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SUMMARY:Landon Elkind (Western Kentucky University)
DTSTART:20231207T190000Z
DTEND:20231207T200000Z
DTSTAMP:20260423T052830Z
UID:OLS/130
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OLS/130/">Pr
 incipia Mathematica\, Negative Types\, and a theorem of infinity for Z-Pri
 ncipia Mathematica</a>\nby Landon Elkind (Western Kentucky University) as 
 part of Online logic seminar\n\n\nAbstract\nI here develop a new\, foundat
 ionless simple-type grammar to replace Principia Mathematica's well-founde
 d simple-type grammar. Rewriting the axiom schemata of Principia in founda
 tionless simple-types\, or Z-types\, gives us a new system\, ZPM. Adding t
 o ZPM a plausible new axiom schema\, Z*107\, allows us prove Infinity in e
 very type. Z*107 is a plausible new axiom schema because\, as I will argue
 \, it is a logical truth of ZPM. Further\, using Z*107 to prove Infinity i
 s not circular: the new axiom alone does not secure a proof of Infinity\, 
 but crucially relies on heterogeneous relations. So using Z*107 to prove I
 nfinity is not question-begging. In this talk I also relate this system to
  earlier discussions of Wang's Negative Types (and its extension by Specke
 r's TA).\n
LOCATION:https://researchseminars.org/talk/OLS/130/
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