Greek mathematics did not know the zero. Without denying this commonplace observation, I would like to explore ways in which Plato’s Theaetetus and Sophist may be read as reaching towards the concept of the zero, if not towards anything like its Hindu-Arabic symbol. This may help connect Plato’s reflections on mathematics with his arguments about Nonbeing.

We reexamine Plato’s use of visual metaphors by considering his own treatment of light and sight, which differed from the later view that the eye is purely passive. Instead, he considered the eye to be active, sending out beams that contact the “outer fire” and then return to the seer. This essential activity of the act of seeing changes the way we should read many passages in Plato based on metaphors of vision, in order to bring forward the fundamental activity (...) of the soul in knowing. Understood in this way, Plato’s words eidos and idea may refer not only to self-subsistent, transcendent “forms” but also to the active process of “seeing” that connects us with them. (shrink)

John Searle e Maurizio Ferraris, due tra i più influenti pensatori in ontologia sociale, a dispetto delle radicali differenze tra le loro teorie circa il fondamento del mondo sociale, sono concordi su un punto: gli oggetti sociali sono fortemente dipendenti dai soggetti ma non sono soggettivi. Tuttavia, tale dipendenza non può essere spiegata a fondo attraverso la logica soggetto/oggetto. In questo senso, il presente contributo offre una visione più dinamica, che prende l’avvio dalla specificità del nostro essere-nel-mondo e dalla relazione, (...) complessa e circolare, tra la mente umana e l’ambiente socionaturale. (shrink)

What happens when people born in a “non-existing” country are faced with Italian burocracy? What happens if they want to get married? This short paper discusses, in a humorous way, some serious problems of our everyday social life made of documents, stamps, statements, licences, certificates, the immense realm where esse est scribi is a basic principle. What comes to light is that documents and data they posess determine our lives in a crucial way, and when they are not updated the (...) past seems to master the present. (shrink)

An exploration of the relationship between quantum theory and concepts of individuality and identity from ancient Greece to the present.

Aiming to provide an accessible introduction to critical changes in the biosphere that have occurred since the origins of life, this text presents an integrated view of our planet's evolution. Fifteen scientists reflect on major events in the history of the Earth.

Hermann Weyl was one of the twentieth century's most important mathematicians, as well as a seminal figure in the development of quantum physics and general relativity. He was also an eloquent writer with a lifelong interest in the philosophical implications of the startling new scientific developments with which he was so involved. Mind and Nature is a collection of Weyl's most important general writings on philosophy, mathematics, and physics, including pieces that have never before been published in any language or (...) translated into English, or that have long been out of print. Complete with Peter Pesic's introduction, notes, and bibliography, these writings reveal an unjustly neglected dimension of a complex and fascinating thinker. In addition, the book includes more than twenty photographs of Weyl and his family and colleagues, many of which are previously unpublished. Included here are Weyl's exposition of his important synthesis of electromagnetism and gravitation, which Einstein at first hailed as "a first-class stroke of genius"; two little-known letters by Weyl and Einstein from 1922 that give their contrasting views on the philosophical implications of modern physics; and an essay on time that contains Weyl's argument that the past is never completed and the present is not a point. Also included are two book-length series of lectures, The Open World and Mind and Nature, each a masterly exposition of Weyl's views on a range of topics from modern physics and mathematics. Finally, four retrospective essays from Weyl's last decade give his final thoughts on the interrelations among mathematics, philosophy, and physics, intertwined with reflections on the course of his rich life. (shrink)

Gregory Chaitin has done seminal work on the foundations of mathematics, especially the meaning of randomness and undecidability. In Meta Maths, he offers his ideas in a new popular version, which has a special interest because it comes directly from their originator. Long associated with the IBM Watson Research Center, Chaitin comes across as a kind of mathematical Richard Feynman, intuitive and high-spirited, irreverent and plain-spoken. Through this jovial persona, he presents many serious ideas in an engagingly dishevelled way, mixing (...) autobiography and reminiscence with exposition and example. He presents his insights so agreeably that it all seems a grand lark. (shrink)

