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METHOD:PUBLISH
BEGIN:VEVENT
DTSTAMP:20191002T155008Z
DTSTART:20191016T140000Z
SUMMARY:Sam Sanders - Plato and the foundations of mathematics
UID:{http://www.columbasystems.com/customers/uom/gpp/eventid/}uqd-k19g5vr
 2-q41ang
DESCRIPTION:Sam Sanders joins us for the Logic Seminar.\n\nPlato is well-
 known in mathematics for the eponymous foundational philosophy ‘Platonis
 m' based on ideal objects. Plato’s 'allegory of the cave' provides a pow
 erful visual illustration of the idea that we only have access to shadow
 s or reflections of these ideal objects. An inquisitive mind might then 
 wonder what the current foundations of mathematics\, like e.g. Reverse M
 athematics and the associated Goedel hierarchy\, are reflections of. In 
 this talk\, we show that the aforementioned are reflections of a much ri
 cher higher-order hierarchy under the canonical embedding of higher-orde
 r into second-order arithmetic. We make use of well-known generalisation
 s e.g. nets versus sequences and the gauge integral versus Riemann's int
 egral.  Philosophical discussion is kept to a minimum. 
STATUS:TENTATIVE
TRANSP:TRANSPARENT
CLASS:PUBLIC
LOCATION:Frank Adams 1\, Alan Turing Building\, Manchester
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