﻿ Peter T. Geach on Sets - Dictionary of Arguments

Dictionary of Arguments

Sets: a set is a summary of objects relating to a property. In the set theory, conditions are established for the formation of sets. In general, sets of numbers are considered. Everyday objects as elements of sets are special cases and are called primordial elements. Sets are, in contrast to e.g. sequences not ordered, i.e. no order is specified for the consideration of the elements. See also element relation, sub-sets, set theory, axioms.

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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 Item Summary Meta data
I 215ff
Classes/Geach: must not be treated as objects (> paradoxes) - Solution:
I 215ff
Relation/Geach: instead of a class: solution to problems - a class may be no object (> paradoxes). Relation: E.g. diameter/Plate: - E.g. father-son-grandson: same relation, but no common subject.
I 221
"is a..."/Geach: no logical relation between an x and an object (class) called "man".
I 222
Classes/Geach: can be viewed as an object only when we say, "the class of A’s may be the same as the class of the B’s, although something is an A, without being a B".

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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.
The note [Author1]Vs[Author2] or [Author]Vs[term] is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition.

Gea I
P.T. Geach
Logic Matters Oxford 1972

> Counter arguments against Geach

Ed. Martin Schulz, access date 2018-12-10