Ludwig Wittgenstein
From Geography
Ludwig Wittgenstein was born in Vienna in 1889, he studied engineering in Linz and Berlin and from 1908, aeronautical engineering in Manchester where he developed his interest for pure mathematics and philosophy. Im 1912 he moved to Cambridge to studylogic and philosophy but in 1913 he suddenly abandoned Cambridge and moved to a farm in Norway.
Early Life
At the beginning of the war he enlisted as a volunteer in the Austrian army and when it finished he was interned in an italian POW-camp (prisoner-of-war camp) until 1919. During those years, since his stay in Norway, he continued thinking about the problems of logic and philosophy and he wrote a short treatise thinking that with it he definitively resolved those problems. The book was published in 1921 in the "Annalen der Naturphilosophie" under the title "Logisch-philosopische Abhandlung" and in 1922 was published the english version "Tractatus Logico-philosophicus" which included an introduction wrote by his friend B. Russell [1]. It became the most influential work of his time.
After the publication, he considered his public philosophical activity completed and returned to Austria where he worked as a teacher between 1920 and 1926 and even as an assistant gardener at a convent. Lately, he returned to Vienna and he resumed contact with philosophy. After a brief encounter with the Vienna Circle and influenced by a conference given by Brouwer, in 1929 he went back to Cambridge and he joined he Trinity College as a fellow presenting the Tractatus as his doctoral thesis. He stayed there until 1936, when he returned to Norway where he started to work on his second book, the "Philosophical Investigations". In 1937 he returned to Cambridge and in 1939 he was given the Chair of Philosophy and became british citizen. In 1975 his mathematics course was published under the title "Wittgenstein's Lectures on the Foundations of Mathematics".
At the start of World War II he was a volunteer in Newcastle. During this period (1937-1944) he worked intensively on the philosophy of mathematics. In 1944 he returned to Cambridge, but in 1947 he resigned from the professorship and moved to Ireland with the intention to work more in the second part of "Investigations". He died in 1951 and his second book was published posthumously in 1953 and had a greater importance than the Tractatus.
Philosophy
His philosophical positions changed throughout his life, so that usually has distinguished between a first period focused on tractatus and a second period, from 1929, whose maximum exponent would be Investigations. Although this separation is excessive, because there is a continuity between the two periods and the change is gradual, it is clear that the point of view is essentially changed. Indeed, the fundamental issue is the same throughout his work: the nature of language, how it represents the world and the implications this has for logic and mathematics.
In the Tractatus, the approach is objectivist. Consider abstract language independent of human activities. Its relationship with the world through logic is formal and static. So in any case, they say nothing about the world, they just show us the nature of language and its properties.
In the second period, however, the emphasis is placed on the subjects, people's actions and the role that language plays in their activities. The language is no longer an abstraction but a set of practices in which the fundamental and defining meaning is the use within the context of everyday social activities, such as asking, advising, etc. These activities are language games (as well as mathematics are a language game, so they do not need external fundamentals but analysis) in which rules are set and interpreted and which together constitute social life forms, sets of established human social practices and lived with their own purposes, implicit rules, patterns of behavior and language use.
This is how Ludwig Wittgenstein's work caused him to be considered as the percusor of social constructivism in mathematics.
References:
Sánchez Navarro J (2000).Las Matemáticas del siglo XX: Una mirada en 101 artículos. Ludwig Wittgenstein. Sociedad Canaria Isaac Newton de Profesores de Mateática. España. Artículo 43.
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