Philosophy and Mathematics: a Journey between Ontology, Epistemology, Aesthetics, and Technique

 

Philosophy's engagement with mathematics traces back to their contemporaneous emergence in Greek thought, continuing to stimulate original reflections on the enigmas posed by the nature and constitution of mathematical ideality. Despite the increasing specialisation in the sciences, numerous thinkers have made significant contributions to both disciplines.

Philosophical investigations into mathematics span various horizons. At an ontological level, inquiries delve into the being of mathematical ideality. From Plato's Timaeus to contemporary physics, debates persist regarding whether and how mathematical objects belong to the world. In the 20th century, against metaphysical or psychologistic explanations, Husserl's phenomenology attempted to reconcile the objectivity and necessity of mathematical entities with their subjective genesis. He studied the intentional dynamics within which idealities are constituted, marking a pivotal moment in philosophical discourse and influencing also epistemology and aesthetics.

Philosophy has also engaged with mathematics from a methodological standpoint. Descartes, Pascal, and, notably, Spinoza regarded the certainty of mathematical science as an epistemological model for establishing an absolutely grounded and rigorously demonstrated philosophy. This endeavour, however, appeared to decline definitively in the pages of the Preface to Hegel's Phenomenology of Spirit, in which he cautioned against importing the axiomatic-deductive method into philosophy, advocating for an approach free from predetermined postulates. Hegelian logic itself represents the peak of attempts to address the longstanding challenge that classical logic and mathematics have failed to fully resolve: the demonstration of foundational principles.

Reflection on mathematical objectivities has also found an important place in aesthetics, not only through the prominent role of mathematical proportions in the figurative arts, architecture, or music but also concerning the concrete practice of mathematical demonstration. As highlighted by mathematician and phenomenologist Gian-Carlo Rota, in the structure of a demonstration there is a particular dimension of beauty, which serves also as a criterion for evaluating the proof itself.

Ultimately, digital innovations have opened up an additional horizon of problems for philosophical reflection. These questions concern the possibility that the new so-called Artificial Intelligence may be capable of making real progress in the field of mathematics. Specifically, beyond merely generating numerous conjectures through probabilistic approaches, the question arises whether AI can produce entirely new proofs and "create" novel mathematical entities. The answer to this question would certainly have implications both on how we conceive the status of mathematical objects and on how we think of the relationship between human intelligence and machines.

This issue of 'Scenari' aims to explore the historical, theoretical, and aesthetic dimensions of philosophical engagement with mathematical science, with a specific focus on innovative and original proposals, while also giving special attention to how phenomenological approaches have influenced studies on the topic.

 

Authors interested are therefore invited to submit contributions on the following topics:

 

- Historical-philosophical analysis of the relationship between philosophy, technology and mathematics.

- Mathematics in the phenomenological tradition.

- Ontological status of mathematical objectualities.

- Relationship between the philosophical method and the mathematical method.

- Relationship between modes of expression such as language and painting and mathematical objects.

- Role of mathematics in artistic production.

- Aesthetic dimension of mathematical demonstration.

- Artificial intelligence and mathematical demonstration.

 

 

Deadline for submitting proposals: December 15, 2024 (andrea.colombo@uniud.it)

 

Notification of acceptance or refusal of the proposal after the peer review process: February 1, 2025.

 

Deadline for submitting the final article (after the potential revisions required by the reviewers): March 7, 2025.