# Psychology Dictionary of Arguments

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Set Theory: set theory is the system of rules and axioms, which regulates the formation of sets. The elements are exclusively numbers. Sets contain individual objects, that is, numbers as elements. Furthermore, sets contain sub-sets, that is, again sets of elements. The set of all sub-sets of a set is called the power set. Each set contains the empty set as a subset, but not as an element. The size of sets is called the cardinality. Sets containing the same elements are identical. See also comprehension, comprehension axiom, selection axiom, infinity axiom, couple set axiom, extensionality principle.
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Annotation: The above characterizations of concepts are neither definitions nor exhausting presentations of problems related to them. Instead, they are intended to give a short introduction to the contributions below. – Lexicon of Arguments.

Author Concept Summary/Quotes Sources

Peter M. Simons on Set Theory - Dictionary of Arguments

I 12
Set Theory: seperate quantities have one element in common: the empty set.
Mereology: here, mereology does not exist.
>Mereology
.
Partial order: here, partial order is the common part of the lower bound.
>Partial order.
Product: a product is the greatest lower barrier: i.e. the individual, that x and y have in common (= average of the set theory, lens in Venndiagram).
Stronger: binary sum: the binary sum is the individual who overlaps iff. it at least overlaps one of x or y (Venndiagram: both circles with lens), e.g. a broom is the sum of handle and head. Any two individuals always have a sum.
>Mereological sum.
I 279
Set Theory/modality/necessity/Simons: there is rigidity of the element relationship: a class can have in no possible world other elements, as it has in the actual world. This is analog to the mereological essentialism for subsets.
>Element relation.
I 332
Set Theory/mereology/elements/(s): elements are not interchangeable but parts are.
>Parts.

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Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution. Translations: Dictionary of Arguments
The note [Concept/Author], [Author1]Vs[Author2] or [Author]Vs[term] resp. "problem:"/"solution:", "old:"/"new:" and "thesis:" is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition.

Simons I
P. Simons
Parts. A Study in Ontology Oxford New York 1987

> Counter arguments against Simons
> Counter arguments in relation to Set Theory