Despite Kempe, the Modest Place of Multisets and Multiclasses in Foundational Theories

Grattan‐Guinness, I.

doi:10.1007/978-3-319-12030-0_3

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On Collections Especially Multisets1

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2015

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“…It is a total mystery to me that such an obvious point is not 'universally' known and accepted long ago; but multisets are still almost unknown among mathematicians and logicians [11]. 2 Computer scientists are rather better served, due to the advocacy by Donald Knuth ([14] and elsewhere).…”

Section: On Collections Especially Multisetsmentioning

confidence: 99%

Is Logic Universal or Hierarchical?

Grattan‐Guinness

2015

Studies in Universal Logic

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Some conceptions of logic claim that they are universal. By contrast, I assume that the applications of any logic are central to its conception, so that it has to comprise a hierarchy of its metalogics, metametalogics, . . . , indefinitely extended but never capped off with some universal logic. I also advocate for the distinction between parts and moments of a multitude as key to this conception, and I query the assumption that set theory provides the most general means of handling collections of objects.

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Section: On Collections Especially Multisetsmentioning

confidence: 99%