Lexicon of Arguments

Philosophical and Scientific Issues in Dispute
 
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Theses I
Theses II

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I 45
Structure/Mathematics/Bigelow/Pargetter: it has sometimes been discovered that structures originating from very different areas are sometimes identical:

I 46
This means that two relations can be coextensive. What only matters is then what they have in common.
>Coextension, >Relations.
Def Set/Bigelow/Pargetter: are what coextensive universals have in common: their extension. This puts them relatively high in the hierarchy. That is why they appeared so late in mathematics.
>Sets, >Set theory.
Special case:
Random sets/Bigelow/Pargetter: have nothing in common with anything else except their elements. That is why they are nothing that coextensive universals have in common.
Hierarchy/Sets/Bigelow/Pargetter: it is controversial, where you should place sets in the hierarchy of universals.
>Universals, >Hierarchies.

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