Point-free geometry and verisimilitude of theories

Journal of Philosophical Logic 36 (6):707 - 733 (2007)
Abstract
A metric approach to Popper's verisimilitude question is proposed which is related to point-free geometry. Indeed, we define the theory of approximate metric spaces whose primitive notions are regions, inclusion relation, minimum distance, and maximum distance between regions. Then, we show that the class of possible scientific theories has the structure of an approximate metric space. So, we can define the verisimilitude of a theory as a function of its (approximate) distance from the truth. This avoids some of the difficulties arising from the known definitions of verisimilitude
Keywords metric spaces  multi-valued logic  point-free geometry  Popper  verisimilitude
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