimonides Review of Philosophy and Religion_ is an annual collection of double-blind peer-reviewed articles, which seeks to provide a broad international arena for an intellectual exchange of ideas between the disciplines of philosophy, theology, religion, cultural history, and literature and to showcase their multifarious junctures within the framework of Jewish studies.

Introduction: in search of a Jewish renaissance -- Jewish philosophy: humanist roots of a contradiction in terms -- The prophetic-poetic dimension of philosophy: the ars poetica and Immanuel of Rome -- Leone Ebreo's concept of Jewish philosophy -- Conceptions of history: Azariah de Rossi -- Scientific thought and the exegetical mind, with an essay on the life and works of Rabbi Judah Loew -- Mathematical and biblical exegesis: Jewish sources of Athanasius Kircher's musical theory -- Creating geographical and political utopias: (...) the ten lost tribes and the east -- Ceremonial law: history of a philosophical-political concept -- The city and the ghetto: Simone Luzzatto and the development of Jewish political thought -- Body of conversion and immortality of the soul: Sara Copio Sullam, the 'Beautiful Jewess'. (shrink)