His sister Gretl and Engelmann now wanted him to work on the design and construction of Gretl's house. Engelmann had already done some renovation work for the Wittgensteins on a previous occasion, and Wittgenstein was to work with him. Wittgenstein designed doors, windows and radiators for this purpose and was subsequently listed in the Vienna city directory as an architect for years.
Wittgenstein's obsessive attention to detail had the engineer working on glass doors according to his requirements in tears, and the radiators took a year to deliver because no one in Vienna could produce them according to his standards. Gretls finally occupied the house at the end of 1928. However, her approval was moderated by the austere mathematical quality of Wittgenstein's design. He had eschewed any external decorations and even strictly rejected carpets and curtains. The rooms used undecorated light bulbs, the floors were of dark stone and the walls a light ochre throughout, and door handles, radiators and window frames were left unpainted.
The house was to become a barracks and stable for Russian forces in 1945, left empty after 1958 and slated for demolition in 1971, finally becoming a Bulgarian embassy building after a campaign to save it. Subsequent decorators have added wood paneling and other elements Wittgenstein would have disapproved of.
Wittgenstein started going out with a certain Marguerite whom he had met in Cambridge. Marguerite was not especially serious or intellectual and did not get on with Wittgenstein's circle. This was especially the case with Paul Engelmann, about whom she made comments with respect to his Jewish origins. Gretl, however, encouraged the relationship. Wittgenstein used her as a model for a bust he sculpted, which he gave to Gretl. Wittgenstein saw this relationship as a preliminary to marriage, though he was much older than Marguerite.
Wittgenstein also returned to philosophy during his stint as an architect, meeting with a professor of philosophy at the University of Vienna, Moritz Schlick. Schlick had previously attempted to deal with Wittgenstein without results. Schlick and his circle eventually had regular meetings with Wittgenstein, but were surprised to find him hostile to positivism and with an unscientific attitude. Schlick wrote that Wittgenstein delivered precepts as if by divine inspiration, not tolerating argument of a kind based on Enlightenment rationality.
One of the topics was Ramsey's attempts to correct the errors in Russell's philosophy of mathematics, using Wittgenstein's ideas. At the same time, Ramsey was defending Russell's general approach of seeing mathematics as reducible to axioms of logic, opposing the "Bolshevik menace" of Brouwer, who used an approach in which a fundamentally different conception of logic and mathematics was needed to reconstruct mathematics entirely, which would lead to the casting aside of many well-established theorems which were not provable within his system.
Ramsey wanted to show that mathematics consists of Wittgensteinian tautologies (using a logical function Q(x,y) that corresponds to x=y) and that mathematical propositions are thus logical propositions. Wittgenstein, however, distinguishes between the 'equations' of mathematics and the 'tautologies' of logic. Having read Ramsey's paper, Wittgenstein attacked his claim that all expressions of identity are either tautologies or contradictions: "The way out of all these troubles is to see that neither 'Q(x,y)', though it is a very interesting function, nor any propositional function whatever, can be substituted for 'x=y'". In short, Wittgenstein thought the attempt to base mathematics on axioms of logic futile. But whereas Wittgenstein saw Ramsey's endeavour as philosophically misguided, Ramsey saw his function Q(x, y) as merely a (so to speak) "semantic" tool defined so as to accomplish the practical function of identity statements within his theory. Wittgenstein saw Ramsey as a "bourgeouis" thinker because Ramsey was considering the possible organization of one particular 'state ' (the 'community of ideas' espoused by Russell and others) and not considering its essence, whereas according to Wittgenstein a philosopher as such is not a citizen of any community of ideas.
Wittgenstein was also corresponding with Keynes, commenting positively on Keynes' survey of the Soviet Union. Curiously. what Keynes and Wittgenstein liked about Soviet Marxism was not its economics, which they thought wrong, but its character as a religious attitude comparable to Christianity. Keynes did however contrast Marxism and Christianity, seeing the former as pointing the way to a non-supernaturalist religion of the future. Russell had also written about the Soviet state and compared it to Christianity, but despised both, and particularly what he saw as their common elements. Wittgenstein was to retain the idea of living in the Soviet Union until the political conditions prevailing from 1937 made it unworkable.
In 1928 Wittgenstein attended some lecturers by the mathematical "Bolshevik" Brouwer. Although he did not "convert" to Brouwer's school, Brouwer's thought was to prove a powerful stimulus to Wittgenstein. Wittgenstein would have nothing to do with Brouwer's Kantian idea of a "basic mathematical intuition" on which his philosophy of mathematics was founded. However, his philosophical attitude and Wittgenstein's were similar, and opposed to that of Ramsey and Russell. Their thinking was closer to that of Schopenhauer than that of the rationalist Vienna circle. They also agreed on rejecting the following ideas:
- the notion of an infinite series in extension.
- the possibility or need to found mathematics on formal logic.
- the need for consistency proofs in a mathematical system.
- the mind-independent reality of mathematics, elements of which can then be 'discovered' rather than 'created'.
According to the biographer, Brouwer's work probably pointed Wittgenstein in the direction that his later philosophical work would go.
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