|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._____________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.|
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Definition necessary identifying/Quantity/Containment/Element/definite description/Millikan: e.g. Superlative.
N.B.: if there are several authors of e.g. Principia Mathematica it is wrong to speak of "the author of Principia Mathematica".
E.g. Brutus was one of several murderers of Caesar.
Wrong: "Brutus murdered Caesar" (!) - wrong: Brutus was the murderer of Caesar.
Solution/Millikan: descriptions that attribute responsibility are necessary indentifying. ((s) They must not vary between singular and plural).
Necessary identifying/definite description/solution/Millikan: refer to parts of collectives, not to elements of sets. ((s) "to be murderer of Caesar" does not constitute a set, but a collective).
E.g. from "Bill is one of John's sons" follows Bill is John's son.
For example, "Brutus was one of Caesar's murderers" does not follow "Brutus was Caesar's murderer". ((s) being-son forms a set, being-murder does not).
Superlative/definite description/unambiguous/Millikan: For example, if there are several largest, that are of the same size, it is wrong to say "everyone is the largest"._____________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.
R. G. Millikan
Language, Thought, and Other Biological Categories: New Foundations for Realism Cambridge 1987