|Classes: identity of classes provided by same elements (extension) - identity of properties by the same predicates (intension)._____________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. |
Ludwig Wittgenstein on Classes - Dictionary of Arguments
Number/Class/Frege/Russell/Wittgenstein: Frege's Definition: Class of classes. A number is the class of all equal classes.
Intension/Class/Quantities/Frege/Russell/WittgensteinVsRussell/WittgensteinVsFrege: the two believed they could handle the classes intensionally because they thought they could transform a list into a property, a function. (WittgensteinVs).
Why were they so keen to define the number?
Measuring: For example, numerical equality of classes or
Calculating: e.g. equal number of roots of a 4th degree equation: one is a measurement,
the other a calculation.
Is there an experiment to determine if two classes have the same number? This may or may not be the case for classes that we cannot get a general view of.
It is a damaging prejudice to believe that when using strokes we are dealing with an experiment.
Classes/Assignment/Wittgenstein: Difference: Assignment in Russell's and in the usual sense:
1. by identity
2. how to assign cups and saucers by stacking.
In the second case, it does not mean that they cannot be assigned in any other way. Could the same be said about Russell's assignment? No, here no other allocation could exist, if that is not given. What I want to draw attention to is not a natural phenomenon, but a matter of grammar.
Allocation/Number Equality/Wittgenstein: the requirement that an actual allocation must be made to declare two classes equal in numbers is worrying.
Classes/Wittgenstein: we must not forget that we do not always talk about the same phenomenon when we talk about two classes containing the same number of elements.
How do you know if some pieces will disappear while they are being counted, or if others will not break?
Classes/Power Equality/Number Equality/Class Equality/Wittgenstein: Question: whether the classes must actually be assigned to the paradigm to have the same number, or whether this only needs to be possible. What is the criterion of existence of the possibility of their assignment?
Classes/Numbers/Wittgenstein: when it is said that you can just as well calculate with the classes as with the rational numbers, actually no substitution has taken place. The calculation is simply done with the rational numbers.
Class/Method/Wittgenstein: we must distinguish between a class of coin tosses and a method (rule) - E.g. irrational number: is defined by a method - it is a process - the square root of two is not an extension but a special rule to produce a fraction.
Classes/Sets/Tractatus: 6,031 The theory of classes is completely superfluous in mathematics.
This is because the generality we need in mathematics is not the random one._____________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 [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.
Wittgenstein’s Lectures 1930-32, from the notes of John King and Desmond Lee, Oxford 1980
Vorlesungen 1930-35 Frankfurt 1989
The Blue and Brown Books (BB), Oxford 1958
Das Blaue Buch - Eine Philosophische Betrachtung Frankfurt 1984
Tractatus Logico-Philosophicus (TLP), 1922, C.K. Ogden (trans.), London: Routledge & Kegan Paul. Originally published as “Logisch-Philosophische Abhandlung”, in Annalen der Naturphilosophische, XIV (3/4), 1921.
Tractatus logico-philosophicus Frankfurt/M 1960