|Generality/Geometry/Wittgenstein: one point is not a concept at all. Then what is the generality in geometry? Two meanings:
1. the geometric rules,
2. the generality of the applications of geometry. The application depends on how the world appears. This generality of applications is also the generality of arithmetic.
Proof/Mathematics/Wittgenstein: two different types of proof:
1. to communicate certain substitution rules (axioms) from one equation to another.
Geometry/Description/Border/Wittgenstein: in geometry we cannot describe a cube or circle, but we can define it. Geometry describes the circle to the same extent as logic describes negation. Geometry provides the grammar of certain contexts.
Facial Space/Wittgenstein: the geometry of the facial space is not Euclidean.
Geometry/Rules/Experience/Wittgenstein: from the consideration of the rules, the geometry of the cube cannot be derived. The rules do not follow from an act of insight. Geometry is not about cubes but about the grammar of the word "cube" because geometry is not physics. Arithmetic: the grammar of numbers - a definition is not a proposition about a thing.
Geometry/Wittgenstein: geometric sentences say nothing about cubes, but determine which sentences about cubes have meaning and which have no meaning.
Geometry/Wittgenstein: what role does the cube play in the geometry of the cube and in the development of this geometry? Two types of examination:
a) Examination of the properties of an object
b) Examination of the grammar of the use of a word.
A geometric examination in the sense of an examination of the properties of geometric lines and cubes is not possible. Geometry is not a physics of geometric lines and cubes, but it is constitutive for the meaning of the words "straight line" and "cube".
The fact that something green or yellow matches the green pattern is part of the geometry and not part of the dynamics of green. In other words, it is not a law of nature, but part of the grammar of "green".
Geometry/Frege/Wittgenstein: according to Frege, geometric lines are always there. That is, "it makes sense to say that a real line has been drawn".
Geometry/Wittgenstein: it has been claimed that constructions with ruler and compasses are always inaccurate.
This objection is not appropriate, but if it were, the same would apply to multiplication: one could object that the forms of the "four" are not exact, that we could never be sure to have written "the arithmetic 4.
Point/Geometry/Wittgenstein: if people had always painted their geometric figures with the brush, they would never have come up with the concept of a class of points. And we would not claim that it is possible to transfer the same division method to the real numbers._____________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.
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