25 APhEx num 25, anno 2022

Per Martin-Löf is one of the most prominent living logicians. The present profile aims to illustrate his main works in an accessible way, devoting particular attention to their philosophical significance. After a brief sketch of his intellectual biography, we shall survey his main contributions to different areas of logic and philosophy. In particular, we shall focus on his most important contribution, the introduction of the Intuitionistic Theory of Types, and we shall analyze his work in proof theory, foundations of constructive mathematics and philosophy of logic.

In this essay I propose a critical profile on the figure of the Oxonian philosopher Mary Midgley, who died in 2018. Her thought has always remained central in the debate on environmental ethics and is recently being rediscovered due of its possible applications to bioethics, environmentalism and feminism. In this profile I conduct a thematic analysis of her thought, trying to connect elements of her epistemology with some of her ethics, especially in relation to the environmentalism for which she is famous. My goal is to highlight how anti-reductionist themes and the emphasis on complexity are the unifying elements of Mary Midgley's thought and the key to understanding its relevance.

The aim of this Profile is to introduce the reader to some of Jerry Fodor's main contributions to the current philosophical-scientific debate. The presentation is divided in two main thematic sections: one devoted to Fodor's conception of the nature of the mind, its processes and states, and one focussed on the issue of the semantics of mental representations. The two sections are preceded by a biographical sketch and followed by a critical assessment of Fodor's intellectual legacy.

Against a decidedly conspicuous academic output on infinity, there are few texts of a purely philosophical nature. Mostly, in fact, works written by mathematicians and physicists with a keen interest in the history of philosophy but no specific background are available. And this is especially true for literature in Italian: as much for books that have become available in translation in recent times (to give just two examples, Barrow (2006) and Aczel (2015)) as for texts originally in Italian (think of the recently reissued classics by Zellini (1980) and Lombardo Radice (1981), or the more recent Bottazzini (2018) and Benci-Freguglia (2019)). Therefore, the publication of this work on infinity, written by two Italian philosophers in four hands, cannot but be greeted with great pleasure; although they themselves privilege themes and issues of a mathematical nature, they excellently frame the theme of infinity in a broader historical and conceptual context, in the writer's opinion indispensable for an effective understanding. Infinity. Philosophy, Mathematics, Physics goes, in other words, to add to a rich list of works on this fascinating subject, but provides the reader with at least a somewhat different point of view, characterized above all by greater comprehensiveness and a better general philosophical framing of the various issues dealt with. Regardless of minimal flaws and shortcomings, which I will try to point out in the course of this critical reading, the result is undoubtedly excellent, both from the point of view of usefulness for the - always hypothetical - 'average reader' and in terms of its ability to examine more complex issues and more recent lines of research for the use of readers who are more knowledgeable or more willing to reread certain passages and deepen specific notions through additional readings.

Rigorous proof is supposed to guarantee that the premises invoked imply the conclusion reached, and the problem of rigor may be described as that of bringing together the perspectives of formal logic and mathematical practice on how this is to be achieved. This problem has recently raised a lot of discussion among philosophers of mathematics. We survey some possible solutions and argue that failure to understand its terms properly has led to misunderstandings in the literature.