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Tuesday, 27 December 2016

The idea of a universal metaphysics

In his Mathematical Review piece on my paper with Alexandre and Edelcio on galaxies that appeared in Studies in Universal Logic in 2015, Andrzej Indrzejczac briefly analyses the content of the paper and diagnoses it as "no more than a manifesto". I guess the paper is a manifesto and we need then whenever new directions are possible or required. We sensed that the research in universal logic was unknown to those doing metaphysics in a (broadly Lewisian) framework of possible worlds and that state of affairs could and should be remedied. Our paper intends to set the stage for a possible metaphysics that considers possible worlds together with logical diversity. It offers a programme and start implementing it. The idea that a logic can be given by pointing at a set of possible worlds - which is proposed but not developed - is itself a glance in the power of diversity in logical systems. In that first paper we wanted to present the idea: that a metaphysics could be informed by universal logic and that such an endeavor would have classical metaphysics as a special case.

I take the opportunity to say something about our work on galaxies since the paper. It's been a rigged road: bouts of intense fermentation followed by long interruptions. The last interruption had to do with the definition of galaxy collapsing into that of valuation spaces given by Hardegree and Dunn and used by James Trafford recently. Our work now, together with Rodrigo Freire, revolves around the consequences of an existing Galois connection between G and L (the class of all galaxies and the class of all logics). The initial paper, as well as Trafford's work, sets the stage for many directions of development. For instance, we believe we can now make precise the idea that we can give a logic by pointing at a class of possible worlds; it is clear now that not all classes of possible worlds can be galaxies and therefore logics in the sense that they could be expressed in languages. There are constellations - general classes of possible worlds - that are not galaxies. They cna be logics, but not in the sense of linguistically expressible devices

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