After Kant the meaning of freedom is considered not so much as inner experience, but rather as a requisite to understand the world. In this regard an act of freedom is not one among many human acts, but their precondition and cause. In its highest reaches freedom thus provides existence with a final possibility in which it presents itself as an aesthetic monolith. Aesthetics of freedom considers its sublimity, one that confronts the misery of suffering its deprivation. The syncope of (...) freedom consists in itself its aesthetic feasibility as a lunge equal to reaching, but not discovering freedom, the same freedom many have viewed differently in numerous moments of aspiration through the ages, but have never discovered it in the entirety of its sublimity due to evading responsibility for it. This presentation attempts to contribute to understanding whether the philosophical concept of freedom is in fact comparable to a square circle. (shrink)

From a more physicalistic point of view the paper gives a brief overview of Boscovich’s thought about the bilayer of space and time, real space and time, and mathematical space and time, without going into philosophical analysis in detail. The paper provides examples of possible correspondence between Boscovich’s thought and physicalist concepts in modern physics.

ABSTRACT Because the modern concept of number emerged within a quadrivium that included music alongside arithmetic, geometry, and astronomy, musical considerations affected mathematical developments. Michael Stifel embedded the then‐paradoxical term “irrational numbers” (numerici irrationales) in a musical context (1544), though his philosophical aversion to the “cloud of infinity” surrounding such numbers finally outweighed his musical arguments in their favor. Girolamo Cardano gave the same status to irrational and rational quantities in his algebra (1545), for which his contemporaneous work on music (...) suggested parallels and empirical examples. Nicola Vicentino's attempt to revive ancient “enharmonic” music (1555) required and hence defended the use of “irrational proportions” (proportiones inrationales) as if they were numbers. These developments emerged in richly interactive social and cultural milieus whose participants interwove musical and mathematical interests so closely that their intense controversies about ancient Greek music had repercussions for mathematics as well. The musical interests of Stifel, Cardano, and Vicentino influenced their respective treatments of “irrational numbers.” Practical as well as theoretical music both invited and opened the way for the recognition of a radically new concept of number, even in the teeth of paradox. (shrink)

Leibniz diskutierte den Nutzen der gerichtlichen Folter, obwohl er von ihr abgestoßen war. Er betrachtete Folter als eine Ermittlungsmethode, die den höchsten Grad an Sicherheit erreichen kann und nutzte sie metaphorisch, um analoge Praktiken in der experimentellen Wissenschaft zu beschreiben. Er befiirwortete jedoch nicht den Mißbrauch der Natur, sondern eher eine unübertreffliche Methode, die die Natur dazu bringt, zu 'gestehen', ohne sie dauerhaft zu schädigen.

Pesic writes a nontechnical, agreeably philosophical introduction to the strange world of Quantum Mechanics. He uses the idea of individuality to explain the perplexing difference between the world of experience and what physics sees. Individuals are known by their difference from others. A world without variation is a world without individuality. The living world is never like that. The whole evolution of life from earliest times depends entirely on small differences distinguishing one organism from another. Step from the simplest single-cell (...) organism to its lifeless atoms and their parts, and you’re in a different world. A world without individuality. Tests accurate to one part in 1034 find no difference between one electron and another. Electrons carry no scars. They have neither trajectory nor history, ideas that presuppose we could differentiate one from another and follow its vicissitudes—exactly what we cannot do. It is only when vast numbers of electrons are organized into a complex system (like an organism) that we can speak of individuality, which is a luxury of the complicated, and comes at the price of death. (shrink)

Tom McLeish’s Music and Poetry of Science adds to along and complex literature looking at the creative powers of human genius. In addition to his own scientific field, McLeish draws on art, poetry, novels, music, and BBC television productions. Although positioned in the line of the ‘two cultures’ debate typically associated with C. P. Snow, McLeish reprises William Beveridge’s earlier contribution to that tradition, perhaps, to be aligned,although this McLeish does not do, with Peter Pesic’s Music and the Making of (...) Modern Science . The task of coordinating music, poetry, and science requires more, such that the material hermeneutics of the late Irish-Belgian physicist and philosopher, Patrick Heelan might have offered a basis for fruitful dialogue, although this,too, was a missed opportunity. Given McLeish’s illustration of the beauty key to mathematics in physics via BBC television, it seems an illustration of technological millenarianism via Andrew MacKendrick’s 1951 film, The Man in the White Sui , updated for today, key in a nano-context, might be helpful in raising issues of material‘instability,’ i.e., environmental detritus, nano-waste and pollution. (shrink)