David Virgili

I am interested in the foundations of mathematics and the historical correlation between mathematics and philosophy.

I am the programme coordinator of INFTY: "New frontiers of infinity: mathematical, philosophical, and computational prospects", an ESF Research Networking Programme. Please, go to our web, http://inftynet.net, for more details. I am also involved in the newborn wiki Young Set Theory Network, http://young-set-theory.net, a meeting point for set-theorists and a place to share research documents.

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My main concern is freedom. It has always been the motor of human development, and as such can be studied in painting, music, poetry, philosophy, etc. But nowadays we can study it mathematically, and hence we have the tools to obtain the most clear and powerful conclusions ever.

We have an almost unlimited power to imagine and create; this also demands us in turn the possibility of refusing previous ideas. The history of Occidental Philosophy has been marked by the creation of successive dominant frameworks for knowledge, most prominently, Christianity-Catholicism and Protestantism, and the simultaneous fight to get rid of them.

Christianity combined several ancient philosophical deep issues in the invention of its dogmas (hellenism, gnosticism, etc.). During the Middle Ages, many philosophers-theologians -motivated in part by the aristotleanism of Avicenna and others- thought about the limitations that it imposed (is god definable? does it make sense to state that human beings have free will?), and the contradictions observed resulted in the whole machinery finally collapsing with Ockham.

This led to an unseen period of freedom in arts and knowledge, even in theology (Nicholas of Kues, our unrecognised "father" of the pursuit of infinite), and reached splendour with Giordano Bruno. In the meantime, the Church regained power and was able to impose its own order by the use of force.

A new period started in philosophy, mostly based on protestantism. Kant and his henchmen imposed the new dogmas in ethics (a moral of intention, against God, instead of a moral of action, against people), in epistemology (turning it into metaphysics), etc.

The fight against this rebirth of dogmatism would achieve some great results, but at the same time would start to move science away from philosophy.

Mathematics has inherited the problems posed by philosophy: "what is true?" is now answered by "what is logically provable", and we can also choose what do we want to mean by "logically provable"; Hilbert's axiomatic method opened the door for freedom in mathematics. "What is real?" doesn't make sense any more in mathematics.

I work in set theory, which is basically -quoting Cantor- the study of the infinite. Set-theorists are interested in freedom: mathematically, everything which is consistent is possible if stronger hypotheses are settled, that is, if larger cardinals are assumed.

There is a top limit for creation, which is inconsistency. The Absolute -which had religious connotations for Cantor- is mathematically intractable. "God" can't be assimilated in the human reasoning (Scotus Eriugena); accepting it in mathematics makes our logic inconsistent, nothing makes sense then.

I like to think that my study is in the boundaries of logical inconsistency to see how to push the limits of knowledge further every time, in order to leave an increasing space for our freedom to create.